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DESIGN STUDY FOR A LARGE BALLOON-BORNE
FAR INFRARED TELESCOPE
By
GILLIAN SUSAN WRIGHT Astronomy Group, Imperial College, London SW7 2BZ
Thesis submitted for the degree of
Master of Philosophy
of the University of London
ABSTRACT
The largest of the present generation of balloon telescopes are
in the 1m class and are limited in their astronomical usefulness by
their aperture. Far-infrared astronomy has now developed sufficiently
so that a strong case can be made for a telescope of much larger aperture.
The increase in sensitivity and angular resolution of a 3m telescope
over a i m telescope and the contributions that the use of such a tele-
scope could make to current astrophysics are examined. A general review
of infrared balloon astronomy and some of the existing balloon telescopes
reveals some of the constraints which a 3m telescope must meet.
Various techniques for making lightweight mirrors were examined
because the weight of the primary mirror is the most important factor in
determining the total telescope weight. An assessment of the state-of-
the-art technology showed that the most reliable design would use a light-
weight honeycomb celled aluminium mirror. This is a compromise between
the techniques for fabricating optical quality mirrors and those used for
mm-wave dishes.
A variety of optical configurations for the telescope were
compared on the basis of the ease with which they could be made to fit
the length criterion, with a readily manufactured primary f-ratio. A
Cassegrain configuration with a spherical primary and an aspheric
secondary was finally chosen. First order alignment tolerances were
calculated for this design.
Finally, the structural problems of the 3 m telescope are
considered. In particular the positions and thicknesses of the honey-
comb ribs of the primary mirror for minimum distortion of the front
surface were investigated and the requirements on the supporting structure
were evaluated.
2
ACKNOWLEDGEMENTS
I would like to thank both my supervisors: Dr R. D.
Joseph for his helpful advice and encouragement and for
obtaining financial support for the project; and Dr R. C. M.
Learner for his interest, practical advice and guidance.
Dr D. Heshmaty-Manesh of the Optical Design Group provided
the ray-tracing for the optical design of the telescope.
Dr P. Kilty of the Aeronautical Engineering Department made
available the finite-element analysis routines used in this
thesis, and I am indebted to him for several helpful discussions
and his interest in this project.
I thank Mrs T. Wright for her efficient and accurate typing
of this thesis, and Ms P. Kerridge for typing Chapter 6. Finally
I would like to thank Dr N. Robertson, Mr T. Jones, Mr M.
Nicholson and Mr S. Mrowka for their assistance and encouragement.
3
C O N T E N T S
Page
ABSTRACT 2
ACKNOWLEDGEMENTS 3
LIST OF TABLES 8
LIST OF FIGURES ^
CHAPTER 1 - Scientific Background and Objectives
1.1 Introduction 12
1.2 Historical Background 13
1.3 Achievements of Far-Infrared Astronomy 15
1.4 Capability of a 3m Telescope 16
1.4.1 Noise Sources 17
1.4.2 Sensitivity Improvement 17
1.4.3 Angular Resolution Improvement 22
1.5 Scientific Objectives 22
1.5.1 Extragalactic Astronomy 23
1.5.2 Line Astronomy 27
1.5.2(i: ) Molecular Clouds 27
1.5.2(ii) H II Regions
1.5.3(1^ Interstellar Dust
30 3 1
1.5.3 The Galactic Centre 3 3
1.5.4 The Cosmic Microwave Background 3 3
1.6 Compatibility with Satellite Telescopes 37
1.6.1 I R A S 38
1.6.2 The Space Telescope (S.T.) 3 9
1.6.3 Infrared Space Observatory (ISO) 39
1.6.4 Shuttle Infrared Telescope Facility 4 0
1.6.5 German Infrared Laboratory (GIRL) 40
1.6.6 Other Telescopes 4 1
4
Contents (Continued) Page
CHAPTER 2
CHAPTER 3
1.6.7 Discussion
1.7 Conclusions
Balloon Infrared Telescopes
2.1 Introduction
2.2 Chopping
2.3 Launch and Landing
2.4 Guiding and Telemetry
2.5 Balloon Telescopes
2.5.1 The Centre for Astrophysics - University
of Arizona Telescope
2.5.2 The University of Arizona Cooled
Telescope
2.5.3 The University of Arizona Linear Scanning
Telescope
2.5.4 The University College 6o" Telescope
2.5.5 The Imperial College Balloon Telescope
2.5.6 Submillimeter Wave Sky Survey Telescope
2.5.7 The University of Gronigen Telescope
2.5.8 The Max-Planck Institute Telescope
2.6 The Constraints on a 3m Telescope
2.6.1 General design considerations
2.6.2 Size limitations
2.6.3 Weight limitation
2.6.4 Conclusions
Lightweight Mirrors
3.1 Introduction
3.2 Properties of Materials
3.3 Glass Ceramics
4 1 4 1
43
4 3
44
4 6
4 7
4 7
4 8
49
49
50
5 1
5 2
53
53
5 3
54 55
55
5 8
6 1
64
Contents (Continued) Page
3.4 Low Expansion Glasses 6 8
3.5 Very Low Expansion Glass 6 8
3.6 Beryllium 7 <5
3.7 Titanium 7 5
3.8 Aluminium ^ 5
3.9 Replica Mirrors 8 2
3.10 Active Optics 8 6
3.11 Membrane Mirrors 8 8
3.12 Figuring 9 2
3.13 Choice for a 3m Balloon Telescope 9 <5
CHAPTER 4 - Optical Design of the Telescope
4.1 Introduction 9 9
4.2 The Prime Focus Configuration 9 9
4.3 The Herschellian Telescope 1 01
4.4 The Newtonian Telescope 1 01
4.5 The Cassegrain Telescope 104
4.6 The Optical Configuration for the 3m 111
4.7 Detailed Design of Cassegrain 1 1 1
4.8 Optical Tolerances 12 2
CHAPTER 5 - A Lightweight Primary Mirror
5.1 Introduction 1 32
5.2 The Problem of Mirror Deflection ] 3 3
5.3 Parametric Analysis of the 3m Lightweight 1 38
Mirror
5.3.1 Faceplate thickness 140
5.3.2 Overall bending of the Mirror 14 1
5.4 Finite Element Analysis 145
5.5 FINEL - The Finite Element Analysis Routines 148
of the Aeronautical Structures Group 6
Contents (Continued) Page
506 Finite Element Models of Mirrors 1 5 0
5.7 A FINEL Model for the proposed ^ ̂ 3
3m Mirror
5.8 Preliminary Results and Conclusions 1 54
on the Mirror Design
CHAPTER 6 - A 3m Balloon Telescope Payload
601 An Estimate of the Weight of a 1 62
Balloon Telescope
6.2 Suggestions for Further Work 167
R E F E R E N C E S 1 7 2
7
LIST OF TABLES Page
1.1 Distances out to which a 3m Telescope could detect
some bright Far-infrared Objects
1.2 Integration Times to detect some predicted infrared
lines from Molecular Clouds and H II: regions with.
S/N = 5
2.1 Typical Balloon Systems
3.1 Mechanical and Thermal Characteristics of Mirror 6 2 *
Materials-
3.2 Figures of Merit for Mirror Materials 65
3.3 Parameters for Cervit Mirror 6 7
3.4 Space Telescope Mirror Parameters 7 3
3.5 A Tinsley Laboratories Mirror 80
3.6 Two Sample Replica Mirrors 85
3.7 Parameters for Actuator Mirror 8 7
3.8 Mirror Manufacturers 9 3
4.1 Different Types of Cassegrain Telescope 105
4.2 Performance' of Different Telescope Configurations no
4.3 The Baseline Cassegrain Design 119
4.4 The Final Optical Design for the 3m Telescope 121
4.5 The Figure of the Secondary Mirror 123
4.6 The Alignment Tolerances 131
5.1 The Initial Mirror Design 146
5.2 Richard and Malvick 0.973) Mirror Parameters 152
5.3 The Final Mirror Design j 5 7
5.4 Summary of Mirror Deformations-
8
LIST OF FIGURES
1.1 Integration times as a function of flux density for 21
various telescopes
1.2 A map of Ml7 32
1.3 fir an<i radio maps of the galactic center 34
1.4 Sensitivity of measurements of the cosmic microwave 36
background
2.1 Different types of chopper 45
3.1 The back of the mount Palomar 200" mirror 59
3.2 a) Plan of Cervit mirror with triangular cavities 67
b) Section A-A
3.3 Thermal expansion properties of ULE 7 0
3.4 Assembly of a ULE eggcrate 71
3.5 A monolithic ULE honeycomb 71
3.6 Production of optical grade beryllium 74
3.7 a) Core drilling pattern in beryllium 76
b) Two pieces brazed to form an 'eggcrate'
c) A thin walled eggcrate
3.8 A radially ribbed aluminium mirror 78
3.9 a) The geodesic pattern of a Tinsley laboratories 80
mirror
b) Cross-sectional view of mirror
3.10 An ESSCO panel 81
3.11 a) Cut away and plan view of the 10 m antenna 83
b) Detail of a honeycomb panel
3.12 Schematic layout of aTalbert laboratories mirror 85
3.13 A stacked actuator mirror 87
3.14 The electrostatically controlled membrane concept 89
3.15 A symmetrical L.W. mirror 9
4.1 A prime focus arrangement 100
4.2 A Herschellian arrangement • 105
4.3 A Newtonian arrangement
4.4 Secondary diameter as a function of primary focal I02
ratio for a Newtonian telescope
4.5 A Cassegrain arrangement 105
4.6 Parameters for the design of a Cassegrain 107
4.7 Overall F ratio as a function of primary F ratio 108
for a Cassegrain telescope
4.8 Overall F ratio as a function of mirror separation 109
for a Cassegrain telescope
4.9 Quantities used to calculate Seidel sums 114
4.10 Spherical aberration coefficients for primary and 117
secondary mirrors
4.11 The spot diagram for the 3 m telescope I20
12 5 4.12 Mirror separation change
4.13 Primary decentre 126
4.14 Primary tilt 127 128
4.15 Secondary decentre
4.16 Secondary tilt 129
5.1 Mirror back support 135
5.2 A two point lateral support 137
5.3 A band support 13 7 13 7
5.4 A sinusoidal support
5.5 Honeycomb mirror cross-section 139
5.6 Faceplate thickness as a function of rib spacing l42
5.7 Rib thickness as a function of mirror depth I44
5.8 The symmetrical shape of the 3 m mirror 146
5.9 Flow chart for a stress analysis 149
5.10 The mirror model 155
5.11 Graph of ULE manufacturing capability 161 10
a) Secondary vanes, telescope vertical
b) Secondary vanes, telescope horizontal
a) Secondary ring telescope vertical
b) Secondary ring telescope horizontal
c) Cross-section of secondary ring
A primary of varying thickness
11
CHAPTER 1
SCIENTIFIC BACKGROUND AND OBJECTIVES
1.1 Introduction
fModernT observational astronomy can be thought of as beginning
in 1609 when Galileo first used his "optik tube" , a telescope with a
lens only 4 cm in diameter and a magnifying power of 10. Since then
telescopes have grown steadily larger, changing from refractors to
reflectors as lenses became too thick and heavy. The history of
astronomy in all wavelengths shows that major advances have accompanied
the building of larger telescopes and improvements in the sensitivity
of detectors.
Work in the far-infrared (30 p. - 1 mm) has been no exception with
the introduction of airborne telescopes of larger and larger aperture.
However, since the early 1970Ts, there has been no further development
of telescopes; the largest still being the in the lm class, although
the sensitivity of detectors has improved by about an order of magnitude
(Soifer and Pipher 1978). With the results from these telescopes
far-infrared astronomy has now developed sufficiently that a strong
case can be made for a much larger telescope.
This project investigates whether the 'state of the art'
technology could be used to produce a feasible large telescope,
given the constraints on complexity, size, weight and strength that
ballooning imposes (Chapter 2). A telescope of 3 m aperture was
chosen for the design study because, as discussed below, this will
bring a significant increase in capability over the existing systems,
while recent developments in light-weight mirror technology (Chapter 3)
suggest that a telescope of this size should be structurally
practicable. 12
1.2 Historical Background
Infrared astronomy began in 1800 with the discovery of infrared
radiation by Herschel. He was investigating the heating powers of
different colours of sunlight when he detected heat beyond the red end
of the visible spectrum (Herschel 1800). It was not until several
years later that Piazzi Smyth detected the full moon in the near infrared
during his 1856 expedition to Tenerife (Smyth 1859).
After these first results there was a lull in the development of
infrared astronomy, due to the opacity of the atmosphere at infrared
wavelengths and the low sensitivity of the available detectors. However
in 1948 Wesslink demonstrated the great potential of infrared astronomy
by using near infrared data on the moon, collected a few years earlier by
Petit and Nicholson (1930), to derive the then controversial result that
the moon was covered in a fine layer of dust.
The subject did not really start to expand, until the development
of the Low bolometer in the early 1960*s (Low 1961). This gallium doped
germanium bolometer, which is cooled to 2°K or less by cryo-pumping liquid
helium, was an order of magnitude more sensitive than the mercury and
copper doped germanium photoconductors then in use for the 5 - 15 ji region.
In addition the Low bolometer can be used over a wide range of wavelengths
and so far-infrared astronomy became possible, while ground-based near-
infrared astronomy began to develop rapidly.
Pressure broadened water and carbon dioxide absorption bands account
for most of the opacity of the atmosphere in the infrared. However there
are a few gaps in this absorption, where the atmosphere is relatively
transparent. Thus astronomical observations are possible from high dry
sites where there is less water vapour and atmosphere. In 1962 the
atmospheric windows between 1 - 5 JI were used by Johnson to define three
photometric bands, and he detected several thousand stars in his investi-
gation of the interstellar reddening laws. The windows at 10 p.
13
(transmission about 0.9) and 20 p (transmission about 0o6) were first
used in 1963 and 1965 respectively (Allen 1975). A 2.2 p survey of
the northern sky was completed and many objects were shown to be
unexpectedly bright in the infrared (Neugebauer, Martz and Leighton,
1965)o This was an incentive for further work at the other infrared
wavelengths accessible from the ground. The two windows at 35 p and
350 |u , with transmissions around 0.3, are very poor and so these are
still only rarely used for ground based observations. The use of the
1 - 20 p atmospheric windows is now well established and over the years
a number of telescopes specifically designed to meet infrared require-
ments (for example a low background and chopping) have been built on
carefully selected sites; for example U.K. I.R.To - the 3.8 m telescope
on Mauna Kea, Hawaii.
The atmosphere is strongly absorbing between 30 p and 1 mm and
so far-infrared astronomy was impossible without the development of
techniques for observations from above the atmosphere. Rockets were
used in the late 1960fs but were severely limited by the very short
observing time available (5-10 minutes) and the difficulties of pointing.
Like rockets, satellites, the most recently developed technique, carry
telescopes completely clear of the atmosphere. Their major disadvantages
are their high cost and the very long Tlead time1 necessary. The first
infrared satellite, I.R.A.S. (Infrared Astronomical Satellite), a survey
instrument, will be launched in 1982 and is expected to find a large
number of new sources.
The two most commonly used techniques compromise between altitude,
observing time and cost. High flying aircraft can lift telescopes to
about 14 km where they are above some but by no means all of the water
vapour and the atmosphere is fairly transparent. The most recent of
these is the Kuiper Airborne Observatory1s 90 cm telescope (Cameron 1971).
14
A lot of far-infrared data has been obtained with balloon-borne
telescope systems. For example, all the far-infrared (FIR) source
catalogues to date have been made using balloon telescopes. Balloons
lift the telescopes to altitudes of ^ 35 km where they are above all
but a few hundredths of a percent of the water vapour. The telescope
systems have developed from the pioneering 1" refractor of Woolf et al.
(1969) to the 1m class telescopes in current operation. Some of
these telescopes are discussed in Chapter 2.
1.3 Achievements of Far-Infrared Astronomy
As in the near infrared, the first far-infrared object to be
detected was the sun (by Beer in 1966 using a balloon instrument),
followed a year later with a detection of the moon (Hoffmann et al3 1967).
Since then Jupiter, Saturn and Neptune have all been shown to be emitting
more power in the infrared than they absorb from the sun (Keay et al3
1973, Nolt et al. 1974, Loewenstein et al. 1977). The presence of an
internal heat source has been taken to imply that the interiors of
these planets are still contracting. Hoffmann, Frederic and Emery
(.1971a) carried out the first 100 p. survey of the galactic plane and
found over 70 sources, many of which they identified with H II regions.
They also produced the first 100 p map of the galactic centre (Hoffmann,
Frederic and Emery 1971b). The first far-infrared measurements of
H II regions were made in 1970 by Low and Aumann, who were able to
estimate their luminosity and show that they emit most of their energy
in the infrared.
More recently, maps of some of the larger H II regions have been
produced and these broadly resemble radio maps of the same region. The
extent and intensity of the diffuse radiation from the galactic plane
has been measured in selected regions. These measurements have been
used to give an indication of the distribution of dust and stars and the
rate of star formation in our galaxy. Molecular clouds have also been 15
shown to be emitting strongly in the far-infrared and measurements of
their temperatures and luminosities have been used in stellar evolution
models (Fazio 1979.), while far-infrared fine structure lines have
recently been used to derive ionic abundances in the nebula M.17.
(Moorwood et al. 1980). Far-infrared absolute temperature measurements
of the sun have been used to study the area between the photosphere and
the chromosphere precisely enough to single out one of the many models
of the solar atmosphere as being the most accurate (Rast, Kneubuhl and
Muller, 1978). Some galaxies and active galaxies have been shown to
have large far-infrared luminosity peaks. The nucleii of some of these
galaxies appear to exceed the maximum luminosity that can be derived
from thermal re-radiation models of dust heated by a normal population
of stars.
Far-infrared astronomy, like near-infrared astronomy, has now
been shown to be a useful tool for studying objects ranging from the
solar system to other galaxies and has already brought advances in many
areas of astrophysics. The viability of balloon telescopes with
sophisticated pointing and stabilization control for exploiting the
potential of far-infrared studies has been clearly demonstrated (Fazio
1979). In the following sections the greater capabilities of a 3 m
class instrument are evaluated and the ways in which it will allow the
potential of far-infrared astronomy to be more fully realized are
discussed.
1.4 Capability of a 3 m Telescope
The 1m aperture of the present generation of balloon telescopes
imposes two limitations on the far-infrared studies that can be be under-
taken at present. One of these is the angular resolution achieved:
diffraction limited at 100 p. to about 25 arc seconds and the other is
the small flux collection of the primary mirror, which makes the detection
of potentially interesting, faint sources impossible. In this section
the improvements in sensitivity and angular resolution that can be
expected from a 3 m telescope are quantified.
1.4.1 Noise Sources
Since all signals include noise, the sensitivity of a telescope
system depends on how much noise it introduces. There are several
sources of noise and these are briefly described below.
All room temperature surfaces radiate in the infrared and statis-
tical fluctuations in the number of such background photons from the
telescope are the fundamental source of noise. This noise can only be
reduced by lowering the temperature of the telescope or reducing the
optical throughput of the telescope or the bandpass of the filters.
The residual atmosphere at balloon altitudes provides a second
major noise source. Both statistical fluctuations in the background
radiation from the atmosphere and fsky noise', random fluctuations in
the emissivity of the atmosphere, can limit the telescope's sensitivity.
However, there are many other noise sources in the system which
may or may not be larger than this background radiation noise. Fluctuat-
ions in the output of the detector itself (Johnson noise, 1/f noise,
phonon noise) can be significant and since the signals have to be
amplified 1/f noise may be introduced by the pre-amplifier.
1.4.2 Sensitivity Improvement
The sensitivity of a telescope is described by the signal-to-
noise ratio it can achieve on a source in a given length of time.
Although a 3 m class telescope will have nine times the flux collection
of a 1m one it is the relative size of the background radiation noise
to the sum of all the other noise sources that determines the gain in
sensitivity that can be expected from the 3m telescope.
17
If the dominant noise source is in the detector and amplifier
system, the signal to noise increases, as the signal does, with the
collecting areaQ This is the case in spectroscopic work where the
narrow bandwidth used ensures that the photon background noise is less
than the noise equivalent power of the most sensitive detectors and
amplifiers presently available. Quantitatively, for a 3 m balloon
telescope, this will be the case for resolutions of less than about -4
4 x 10 o Hence for far-infrared line astronomy a 3 m telescope would
bring an improvement of nine times in sensitivity over a i m one.
noise from the telescope is sufficiently large that the telescope is
background radiation noise limited. In this case the gain in sensitivity
from a 3 m telescope depends on the relative throughput or etendue A Q ,
as shown below.
Assuming Poisson statistics the power fluctuation at the detector
where N is the average number of photons reaching the detector from
the background.
Thus
On the other hand, for broad band photometry the photon shot
is
P noise
P noise a where
Bv(T) is the Planck function \) -l
A is the detector area d
Q ^ is the solid angle subtended by the mirror at the detector
Av is the bandwidth and £ is the emissivity
18
But
where
A O , = A O d d m s
A^ = area of primary mirror
Q = field of view of telescope.
Thus
P . o < JA^A DlW s (1.2) noise
where
D = telescope diameter.
O -rr , ,2.44A 2 For a diffraction limited field of view "s = 71 / l ( )
D l 2 and so A n ^ 3.7 A „ m i,s s
So for a diffraction limited field of view the background noise
power is independent of the telescope aperture. Thus if both telescopes
are operated with a diffraction limited field of view, a gain of nine
times in sensitivity over a i m telescope is made by using a 3 m tele-
scope for broad band work. If the larger telescope is operated with
the same field of view as a 1m telescope it is evident from equation (1.2)
that there is still a gain of three times in sensitivity because the
noise increases as the diameter, while the signal increases as the
diameter squared. For some studies, such as photometry of extended
objects, a diffraction limited field of view is not required. Also the
pointing requirements for diffraction limited operation of a 3 m class
telescope are very precise ( - 8 arc sec) and even 1m telescopes are
often not used at the diffraction limit if the pointing and stability of
their platforms are not good enough.
Thus for both narrow and broad band work the sensitivity of the
present generation of telescopes will be improved upon by a telescope of 19
three times larger aperture. However for broad band work where we are
background noise-limited, it could be argued that the sensitivity could
be improved more by cooling the telescope and so decreasing the back-
ground noise (see Eqn.1.1). Cooling a balloon telescope involves over-
coming the problems of condensation and even then, in general there is
little gain because the atmosphere itself becomes the dominant noise
source (when T = 70K)• Because the temperature across the primary
mirror must be constant, cooled telescopes tend to be small 1 m),
A small cooled telescope in space (for example I.R.A.S.) will however
allow the full advantage of cooled optics to be used.
All of the various possibilities are summarized in Figure 1.1,
which shows the integration times required to reach a signal to noise
ratio of 5 on a source of a given flux density for broad band photometry
at 100 p with a i m warm, 3 m warm, 60 cm cooled (atmospheric limited)
balloon telescopes and a 60 cm cooled telescope in space. All of the
telescopes were assumed to have an overall efficiency of 10% and a
diffraction limited field of view. The emissivity of the warm telescopes
was taken to be 0.02. The cooled balloon telescope was assumed to be
cooled until the residual atmosphere was the limiting factor and the
background radiation shot noise was estimated from the results of Traub
and Steir (1976). The cooled space telescope was assumed to be cooled
to ~ 12 K when the noise from the thermal emission of the telescope
became less than the N.E.P. (noise equivalent power) of an infrared -17 -1/2 detector (taken as 3 x 10 W Hz ' ).
A measurement that would take an hour with a i m class telescope
could be done in only a few seconds with a 3 m telescope. It is not
practical to use a small telescope for a long integrating time to obtain
the same result on a faint object as could be achieved with a large
telescope in a much shorter time because systematic problems such as
slow drifts could occur and these cannot be eliminated with a long
Figure 1.1 Integration times as a function of flux density for various telescopes.
integration. Also very long integration times are impossible because
of the accuracy with which a balloon telescope can track an object. The
small cooled telescope in space is two to three times more sensitive
than a 3m warm telescope for these broad-band measurements, but as
discussed above, would have about 25 times less sensitivity than the 3m
for narrow-band work where the sensitivity depends only on the collecting
area. Such a telescope would therefore be complementary to, as opposed
to an improvement on, a 3m balloon telescope. In conclusion, a 3m warm
balloon borne telescope will provide a major improvement in sensitivity
over existing systems for both far-infrared spectroscopy and photometry.
1.4.3 Angular Resolution Improvement
A 3m class telescope, diffraction-limited at 100 p to - 8.5 arc
sec., would bring an improvement in angular resolution over that of a
lm telescope by a factor of at least 3, The angular resolution that
can be achieved in practice with a telescope depends on the sensitivity,
because with greater flux collecting power the same signal to noise ratio
can be obtained on a smaller area of sky. Since the increased aperture
of the 3m telescope will also bring almost an order of magnitude increase
in signal strength from the source, its angular resolving power in practice
can be expected to be rather more than 3 times that achieved with a i m
telescope (providing the source is unresolved).
1.5 Scientific Objectives
It is difficult to predict in detail what observations will be
the most interesting by the time a large balloon telescope is built.
There are many examples in the history of astronomy where previously
unthought-of investigations were stimulated by the results obtained on
a new telescope. Thus some of the scientific problems that the telescope
could help solve probably cannot be defined at present. However in
terms of our current knowledge of astrophysics and infrared astronomy it 22
is possible to discuss how the telescope could contribute in several
important areas of research.
1,5,1 Extragalactic Astronomy
This is one of the most exciting areas to benefit from the
increased sensitivity of a 3 m telescope because very strong mid- and
far-infrared fluxes have been observed for a variety of extra-galactic
sources ranging from elliptical galaxies to quasars and Bl-Lac type
sources, A recent survey (Reike and Lebosfoky 1978)suggests that for
40% of normal spirals, including our galaxy, the luminosity peaks in the
infrared, while more complex systems such as interacting galaxies are
even more luminous. Although there have been extensive ground-based
near- and mid-infrared surveys of galaxies, only the dozen or so brightest
have been detected at far-infrared wavelengths, mainly due to sensitivity
limitations, despite the fact that the spectra of several galaxies appears
to continually rise towards longer infrared wavelengths. It is now
accepted that observations at all infrared wavelengths are necessary for
even an elementary understanding of extra-galactic sources, because they
provide information on source strength and emission mechanisms.
Thermal re-radiation by dust grains heated by stars is thought to
explain the infrared emission from H II regions and molecular cloud
complexes in our galaxy. Since extinction studies show that many other
galaxies contain large amounts of dust, it appears that the infrared
luminosity in these objects is also due to thermal re-radiation by dust.
The general shape of the far-infrared spectra of M82 and NGC 253 has
been found to be similar to that of galactic H II regions (Telesco and
Harper 1980) which lends support to this theory. However the details
of these processes are very uncertain. Some galaxies appear to be
emitting more radiation than can be accounted for by a normal population
of stars, and so models involving recent bursts of star formation have been
23
suggested. The ratio M/L (total mass to infrared luminosity) can be
used to put constraints on the energy generation mechanisms: e.g.
M/L - 0.5 signifies recent star formation. The M/L ratios of some
galaxies detected are too low ( 0.002) for these galaxies to continue
to radiate at this level via thermonuclear reactions for a normal
galactic lifetime. Obviously more detailed studies, such as a 3m
telescope would be capable of (see later), will provide the basis of
more realistic models.
Active galaxies such as Seyferts and quasars also have in common
a high infrared luminosity, rising steeply towards longer wavelengths.
The emission processes in these objects are even more uncertain. For
most type 1 seyferts and for QSO's it is not at present possible to
decide whether the emission mechanism is thermal, non-thermal or a
mixture of both.
The increased photometric sensitivity of a 3m telescope would
allow the far-infrared luminosity and the constraints it provides on the
energy generation and emission processes to be obtained for many more
galaxies than at present. To illustrate this, Table 1.1 shows the
distances out to which some far-infrared sources could be moved before
the telescope would be unable to detect them with a S/N of 5 in a
10 minute integration. Most of the galaxies detected at -100 p. to
date must be exceptionally bright, otherwise more would have been detected
with 1m telescopes. Thus to suggest that, for example, the 3m
telescope could detect all seyfert type 2 galaxies out to ~ 1000 Mpc
would be very over optimistic. Probably as important, with a 3m
telescope (diffraction limited) objects about an order of magnitude
fainter (at similar distances to those already detected) could be detected
than with a i m telescope. The more galaxies we can study, the more
detailed are the models we can make. Table 1.1 also suggests that it
should be possible to detect sources similar to Orion or M17
24
TABLE 1.1
Distances out to which a 3m telescope could detect some bright Far-
Infrared Objects
Object Type Actual Distance Maximum distance detect-able with S/N = 5in lOmin at 100 u
c M 17 Giant H II 1.6 kpc 6 Mpc
M 42b H I Region 0.45 kpc 1.25 Mpc
NGC 253a Sc Spiral 3.4 Mpc 942 Mpc
M 83a Sc Spiral 8 Mpc 803 Mpc
M 51a Interacting 9 Mpc 378 Mpc
M 82a Irregular 3.3 Mpc 1000 Mpc
3C 273a Q.S.O. 950 Mpc 10,000 Mpc
NGC 1068a Seyfert Type 2
20 Mpc 2000 Mpc
NGC 4151d Seyfert Type 1
18 Mpc 300 Mpc
Note - Data taken from
(a) Telesco and Harper 1980,
(b) Werner et al. 1976.
(c) Harper and Low 1973.
(d) Telesco and Harper, 150th A.A.S. meeting.
25
in galaxies in the Local Group*
Active galaxies (e.g. 3C 273) could be monitored for possible
variations in flux level at long wavelengths (10-100 p) to distinguish
between thermal and non-thermal emission mechanisms. There is already
some evidence in the form of variations at 10 p for a non-thermal
emission mechanism for 3C 273. However the change detected was small
and doubling the estimated errors would seriously reduce the case for
variations (Reike and Lebofsky 1979).
The increased angular resolving power of the 3 m telescope will
also bring advances in the study of galaxies.
The sizes of the far infrared flux-emitting regions in galaxies
need to be measured for calculating M/L ratios. For some galaxies
showing a very low M/L value, the mass has had to be estimated because
the size of the emitting region is unknown and this could, at least in
part, account for the smallness of the ratio. For nearby spiral galaxies,
the sizes of the emitting regions that have been measured are in the
range 150-600 pc across. Sources - 500 pc across could be distinguished
by a 3 m telescope out to 12 Mpct whereas with a i m telescope the
distance is 4 Mpc. Also the - 8" resolution of the 3 m telescope
means that the central area of a nearby galaxy like M82 could be mapped
on a spatial scale of - 100 p.c . which might reveal structure in the
emitting material. Maps of infrared dust emission from nearby galaxies
could be made to locate star formation regions in their spiral arms.
In interacting galaxies, which are very bright throughout the
infrared, it is thought that tidal interaction triggers episodes of star
formation. Here a knowledge of precisely where in the system the far
infrared flux originates, such as could be achieved with the greater
angular resolution of a 3m telescope, would allow this theory to be tested.
In recent measurements at 80 p of M51 a beam diameter of 30" was used
(the diffraction limit of a 1m telescope). However, M51 can be divided
26
into two regions with very different optical properties: an inner
region - 7" across and a "ring" of early type stars out to - 20"
radius. Thus the interpretation of the far-infrared data is ambiguous
because the beam diameter was large enough to include approximately
equal portions of both regions (Telesco and Harper 1980). A 3 m telescope
would be able to resolve the central region, and thus make the origin of
the far-infrared emission clear.
1.5.2 Line Astronomy
Spectroscopic work, which provides detailed information on
conditions in the interstellar medium, is another broad area of research
that would benefit from the use of a larger telescope. High resolution
spectroscopy in the infrared is important because most vibrational and
rotational transitions of molecules, as well as many atomic and ionic
fine structure transitions and recombination lines occur in this wave-
length region. The most important use of fine structure lines is the
determination of very accurate relative ionic and atomic abundances and
electron number densities. Values determined from infrared measurements
are more accurate than those from optical forbidden line measurements
because dust extinction in the infrared is almost negligible. Molecular
lines provide information about abundances and the chemical processes
of molecule formation for those parts of the interstellar medium that
are cool enough and dense enough for molecules to form.
1.5.2(i) Molecular Clouds
These objects, which consist mainly of molecular hydrogen,
emit no visible or radio continuum emission and can only be studied
through their infrared continuum and infrared and radio line emission.
Star formation occurs when a dense cool cloud starts to collapse under
its own gravitation. Thus a knowledge of the molecular and atomic species
27
present in a molecular cloud can provide information about the very early
stages of star formation, since molecules are the building blocks of dust
and condensed matter . The heating mechanism in these regions is not
fully understood but possible energy sources include cosmic rays, star
light, and gravitational contraction energy. The main mechanism for
energy loss is infrared radiation from collisionally-excited molecules.
Since in equilibrium the heating and cooling rates are equal, studying
the molecular emission can put constraints on the possible heating
mechanisms. Many models of these regions have been made, which suggest
that molecules such as CO, H^ are important coolants, and predictions
of line fluxes from molecular coulds have been made.
The most abundant molecule, H^, is only directly detectable in
the infrared, while HD is similarly observable. These two lines are
very interesting because a measurement of their relative intensities
will allow the H/D ratio to be deduced. This is cosmologically important
because the amount of deuterium in the present universe is very sensitive
to the density of the very early universe. Predicted fluxes for the
28 ju H^ line and the 112 p. HD line from the molecular cloud near Sgr B2
are shown in Table 1.2 (taken from Kessler 1981), together with estimated
integration times for a 3 m and a i m balloon telescope. It can be seen
that the fluxes are just on the threshold of what is presently possible -15 -2
(recently detected line fluxes are about 10 W cm ) and of course the
models may be predicting values that are too high.
The ability to measure the spatial distribution of species and
to search for centres of local heating is also important, and here the
greater angular resolving power of a 3 m telescope will be invaluable.
For a detailed knowledge of the processes in molecular clouds it is
important to map for each molecule detected the regions where its
different energy levels are excited. A 3m telescope will be useful
28
TABLE la2
Integration times to detect some predicted infrared lines
from Molecular Clouds and H II regions, with S/N = 5
Object Species Wavelength Flux Integration Integration u -2 cm time time u -2 cm 3m telescope 3m telescope
Molecular Cloud HD 112 1.62xl0"16 9.5 sec 13 min near near Sgr B2 H 2 28 1.87xl0"16 7.2 sec 9.7 min
NGC 7027 0 III 88.35 21xl0"18 9.5 min 12.9 hours
W3A/IRS1 0 III 88.35 1.22xlO~16 16.8 sees 23 min
G45.5 + 0 III 88.35 2.08xl0"17 9.6 min 13 hours 0.1
G29.9 - 0 III 88.35 1.87xl0"17 12 min 16 hours 0.0
Notes : (i)
Cii)
(iii)
References for line flux predictions are in text.
Both telescopes were assumed to be detector noise limited
(taken as 10 W / J 1 T ) and to have 10% efficiency.
Integration times are for 1 spectral bandwidth so total
observation time will be much longer.
for this both because of its angular resolution and because its greater
flux collection will be needed to detect the molecular lines since they
are faint.
1.5.2(ii) H II Regions
H II regions are also intimately linked with star formation
as these clouds of hydrogen are ionized by radiation from recently formed
0 and B stars. Measurements of the infrared line emission from these
regions, which are usually obscured by dust in the visible, can yield
information on the atomic abundances, ionization structure and electron
densities in the plasma. A substantial amount of theoretical work,
using estimates for these properties, has lead to many predictions of
line fluxes from these regions. Where tested many of the predictions
have been inaccurate. Conversely by adjusting models to fit the
observations, they can be interpreted in terms of excitation conditions
in the regions. A few far infrared lines have been detected from H II
regions; for example Dain et al. (1978) measured an 88 u 0 III line -15 -2
flux of 1 x 10 Wcm from M42, while Moorwood et al. find a flux of -16 —2
6-1 x 10 Wcm for 0 III. from MI7-
Simpson (1975), used observed line spectra to calculate ionic
abundances for S IV, Ne II and Ar III. This procedure is then reversed,
and using a model for ionization structure, line intensities for several
planetary nebulae are predicted. Her prediction of the 88 p. 0 III
flux from N.G.C. 7027 is given in Table 1.2. Zeilik (1977) developed
a model for four compact H II regions, that matched their observed radio
and near-infrared emission and used it to predict the emissivity of many
lines. For the 10 p atmospheric window his values, where tested, are
too low but at larger wavelengths they are consistent with observations
(Kessler 1981). Some of his predictions for the 88 p 0 III line are
shown, with integration times in Table 1.2. In general the predicted
fluxes from H II regions suggest that many lines are an order of magnitude
too faint to be detected with present telescopes. Thus the order of
magnitude improvement in sensitivity possible with a 3m telescope should
allow the full development of this work.
High angular resolution in far infrared studies of H II regions
is also important. For example it is not possible to test models of
compact H II regions by observing where the far infrared flux originates,
to decide if the source is clumped or diffuse. The sizes of interest
fall in the range - 0.1 pc to -1 pc, A 3m telescope could resolve
100 p features of these sizes at distances out to the range 2.5 kpc
(0,1 pc objects) to 25 kpc, whereas for a i m telescope these distances
are 0.8 to 8 kpc. At present far-infrared measurements have the
double penalty of longer wavelengths and smaller telescopes when compared
with ground based ones. This is illustrated by Figure 1.2 (Wilson et al.
1980), which is a map of Ml7 made with a 102 cm telescope. A 3m balloon
telescope would be capable of mapping H II regions with high enough
spatial resolution to resolve physically distinct sources - so that the
energy sources and development of an H II region could be more fully
described.
1.5.2(iii) Interstellar Dust
Infrared observations can be used to measure the properties
of interstellar dust. Either by comparing predicted and measured fine
structure line ratios for a source of known properties, or by comparing
the intensities of infrared recombination lines and their radio equivalents,
the wavelength dependence of interstellar dust absorption can be evaluated.
At present, it is very uncertain whether this is a 1/ X or a
law. It is important to know the behaviour of the dust absorption at
infrared wavelengths because even at 100 p the optical depth to the
galactic centre is 1.6 (Erickson et al. 1977). By using a 3m telescope
31
Figure 1.2
-!6e GO-
-16° 7.'5-in <7>
2 O
-•S® 15 I-
RIGHT ASCENSION (1950.0)
A map of Mi7
32
the interstellar medium could be studied to further distances as more
remote sources (fainter) will be available to supply the emission against
which the interstellar absorption can be observed.
105.3 The Galactic Centre
Because the centre of our galaxy is obscured by dust in the
visible, it can only be studied at infrared, radio and X-ray wavelengths.
Existing infrared maps need to be improved with higher spatial resolution
to resolve the complex structure of sources for clearer comparison with
radio maps. This is illustrated by Figure 1.3 which shows far-infrared
and radio maps of the galactic plane. A 3m balloon telescope at 100 jLi
will have an angular resolution that is more nearly comparable to that
achieved from the ground on millimetre wave telescopes.
1.5.4 The Cosmic Microwave Background
The "big bang" theory of the universe predicts that the decoupled
radiation would continue to expand and cool to form a remanent background
radiation. The existence of the apparently thermal microwave background
and the fact that its spectrum is approximately that of a 3 K black body
as predicted is observational confirmation that simple models based on
a homogeneous, isotropic expanding universe can describe the development
of the universe. A major question is how the observed structure in the
universe (clusters, galaxies, stars) could arise from an approximately
homogeneous initial state.
This structure is thought to have formed through the growth of
density perturbations due to gravitational instability. The theories
suggest that there can be no features of the sizes of interest (e.g.
galaxies) before the end of the radiation dominated era. Thus, in order
to explain the observed structure of the universe small "seed" fluct-
uations must have been present when the radiation and matter decoupled,
after which they could start to grow. However if the simple model of
33
Figure 1.3 FIR and radio maps of the galactic centre
the universe is used a region of density enhancement grows algebraically
(slow). Given a size of feature in current epoch the theory then
predicts (working backwards in time) the minimum necessary size of
'seed' perturbation. On scales corresponding to galaxies, the pertur-
bations have 10 , where P = density, and this would cause
a temperature anisotropy in the radiation of a similar magnitude
(Longair 1978).
It is therefore important to search for temperature fluctuations
in the cosmic microwave background on scales predicted by the theories
to correspond to the sizes of present features. .Figure 1.4 shows the
fractional r.m.s. temperature fluctuations A T/t of the background
as a function of angular scale Cor mass of feature), calculated by
Sunyeav and Zeldovich (1970), for a number of different values of Q o
(the density parameter P /pcr. ). The horizontal bars on the graph
represent current observational limits (references to be found in
Bonyton 1978). Galaxies have masses M M 0 and for an
Q = 0.1 universe the expected fluctuations are shown on Figure 1.4 as
the doubly hatched region. Any experiment which penetrates this region
(or its lower extension) should detect fluctuations. A more general
region (for varying Q ) for the detection of fluctuations is shown
singly hatched. Neither region has been reached by current observations.
The 3 m balloon telescope is diffraction limited at 1 mm to
~ 1.5 arc minutes. Operating at 1 mm with A A = 0.4 and a
2 arc minute field of view it would be detector noise limited. Assuming
a detector N.E.P. of 10 W/ jHz , the 3 m telescope could be used to A S . —5 detect a variation in flux ( ) corresponding to AT/t — 10 in S
2.5 hours with a signal-to-noise (S/N) of 3. Again at the S/N = 3 —6
level AT/rp ~ 5 x 10 could be achieved in ~ 9 hours, i.e. about
the time allowed on a balloon flight. The 3m telescope is therefore
35
Figure 1.4
Sensitivity of measurement of the cosmic microwave background.
36
capable of detecting small scale fluctuations in the microwave background
with a sensitivity and spatial scale in the range where theories predict
such fluctuations should occur.
These types of measurements can also be used to study the "Sunyeav-
Zeldovich" effect. Here, relativistic electrons in a hot intra-cluster
gas such as is found in X-ray emitting galaxy clusters inverse-Compton
scatter the cosmic microwave photons to higher energies. Thus in the
direction of an X-ray cluster the background spectrum will have a
distorted shape, showing a slight decrease in intensity on the long
wavelength side of maximum and a corresponding increase on the other
side. There have been several attempts to measure this effect at
~ 3 cm and ~ 9 mm wavelengths and with one unconfirmed exception these
have failed to detect fluctuations down to ZaT/T 10 However
the Sunyeav-Zeldovich effect could have been masked by systematic effects
(for example bright radio galaxies in the cluster) and so it has been
suggested that the measurements should be attempted at around 1 mm
wavelength where these complications would be reduced and wider band-
widths can be used (Lake and Partridge 1980). The advantage of using
a 3 m balloon telescope for these measurements is that it will be above
almost all of the atmosphere so that the study is not restricted by the
use of the atmospheric windows or by atmospheric fluctuations. At the
same time the spatial scale possible with a 3 m balloon telescope will
be better than that with a i m telescope and its greater flux collection
will mean that it could detect a smaller effect than a i m telescope
could.
1.6 Compatibility with Satellite Telescopes
Satellites are the logical extension of using balloons to lift
telescopes above the atmosphere. By cooling the telescope a satellite
instrument can be made extremely sensitive because of the reduced
37
background in space. The total freedom from the atmosphere can also
be very important for spectral work where the precise details of the
atmospheric absorption spectrum can be very important. Because infra-
red detectors are cryogenically cooled there have been severe technical
difficulties in designing a satellite where the cryogens do not boil
off in a few hours or days. These have now been overcome and the first
infrared satellite, IRAS, is due for launch in 1982. Thus by the time
the 3m telescope is built, satellite observing time will also be avail-
able, and so it is important to show that a 3 m balloon telescope will
not become redundant.
A typical satellite mission can be expected to last for 1-2 years,
depending on its cryogen hold time, and the cost of ~ £50 million
means that they will be rare, so very little time will be available to
any one astronomy group. Also a satellite payload is seldom innovative
because the lag time between an experiment concept and its execution is
very long ~ 5-6 years. Once a balloon telescope is built however
its auxiliary instrumentation can easily be changed allowing greater
flexibility in its scientific uses. The few IR satellites planned and
under consideration are briefly described below and the relationship of
a 3m balloon telescope to their scientific objectives is discussed.
1.6.1 I.R.A.S.
This joint UK-Netherlands-NASA 60 cm cooled satellite telescope
has as its aim the first all sky survey at mid- and far-infrared wave-
lengths. A circle on the sky is scanned at a rate of 3.6 arc min. per
sec. in each orbit and the whole sky is covered in ^ 6 months (Moorwood
1978). If necessary the entire survey can be repeated in a second six
month period. The I.R.A.S. photometric bands have been fixed at
8-15 AI, 19-30 p, 40-80 ju and 83-119 p. and in addition two low resolution
spectrometers will provide information in the 7-14 and 13-24 p bands to
aid in identifying and classifying sources. As well as providing the
first census of known infrared object types, I.R.A.S. will hopefully
also discover new classes of objects. There will be a large amount of
follow-up work in all wavebands; confirming, identifying and studying
the new sources. The results of the survey will increase the demand for
telescopes capable of high spectral and/or spatial resolution investigat-
ions of the new sources and will be very important in determining the
uses of other I.R. telescopes, including a 3m balloon telescope.
1.6.2 The Space Telescope (S.T.)
Designed to take advantage of the absence of atmospheric turbu-
lence in space for optical astronomy this is a 2.4 m, warm (294 K), F/24
Cassegrain telescope. It will be possible to use the S.T. for infrared
observations if a focal plane chopper is used (Kleinmann 1975). The
S.T. will be deployed from the shuttle and is expected to last ~ 15 years
because further shuttle flights will enable its instrumentation to be
repaired or replaced. An infrared photometer system will probably be
included in the focal plane instruments at the first refurbishment in
the mid-19901s, and cooling of the detectors for about a year should be
possible. The main reason for using the S.T. in the infrared is its
angular resolving power, since it does not have cooled optics. A 3m
balloon telescope with a good pointing system could have equal angular
resolution and a similar sensitivity.
1.6.3 Infrared Space Observatory (I.S.O.)
This is a 60 cm cooled telescope with photometric bands out to
about 120 ju and two high resolution Ntichelson interferometers for
2-30 p spectroscopic work and is intended as an I.R.A.S. follow-up
mission (E.S.A. Sci(79) 6). Its long list of wide ranging objectives
include several speculative observations, made possible by its high
sensitivity, such as directly observing planetary systems forming in
young stellar objects and searching for protogalaxies at cosmological
39
distances. A 3m balloon telescope will be complementary to this
mission,since ISO will be unable to perform high angular resolution
studies, and for high resolution spectroscopy at wavelengths beyond
30 ju a warm 3 m telescope will have about 25 times more sensitivity
(Section 1.4.2).
1.6.4 Shuttle Infrared Telescope Facility
S.I.R.T.F. is a 1.16m cryogenically cooled telescope, designed
for repeated Shuttle/Spacelab flights. The telescope configuration
is basically Gregorian but with two additional plane folding mirrors.
This is unusual for a space telescope, because Gregorian configurations
tend to be longer than the equivalent Cassegrain, but the design has
the advantage of allowing a cold central baffle to be used for stray
light protection. S.I.R.T.F. will be ideally suited to photometric
observations of intrinsically faint and very distant objects and to total
flux measurement of extended sources (Moorwood 1977). It is hoped
that SoI.R.T.F. can be used to follow-up to the I.R.A.S. survey with
very deep surveys of limited parts of the sky. S.I.R.T.F. will be
more sensitive than a 3 m balloon telescope for photometric observations
but the balloon telescope will have about seven times more sensitivity
for high resolution work, as well as an angular resolution advantage.
1.6.5 German Infrared Laboratory (G.I.R.L.)
G.I.R.L. is scheduled for launch in 1986. It is a 0.4m cooled
telescope and will be used for both astronomical and atmospheric studies.
An important research area for G.I.R.L. will be the study of regions of
stellar formation, which includes the investigation of maser sources
and young stars. One focal plane instrument will be devoted to the
search for instellar molecular hydrogen, while aeronomic investigations
are aimed at improving our knowledge of the earth's middle atmosphere
40
(Lemke et al. 1979). Because G.I.R.L. is so small there will be no
overlap of proposed studies with the uses of a 3m balloon telescope.
1.6.6 Other Telescopes
There have been numerous other proposals for small cooled infra-
red telescopes with very specific objectives. For example a liquid
helium cooled 15 cm telescope is now approved for Spacelab 2 (Koch 1979)
with the aim of studying the quality of the spacelab environment for
infrared observations.
In addition a NASA supported design survey for a large (10-15
meter) space based telescope, diffraction limited at 2 ji, is underway
(Werner 1979). This would represent an improvement of an order of
magnitude in sensitivity over a 3 m telescope and more than three times
in angular resolution, and such a telescope would have unique capabilities.
1.6.7 Discussion
Since all except one of the approved telescopes are small, a
3 m balloon telescope will fill an important gap by being capable of
higher angular resolution work. In terms of sensitivity the distances
in Table 1.1 are of the same order of magnitude as those presented by
Van Duinen (1977) for I.R.A.S,, (since I.R.A.S. does not perform long
integrations) and so follow-up work on all the I.R.A.S. sources will be
possible. For example, the higher angular resolution of the 3m
telescope will allow the positions and sizes of I.R.A.S. sources to be
determined more accurately, so that possible identifications of I.R.A.S.
sources with optical or radio objects can be confirmed.
Since the S.T. is uncooled its sensitivity is almost the same
as that of a 3 m balloon telescope and the distances calculated by
Kleinmann (.1975) for the S.T. are very similar to those of Table 1.1.
Unlike the S.T., for spectroscopic work a balloon telescope is limited
41
by the residual atmosphere, however there are many astronomical infra-
red lines that do not coincide with atmospheric absorption features.
Although the 3 m balloon telescope will not have the capabilities
of the proposed 10m antenna, there are many important observations
which are impossible with a i m class telescope, yet do not really
require the sophisticated capabilities of a 10m telescope, and these
are included in the scientific objectives (Section 1.5). Thus if a
10m telescope is built a 3m balloon telescope will be needed to bridge
the gap between the present balloon and proposed space telescopes and a
very large space telescope. It is proposed to build a — 3 m prototype
for the 10m telescope and this will of course have similar capabilities
to a 3m balloon telescope. Also a 3m balloon telescope could be
operational for many years before the advent of a 10 m space telescope
and/or before the S.T. has an infrared photometer.
1.7 Conclusions
The largest of the present generation of balloon telescopes are
in the lm class and are limited in their uses by their size. There is
a strong case for a 3 m class balloon telescope which would bring almost
an order of magnitude increase in sensitivity and an improvement in
angular resolution by a factor of 3 over existing systems. These
improvements mean that the telescope will be able to carry out many
observations that are beyond the reach of present telescopes. The
scientific objectives of a 3m balloon telescope range from high spatial
resolution mapping of sources in our galaxy, line astronomy and sensitive
photometry of other galaxies to searching for small scale anisotropies
in the relic radiation. A 3 m balloon telescope is also complementary
to all the proposed satellite programmes. Altogether a 3m balloon
telescope would be an investment expected to bring (at present) some
unique scientific returns.
42
CHAPTER 2
BALLOON INFRARED TELESCOPES
2.1 Introduction
The two obstacles to far-infrared astronomy are the virtually
complete absorption of the radiation by the atmosphere and the fact
that the telescope and overlying atmosphere are themselves sources of
far-infrared radiation. This means that the telescopes have to be
lifted clear of the atmosphere and balloons, rockets and aeroplanes
have all been used (cf. Section 1.2).
Balloon telescopes are usually launched from the National
Scientific Balloon Facility (N.S.B.F.) in Palestine (Texas), although
facilities for ballooning also exist in the South of France and Central
Australia. In this chapter some of the general techniques and problems
of balloon infrared astronomy are described. A review of some of the
larger or more innovative balloon telescopes is included, to illustrate
those features which directly affect the feasibility of a 3m telescope.
The final section collects all these features together, to set down the
design criteria for a 3m balloon telescope.
2.2 Chopping
The need to keep the infrared background as low as possible, from
the point of view of noise, has already been mentioned in Section 1.4,
Typically the signals to be measured are - 10 times smaller than
the background, so the performance of the telescope is dependent on its
ability to reject background fluctuations, and all infrared balloon
telescopes must include some means of doing this.
Ideally the telescope should be alternately moved from background
only to source plus background and the difference taken between the
two measurements. This is not generally practicable because the
43
telescope's inertia is so large that this type of modulation must be
done at low frequencies ( ̂ 1 Hz). At these frequencies the background
may change significantly during the sample period, and the detector
noise will be much higher than at frequencies ^ 10 Hz. The two
classes of solution which permit wobbling the telescope beam between
two sky positions at higher frequencies are secondary mirror choppers
and focal plane choppers.
Focal plane choppers use a third (or fourth) mirror near the
focal plane to move the beam seen by the detector back and forch across
the sky. Figure 2.1 shows schematically three arrangements for focal
plane choppers (Low and Reike 1974)„ Secondary mirror choppers rock
the secondary mirror about an axis orthogonal to the telescope optical
axis and so have to move a much larger and heavier mirror. To keep
power consumption low and reduce unwanted vibrations resonant systems
are often used. Secondary mirror choppers have the advantage that it
can be easier to obtain a large angular throw on the sky, and no extra
mirror, with its added background emission, is needed.
2.3 Launch and Landing
A variety of launch techniques are used by the NSBF, depending
on the size and weight of the payload. The most commonly-used
technique is a dynamic launch which results in a minimum jolt on the
payload at launch. The balloon is filled with just enough He gas for
about 10% lift. This "bubble" at the top of the balloon is released
and a launch vehicle manoeuvers the payload until it is directly under
the ascending balloon. When the balloon is fully extended above the
payload it is released from the vehicle. The largest launch truck,
'Tiny Tim' , can accommodate gondolas as tall as 10m, with up to 20 m
in one of the horizontal directions. Weights of up to about 3000kg
have been successfully launched in this manner. Very heavy payloads
of 6500 kg have been launched by a static technique which is capable 44
Figure 2.1
REFERENCE^) SOURCE
CHOPPER DISC
A A
r • , >
/
Different types of chopper.
45
handling up to 18 000 kg. (Kubara 1974).
During the float to altitude the temperature of the payload
changes by about 70°k, on a relatively short timescale. When the
mirrors and telescope structure undergo a temperature change AT, the
focal length, f, of the telescope changes by At = f(a - Ct ) A T
where ct g and ^ are the thermal expansion coefficients of the
structure and mirror materials respectively. Thus potentially large
focal shifts must be compensated for, either in the design or in aligning
the optics just before launch.
Accurate position reports are essential and are accomplished by
radar and radio direction finding.
In the final stages of a flight the balloon is followed by a
light aircraft and the flight is terminated by a telecommand (sent from
the aircraft) which separates the balloon from the parachute and gondola.
The gondola descends with a terminal velocity of about 7 meters per
second. A 3g acceleration on parachute opening is not uncommon and
most payloads are designed and rigged to withstand lOg. The pilot
of the recovery aircraft directs the recovery team on the ground to the
impact location, and the payload is disassembled and returned to the NSBF.
2.4 Guiding and Telemetry
Another major disadvantage of a far-infrared telescope is the
total lack of access by the experimenter to the payload during operation.
As for a ground-based telescope, to achieve useful scientific goals it
is necessary to point the telescope to any given- celestial source in
the sky, some of which are optically invisible. A balloon gondola is
subject to transient jerks and rotations produced by the balloon's motion
so that pointing a telescope mounted on it presents a severe servo-control
problem. Various methods of providing positional information for control
have been developed and these are described, where appropriate in the
sections describing individual telescopes. 46
The ability to have remote control over the payload and to
recover data accurately from the telescope are very important, so the
NSBF provides a telemetry and command system for this purpose. This
is based around a pulse-cooled modulation (P.C.M.) system with data
encoders and decoders. Commands and data are transmitted to and from
the telescope over an h-band R-F carrier.
2.5 Balloon Telescopes
In this section the general features of several balloon telescopes,
which illustrate the current state of the design,are described. Innovative
features and points which might be considered for a large balloon
telescope will be particularly noted.
2.5.1 The Center for Astrophysics - University of Arizona
Telescope (102 cm)
This telescope, an f/13.5 Cassegrain, has a f/2 spherical,
aluminium alloy primary and a Pyrex aspheric secondary which is used
as the chopper. The telescope is mounted in a rectangular, tubular
aluminium frame gondola which is about 5m high and 3m wide, including
protective crash rings. The structure is very massive so that the
frame can easily stand repeated use without misalignment of the telescope
axes. The payload weighs about 1800 kg (Fazio et al. 1974).
The telescope is positioned and controlled by means of servo-
controls on the elevation and azimuth axes. In azimuth the reaction
forces are provided by a large reaction wheel mounted on the gondola
centre line below the telescope. For coarse pointing, azimuth is
determined with respect to the horizontal component of the geomagnetic
field, and altitude with respect to the local vertical. Fine pointing
is controlled by two precision rate-integrating gyroscopes mounted on
the base of the tube. The telescope can track any point in the sky
with an accuracy of ~ 8 arc sec per minute (Fazio 1977).
47
This telescope has been used to make high resolution far-infrared
maps of H II regions and the galactic center,as well as observing the
planets and extra-galactic objects.
2.5.2 The University of Arizona Cooled Telescope
This Cassegrain telescope is unusual because it is small and
cooled. The entire telescope is mounted in a liquid helium dewar with
an 18-inch diameter opening. The boil-off flow of helium gas is not
sufficient to prevent air entering and condensing on the optics. To
overcome this the top of the telescope is covered with a 5 u thick
polyethylene window. The membrane's thermal emission is negligible
in comparison with the sky. Twenty-seven litres of helium are held
in a stainless steel reservoir behind the primary mirror and the tele-
scope is cooled by the boil-off gas, while the detectors and filters
are on copper heat sinks directly in the liquid. (Campbell 1979).
The telescope is mounted on an elevation drive which is in the
centre of the gondola and the electronics and telemetry package is used
to counter-balance the telescope. The gondola is stabilized in
azimuth against the earth's magnetic field and is always operated in a
scanning mode in altitude. Positional data is provided by stars
detected by a visual photometer mounted on the telescope framework.
(Frederick et al. 1974).
Tests have shown that the telescope, with a large field of view,
is atmospheric noise limited and it could be used at higher altitudes
than normal (140,000*) to reduce the background still further and
improve sensitivity. This is important because the main purpose of
this telescope is to survey the galactic plane at four colours with as
high a sensitivity as possible, to discover new sources of far-infrared
radiation and to map low surface brightness emission. (Campbell 1979).
48
2.5.3 The University of Arizona Linear Scanning Telescope
Like the University of Arizona telescope described previously
(2.5.2) this telescope is small and uses novel techniques to reduce
the background. A 20 cm diameter spherical mirror is used as a
Herschellian telescope (off-axis angle 5°) to avoid any non-reflecting,
high emissivity surface within and around the beam. An essential part
of this telescope is the dewar window which consists of a membrane only
4JJ thick, which produces negligible background. At low altitude it
is protected from ambient pressure by a cover which can be removed in
flight. (Low, Poteet and Kurtz 1974).
The mounting is of the alt-azimuth type with azimuth angle
controlled by a magnetometer fixed on a turntable which can be steered
by a command signal from the ground. (Nishimura, Low and Kurtz 1979).
The instrument itself is very light (about 350 lbs) and can easily be
taken to high altitudes to achieve low background levels.
The telescope is designed to survey the galactic plane over a
large area and has been used to produce detailed far-infrared maps of
some parts of the galactic plane. An interesting feature of the design,
which facilitates surveying, is that chopping is achieved by rocking the
primary mirror to produce a linear displacement of the beam at the
speed of 5° per second on the sky in the cross-elevation direction.
2.5.4 The University College 60" Telescope
Glass mirrors mounted in an aluminium alloy tube are used for
this Cassegrain telescope. In order to compensate for temperature
changes, the telescope is defocussed in the appropriate direction
before launch.
The telescope is placed within a strong frame which is itself
within an outer protective framework of small aluminium members. During
flight additional roll bars and protective panels are added as required.
49
The mounting is basically alt-az, but the telescope is supported in
an elevation/cross elevation gimbal assembly. Three orthogonal
directions are thus available for fine control.
Coarse stabilization uses error signals from a small magnetometer
for azimuth control and from a potentiometer on the elevation axis
for elevation. Fine guidance is achieved with two star sensors
mounted on the telescope barrel. Initially the system is locked onto
a bright star using a star sensor with a wide field of view (2°). The
second star tracker, with a 10T field is now brought in by offsetting
it from the first star sensor and pointing it towards the second
(fainter) guide star. The limiting magnitude of these star trackers
is about 7-8 (Furniss et al. 1976), so guide stars close to an object
of interest can usually be found.
The overall weight of the system, excluding telemetry is about
950 kg. Photometric and spectroscopic studies are carried out using
this telescope.
2.5.5 The Imperial College Balloon Telescope
This f/7, 41" Cassegrain telescope has a spherical primary and
secondary. The spherical aberration was kept smaller than the
diffraction limit by the appropriate choice of mirror radii of curvature
and separation. Both focal plane and secondary mirror choppers have
been used with this telescope.
Since it is constructed entirely of aluminium alloy (including
the optics) , there is no need to refocus this telescope at altitude
Additionally the use of solid aluminium, rather than glass optics offers
a factor of 10 more resistance to permanent damage on landing (Joseph
et al. 1977). The telescope tube is an open structure using conventional
serrier trusses, while the primary cell is constructed of hollow tubing,
so it is a relatively light design.
50
The telescope is designed to be flown on the SERC stabilized
balloon platform. This platform is stabilized in three axes; azimuth,
elevation, and roll, about a central gimbal torque motor cluster which
is suspended from the balloon. Instead of using a reaction wheel the
platform is driven against the inertia of the balloon itself.
Astronomical programmes with this telescope include far-infrared
photometry, polarimetry and high resolution spectroscopy.
2.5.6 Submillimeter Wave Sky Survey Telescope
This 1.2 meter Cassegrain telescope is designed for surveying the
galactic plane at wavelengths longer than 100 p. It has a chopping
secondary mirror which can produce a beam separation of up to one degree
on the sky. It is one of the most recent balloon telescopes to be
built and makes substantial use of microprocessors to maximise its
observing efficiency and flexibility. The detector system consists
of a linear array of three bolometers mounted in a helium dewar on a
line which is perpendicular to the direction in which the telescope
scans and chops. This is described in detail by Silverberg et al. (1979).
An alt-az mount is used, the elevation drive consisting of two
D C torque motors, while azimuth is controlled by driving a reaction
wheel. A null magnetometer and a local vertical reference are used
for coarse stabilization and finding .whereas a two-axis gyro is used
as an inertial reference during scanning of selected sky regions.
The overall gondola is very similar to the Center for Astrophysics
University of Arizona payload (2.5.1). It is 4.3m high and 3.4 m in
diameter including an outer crash ring. An inner gondola made of
aluminium tubing supports and protects the telescope and the outer
crash rings are made of thin walled tubing to act as shock absorbers
when the telescope lands. The full payload package, exclusive of the
balloon, weighs approximately 1900 kg at lift-off.
51
Microprocessors are used to control flight sequencing, telescope
pointing (both altitude and azimuth), servo-systems and the formatting
of data for telemetry. Should this system fail, the microprocessors
can be overriden and slews in both azimuth and elevation can be commanded
from the ground
The sole purpose of this telescope is to perform a high sensitivity,
moderate spatial resolution survey of the Galactic plane at wavelengths
larger than 100 u.
2.5.7 The University of Gronigen Telescope
The f/2 primary mirror of this 60 cm Cassegrain is made of diamond-
turned aluminium and weighs about 20 kg. The all-up payload weight is
about 1000 kg.
It has an alt-az mount in which the landing platform provides
the inertia for the azimuth servo to react against. Fine guiding is
accomplished using an image dissector star tracker, sensitive to 5th
magnitude stars, which is mounted so that the centre of the 8° star-
tracker field of view is aligned with the axis of the infrared telescope.
Electronic gimballing is used to offset the telescope towards the
infrared source. This is accomplished by inserting electrical bias
signals into one or both of the servo-control loops. Error signals
are then required from the star tracker to satisfy the servo null
condition, so the control system rotates the telescope until the tracker
output error signals are equal and opposite in sign to the input
bias signals.
Scientific instruments which have been designed for use with
this telescope include a 4-channel photometer, a 2-channel, 2-detector
simultaneous photometer, a variable aperture field stop, and a civo ~
genically-cooled Fabry-Perot interferometer with a resolution of 2 000.
52
285O8 The Max-Planck Institute Telescope
This is a lm aperture f/14 Cassegrain with a chopping secondary-
mirror and a 1 arc min field of view. It is unusual because it is the
only balloon telescope to date with a light weighted primary mirror.
This 100kg, gold coated, honeycomb Cer-vit mirror which was designed
and manufactured by Owens-Illinois and figured by Zeiss, is lighter by
a factor of 2 than an equivalent solid mirror.
The telescope is housed in an open-framed structure suspended
by a 3-axis inertial gimbal. A similar structure surrounds the
electronics package which is used to balance the payload. Despite the
light weighted primary the total weight of 1950kg (including ballast)
is typical of others in its class.
Two star trackers with fields of view 90° apart on the sky
provide a pointing accuracy of less than 1 arc minute with a stability
15 arc sec (Drapatz 1980). It is intended to use this telescope to
carry out a wide variety of studies which include low resolution mid- and
far-infrared spectroscopy, polarimetry and heterodyne spectroscopy.
2.6 The Constraints on a 3 m Telescope
2.6.1 General design considerations
The designs described in Section 2.5 show that even the most
recently built telescopes are of a rigid, heavy construction. Most
telescopes have an alt-az type mounting and are stabilized in two axes.
For a large (i.e. 3m) telescope this configuration is essential as it
is much easier to balance an alt-az telescope and control the tube
deflections, since gravity is always in the same direction.
Although some telescopes are launched with the telescope tube
horizontal, most telescopes have a vertical tube during launch and
descent. Landing with the primary mirror horizontal results in a more
even distribution of stresses across the mirror and so decreases the
53
possibility of permanent damage. Thus from the point of view of
structural rigidity the 3 m telescope payload should land with the
tube upright.
Roll bars and crash padding are an essential part of any gondola
as payloads do not always land on a convenient site. For example they
have landed in forests and marshes, and so it is very important to
protect the optics and instrumentation as much as possible.
Another feature of existing systems that must be adapted to a
3m telescope is structural simplicity. To aid recovery, the roll bars
and padding of the telescopes are easily removed from around the instru-
mentation. Similarly the mirror mountings are simple, so that if
necessary they can be removed at the impact site. If more than one
balloon flight is required it is also important to be able to easily
replace damaged parts of the telescope when it is returned to the NSBF.
2.6.2 Size Limitation
If the telescope has the general design features described above,
the size of the telescope is constrained by the size of the launch truck.
For a dynamic launch; the most favourable method, this allows a maximum
payload height of about 10m. For a launch with the tube vertical,
allowing for crash padding underneath the primary mirror and clearance
between the tube and the top of the gondola a reasonable telescope length
would be 7 m.
Although the truck could accommodate up to 20 m in a horizontal
direction, the 10m height is still a limiting factor since the telescope
must be able to swing up towards the vertical when in use (often to
within 30° of it). Since the centre of gravity will be near the mirror,
even if the launch/landing forces for a horizontal launch were found to
he tolerable the gain in allowable length would be relatively small
( 4: 1 m) . Additionally, it will be easier to maintain alignment
54
tolerances with a * short* 'light tube, since the deflection for a given
stiffness will be less than for a long tube.
The criterion used in the optical design of the telescope is
therefore that its length should be limited to 7 meters.
2.6.3 Weight Limitation
The weight of the telescope is limited not only by the
capabilities of the launch truck, but also because the telescope must
be lifted above most of the atmosphere. Payloads with weights in
excess of 3000 kg have been flown to altitudes beyond 34 km using 6 3
* ordinary* 21 x 10 ft balloons. Altitudes of about 28 km are
sufficient for most far-infrared work. Table 2.1 shows some balloon
sizes for different payload weights and altitudes. A reasonable weight
for a dynamically launchable 3m telescope seems to be about 3000-4000 kg.
Although this could be much higher if a static launch is used (of 2.3),
the payload weight should, ideally, be as low as possible to minimise
handling problems.
The weights of the telescopes described in Section 2.5 show that
a simple * scaling—up* of these designs would not be feasible and so a
more efficient structure is necessary. A light weighted primary mirror
will be an essential feature of a 3m telescope, because for equal
stiffness solid mirrors the weight of the mirror is proportional to the
diameter cubed. With the use of a lightweight primary, a careful
analysis of the deflections, and stresses in the gondola on landing,
should allow a minimum weight-maximum rigidity payload to be designed,
which will fit this weight budget. 2.6.4 Conclusions
Balloon telescopes have to be rugged enough to withstand launch
and landing forces, and reliable enough to maintain pointing accuracies
55
TABLE 2.1
Typical Balloon Systems
Inflated Volume of Balloon (106 ft3)
Suspended Load (kg)
Altitudes (km)
4.3 1179.3 30.7
5.1 1905.0 29.0
11.6 1451.5 35.7
14.6 2086.5 35.2
20.8 2267.9 36.0
26.6 1088.6 40.7
32.1 4535.9 33.5
24.6 3460 34.1
21.6 3029 34.4
From: Winzen Research Inc.Ready Reference on Ballooning.
56
of a few seconds of arc. Thus the structure of the payload must
provide adequate protection for the instrumentation. It should he
possible to partially disassemble and reassemble a 3m telescope so
that it can be more easily recovered and refurbished after a flight.
The two principal design constraints on the telescope are length and
weight. In order to launch the telescope with the mirror horizontal
the length of the optical configuration must be less than 7m. The
maximum payload weight should be approximately 4000 kg so that the
telescope can be readily lifted high enough to carry out the scientific
objectives described in Chapter 1. This weight limit means that a
light weighted primary is essential. In the following chapters the
various design options for the mirror, optics and structures are
evaluated and compared.
57
CHAPTER 3
LIGHTWEIGHT MIRRORS
3.1 Introduction
The most important constraint on the design of a 3 m balloon
telescope is the total payload weight (Section 2.6). The weight of
the primary mirror determines the overall weight for the telescope,
because the lighter the mirror, the lighter its support system and
hence the whole telescope. So the feasibility of the 3 m telescope
is strongly dependent on the achievable minimum weight for the optics.
The aim of this chapter is to present an overall view of the current
state-of-the-art of lightweight mirror manufacture so that a feasible
baseline mirror for the 3m telescope can be chosen for further study.
Traditionally, astronomical mirrors are made in the form of right
circular cylinders. The self-weight deflection of such a structure 2 2
is proportional to (D /H) where D is the diameter and H is the thick-
ness of the mirror, and so large high performance systems require very
thick and heavy mirrors to maintain the desired mirror shape. Since
the late 1920*3 many scientists and engineers have experimented with
small specimens of ideas for the production of lightweight mirrors.
The primary mirror of the 200 inch Hale telescope was the first example
of a large lightweight astronomical mirror, and its design embodies much
of the technological reasoning used today in lightweight mirror design.
This mirror was designed with a ribbed back (Figure 3.1) mainly in order
to increase the surface area in contact with the surrounding air and so
decrease temperature gradients across the mirror surface and the
distortion they cause. The ribbed design also allowed for a weight
reduction of 50% without a proportional loss of stiffness. For an
equal deflection under its own weight a solid disc would be 14" to 15"
58
Figure 3.1
The back, of the Mount Palomar 200" mirror
59
thick and would weigh about 40 tons (Loytty 1969). However from a
weight/rigidity standpoint this structure is very inefficient because
the back is- not closed off, and modern lightweight mirrors, with weight
reductions of up to 80%, are designed with integral front and back
plates.
In recent years there has been a growing interest in both fast
and lightweight mirrors and many advances in lightweight mirror tech-
nology have been made. For space-borne telescopes such as the S.T.
(Section 1.6.2) the main problem to be solved was that of weight and
this has been a large driving force behind the development of extremely
lightweight optics. The need for a new telescope technology using
lightweight primaries has also arisen from the trend towards larger
ground based telescopes. It is well known that without the use of new
design features the cost of a large ground based reflecting telescope
rises as the 2.6th power of the mirror diameter. In general a reduction
in cost requires a reduction in weight which, in turn, means a reduction
in telescope length (fast optics) and the use of a lightweight mirror.
The very large telescopes currently under consideration, such as the
Texas 7.6m or the National New Technology Telescope (N.N.T.T.), would
be prohibitively expensive if their designs did not incorporate these
features. The next generation of space-borne telescopes such as the
proposed 15 meter millimeter-wave telescope (Section 1.6.6) will require
a further development in lightweight mirror technology.
In 1977-78 Matra Espace Ltd. carried out a survey of lightweight
mirrors for the European Space Research and Technology Centre. They
gathered together the available technical information on several types
of mirrors, so that those areas in which further development work was
needed for the production of space optics could be identified. This
chapter, while including many of the general findings of the Matra survey,
60
brings up to date the details- of achievements in lightweight mirror
technology and includes- some techniques not covered by the Matra survey.
In Section 3.2 some general design considerations for a telescope mirror
are discussed and the properties of some commonly used lightweight mirror
materials are summarized. This forms the background to the following
sections, in which each of the various types of lightweight mirrors and
the techniques involved are described and their suitability for a balloon-
borne telescope assessed.
3.2 Properties of Materials
In order to achieve diffraction-limited performance, there are
very small tolerances on the shape of an astronomical mirror. If we
assume that we start with a mirror of perfect geometry then spherical
changes of 1/4 of a wavelength in surface displacement will cause a
shift in focus, and non-spherical changes of the same amount will
noticeably affect the aberrations in the image. The generally accepted
standard for a diffraction-limited astronomical mirror is that its figure
should be accurate to < A / 2 0 r.m.s. deviation i.e. about 3 p. for the
far-infrared telescope of this study (Section 4.8). Four important
design considerations for astronomical mirrors (for any type of telescope)
are therefore thermal stability, thermal expansion, ease of obtaining
and retaining surface finishes, and the mechanical characteristics of
the material used to fabricate the mirror. The parameters of interest
for mirror materials are density (/?), elastic modulus (E), thermal
conductivity (K), specific heat (C) and the coefficient of thermal
expansion (Ct). These properties are listed in Table 3.1 for some
materials that are commonly used to make lightweight mirrors. To
facilitate the comparison of different mirror materials some figures of
merit can be derived from the basic material properties (Barnes 1977) by
considering the mechanical and thermal behaviour of a mirror.
61
TABLE 3.1
Mechanical and Thermal Characteristics
of Mirror Materials
Material P E K c O< Material , 3 g/cm N/cm2 x 106 V J / M K J/KgK do" 6 K " 1 )
Fixed Silica 2.2 7.32 1.37 741 0.56
Pyrex 2.35 6.8 1.02 835 3.2
U.L.E• 2.20 6.88 1.31 766 0.03
Cervit 2.5 9.18 1.70 840 0.03
Beryllium 1.85 28 220 1.82 xlO3 12.4
Aluminium 6061-T6 2.71 6.90 171 960 23.0
Graphite Epoxy G9-70/x-30 1.78 9.3 35 (in )
(plane) - 0.02 "Isotropic"
Note: Data compiled from Barnes (1979) and Kaplan et al. (1978).
62
Mechanical distortions of balloon telescope mirrors have in
general two different causes: the action of external forces on the
mirror from its mount during the operation of the telescope (self-
weight deflections) and the action of launch and landing stresses
which must not exceed the elastic limit of the material. The self-
weight deflections cannot be allowed to deform the mirror either in
use or during polishing operations and so the stiffness-to-weight ratio
^/p is a very important criterion for material selection. The
higher the value of E/P the better the stability of the mirror under
stresses.
Thermally-induced deformations can arise as a result of uniform
heating (or cooling) across the face of the mirror, leading to overall
changes in mirror curvature. Radially non-uniform face heating will
cause surface irregularities. The magnitude of the thermal expansion
coefficient Ct is important because it affects the magnitude of both
surface variations and gross curvature changes. A high value of the
ratio K/ ct means that the dimensional change caused by thermal
expansion is minimal for uniform heating conditions. The higher the
value of K/Ca the better the overall stability of the material to
temperature changes, since this ratio also takes into account the time
taken to reach thermal equilibrium. This is an important consideration
for a balloon telescope since it undergoes a temperature change of about
75°C in the two hours or so it takes to reach float altitude (Section 2.4).
Another important figure of merit is the thermal diffusivity
D = K/pC. The lifetime of a thermal transient is proportional to D,
while the magnitude of the induced thermal distortion is proportional Ct
to /D. Thus, in order to minimise thermal distortion one either
uses a material with a very low Ct and a very low D or a material of
high diffusivity for which Ct is also higher. Low expansion glasses
fall into the first category while metals are mainly in the second. 63
Table 3.2 lists figures of merit for some typical lightweight mirror
materials-.
The microscopic properties of a material may also be very
important. Barnes (1979) has shown that a strain level as low as -5 . . .
10 may significantly affect the optical performance of a large mirror.
Thus microcreep, the permanent dimensional change of the material under
an applied stress, can be important. The microyield stress, viz, the —6
stress required to produce a permanent strain of 10 , is often used as
a measure of how easily this can occur and is therefore included in
Table 3.2. If the microyield stress is low it is likely that residual
stresses will relax in service and there is then a high probability that
dimensional changes will occur. These instabilities can be greatly
reduced by proper stress relieving through chemical etching or heating
processes after the machining and figuring of the mirror. A further
problem arises if the material has a thermal anisotropy - a difference
in direction and magnitude of the thermal expansion coefficient as a
function of position in the structure. Such a material will change
its shape with a uniform temperature change even in the absence of
thermal gradients. This is particularly a problem for beryllium, which
even after careful processing has a thermal expansion anisotropy in -6
3 orthogonal directions of 0.1 x 10 per degree K, and for graphite
epoxy materials where the expansion coefficient along the direction of
the grains differs greatly from that in the other two directions. This
is discussed in more detail in the relevant sections below.
In the following sections different concepts in lightweight
mirror design are examined from the point of view of the materials and
manufacturing processes involved and the state-of-the-art reached.
3.3 Glass Ceramics
This category of materials is primarily represented by ''Cervit",
made by Owens-Illinois in the United States, and Zerodur, made by Schott 64
TABLE 3.2 - Figures of Merit for Mirror Materials ^ ^
Material E/J olO6 K/A< .106 K/CO( ,103 D = K(jPC
•104 Microyield Stress
107 N/m2
Fixed Silica 3.32 2.44 3.29 8.40 5
Pyrex 2.89 0.31 3.71 5.19 8
U.L.E• 3.12 43.66 56.9 7.7 5 ( i )
Cervit 3.67 56.6 67.3 8.09 6 <*>
Beryllium 15.13 17.7 9.72 653 1.7
Aluminium 2.54 7.43 7.73 657 12 - 14
Graphite Epoxy G -70 x-30 "Isotropic"
5.22 (May be as high as 16)
1750 - - -
Notes: (i) Greater than the ultimate tensile stress,
(ii) References as for Table 3.1.
in Germany. Glass ceramic is defined as an inorganic non-
porous material containing both glass and crystalline phases, and is
characterised by its method of production. A base glass is produced
by the standard melting procedures of the glass industry and formed in
the usual way by casting or blowing. Small, randomly distributed
crystals are then formed in the glass by a complicated heat treatment.
The properties of the material are principally determined by the
properties of the crystals and their separation.
The excellent transparency and polishing qualities of Zerodur
are obtained by ensuring that the chemical compositions of the crystal
and glass phases are very similar, so there is little difference in
refractive index and hardness between the crystals. In Cervit the
average crystal size is of the order of a wavelength of visible light,
and this material can be polished to a smoothness of 7 X r.m.s. Both
crystal size and thermal expansion coefficient are controllable by
additives such as aluminium and lithium and the composition used in
these ceramics has a temperature coefficient constant to within
i 1 x 10 7/°C over a temperature range from -80°C to 150°C. (Simmons
1969).
The lightweighting technique developed for glass ceramics is to
machine cavities into a solid blank. Holes are drilled into the back
of the mirror, corresponding to a chosen web arrangement. Machine
tools then operate through these holes, undercutting the backplate and
enlarging the holes into accurately positioned cavities (Figure 3.2a,b.
and Table 3.3). A wide variety of cavity sizes and shapes are
possible as the web thicknesses and location are freely variable.
After removing the desired material the mirror is finished as an
ordinary glass blank and then acid polished to remove any surface
imperfections. This method results in a completely monolithic
structure with large 1 fillets' between the webs to further stiffen
66
Figure 3.2
3 W o i / V / V / J '/ I J \
a) Plan of Cervit mirror with triangular cavities
b) Section A-A
TABLE 3.3 Parameters for Cervit Mirror
Diameter
Cavity Entrance Hole
Rib thickness
Fillets
Center to center distance between fillets
Number of Cavities
Weight
64"
2J" diameter
0.20"
3/4,f radii, 1|"diameter hole
7.30"
138 large
55 small cylindrical
1068 lbs. From Simonen 1969. 67
the structure. Since 1969, tools that will operate through much
smaller holes than those shown in Table 3.3. have been developed and
the removal of up to 75% of the weight of the solid blank is now
readily achieved (Kaplan et al. 1978).
3.4 Low Expansion Glasses
These include Pyrex (Corning Glass Works) and Duran 50 (Schott),
both of which are borosilicate glasses made conventionally by melting
oxides. Their thermal expansion coefficients tend to be high when
compared to the other glasses (compare Pyrex with Cervit in Table 3.1).
Mirrors made of these materials may be subject to thermal distortion
problems. In addition they are very difficult to process. The cost
is about a factor of 30 lower than that of glass ceramics and very low
expansion glasses, and for this reason experiments with honeycombed
pyrex panels are being conducted at the University of Arizona. By
using a honeycomb, thermal distortion will be minimised while the
structure is kept light. It is hoped that such mirrors can be used
in a larger version of the Multiple Mirror Telescope.
3.5 Very Low Expansion Glass
The two most commonly used materials in this category are high-
purity fused silica and a 7% titanium-doped silica glass (Corning U.L.E.).
Fused silica is a synthetic amorphous silicon dioxide manufactured by
flame hydrolysis. It has a very low thermal expansion coefficient
(Table 3.1) over the range 0 to 300°C, while at low temperatures (-100°C)
it is essentially zero. Fused silica is therefore a very attractive
choice for mirrors which have to work at these low temperatures. U.L.E.,
a synthetic amorphous silica glass manufactured by the same process as
fused silica, comes from the furnace in discs about 6 feet in diameter
and 6 inches thick which can be fused together to form solid mirror
68
blanks of theoretically unlimited size (De Voe 1969). Because the
titanium impurity ions substitute for some of the silicon ions in the
glassy network, U.L.E. has a coefficient of thermal expansion fifteen
times less than that of fused silica (Table 3.1). Figures 3.3(a) and
(b) show the thermal expansion of U.L.E. over the range -200 to +200°C
and its thermal diffusivity over the range 0-800°C. U.L.E. was chosen
as the mirror material for the Space Telescope because of these excellent
thermal properties, as well as the fact that it may be light-weighted.
The construction of lightweight, rigid mirrors using fused silica
and U.L.E. is possible because pieces can be fused together without
destroying their shape. At temperatures of 1600-1700°C these materials
soften just enough that two pieces will flow into one another, and
Corning have now developed a technique which allows the heat to be
applied to specific areas only, so that monolithic cores can be fabricated.
However, the basic technique (used for most mirrors to date) is to build
an eggcrate assembly as in Figure 3.4 by fitting precision ground
struts together. The top and bottom plates are then fused to this
assembly (which is not completely monolithic). Up to 70% lightweighting
over a solid mirror of equivalent rigidity has been achieved (Kaplan
et al. 1978).
The Space Telescope mirror substrate represents the current state
of the art of large lightweight 'glass' mirrors. A monolithic core was
made by fusing together accurately machined parts into a square celled
honeycomb pattern (Figure 3.5 ). By removing the discontinuities
of the ribs and providing a continuous shear path, a much greater stiff-
ness-to-weight ratio, compared to the basic eggcrate design, was achieved.
The rings for the outer and inner edges were made by sagging plane
strips of U.L.E. over a mould (Lewis 1980). The completed parts were
then placed in position and the entire assembly heated to 1600°C to fuse
it into a completely monolithic structure. Table 3.4 lists the
69
Figure 4.10
(ajThermal Expansion -200° to + 200*0 140 120 100 80
60 40 20 0
- 2 0 - 4 0 —60 - 3 0 -100
1 1 1 I I i
1 1 I I N ! 1 1 1 i 1
1 1 II 1 M 1 1 1 1 1 1 1 M M
i 1 M I I | —20(J -100 0 100 femoeralure—*C
Specific heat. 25rC cal/gm'C 0.183
Thermal conductivity. 25°C. cal cm/cm' sec *C 0 00313
Thermal diffusivity. 253C. cm'/sec. 0.0079
200
fb^Thermal Diffusivity
0 100 200 300 400 500 600 700 300 Temoe'Jturf - *C
Thermal expansion properties of ULE
70
Figure 4.10
Assembly of a ULE eggcrate
Figure 3.5
A monolithic ULE honeycomb
71
structural parameters of the S.T. mirrors.
Because U.L.E. is an ideal material for space applications, work
has now begun on techniques for making much lighter mirrors. For
maximum weight reduction the core cells must have the greatest possible
area, the thickness of the core walls must be as thin as possible and
the thickness of the front and back plates must be kept to a minimum.
The possible reduction of wall thickness in the core is at present
limited by the techniques used. For very thin walls the local heating
needed to cause fusion also makes the wall sag, destroying the honey-
comb structure. Recent advances in the technique of frit bonding, the
use of a glass 'solder' which has similar properties to U.L.E. and bonds
strongly to it, at a lower temperature (900 C), suggest that large
mirrors with an overall density of approximately half that of the S,T.
substrate will be possible by the 1990's (Murphy et al. 1980).
3.6 Beryllium
For lightweight structures beryllium stands out because it has
a stiffness/density advantage of about a factor of five over any of
the other materials (Table 3.2). Unfortunately beryllium crystallises
at low temperatures with a hexagonal crystal structure that leads to
an anisotropy in many of its physical properties. For example the
thermal expansion coefficients that are parallel and perpendicular to —6 o
the crystal axis differ by about 3 x 10 per C. Highly expensive
"pressureless sintering" techniques (Figure 3.6) produce a random
orientation of crystals but at present this imposes an upper limit of
1.6m on the size of blank that can be produced (Kaplan et al. 1978).
It is possible to polish bare beryllium surfaces (Paquin and Goggin
1972) so that coating is not necessary, but beryllium has a low micro-
yield stress (Table 3.2) and stress relaxation when in use could cause
instability. A beryllium mirror must be subjected to extensive etching
72
TABLE 3.4
SPACE TELESCOPE MIRROR PARAMETERS
Diameter 98" (2.4 m)
Front and backplate thickness 1" (2.5 cm)
Core Depth 10" (25 cm)
Strut thickness 0.20 (.5 cm) 2 Weight 400 lb/m = 820
From Lewis, 1980.
73
Figure 3.14
74
and heat treatment to reduce residual stresses. A major disadvantage
of beryllium is that it is very toxic when in the form of small
particles or vapours, and it is therefore difficult to handle and
machine. However, despite the expense, beryllium was chosen as the
substrate for both I.R.A.S. and I.S.O. because the good heat transport
properties of this metal, coupled with its high stiffness-to-weight
ratio, make it an ideal choice for small cryogenic mirrors.
Some of the advantage of the low density of beryllium is lost
because the lightweighting must be achieved by machining out solid
blanks and this results in less efficient material removal than with
the UoL.Eo techniques. The most commonly used method is to machine
out the back of a mirror as in Figure 3.7(a) and then close off the
back with a similar piece of material with the braze joint along the
neutral axis as in Figure 3.7(b). For very thin walled 'eggcrates'
at the limit of this technique, a mid-section 'splitter1 plate is used 3
(Figure 3.7(c)). Mirrors with a bulk density as low as 120 kg/m and
a flatness of 150 & have been produced by this method, which is limited
to sizes of up to 1.6m diameter because optical-grade beryllium is used. 3.7 Titanium
Recently Spawr Optics have developed a method of making large,
stiff lightweight mirrors from titanium, using a honeycomb technqiue.
In response to an initial enquiry it was estimated that a 3 m,-f/2 sphere
would weigh about l/6th of the weight of a similar beryllium mirror.
Despite further enquiries no more details of the structure, cost or
weight of one of these mirrors is available.
3.8 Aluminium
The availability, good strength (especially when annealed),
weldability, machinability and low cost of aluminium make it a parti-
cularly attractive material for a balloon telescope mirror. The main
75
Figure 3.7
a) Core drilling pattern in beryllium
^ TA YA /
s \ V T v \
b) Two pieces brazed to form an 1eggcrate1
• S S S V S S S . S S S
TT ^=='splitter plate*
f ; / ; Vs y ; ]>-7-r jL
c) A thin-walled eggcrate
76
problem with using aluminium as a mirror material is that it cannot be
polished to a good quality surface using standard polishing techniques.
It can, however, be accurately figured using single-point diamond
turning techniques and if the raw surface quality is not sufficient an
electroless nickel coating is deposited on the figured surface and
final figuring and polishing is performed on this layer. It has been
suggested by Barnes (1966) and others that aluminium is a poor choice
as a mirror material due to the bi-metallic deformations which will
occur between the aluminium substrate and the nickel surface coat.
Two one-piece 1.5m aperture lightweighted aluminium telescope
mirrors have been fabricated at the Lunar and Planetary Laboratory and
are regularly used at the Catalina Observatory without this problem
(Forbes 1969). The high thermal conductivity of aluminium means that
differential thermal effects are negligible for these telescopes.
A 40 cm, f/3, welded segment lightweight mirror, made at the
University of Arizona, was thermally cycled from 30° to -35°C several
times and then tested at -35°C (Forbes 1969). The mirror was welded
using a material of identical coefficient of expansion to the aluminium
used and has a radial rib construction, (shown in Figure 3.8), the final
figuring being performed on a 76 p layer of nickel. The tests showed
that the mirror figure changed by less than one wavelength, a factor
of 10 less than the bi-metallic theory predicts. Forbes concludes that
the technique of using ribbed and welded segments, with a central support
system, could be extended to considerably larger structures in the
3-4m class.
Because aluminium can be easily welded, unlike beryllium, it is
possible to use the same sort of lightweighting methods as are used for
U.L.E. Additional mounting blocks can be welded into the structure
whenever they are required.
77
Figure 3.7
O -
\
A radially ribbed aluminium mirror
78
Large blanks of aluminium have been cast by Tinsley Laboratories
and used to make light weight solar reflectors of up to 18 ft. diameter.
Table 3.5 lists some typical dimensions of these mirrors. For maximum
rigidity and uniformity of loading, a geodesic pattern of connected
ribs with a terminating rim (Figures 3.9(a,b)) is attached to the
circular disc which forms the mirror surface . The mirrors are made
from 5086 aluminium alloy because it has a very stable crystalline
structure and the construction methods used are basically those of the
heavy metal industry (Taylor 1975). The front disc is made of two
semicircular plates that have been hydraulically formed to approximately
the right curvature. After attaching them to an assembly jig they
are automatically welded together, and the rib structure is constructed
on the back. All intersecting surfaces, rib-rib, rib-dish, rib-rim,
and rim-dish are then welded, working progressively away from the center.
Final optical grinding and polishing is carried out on an electrolytically-
plated nickel layer.
Electronic Space Systems Corporation (E.SS-C.O.) use a similar
technique to construct lightweight, all-aluminium panels for radio and
ran wave telescopes. The panels have a thin face sheet bonded to an
array of channel-shaped grillage members (Figure 3.10), The technology
is capable of 25 p r.m.s. surface accuracy on a panel with a surface 2
area of 21 ft that weighs about 1.76 lbs. per square foot of surface
area. Although a reflective surface of optical quality and accuracy
has not been made to date, it should be possible to do so on a single-
piece 2^/2 - 3 meter dish made by this technique if a nickel coating
were lapped and hand finished in the standard optical manner (Rhoades
1978).
Another interesting technique, which might be adapted for a 3m
balloon telescope, has been developed by R.B. Leighton at the California
79
TABLE 3.5 - A Tinsley Laboratories Mirror
Diameter
Spherical Concave Radius of Curvature
Accuracy of Curvature
Slope Error
up to 18 ft.
120 ft.
± 0.3%
4 - 6 arc sec,
From Taylor 1975,
Figure 3.9
a) The geodesic pattern of a Tinsley Laboratories mirror
b) Cross-sectional view of mirror
80
Figure 3.10
An E. S. S. C. 0. panel
81
Institute of Technology and has been used to build 10 m, antennae
suitable for submillimeter work down to 300 u wavelength (Leighton
1978a). The dish consists of a number contiguous aluminium
honeycomb panels attached to a steel support structure which is a
tubular framework based on a lattice of equilateral triangles. This
is illustrated in Figures 3.11(a) and (b) . All the members are fabri-
cated to precise, computer-calculated lengths, and while the structure
can be wholly or partially disassembled and reassembled with negligible
dimensional change, it is mechanically rigid. The open upper surface
of the honeycomb is machined to shape using a high speed knife-edged
cutter. The reflecting surface of 0.040" sheet aluminium, selected
for its uniformity and freedom from surface irregularities, is pre-
sheared to the correct outline, coated with epoxy and elastically
deformed to mate with the honeycomb surface. After the top skins
are cemented to the honeycomb panel faces, the panels are re-mounted
on the support frame and the dish surface and shape is measured by an
electronic linear transducer. The resulting signal is transformed
into a contour map of the dish surface, drawn on the dish itself, via
a chart recorder and a series of coloured pens. Optimisation of the
overall dish shape is achieved by adjusting the panel-support screws,
while the various high areas of each panel are etched away by dilute
Na Qh. Providing enough care is taken in the mechanical design of the
supporting truss, this method could be adapted to smaller telescopes,
to be used at shorter wavelengths and perhaps an all-aluminium arrange-
ment would be possible (Leighton 1978b).
3.9 Replica Mirrors
Replication is basically a technique for making a large number
of high accuracy mirrors from a traditionally polished master mould.
The replication of large mirrors has recently been demonstrated by
82
Figure 4.10
su PPORT F R AMI HON EYCOM • PANELS
a) Cut-away and plan view of mirror
83
Talbert Reflectors and their manufacturing process is briefly described
below (Talbert 1977).
A steel dome forms the mould support for overall shape control,
and an acrylic liner overlaid on the dome is the optical surface on
which the mirror is cast. The liner is held in place by a vacuum
and optically ground and polished to the desired finish, after which
all except the desired reflector area is masked off. The front
surface of the mirror is formed by pouring several thin layers of epoxy
onto the optical surface, the epoxy being cured when the overall
thickness is 0.05". To provide the structural rigidity of the mirror,
a substrate consisting of two epoxy-fiberglass laminates enclosing an
aluminium honeycomb core- is fabricated separately. The substrate and
front surface are sealed together with a thin layer of silicon rubber.
Releasing the vacuum allows the liner and mirror to be separated from
the steel dome, and thermal stress is then used to remove the liner
from the mirror. Figure 3.12 shows a schematic layout of one of these
mirrors.
In principle there is no size or shape limitation, but individual
reflectors are at present limited to dimensions of about 3 x 4 m due
to tooling constraints. Mounts can be attached anywhere on the back
skin without affecting the surface. The structure is inherently
lightweight and stiffness can be varied considerably without corresponding
weight penalties. Table 3.6 shows the structural characteristics of
two nominally stiff mirrors. Their very low weight makes this type
of mirror very attractive for a large balloon telescope. However
thermal coefficients for figure change have not been assessed either
theoretically or in practice. Considering the wide variety of materials
used it seems likely that the mirrors will suffer from thermal distortion
problems.
84
Figure 4.10
Schematic layout of a Talbert Laboratories mirror
Al H O N E Y C O M B 2 - 8 " THICK
6 P L I E S F I B E R G L A S S C L O T H A N D C O R E - B O N D I N G \
R E S I N . 30* F I B R E ROTATION
B E T W E E N EACH PLY
0-05* EfOXY
' B A L A N C I N G L A M I N A T E '
F I B R E S I N OPPOSITE
D I R E C T I O N TO P L I E S
BE LOW
/
0-0 IS M O X T
1/ R̂.T.V S I L I C O N R U B B E R
Size
6 x 10.75 ft.
21 x 41 in.
TABLE 3.6 - Two Sample Replica Mirrors
Thickness Weight
63/8"
23/ 8"
200 lbs.
20 lbs.
Density
3.1 lb/ft'
2.7 lb/ft'
From Talbert 1977
85
3.10 Active Optics
The active mirror concept involves the continuous correction
of a mirror figure which is allowed to deform under its own weight.
Either the mirror is divided into separate segments, each of which is
moved as a rigid body until the optimum arrangement for the whole is
reached, or a single mirror is fitted with a large number of Tpush-pull'
actuators on its back to deform the surface into a diffraction-limited
figure. In any active optical system accurate figure sensing and
sophisticated computer systems are necessary. Figure sensing is
based on using interferometric techniques, with either a laser or
distant point s-ource providing the reference wave. Wavefront errors
which are detected in this manner are used to control the actuators.
Many different concepts have been reported in the literature but very
few experimental efforts have been successfully completed (Barket and
Jones 1980). In general, for sizes up to a few meters in diameter
continuous faceplates with actuator control are proposed, while for
larger sizes the only feasible approach is to use segmented mirrors
because of manufacturing problems.
The thin continuous mirror approach has been confirmed to infra-
red wavelengths with the building and testing of a stacked actuator
deformable mirror (Everson et al. 1980). Figure 3.13 is a schematic
diagram of the mirror and Table 3.7 lists the device parameters. A
plane mirror was made, and surface deformations of up to 8.5 p. , into
predetermined shapes, were achieved. On the Space Telescope the
primary mirror is fitted with 24 actuators as a backup system in case
a long term distortion occurs (Cuneo 1980). The Multiple
Mirror Telescope is the only telescope to date which puts into practice
a figure sensing mechanism. Its active correction system was not as
successful as planned but fortunately it was found to be adequate
86
Figure 3.13
A stacked actuator mirror
actuator stacks
TABLE 3.7 - Parameters for Actuator Mirror
Clear Aperture
Actuators
Maximum Volts
Surface Deformation
Mirror thickness
Reference
23 cm
37 on inner 16.5 cm only
1500
8.5 p max.
0.3 cm
Emerson et al, 1980.
87
(Shannon 1981). In view of the undeveloped state of the art active
mirrors, although they would be very light, cannot be envisioned for
a large balloon telescope.
3.11 Membrane Mirrors
Membrane mirrors are an extension of the active control idea
to the control of the shape of a thin, optically-coated membrane by
either electrostatic or hydraulic means. They are included in this
survey for completeness, as the technology is still in its infancy.
However a membrane mirror is the lightest mirror concept to-date and
could be seen as a technique of the future for balloon telescopes of
aperture even greater than 3 m.
The electrostatically controlled membrane mirror (E.C.M.M.)
is a thin electrically conducting membrane that is accurately tensioned
and positioned by electrostatic forces. Reflector shape is maintained
by varying the electrical potential between the membrane and segmented
electrodes behind it, using closed-loop control. An important
component of this adaptive structure is the figure sensor that monitors
the surface quality to furnish error signals to the control loop. An
E.C.M.M. is shown schematically in Figure 3.14. When a voltage is
applied between the unstressed membrane and the back electrodes, the
electrostatic attractive force draws the membrane inwards. By selecting
the number of control segments and the voltage applied to each any
surface figure can be generated (Mihora 1980). Tests have been made
on small scale models (up to 1 m) and the electro-mechanical stability
of the membrane has been investigated. To avoid the problems of
resonances a high natural frequency is required, and this will be
achieved by increasing the pressure on the membrane, by increasing the
electric field behind the membrane, on a 4m prototype to be built in
the near future. In addition, Forward (1979) has developed an
88
Figure 3.14
The electrostatically controlled membrane concept
90
electronic technique to damp out very low amplitude vibrations, (for
any type of membrane mirror).
An axisymmetric surface can be created by stretching an elastic
membrane over a circular frame and then applying a uniform pressure to
one side. The resulting surface is stiff and stable, actual character-
istics depending upon the TbowlT depth-to-diameter ratio, the modulus
of the material, the thickness-to-diameter ratio of the membrane and
the amount of prestretch in the membrane before pressure is applied.
Talbert Reflectors have constructed an experimental 30 cm diameter
diaphragm mirror with 0.025 mm thick aluminised polyester film. Initial
tests indicate that, without degradation of the coating, the radius of
curvature may be varied continuously and repetitively from 1m concave
through flat to 1m convex (Talbert 1978) , with a surface smoothness
suitable for visual applications. The membrane shape, for a given
radius of curvature depends on the amount of prestretch and is not
therefore a simple parabolic or spherical form. Vaughan (1980) has
derived an analytic solution for the membrane shape and used it to
predict the image aberrations of a membrane mirror. This theory was
tested against an 0.8 m diameter mirror with a depth of 0.08 m, and
is only valid for shallow bowls (f/2). Experiments with servo control
of the mirror figure are being conducted by Talbert Reflectors.
Casal et al. (1981) are pioneering another variation on the
membrane technique, for solar collectors and millimeter wave telescopes.
By inflating large envelopes, composed of cylindrical gores cut out of
rolls of polyester film,beyond the elastic limit, spheres several meters
in diameter can be formed by a plastic deformation process. The films
utilized are a few dozen microns thick and become elastic once more
after the deformation. They have developed a method for determining
the profile the gores should have so that when subjected to uniform
91
pressure the membrane deforms into a selected profile. Experimentally,
the method was verified on a cap of 1,8m diameter cut from a 4m diameter
sphere made up of 32 gores each 36 um thick. Agreement between theory
and experiment was excellent, except at the gore joints.
In summary there are numerous technological problems to be
solved. In particular,although the behaviour of membranes themselves
have been controlled,the backup support systems have not yet evolved
beyond laboratory Ttest rigs1. For example, the inflatable membrane
mirror described by Vaughan was made by stretching the membrane over a « i
massive steel pressure vessel so the total system is hardly lightweight.
Large electrostatic mirrors require the fabrication of precision
membranes. For this reason studies on Parylene, which can be vacuum
polimerised onto an optical glass surface and then removed, have been
initiated (Mihora 1980). Thus it will be several years before membrane
mirrors can be envisaged on the ground or in space.
For reference Table 3.8 lists manufacturers of lightweight mirrors
and their products. However, before selecting the mirror type for
the 3m balloon telescope, the figuring of mirrors is reviewed since
this has important implications for the optical configuration of the
telescope. 3.12 Figuring
In order to assess the feasibility of different optical designs
the technological limits on the f-ratio and asphericity of the primary
mirror need to be known.
Fused Silicon and U.L.E. mirrors are approximately figured by
sagging over a male mould, and final figuring is done in the traditional
manner by hand grinding and polishing. This technique was used for
both the S.T. mirror and the mirrors for the M.M.T. The mirrors are
sagged to a sphere with approximately the right radius of curvature
92
TABLE 3.8
Mirror Manufacturers-
Company Material Supplied Type of Products
S cho 11, Germany Zerodur Plain Blank supplied.
Zeiss, Germany None Lightweighting of Zerodur.
Owens-Illinois, USA. Cervit Plain Blank supply.
Corning, USA ULE, Fused Silica Lightweight Blank supplied.
Haeraus, Germany Fused Silica Lightweight Blank supplied.
ITEK, USA. None Lightweighting of Glass and Ceramics.
Perkin-Elmer, USA. None Lightweighting of Glass, Ceramics and Metals.
Electro Fusion, USA. None Lightweighting of Beryllium.
Speedring/Shiller, USA.
None Lightweighting of Beryllium.
B.A.C. U.K. None Lightweighting of Beryllium.
RoEoOoS.Co France None Undercutting of Glass Ceramics, Large Size Polishing.
Dornier, Germany ) )
H.S.Do U.K. ) \
A1 Honeycomb C.F.R.R Coated
Antennae
) Ford Aeronautics, )
USA )
E.S.S.C.O. None Large Size A1 Antenna.
Tinsley Laboratories None Large Size Solar Collectors.
California Institute of Technology
None 10 Meter A1 MM Wave Telescope
Talbert Reflectors-, USA.
None Large Size Replica, Membrane Mirrors
93
and so any asphericity is introduced at the grinding stage. Thus
although spheres as fast as f/1.5 to f/2 could be made, highly aspheric
figures or off-axis mirrors are not possible.
Metals are figured by single point diamond turning a solid
blank, or cutting of a honeycomb (Leighton). For a given asphericity
the amount of material to be removed in aspherizing is proportional to 3
(l/frat£Q) . Modern computer controlled machines coupled with
*real time* testing methods that provide accurate contour maps of the
surface now make possible the production of mirrors as fast as f/1.5,
although this is extremely difficult (Meinel 1980).
The two *dish type* techniques described figure the reflectors
by preforming the panels before the supporting ribs are attached.
Tinsley Laboratory reflectors typically have f-ratios in the range
2 to 3 and are spherical (Taylor 1975). However,one of the E.S.S.C.0,
designs has an f-ratio of about 0.4 for the primary dish (Kaufmann and
D*Amato 1973).
A further problem with fast ( - f/2), on-axis mirrors is that
they are more susceptible to large self-weight deflections. This is
because the curvature of the mirror causes a curved 'neutral axis' with
an offset center of gravity. If the mirror is traditionally mounted by
points on its back surface this can cause an unacceptable gravity sag
when the mirror is on edge. This problem was recently overcome for a
small (20 inch), f/1.7, lightweight fused silica mirror, by using
symmetrical front and back plates as shown in Figure 3.15 (Pepi and
Wollensak 1979). Such a design has a straight neutral axis and the
center of gravity is directly in its line of action.
Traditionally, an off-axis aspheric is made by cutting the required
portion out of an axisymmetric mirror, thus making fast off-axis mirrors
impossible. Computer controlled machinery has now made it possible to
94
Figure 4.10
A symmetrical L. W. Mirror
95
grind an asphere directly into the surface. Erickson (1979) reports
off-axis mirrors made on a conventional milling machine, and gives as
an example a f/5 parabola, diffraction limited at 20 p. Recently a
process for single point machining of glasses has been developed (Sangar
and Baker 1980) and so this capability should be possible in glass too.
For replicated optics there is in principle no limit on the speed of
asphere that can be produced.
The most recent innovation in figuring art is the method
developed by Lubliner and Nelson (1980). In general the idea is to
apply an appropriate set of forces to a mirror blank so that after a .
sphere has been ground and polished into the blank the forces can be
removed and the polished spherical surface deforms elastically into the
desired non-axisymmetric (i.e. off-axis) surface. The method assumes
that the mirror is uniformly thick and solid, and so although it allows
the production of fast off-axis parabolas (f/2 for the segment) it is
not applicable to the types of mirrors being considered for a 3 m balloon
telescope.
In conclusion, spherical mirrors .and on-axis, slightly aspheric
mirrors as fast as f/1.5 to f/2 are possible, although there may be
mounting and self-weight deflection problems for mirrors faster than
about f/2. Replica mirrors are still the only method of producing
fast, far off-axis aspheres.
3.13 Choice for a 3 m Balloon Telescope
The mirror chosen for the 3 m telescope should be as light as
possible and readily manufactured. Membrane mirrors, active mirrors
and titanium mirrors are not sufficiently developed (3.11, 3.10, 3.7),
while large replica mirrors have uncertain thermal stability (3.9).
Thus the potentially most lightweight mirrors cannot be considered, at
present, for a 3m balloon telescope. Glass ceramics and low expansion
96
glasses are the heaviest of the mirrors reviewed because the light-
weighting technique used (coring out the back) is not as efficient as
those used with other materials.
Because the optical components in a telescope have stringent
spacing tolerances between them it is a considerable design advantage
to have mirrors and connecting structures made from the same materials,
to minimise thermal adjustment problems, (Section 2.4). Thus the
choice for the 3 m balloon telescope is limited to an all-beryllium
telescope, an all aluminium telescope, or a U.L.E. mirror with a carbon
fibre support, since the thermal coefficient of carbon-fibrous material
can be chosen so that it is a good match to that of U.L.E.
An all-beryllium structure is not an attractive prospect, not
only because beryllium is very expensive, but also because of the handling
difficulties mentioned in Section 3.6. It is important that a balloon
telescope can be refurbished on site, if necessary, and this would be
difficult with a beryllium telescope. Additionally, manufacturers of
lightweight beryllium mirrors use optical-quality, isotropic beryllium
which at present limits the size of mirror to about 1.7m.
A U.L.E./carbon-fibre construction would be very expensive and
the weight of a U.L.E. mirror, although much less than that of a solid
mirror, is still substantial. This is because they are designed to
meet optical specifications, which are about a hundred times more stringent
than those for a far-infrared mirror. The aluminium techniques used
for mm-wave antennas (Tinsley, E.S.C.O.) are just a coarser version of
the fU.L.E. method*. For the 3m far-infrared telescope of this study
a surface accuracy between those of optical and mm-wave mirrors is required.
Thus the most cost-effective approach, and the one offering potentially
the greatest weight-saving, is to take as a baseline design an all-
aluminium welded honeycomb mirror. Such a mirror uses the structure
97
of a UoLoEo or beryllium mirror, but is made in aluminium. This single-
piece mirror is therefore very similar to the one suggested by Rhodes of
Electronic Space Systems Corporation (3.8). It is a compromise between
the stiffness- of structure used for optical and mm-wave mirrors.
Because the 3 m mirror requires a greater surface accuracy than a
mm-wave dish, the f/0.4 figure of one of the E.S.C.O. mirrors would not
be possible and the f-ratio of the mirror chosen should not be faster
than f/2. This is compatible with achievements for optical quality
mirrors and should avoid the problem of excess gravity sag mentioned in
Section 3.12. Since none of the lightweight techniques considered have
been used to make highly aspheric or far off-axis mirrors, the 3m
telescope mirror should have a figure that is within the capability of
conventional techniques, which allow a deviation of a few millimeters
from a sphere.
The baseline mirror design is a half-way point between the designs
of Tinsley Laboratories and E-S.S.C.O., and the welded radially-ribbed
design. Further details of the mirror structure are discussed in
Section 5.3.
98
CHAPTER 4
OPTICAL DESIGN OF THE TELESCOPE
4.1 Introduction
Optical design is the selection and arrangement of the curvatures
and spacings of the elements of an optical system so that the physical
features of the arrangement and the characteristics of the image produced
by the system are suitable for its intended application. The optical
system of a reflecting telescope consists of a primary mirror to gather
and focus the radiation, and secondary optics, if required, so that the
desired f-ratio is achieved with the focus in a convenient position.
There are four general categories of optical configurations for telescopes:
Prime focus, Cassegrain, Newtonian and Herschellian, all of which have
advantages and disadvantages for a three meter far-infrared telescope.
For any infrared telescope the infrared background should be as
low as possible and for the 3 m balloon telescope there is an additional
constraint on the optical design because the total length is limited to
7m (Section 2.6). In this chapter the different telescope configurat-
ions are assessed and compared in terms of size, f-ratios, weight and
infrared performance. The preferred system is then analysed in more
detail, including the evaluation of alignment tolerances for the final
design.
4.2 The Prime-Focus Configuration
This is the simplest telescope design, consisting of only a para-
bolic primary as shown in Figure 4.1. The length criterion is easily
met with an f/2.3 parabola which is within the manufacturing capability
for a lightweight aluminium mirror (Section 3.12). In addition it has
a significant weight advantage over designs which require secondary
optics. The major drawback when compared with other designs is that
99
Figure 4.1
A prime focus arrangement
Figure 4.2
A Herschellian arrangement.
100
there will be a very large infrared background emission from the focal
plane instruments and their supporting structure, which will be directly
viewed by the detector. Additionally a focal plane chopper would have
to be used (cf. Section 2.2). Because of its infrared background
problems a prime-focus telescope would not be the best design choice
for a far-infrared balloon telescope.
4.3 The Herschellian Telescope
An off-axis segment of a parabolic mirror is used as the primary
mirror in this design (Figure 4.2). Because there is no central
obscuration, it will have a very low infrared background. The slowest
Herschellian telescope which will fit the length criterion will be about
f/2.3, and the parabolic segment must be far enough off-axis that the
focal plane instruments and their supports are clear of the edge of the
primary mirror. Taking this distance as a minimum of 30 cm, the mirror
is an off-axis section of an f/1 parabola, and the asphericity at the
edge corresponds to a deviation of about 18mm from a sphere. The
removal of so much material is well beyond conventional polishing
techniques which can make mirrors only as fast as f/1.5 (Section 3.12)
In view of the typical speed of a Tinsley Laboratory mirror (Section 3.8)
and the welded honeycomb design chosen for the 3 m telescope mirror
(Section 3.13), the mirror required for a Herschellian telescope does
not have a realistic speed. So a Herschellian configuration would not
be suitable for the 3 m telescope of this study.
4.4 The Newtonian Telescope
This is the simplest of the two-mirror configurations. The
secondary mirror is a flat at 45° to the axis of the parabolic primary
so that the beam emerges at 90° to the axis, as shown in Figure 4.3.
By using this configuration it is possible to place the detector clear
101
Figure 4.3
A Newtonian arrangement
diameter of secondary (m) Figure 4.4
1 _L I J. 1 2 3 4 5 6
primary focal ratio
Secondary diameter as a function of primary focal ratio for a Newtonian telescope.
102
of the primary mirror, without the length problems of the Herschel
design, but at the expense of some obscuration of the primary by
the secondary.
The diameter of the secondary mirror is a function of the
primary f-ratio and the separation of the two mirrors, the minimum
diameter for a given f-ratio corresponding to the maximum separation
of the mirrors. For a 3m telescope the choice of mirror separation
is governed by two constraints: the focus and instrumentation must
be clear of the primary mirror edge (30 cm, as for Herschellian), and
the maximum possible mirror separation is 7 meters. Figure 4,4 is
a graph of the minimum possible secondary diameter as a function of
the primary f-ratio (F ), For F ^2.8 it was assumed that the P P
focus is at the minimum possible distance of 1,8 m from the optical
axis, while for F^ 2.8 the separation is fixed at the maximum
of 7 m. Because the secondary is at an angle to the primary axis
it will be elliptical and the secondary diameters in the graph are
the lengths of the major axis of the ellipse.
The smallest possible secondary has a major axis of 0.94 m
and a minor axis of 0.64 m, corresponding to an f/2.8 primary.
Since a small obscuration is very important and the secondary diameter
increases rapidly on either side of this minimum, this combination is
the only Newtonian design that is worth considering as a far-infrared
balloon telescope, A 45° angle between the flat and the telescope
axis means that a rigid support system is needed to maintain tight
tolerances on the position of the mirror. The telescope tube must
also support the instrumentation, because of the position of the focus.
Newtonian telescopes therefore have a weight penalty when compared to
103
the other two mirror designs where the tube has only to support the
secondary.
4.5 The Cassegrain Telescope
In the Cassegrain configuration the secondary mirror is convex
and so the focus can be located conveniently behind the primary
mirror (Figure 4.5). Several systems have evolved which correct for
one or more of the Seidel aberrations by the appropriate choice of
conic sections for the mirrors. Table 4,1 shows the different classes
of Cassegrain telescope and the aberrations for which they are corrected.
The classical configuration is often used because the mirrors are
easy to figure by conventional methods and it can also be used at
prime focus if required. Dall Kirkham systems have a smaller field
of view than the classical Cassegrain, third order coma being about
four times worse (Meinel 1969), but have the manufacturing advantages
of spherical mirrors. The Swarzchild designs have the widest field
of view, being corrected for three aberrations, but the final image is
usually located inconveniently between the two mirrors (W.etherell and
Rimmer 1972). Ritchey-Chretien designs have larger fields of view
than the classical Cassegrain and are often the preferred choice for
space telescopes. Systems with two curved mirrors are very versatile
because they allow greater freedom in the choice of overall f-ratio and
tube length than any other configuration.
For infrared telescopes the actual design is constrained by the
need to keep the background radiation as low as possible (Section 2.6),
and so a variety of techniques for minimising the background from
Cassegrain telescopes have been developed. Unlike optical telescopes in
which an oversized secondary is used to prevent vignetting, an infrared
Cassegrain has an undersized secondary to prevent the detector seeing
radiation from the structures around the edge of the primary. A wide
104
Figure 4.5
A Cassegrain arrangement.
Name Type of Primary Type of Secondary Corrected for
Classical Cassegrain
Parabola Hyperbola Spherical
Gregorian Parabola Concave hyperbola placed beyond prime focus
Spherical
Dall Kirkham
Spherical elliptical
Conic sphere
Spherical
Swarzchild Aspheric Aspheric
Spherical, Coma Astigmatism, or Spherical,Coma
Ritchey Chretien
HyperBoloid with eccentricity
1.05 to 1.15
Hyperboloid Spherical Coma
TABLE 4.1 - Different Types of Cassegrain Telescope
105
field of view is less important for an infrared telescope because large
images are not required and the detector is almost always placed on
the optical axis. The background can be further reduced by ensuring
that the detector does not receive radiation from the warm supports
of the focal plane instrumentation or the secondary optics. This is
done either by making a central hole in the secondary, which matches
the shadowed region of the primary, or by placing a tilted flat mirror
at the centre of the secondary mirror. In both cases the detector
then views the cold sky instead.
The constraints applicable to a Cassegrain design for the 3 m
balloon telescope are now described. At 100 p. the angular diameter
of the Airy disc is - 17 arc sec, while a typical detector size
is ^ 1,5mm. Matching angular resolution to detector size therefore
requires a plate scale of the order of 12 arc sec mm \ which implies
a focal length of the order of 16 m. Ideally the design chosen
should have an f-ratio in the range 6 to 9. The primary mirror focal
ratio (Fp) should be greater than or equal to 2, so that the mirror
can be readily manufactured. Taking account of the mirror thickness
the back-vertex-focus distance b (shown in Figure 4,6), which has to
allow room for the mounting of instrumentation behind the primary
should be in the range 0,5 to 0,9m. Since the total telescope
length, including the back focal distance, is limited to - 7 m,
the separation of primary and secondary mirrors should be limited to
less than 6.5 m. The secondary diameter should be as small as
possible within these constraints.
A minimum of four design parameters are needed to specify
completely the optical configuration of a Cassegrain telescope. To
evaluate the possible configurations for a 3m telescope the dependence
of the overall f-ratio Fm on the secondary diameter D , mirror T s
separation S, back focal distance b and the primary f-ratio F^ was
106
investigated. These parameters are illustrated in Figure 4.6 below.
Figure 4.6
Parameters for the design of a Cassegrain.
The first order equations can be written as
F_ = k/D + F C ' V - 1) »•!«) T S P S
and Ft = b/Dg + S/Dg . ( 4 # l b )
Figures 4.7 and 4.8 illustrate these relationships, the
hatched area representing the range of parameters that will fit the
constraints described above. Figure 4.7 shows that for a given overall
107
f I 3 k S
PRIMARY FOCAL RATIO
Overall F-ratio as a function of primary F-ratio for
a Cassegrain telescope 108
Figure 4.8
Overall F-ratio as a function of mirror separation
for a Cassegrain telescope
109
Infrared Background
Total Length ( <7m)
Primary Focal Ratio
BEST Herschell Cassegrain Cassegrain
Cassegrain Prime Focus Newtonian
Newtonian Newtonian Prime Focus
•4/ WORST Prime Focus Herschell Herschell
TABLE 4.2 - Performance of Different Telescope Configurations
110
focal ratio F^ the minimum secondary diameter occurs for an F/2 primary,
and is not very sensitive to the value of b. The minimum possible
secondary diameter is 0.6 m. Figure 4,8 shows that any of the allowed
combinations of telescope f-ratio and secondary diameter Dg in
Figure 4.7 will also fit the limit on the separation of the two mirrors.
In conclusion, it is possible to design a Cassegrain telescope that will
fit all of the constraints on the 3m balloon telescope, including the
preferred overall f-ratio, and techniques for reducing the background
radiation from the secondary optics can be used.
4.6 The Optical Configuration for the 3 m Telescope
In Table 4.2 the telescope designs discussed above are compared from
the point of view of length, background and primary f-ratio. It is
evident that a Cassegrain configuration would be the best choice for a
3m balloon telescope. In general, for a given value of F , a
Cassegrain telescope will have a smaller secondary (in terms of area)
than a Newtonian, and hence a lower background. It will be lighter
than a Newtonian, not only because of the smaller secondary, but also
because the focal plane instrumentation does not need to be supported on
the telescope tube. The design of a Cassegrain telescope is now
analysed in more detail, so that the optimum configuration for the 3m
telescope can be found.
4.7 Detailed Design of Cassegrain
For the full scientific potential of the 3m balloon telescope to
be realized, it is very important that it can be used with a diffraction-
limited field of view (cf. Chapter 1), and this sets limits on the geomet-
rical aberrations of the optics. At the geometrical focus of a perfect
system, 84% of the energy of the incoming radiation falls within the central
region of the Airy disc. The aberrations introduced by a system are the
111
distortions of the converging (i.e. focussed) wavefront from its correct
spherical shape, and these distortions will change the diffraction pattern
produced by the system. While large aberrations completely change the
appearance of the diffraction pattern, the effect of small aberrations
will be a drop in the central intensity and a redistribution of the energy
into the outer diffraction rings, without affecting the diameter of the i
first ring. A central obscuration has a similar influence on the
diffraction pattern.
The generally-accepted tolerance, proposed by K, Strehl, is that
the image will be sensibly perfect if the intensity of the central maximum
does not fall below 0.8 I , where I is the intensity of the central P P
maximum for a perfect diffraction pattern. When the diameter of the
geometrical blur circle containing 100% of the rays is less than the
diameter of the Airy disc, the aberrations have an effect which is
negligible in comparison with diffraction, the Strehl limit is met, and
the system is said to be diffraction-limited. The central obscuration
must be as low as possible, to maintain the diffraction limit. For the
Strehl limit to be met, the ratio of the diameter of the secondary to
primary mirror must be less than 1/3 (Calculated from Offner 1969).
For the 3m telescope the geometrical blur spot must be less than
0.9mm diameter, the size of the diffraction limited disc at 50 p 7 and
the secondary mirror diameter is restricted to less than 1 m.
Because off-axis image quality is unimportant (Section 4.4) only
spherical aberration has to be corrected. If two mirrors are used to
correct one or two third-order aberrations, their profiles are always
conic sections and so it may be possible to correct sufficiently the
spherical aberration of the telescope design using two spherical surfaces,
because the diffraction disc is relatively large. A design using two
spherical surfaces is attractive because both mirrors will then be more
112
easily and cheaply manufactured. This is particularly important for
the primary mirror which, as shown in Figure 4.7, must be fast if the
secondary is to be kept small. To investigate the use of two spherical
surfaces for a 3 m balloon telescope the third order spherical aberration
Seidel coefficients for the primary and secondary mirrors were written
in terms of the four independent parameters: primary diameter (D^),
primary focal ratio (F ), mirror separation (S) and back focal distance (b) P
The spherical aberration Seidel coefficient for each surface in a system
is defined (using the Cartesian sign convention) as
where ,
S = - A 2 h A (U/n) (Kidger 1978) (4.2)
A = n(hc + u) = n'(hc + uT)
n
u = ^ L = angle of incident ray to optical axis
n = index of refraction for incident ray
/L = angle of deviated ray to optical axis
n* = index of refraction for new medium
h = height of incident ray above the axis
c = curvature of surface
L = vertex to object point distance
t . . . L = vertex to image point distance
T - h / _ » u =
113
The quantities u, u?, L, L* and h are illustrated in
Figure 4.9. below,
Figure 4.9 Quantities used to calculate Seidel sums.
To find the spherical aberration coefficient of a complete
system the coefficients found from equations 4.2 for each surface
are summed. The transverse spherical ray aberration for the ray at
full aperture (i.e. the radius of the spherically aberrated
geometrical blur spot) is given by
Is 8 = ! 2 n ' u * ( 4 - 3 )
where u* is the final convergence angle of the ray, and n* is
the refractive index in the final medium.
For the 3 m telescope the Seidel aberration is
s i = 3 IP + s i s
114
where IP
IS
Seidel coefficient of primary mirror calculated
from Eqn. 4.2.
Seidel coefficient of secondary mirror calculated
from Eqn. 4.2
Substituting into 4.2 for the primary mirror, noting that the
curvature of the primary mirror is 1/2D F , we have P P
Similarly,
IP 64 F,
= "D C ' is 5 (C - l / L R
8
(4.5)
where
D = diameter of primary
F = f-ratio of primary
D = diameter of secondary
C = curvature of secondary
L = D F - S P P
S = separation of mirrors
Equating the first order equations 4.1 (a) and (b) and solving
for the secondary diameter gives
S / D = D - F (4.6) s p p
Writing the conjugate distance equation for the secondary mirror,
taking account of the sign convention we have 115
1 1 (D F - S) (S + b) P P
/fs (4.7)
= 1/zc S - * 5
and
where f - focal length of secondary
b = back focal distance.
Solving Eqn.4.7 for the secondary curvature C and substituting o
Eqns.4.7 and 4.6 into equation 4.5 the spherical aberration Seidel
coefficient for a Cassegrain telescope with two spherical mirrors can
be written as
D D F - S 9 ST = E-*. - P P , T (2S + b - D F ) (2b + D F ) 1 64 F 3 64 F 4 (S + b)3 P P P P
P P
Figure 4.10 shows the Seidel coefficients S and S of the
primary and secondary mirrors as a function of F^ for the allowed
range of separations S, and a back focus distance b = 50 cm. Comparing
Figures 4.7 and 4.8 shows that S must be in the range 4.5 to 6 while
to keep the secondary small F^ must be in the range 2-3. One curve
with b = 80 cm is shown to illustrate that the equation is not strongly
dependent on the back focal distance. For an F/2 primary with a 0.6m
secondary the Seidel coefficient from the graph corresponds to a spot
size of the order of 40 mm. For an F/3 primary, a separation of 6 m
and a 0.9 m secondary the spot size is about 17 mm. Relaxing the
constraint on the mirror separation S or the size of the secondary
mirror by a small amount is unlikely to lead to a configuration with an
acceptable spot size. Relaxing the constraints by a large amount will,
116
Figure 4.10
Spherical aberration coefficients for primary and secondary mirrors..
117
of course, result in a design that is unsuitable for a 3 m balloon
telescope. Thus the graph shows- that, within the constraints on the
3m telescope, it will not be possible to correct the image aberrations
of a Cassegrain design using spherical mirrors alone.
In view of the manufacturing advantages of a spherical primary
mirror, it was decided to figure the secondary to correct the aberration.
Based on Figures 4.7 and 4.8 a Cassegrain configuration with the smallest
possible secondary diameter was chosen as the starting point for the
optimisation of the optics. The first-order parameters for this system
are given in Table 4.3. This design was optimised using the ray tracing
and optimisation routines of the Optical Design group of Imperial College.
Firstly, the best combination of spherical mirrors, within the constraints
was found and then a conic secondary was substituted to give the required
spot size. This results in the minimum amount of figuring of the mirror.
The spot diagram for the final design is shown in Figure 4.11, while
Table 4.4 is a list of the final parameters.
The surface of the secondary is specified by a sag function Z(r),
which defines the sag of the surface from a plane tangent to its vertex
as a function of the radial distance r from the optical axis. For
conic sections the function is of the form
Cr 2 Z C D = C R
1 + 1 - (1 + k)C2 r 2 V 2
Where C = vertex curvature and k defines the various curves
as follows
k > 0 oblate spheroid
k = 0 sphere
0 7> k > -1 prolate ellipsoid
k = -1 paraboloid
k ^ -1 hyperboloid
118
TABLE 4.3
The Baseline Cassegrain Design
Primary Diameter D = 3m P Secondary Diameter D = 0.6m s Primary Focal Ratio F = 2 P Primary Radius of Curvature 12m
Mirror Separation S = 4.8 m
Secondary Radius of Curvature - 3.102 m
Back Focal distance b = 0.5 m
Overall f-ratio Ft = 8.8
1 19
Figure 3.14
yn tn. CFKLE.
The spot diagram for the 3m telescope.
120
TABLE 4.4
Final Optical Design for the 3m Telescope
Primary Diameter
Primary F-ratio
Secondary Diameter
Secondary Radius of Curvature
Secondary Conic Constant
Mirror Separation
Back Focal Distance
Diameter of Primary Hole
Plate Scale
Max, Field Angle.
Overall F-ratio
(i)
D = 3m P Fp = 2, spherical
D = 71o4 cm s -4o053m
£= 9.063, oblate spheroid
S = 4.54 m
b = 61^7 cm
= 8.8 cm
9 arc sec mm
5 arc min.
FT = 7.5
-1
Note : (i) Calculated from the equations for third order coma
and astigmatism for a two-reflector telescope given
in Smith, 1974.
121
The conic constant 6 calculated by the ray trace routine and given
in Table 4.4 is equal to k + 1. Table 4.5 shows the shape of the
secondary mirror, compared to that of a sphete with the same vertex
curvature. The maximum amount of material to be removed from the
secondary compared to a sphere is about 0.2 mm (at the edge) and so
the secondary can be figured by conventional methods (cf. Section 3.12).
In conclusion, a Cassegrain design with a spherical primary and
a conic secondary was chosen for the 3m telescope. The spot size
(Figure 4,11) is about 0.25 mm at the focus and so the telescope will
be diffraction limited for wavelengths beyond 50 p.
4.8 Optical Tolerances
The final stage of the optical design of the telescope is to
calculate the optical specifications that must be met in operation,
viz. the maximum misalignment of the system, and the accuracy of the
mirror surface for which the performance is still diffraction limited.
For a general misalignment of the optics, the image will be
displaced and aberrated and so the usual method of determining the
alignment tolerances is to use ray tracing routines. However a facility
for misaligning the mirrors does not exist m the routines of the
Imperial College Optical Design Group. An alternative method is to
use geometrical optics and third order aberration theory. For the
case of a Cassegrain telescope Huber (1979) has found that the amount
of image displacement is much greater than the amount of image blur for
any given tilt or decentre error. So, a first order (i.e. displacement)
analysis will be sufficient to define the tolerances so that the
constraints on the structural design of the support system can be assessed.
The Strehl limit is used to quantify the amount of image displace-
ment tolerable before the diffraction limit is lost. For image motion 1 2 along the axis of the telescope the depth of focus is given by 1— A F ,
122
TABLE 4.5
The Figure of the Secondary Mirror
r (m) 0.05 0.10 0.15 0.2 0.25 0.3 0.35
Z ̂ Secondary -3.071 -1.23 -2.85 -4.95 -7.75 -1.12 -1.54
(m) -4 -3 -3 -3 -3 -2 -2 (m) xlO xlO xlO xlO xlO xlO xlO
Z ^ Sphere -3.086 -1.234 -2.78 -4.94 -7.72 -1.11 -1.51
(m) -4 -3 -3 -3 -3 -2 -2 (m) xlO xlO xlO -10 xlO xlO xlO
123
where F is the overall telescope f-ratio (Born and 1964). In
a direction perpendicular to the optical axis the image can be displaced
by up to 1/2 the radius of the diffraction disc, at which point the
intensity at the detector has fallen by 20% (from the tables in Born and
WQ (1964), assuming that angular resolution and detector size are
matched). The Strehl limit is also used to define the required figure
accuracy for the mirror. The root-mean-square (rms) value for the
deviation of the surface from ideal can be statistically related to the
amount of energy distributed outside the diffraction image. 10% outside
the fir ring of the pattern corresponds to A /20 rms. (Meinel 1969).
For the 3m telescope with A = 50 ji the tolerable displacements
for optical misalignment are:
depth of focus (along axis) = -1.4 mm
image motion perpendicular to axis '= -0.21mm.
As mentioned in Section 3.6, the 3m telescope mirror must maintain its
figure to about 2.5 u.
The tolerable image displacements are used in the following para-
graphs to estimate the alignment tolerances for change in separation of
the mirrors, primary mirror tilt and decentre and secondary mirror tilt
and decentre.
The tolerances on the position of the detector are, by definition,
the two depths of focus given above.
124
A change in the separation of the mirrors, As, results in a change,
Af, in the position of the focus. This is illustrated in Fig.4.12
below. The largest tolerable new value of the back focal distance b
is b + 1.4 mm. This value is substituted into the conjugate distance
equation 4.7 giving,
1 1 / f s D F - S1 S1 + (b + 1.4 mm)
P P
where D^ = Diameter of primary mirror
S1 = New separation of mirrors
b = Design back focal length
fg = Focal length of secondary
The difference between S* and S, the design separation, is the
maximum possible separation change. Inserting the parameters for the
3m telescope, the tolerance on mirror separation is S = I ^
Figure 4.12
Mirror separation change.
125
If the primary is decentered by a distance A , the prime focus
is shifted off the axis by a distance A and after reflection from P the secondary the final image moves m A off the axis, where m is
F / the secondary mirror magnification (= /F = 3.75). This is
illustrated in Figure 4-13 below. To third order, Coma and Astigmatism
will be increased. Equating, m A to 0.21 mm gives the tolerance P on primary mirror decenter Ap = " 84 ju.
Figure 4.13
Primary decentre .
126
As illustrated in Figure 4. 14 below, a tilt of the primary through
angle Q m o v e s the prime focus f0 off the axis, where f is
the telescope focal length. This distance is magnified by reflection
from the secondary, so the final image displacement is mf Q
Setting mf = .21 mm gives the primary tilt tolerance + 0 = - 0,8 arc sec. P
Figure 4.14
Primary tilt.
127
Figure 4.15 shows a secondary decenter A • In this case the
prime focus is a distance A f r o m the secondary axis, so the final
image is a distance ra from the secondary mirror axis and hence
a distance (m-1) A from the telescope axis. (m-1) A = 0.21 m s s + gives A s = " 140 p.
Figure 4.15
Secondary decentre.
128
The angles for evaluating the secondary tilt are shown in Fig.4.16
below. If the secondary is tilted about its vertex by angle Q , s the image moves through 2 0 i.e. a linear distance of 2 L0%
where L is the sum of the mirror separation s and the back focal
distance b. The tolerance on secondary tilt, = - 3.9 arc sec,
is obtained by equating 2 L Qs to .21 mm.
Figure 4.16
Secondary tilt.
129
Any general displacement of a mirror relative to the axis can be
expressed as a sum of displacement, tilt and separation change. If
both secondary and primary are misaligned, the secondary tilt or
decentre may partially cancel the effect of primary tilt or decentre <,
(for example compare Figures 4.13 and 4.15). However, they could also
add and so to allow for this the separate tolerances were halved.
The final specifications for alignment of the optics are given in
Table 4.6. The tolerances on decentre are quite small ( - 10!s of p)
however they seem large when compared to tolerances for optical
telescopes which are typically only fractions of a micron, corresponding
to image deviations of - 0.3 arc sees, (Meinel 1969).
In conclusion, the best optical configuration for a 3m far-infrared
telescope was found to be a Cassegrain with a spherical primary. A
telescope with all spherical optics is not possible because the f-ratio
of the primary is too fast (<. ~ f/5). The design was optimised using
ray tracing routines and a secondary with a conic constant of 9.06 was
used to correct the spherical oberration. First order alignment
tolerances have been calculated for this design and these will be used
to put constraint on the structural behaviour of the telescope in
Chapter 5.
130
TABLE 4.6
The Alignment Tolerances
Depth of focus along axis
Depth of focus perpendicular to axis
Separation of mirrors
Primary Decentre
Primary Tilt
Secondary Decentre
Secondary Tilt
— 2,3 mm
- 0.21 mm
- 1.43 cm
- 42 u
-0.4 arc sec.
- 70 u
- 1.95 arc sec.
131
CHAPTER 5
A LIGHTWEIGHT PRIMARY MIRROR
Introduction
There is a severe weight restriction for a dynamic launch of
3000 -4000 kg, only about twice the weight of typical lm telescope
payloadSo So, achieving maximum structural strength for minimum
weight for all the telescope components is crucial to the feasibility
of a 3m balloon telescope. As described in Chapter 3, the weight
of the primary mirror effectively determines the weight of the overall
structure and so the most important task is the design of a sufficiently
stiff and lightweight primary mirror.
Structurally, if the primary mirror were to weigh less than
about a quarter of the total allowed weight, a light, strong gondola
and cell to support it could be devised within the weight budget.
Optically, to maintain diffraction-limited performance, the overall
r.m.s. surface quality of the mirror must be better than A/20
(Chapter 4)• ' This has to include residual surface errors from
polishing the mirror, as well as mount-induced deformations. It is
usual therefore, to require that the residual errors are reduced to
less than ^ 5 0 the mount-induced deformations to about -^/sq
r.m.s. deviation from the best-fitting sphere. Thus the 3m mirror
should weigh less than 1000 kg and maintain its figure to - 2 JJ r.m.s.,
for any orientation, when supported in its cell. The mirror should
be as light as possible and the support system as simple as possible,
so that handling problems, particularly after it lands, are minimised.
In the following sections the general problems with and
techniques for mounting telescope mirrors are briefly summarized.
The details of the design of a light primary mirror and a proposed
132
support system are then described. It is the aim of this chapter
to demonstrate that a primary mirror can be made which is sufficiently
light that a 3m balloon telescope is indeed feasible.
5.2 The Problem of Mirror Deflection
The ability to predict accurately the magnitude and nature of
the elastic deformations of astronomical mirrors under various support
conditions becomes increasingly important as the sxze of the mirror
increases. This is because the flexure of a circular disc under its 4 2
own weight increases m proportion to D ft where D is the diameter
and t the thickness of the mirror. Even if the standard practice
of maintaining a ratio of t/D about is followed, the deflection
still increases as the square of the diameter. Thus for large
mirrors, a large number of supports are needed, and the behaviour of
the mirror between them becomes increasingly sensitive to their precise
locations. For realistic boundary conditions analytic solutions to
the theoretical three-dimensional equations of elasticity do not exist.
Analytic solutions have been obtained by making simplifying approximations
for the mirror geometry and boundary conditions and restricting the
orientation of the mirror. Recently, finite element analysis has been
used successfully to predict, with a more reasonable degree of accuracy,
the behaviour of mirrors under a variety of realistic support conditions.
An interesting example, which shows the need for accurate
analysis of support conditions, is the Mount Palomar 200" telescope.
Its primary mirror was designed to be supported on 36 counter-balanced
pads, and this meant that the support system had to be considered as
an integral part of the mirror. It was therefore decided to perform
the final figuring with the mirror in its cell (on site) to try to
avoid the previous experience that large reflectors did not meet their
design specifications in practice (Bowen 1952). However, it took
133
nearly 1| years of manual adjustment and modification of the supports
before the optimum arrangement was found and the figuring could be
done.
Before considering the behaviour of the type of lightweight
mirror proposed for the 3m telescope, different support configurations
for astronomical mirrors are briefly reviewed. This shows the types
of restraining forces that must be modelled and illustrates how a
proposed support condition for the 3m telescope mirror could be realized
in practice.
The aim of the mirror support system is to hold the mirror
firmly in place while minimising the mounting pressure and bending
moments which cause distortion of the optical surface. It takes
three points to define a plane and so the simplest mechanical arrange-
ment is to bolt the mirror rigidly to its cell in three places. A
more sophisticated support uses three pads with each pad self-aligning
against the mirror back to support it along the optical axis, together
with some form of lateral support.
For larger mirrors the load at each of just three points becomes
very high, and so multiple points are used to support the mirror both
along the axis and laterally. The three-point support idea is
extended by using six or nine pads in groups of two or three, each
group and each pad being self-aligning on each of the three ultimate
attachment points. If these systems are still not sufficient, eighteen
or thirty-six individual counter-weighted support pads are often used.
Each support pad is pivoted on a precision low friction ball-bearing
unit. The structure of the back support including the required
counterweights means that this type of support increases the weight
by about 30% of the weight of the mirror (Meinel 1969) and a complicated
mirror cell is required to accommodate the sets of levers and weights.
The range of back-support configurations with from 3 to 18 supports is
134
Figure 5.11
Mirror back supports.
135
shown in Fig.5.1. Troubles experienced with delicate counter-weights
have led recently to the use of annular air bags or rings of pneumatic
cylinders to support large optical quality mirrors.
The simplest lateral support system is to rest the mirror on
two supports 60-90° apart, as shown in Fig.5.2. The supporting force
in this case can be either vertical or radial. A large number of
support points along the edge of the mirror can be used with a series
of radial counterweighted edge supports, if necessary. However,
simpler solutions to providing multipoint lateral supports for large
mirrors have been devised. The first of these is the simple band
support in which the mirror is 'hung* on a band round its lower edge
as shown in Figure 5.3. This provides any desired number of-radial
supports. Most of the deformation arising from this type of support
can be focussed out (Malvick 1972). A sinusoidal edge support,
illustrated in Figure 5.4, is very close to the theoretical optimum
edge support condition. It can be achieved with a series of gravi-
tationally activated levers or springs whose deformations are small in
comparison to their lengths.
For the 3m balloon telescope the problems of mirror support are
less difficult than for large ground based optical reflectors, because
the surface quality of the mirror can be a factor of ten worse. The
use of an alt-az mount is also simplifying because the gravitational
vector is always in one plane relative to the telescope axis. On the
other hand, the mounting technique should be as simple as possible to
allow for any dismantling of the telescope, and this together with the
weight limit makes the use of counterweighted pads very unattractive.
The large diameter of the primary mirror means that the simple three
point back support will almost certainly induce deflections that are
too large. It was therefore decided to design a lightweight primary
which was stiff enough to maintain optical tolerances when resting on
136
137
a nine-point back support, together with either a two-point or a
simple strap edge support. In the following section some simple
analyses of the elastic behaviour of a lightweight primary are used
to define an initial design.
Finite element analysis will then be used to analyze its
detailed behaviour in the support system described above,
5.3 Parametric Analysis of the 3m Lightweight Mirror
The conclusion reached in Chapter 3 was that a welded aluminium
mirror with square, triangular, or hexagonal cells would have the
minimum weight while maintaining the optical tolerance. In order to
show conclusively that such a mirror with a reasonable weight is
feasible, it is necessary to investigate the elastic deformation of
the mirror under the proposed support condition. As has already
been mentioned in Section 5.2, analytic solutions for the bending of
mirrors exist only for a few special cases. Barnes (1969) has
derived an approximate solution for the case of a horizontal circular,
flat, sandwich mirror with a continuous edge support. Selke (1971)
has derived an expression for the deflection under its own weight of
a honeycomb-celled mirror supported horizontally by a ring at its
central hole. In both cases the equations are complex and cannot
easily be used to establish a balance between weight and stiffness
requirements for the mirror.
A cross section of the honeycomb construction (in one direction)
is shown in Figure 5.5. When it deforms elastically under its own
weight or in accordance with an applied load, two separate types of
bending can take place. The first is the sag of the faceplate relative
to the ribs resulting in the surface shown (exaggerated) in Figure 5.5.
The second is the overall bending of the structure against its supports.
In general the minimum faceplate thickness is determined by the need
138
Figure 5.11
Honeycomb mirror cross-section
139
to keep the local sag between cell walls to a minimum during polishing
operations, while the rib thickness and depth determines the overall
bending behaviour of the mirror. By treating the faceplace separately
from the core it is possible to describe in a simple fashion the
bending behaviour of the mirror and the limits that this places on
faceplate thickness, rib thickness, rib depths and spacings to meet
the optical tolerances.
5.3.1 Faceplate Thicknesses
For a given faceplate thickness the amount of sag depends on
the distance between the points on which it is supported. Thus the
spacing between the cell walls determines the minimum acceptable face-
plate thickness. Assuming that the rib spacing is small in comparison
to the diameter of the mirror, the equations derived in Timoshenko
(1959) for the deflection of a thin flat plate supported by rows of
equidistant 'columns' can be used to evaluate the faceplate sag.
The deflection at the center of a section of faceplate (i.e. the 4
maximum) is given by CO = & q b /D 3 2
where D = Eh /12(1- V ) is the flexural rigidity
CO = the deflection
= a numerical factor describing the supports
q = the load per unit area
b = the space between the ribs
h = the faceplate thickness
E = Young's modulus
and V= Poissons ratio.
The value of Ctis 0.0026 for equally-spaced lines of support.
If the faceplate sags excessively under a polishing load, too
140
much material will be removed at the cell walls, resulting in a poor
surface quality. Pepi and Wollensak (1979) suggest that to obtain
a good quality surface the r.m.s. sag under a polishing load should
be limited to about A/ IQQ % For this approximate analysis it there-
fore seems reasonable to limit the maximum deflection to be about 6 p. 2
In their design study Berggren and Lenertz (1975) take 3 000 N/m as
a typical polishing load for conventional polishing operations. Using
this value for q, setting CO = 6 p. and substituting into the
equation the material properties of aluminium the equation
3 -7 4 3 ti = 2.58 x 10 b mm
can be derived, where h is the faceplate thickness and b is the cell
spacing. A similar expression can be derived relating h to b in
the case of self-weight sag of the mirror faceplate. Figure 5.6 shows
a graph of minimum acceptable faceplate thickness as a function of
cell spacing for both self-weight and polishing loads. The graph can
be used to select a reasonable faceplate thickness for any chosen cell
spacing.
5.3,2 The Overall Bending of the Mirror
Analyzing the overall bending stiffness of the mirror is much
more difficult. The simplest expression derived by Barnes (1969)
for the self-weight deflection at the center of a honeycomb mirror
supported at its edge is
r/b)(l-2h/H)3
S = 3(5 +v)(l + v) P a4
16 EH2
141
Figure 5.11
Faceplate thickness as a function of rib spacing
142
where 8 is the deflection
V is Poissons ratio
E is Young's modulus
a is the mirror radius
h is the faceplate thickness
H is the mirror depth
r is the rib thickness
and b is the spacing between the ribs.
In this equation it is assumed that the cell spacing is small in
comparison to the mirror diameter and that the overall thickness to
diameter ratio is less than one tenth. For any chosen cell spacing,
a minimum faceplate thickness can be found from Figure 5.6 and the
only two free parameters determining the stiffness are the rib thickness
and mirror depth. A pocket calculator program was therefore written
to solve this equation for rib thickness when given the rib spacing,
the overall mirror depth and a desired deflection 8 • Figure 5.7
is a graph of rib thickness as a function of mirror depth for different
rib spacings and a center deflection 8 of about 6 p. Some of the
rib thickness found in this way are too small to be used in practice.
For example, a 1 mm thick rib would distort if it were welded to a
bottom plate.
Figure 5.7 shows that a mirror depth of 20- 25 cm gives a
reasonable rib thickness for any cell spacing, while Figure 5.6 shows
that a cell spacing of from 10 to 20 cm results in a faceplate which
is not excessively thick or heavy. If the cell spacing is too small
then there will be many ribs contributing to the weight, while if it is
too large the faceplate is the major contribution to the weight. Based
143
Figure 5.7
Rib thickness as a function of mirror depth.
144
on Figures 5.6 and 5.7 a suitable compromise seems to be a 15 cm cell
spacing with an overall mirror depth of 20 or 25 cm. A mirror with
the parameters shown in Table 5.1 was therefore selected as a baseline
design for further study. The faceplate has been made thicker than
that recommended by Figure 5.6 to allow for the approximate nature of
the theory, so that it can be made thinner, if necessary to reduce over-
all deflection and weight. The mirror has an overall symmetrical shape
as shown in Figure 5.8, with a back plate of the same thickness as the
front plate for maximum rigidity. An analogy to the use of mirrors
with backplates, is the use of I-beams rather than T-sections for
applications where bending must be minimised. To study in detail the
behaviour of a mirror like that in Table 5.1, it was necessary to set up
a finite element model of the mirror using the analysis routines of the
Imperial College Aeronautical Structures Group. The technique of
finite element analysis and the capabilities of the routines used are
briefly described in the next two sections. The mirror model and the
results obtained with it are then discussed,
5.4 Finite Element Analysis
The finite element method is the most sophisticated method of
analysing the deformation of, and stresses and strains in, complex
3-D structures. The method operates by dividing a two or three-
dimensional continuum into small segments, triangles or rectangles, over
which it is assumed that the strain is uniform or distributed according
to some known variation. The individual force-deformation response of
a segment (called an element) is then known from simple elasticity by
using the assumed strain function.
Any structure can be regarded either as a large number of small
elements or a small number of large ones. If small elements are chosen
then the number of variables in the analysis will be large, but a
145
Table 5.1
The Initial Mirror Design
Faceplate thickness 1 cm
Rib spacing 15 cm
Rib thickness 4 mm
Mirror depth 25 cm
Backplate thickness 1 cm
Figure 5.8
The symmetrical shape of the 3m mirror. 146
relatively crude, approximate theory can be used to predict the
behaviour of each individual element. If large elements are chosen
then the number of variables needed to describe the overall behaviour
of the structure will be less, but the characteristics of the elements-
will need to be represented more exactly.
In practice, the analysis is broken down into a few discrete
steps. The first stage is to express the properties of an individual
element as a relationship between loads and displacements at the nodes,
the nodal loads being statically equivalent to the stresses which occur
in the element. Nodes are the points in the structure that subdivide
it into elements.
When a number of finite elements are assembled to form a structure
the physical process of joining the elements together corresponds to
imposing conditions of displacement compatibility and stress continuity
across the boundaries. The second stage of finite element analysis
is to replace these boundary conditions by conditions of compatibility
at the nodes only. External loads acting on the structure are replaced
by statically equivalent nodal loads and the equilibrium condition that
at each node the external load is equal to the sum of the nodal loads
is applied.
By combining the nodal compatibility equations with the element
load/displacement equations and then substituting into the equilibrium
equations, a set of equations relating the external loadings to the
nodal displacements can be derived. These are expressed in matrix
form and a computer can then solve for the displacements. In the last
step the loads and stresses in each element are found from the
individual element equations. The most important factors are that the
correct element type for the problem is chosen, and that the model
contains a large enough number of elements to supply an accurate solution.
The only way to test that the number of chosen elements is adequate is
147
to increase the number of elements until no significant change is
detected in the computed results.
5,5 FINEL ~ The Finite Element Analysis Routines of the
Aeronautical Structures Group
'Finel* is a general purpose finite element program organised
as a series of modules, each of which performs one step in the finite
element analysis. The standard analysis facilities provided by the
program may be used to perform: a linear elastic, static stress analysis
for a variety of loading cases, including point, pressure (on edges
and surfaces), displacement and temperature loads; a dynamic stress
analysis including velocity and displacement structural response, and
free vibration eigenvalue/vector calculation; transient and steady
state heat conduction calculations; and non-linear structural response
analysis. If the program does not provide a facility for a particular
analysis temporary additions or modifications can easily be made to
the program, without affecting any of the permanent modules. Finel
was developed by D. Hitchings of the Aeronautical Structures Group and
the capabilities of the routines are fully described in the Finel manual.
A basic flow chart for a finite element stress analysis is
shown in Figure 5.9 , which also shows the names of the Finel modules
which carry out each specific task. Each step must be completed before
the next can be solved. This module list is automatically assembled
within Finel by the specification that the analysis type is a static
stress one.
As each module is called it must receive the correct input data
and so the basic order of the input data is defined by the module
sequence. The input data is specified by two words, the first defining
the module for which it is intended and the second defining exactly what
type of data follows. There is no specified system of units within
Finel and so care must be taken that all the input data are given in 148
Figure 5.7
Flowchart for a stress analysis.
Problem definition
Mesh generation \ ra
\ Formation, arid assembly of the Structual
Stiffness Matrices(ASMB)
\ Specification of the Necessary Boundary
Conditions(BNCN) I Factorization of the Structural Stiffness
Matrix(CHOL)
Specification of loadings(LOAD)
l i Solutions of the displacements(SLVE)
Calculations of the strains and stresses from
the displacements
149
in a consistent set of units. Commands are also used to specify
which of the many different finite elements in the Finel element
library are to be used, as well as the region it is to occupy and
the type of loads the structure is subject to. Typical Finel commands
are ELEMENT QD04 Ot , specifying a four noded membrane element of
thickness OC and LOAD POINT F i j, specifying a point load of magnitude
F at node i in direction j. Once the basic geometry and properties
of the element to be used and the number of such elements in a given
region are defined, Finel automatically generates the mesh of nodes
used for the analysis and assigns each node a number. These numbers are
then used to specify the points at which the various loadings are
applied, as well as to identify the points in the grids when outputting
the displacement data. To reduce the volume of input data it is
always assumed that any parameter remains constant until it is redefined.
The use of finite element analysis to study mirror behaviour is now
briefly discussed, before presenting a model for the 3m mirror .
5.6 Finite Element Models of Mirrors
Finite element analysis is now used routinely to predict the
magnitude and nature of the elastic deformations of mirror surfaces
due to mechanical and thermal loads, both when the mirror is mounted
in its cell and when it is in the optical shop.
A recent example of the use of the finite element technique
to study the behaviour of a mirror under various support conditions is
the study by Mack (1980) for the U.K. 4.2m optical telescope being
planned for La Palma. He uses two separate models, one for the axial
flotation of the (solid) mirror and one for the transverse supports,
taking advantage of symmetry to reduce the amount of calculation. By
using finite element analysis, the optimum back support radii and
form of the transverse support forces could be determined, to keep the
150
mirror figure within 30nm of the true paraboloid at all altitudes.
Such an analysis would have been extremely difficult using (thick)
flat-plate theory techniques, because 'simple1 analytic solutions exist
only for a few special cases. This is also the case for lightweight
mirrors because of their structural complexity and a finite element
model for the 3m mirror can similarly be used to find the best support
conditions for it.
For a lightweight mirror the finite element method makes it
possible to conveniently study the effects of varying several
geometrical parameters of the mirror, such as depth, top and bottom
plate thickness, cell configuration and its width for different support
conditions and mechanical and thermal loads. Richard and Malvick
(.1973) compared computed and experimental deformations of lightweight
mirrors under various support conditions, and their conclusions are
now summarized.
The mirrors used for the analysis had the properties shown in
Table 5.2, with rib thicknesses adjusted so that all have the same
total weight. The structural behaviour of these mirrors was modelled
by using linear edge-displacement membrane rectangles wherever possible,
and constant-stress membrane triangles in all other areas. One
element was used for each face of a cell. The shape of the cells was
found to have very little effect on the overall bending behaviour.
Models were then set up using elements with additional bending and
twisting capability and the two sets of results were compared. These
were found to be essentially identical (to less than 2%). A coarse
( - 40 cm) grid was also modelled and found to be about 10% too stiff,
thus establishing an upper limit to the cell size it was possible to
model with just one element for each face.
On the basis of these results a program to automatically generate
mirror models using constant-stress membrane triangles (for ease of
151
Table 5.2
Richard and Malvick (1973) Mirror Parameters
Mirror diameter 186.7 mm
Mirror depth 32 .5 cm
Top-plate thickness 3.3 cm
Bottom-plate thickness 2.7 cm
Rib spacing (1st case) 7.6 cm
Rib thickness (1st case) 6.4 mm
Rib spacing (2nd case) 15 cm
152
modelling curves) was set up. Model predictions for a mirror with
the properties shown in Table 5.2 were then compared to the experimental
results, for various support conditions. The comparison was made for
deviations of the surface from a best fit sphere, which is the most
stringent test for the model. Despite the fact that some of the
mirror webs had poor bonds and the web plates were not connected to
the outer plates (which the model assumes), the model was found to be
predicting the deformation very well. Quantitatively, the predictions
were about 20% less than the observed deflections in some cases, and
it is evident that much better agreement would have been achieved for
a mirror without the structural weaknesses of the core used.
5.7 A Finel Model for the proposed 3m Mirror
The purpose of setting up a finite element model for the
proposed 3m mirror is to demonstrate the feasibility of a 3m mirror
which is stiff enough and light enough to be used for an infrared
balloon telescope. The model can be used to investigate possible
support configurations and geometrical shapes for an optimum light-
weight infrared mirror, and is briefly described below.
A model for a mirror with square cells was set up because this
was most easily accomplished with Finel. In view of the fact that
Richard and Malvick (1973) find that the shape of the cells have little
effect on overall bending behaviour, a fact which was also noted by
Barnes (1969) and Selke (1971), conclusions based on this model should
be equally valid for mirrors with triangular or hexagonal cells.
These may prove to be more convenient from a manufacturing point of view.
After consultation with Dr. P. Kilty of the Aeronautical
Structures Group at Imperial College it was decided that the best Finel
element to use in modelling the structure was a four-node linear
membrane element, joined at the rib intersections. A simple triangular
153
element was used, when necessary, to fill in the edge of the mirror.
This model is therefore similar to the one set up by Richard and
Malvick. Because the proposed support point arrangements were
symmetrical about a diameter of the mirror, it was only necessary to
model half of the mirror in order to study its behaviour.
As described in Section 5.5, the input data describing the
mirror geometry and the arrangements of the elements must be in a
specific order, preceded by the correct commands. Because of the
large number of nodes ( ~400) and elements ( ~7Q0) necessary to
model the mirror, it was decided to write a computer routine to auto-
matically generate the nodes and input statements for the mirror model.
In this way the basic geometry of the mirror can be easily changed.
The program calculates the nodal coordinates for any cell
width, and writes the element and node configurations in an efficient
order onto the input file for the Finel routines. Any mirror
curvature, top and bottom plate thickness, rib width and overall mirror
depth can be specified. Plotting information for the Finel plotting
routines is also written out. This is because the first stage of a
stress analysis using Finel is to plot the input mode of elements.
After the model geometry and the elements have been specified, Finel
automatically re-numbers all the nodes and these new node numbers are
listed in the plot output. It is the new node numbers that are used
to specify the boundary conditions and load conditions on the model.
The input file is then edited to include the chosen support conditions
and a full self-weight deflection and stress analysis is then run.
Figure 5.10 shows a plot of the mirror model for a 15 cm rib spacing.
5.8 Preliminary Results and Conclusions on the Mirror Design
Based on the analytic work in Section 502, the first mirror
analysed had the basic geometry shown in Table 5.1. This mirror was
154
Figure 5.10
The Mirror Model
155
supported on its back using a traditional nine-point support pattern,
in which each back support carried 1/9 of the weight of the mirror,
as shown in Figure 5.1. The position of the supports- was modified
very slightly so that each support point coincided with a rib inter-
section, which is where the mirror is strongest. In the model, the
nodes at these points are fixed in both the vertical and the two
horizontal directions. Thus the mirror is assumed to be supported
on nine fixed geometrical points. The deformations of the mirror
surface are therefore greater than those resulting from a real support
which would have a larger bearing area. The r.m.s. deformation of
the mirror was estimated from the displacement output of the program
by calculating the standard deviation of the displacements about the ir
mean value. Again this will tend to give an over-estimate of the
mirror surface quality, which is normally considered as the r.m.s.
deviation of the deformed surface about the best-fitting sphere. The
small focal length change between the original mirror surface and the
best fit to the deformed surface can be compensated for by moving the
secondary mirror when the telescope is aligned. For this mirror,
shown in Table 5.1, the mean deviation was 7 p with an r.m.s. surface
quality estimated to be 2.6 p . This does not meet the A/50 criterion
described in Section 5.1, and although it is probably an overestimate,
it was decided to design a slightly stiffer mirror, for a better overall
performance.
The second mirror for the analysis had the geometry shown in
Table 5.3. This was chosen because, thickening the ribs, while reducing
the weight they have to support will probably result in a stiffer mirror.
For this mirror the mean sag was 5.2 p with an r.m.s. of 1.8 p,
and so it meets the design criterion when it is horizontal on a
traditional nine point support.
156
Table 5.3
The Final Mirror Design
Faceplate thickness 2 cm
Rib spacing 15cm
Rib tickness 6mm
Mirror depth 20cm
Backplate thickness I cm
157
To evaluate this mirror's behaviour when vertical two different
supports were modelled. In the first case two points (one on the
front and one on the back) on the lower edge of the model were fixed
in the y-direction. The point chosen was a strong point where a rib
join meets the edge. This is equivalent to supplying a vertical face
to the mirror edge to keep it in place. The r.m.s. deviation in this
case was 0.8 p about a mean of 2 ji . In the second support system
considered, a radial force was applied, such that the vertical component
equalled the weight of the mirror, at the same point as in the first
case. With this support the r.m.s. surface error was 0.7 p about a
mean of 3 p .
In order to analyse further the stiffness of the mirror when
it is mounted in a real cell, distortions of the back surface were
applied. The fixed point representing the supports for the horizontal
mirror were displaced fixed amounts in the vertical direction to
represent the flexure of the cell. Two cases were tried. The first,
in which the two inner supports of the half-mirror were moved by 4 p
and the outer by 2 p, increased the mean deviation to 7 p but did not
affect the r.m.s. surface quality of -1.8 p. In the second case the
innermost points were moved by 10 p and the outer by 5 p, increasing
the mean to -11 p and the standard deviation to 2.3 p . This r.m.s.
value is only just acceptable, and so a differential sag across the cell
of 5 p seems to be about the largest that can be tolerated. The
absolute magnitude of the sag is not important, since this can be
compensated when focussing the telescope.
To summarize, an aluminium honeycomb mirror, weighing - 504 kg
with the geometry specified in Table 5.3 will meet the design criterion
when supported axially by 9 points and radially on its edge, The
mean deformations and r.m.s. surface qualities of the mirror in all
the configurations described above are summarized in Table 5.4. For
158
Table 5.4
Summary of Mirror Deformations
Support Mean (jU) RMS deformation (jU. )
9-point back support 5.2 1.8
Edge points fixed 2 0.8
0 . 7 Radial edge support 3
9-point distorted back support, 2jU differential 7 1.8 sag
As above, but with 5/X 11 2.3 differential sag
159
all the cases analysed the stresses were found to be a factor of 10
or more less than the microyield stress. The proposed 3m mirror
is therefore the one described by Table 5.3, and its areal density
is shown in Figure 5.11 on a graph showing the capabilities of U.L.E.
honeycomb mirrors, drawn for a design study by Lockheed (1980). The
faceplate of the proposed mirror is just on the borderline of what
is acceptable from a polishing point of view, but its weight is
sufficiently far inside the weight budget that it may be possible to
thicken this if necessary.
A test of the number of elements used in the model has not
yet been made since this requires modification of Finel so that it
can accept more than the present limit of about 500 nodes. On the
basis of Richard and Malvick*s results (Section 5.6) the use of one
element per cell face for a 15 cm grid should be acceptable. Similarly,
considering the comparison of their model to a real, but structurally
poor mirror and the over-estimates explained above, the results for
the deformation of the mirror are probably accurate to ^10% or better.
In conclusion a primary mirror for a far-infrared telescope
weighing only - 500 kg seems entirely feasible. No attempt has
been made to further optimise the mirror and a slightly lighter mirror
could probably be designed. Since this is the heaviest part of the
telescope and the weight budget is 3Q00- 4000 kg, we can conclude
that a 3m balloon telescope will be possible within the design criteria
set out in Chapter 2. In the following chapter some suggestions for
further reductions in the weight of the primary mirror are made, as
well as some preliminary comments on the design of the rest of the
payload.
160
Figure 5.11
200
CURRENT FUSION WELDED
MIRROR TECHNOLOGY
150
CURRENT FRIT BONDED
MIRROR TECHNOLOGY 100
PROPOSED 3M MIRROR
50
PREDICTED IR FRIT BONDED MIRROR
D IAMETER (METRES)
Graph of U.L.E. manufacturing capability.
161
CHAPTER 6
A 3 m BALLOON TELESCOPE PAYLOAD
6.1 An estimate of the weight of a 3 m balloon telescope
The aim of this chapter is to show that the total weight of a
3 m balloon telescope can be kept within the weight limits imposed
by current balloon launching techniques. In the following paragraphs,
each of secondary ring, serrurier trusses and primary cell are
considered in turn and an estimate of the required weight is obtained
by using standard beam bending equations. All the equations quoted in
this chapter were taken from Roark (1965). An assessment of the
relative weights of these components will show those components for
which further design effort in weight reduction would be profitable.
Assuming a thickness to diameter ratio of ^/10, the weight of
the 70 cm secondary selected in Chapter 4 is 72 kg. For this preliminary
analysis, this is taken as the weight of the secondary assembly.
The secondary is supported in its ring by four vanes, which
are as thin as possible to minimise the thermal radiation they emit,
and this paragraph considers the strength requirements of the vanes.
It is vitally important that the vanes do not break when the telescope
lands, as this could result in the secondary falling onto the primary
and damaging it. If the vanes are considered fixed at the ring with the
weight of the secondary acting in the centre, as shown in figure 6.1a),
the maximum stress in a vane is | ̂ / Z where W is the load (N) , 1 the
length of the vane, and Z the moment of inertia of the cross-section,
divided by the distance from the neutral axis to the edge. Under a 5 g
acceleration the load, W, is equal to 2.5 times the weight of the
secondary mirror. Vanes 11 cm deep by 6 mm thick will support the
162
SECONDARY-^)
VANE
w RING
I w
Figure 6.1a) Secondary vanes,telescope vertical
Figure 6.1b) Secondary vanes,telescope horizontal.
163
secondary with a safety factor of over the breaking stress of 2 aluminium (T31 alloy, 290 N/mm ). Alternatively the vanes provide
a safety factor of about 3 for a 10 g acceleration. The deflection 2
of the vanes is found from 6 = W1 /192EI, where E is the modulus of
elasticity, I is the moment of inertia of a cross-section, W is the
load, 1 is the span, and 5 is the deflection. This gives a change of
separation of primary and secondary of less than 1 y, which is well
within the tolerance of 1.4 cm derived in section 4.7.
On the other hand, if the telescope is horizontal, as in W /—
figure 6.1b), the tension in a vane is //2, where W is the weight 2
q of the mirror, and this gives a stress of 'MD.S N/mm . Here the
main requirement is that the vanes are strong enough to maintain the
alignment of secondary and primary. The amount each of the two T1
uppermost vanes stretch is dl = /AE where T is the tension, 1 the
length, A the cross-sectional area,, and E is Young's modulus. The
vertical distance moved by the secondary is /2 dl, and for the
11 cm x 6 mm vanes discussed above this distance is ^22y, about a third
of the tolerance of 70y on this motion. The weight of these vanes is-9 kg.
The secondary ring is more difficult to analyse because
it is subject to twisting moments as well as bending moments. For a
very crude, order of magnitude analysis, we ignore twisting of the
ring and approximate it by a square. In the case when the telescope is
vertical, as illustrated in figure 6.2a), the 'ring' is subject to
both axial tension and a transverse force. The maximum stress in the 125 ring is therefore /A where A is the cross-sectional area, and 125N
is one quarter the weight of the secondary (500 N). Clearly this will 2
be several times less than the breaking stress (^250 N/mm ). If the
ring is apprximated by the square shown in figure 6.2b), when the
telescope is horizontal, the maximum stress in the top section is { ^/Z,
164
assuming its ends are simply supported. A ring with a rectangular
cross—section with the dimensions shown in figure 6.2c) will provide
a safety factor of 20 over the breaking stress, if the stress in the
ring is calculated in this manner. The high factor of safety is
allowed because of the rather crude approximation used.
The weight of this ring is about 46 kg and so the total weight
of secondary vanes and ring was taken as 46 + 72 + 9 = 127 kg for the
analysis of the serrurier trusses.
If the load on the truss is W then the tension in the truss is
l W/sin 0, where 0 is the half-angle of the A-frame. For the final
optical design of section 4, the mirror separation is 4.54 m and so
the truss length is about 4.8 m. Thus the tension T is XL. 6 W, where 127
W is /2 kg, assuming each of two A-frames carries half the load. IT
The extension of the truss can then be calculated from dl = JAE,
as before. For an A-frame made of solid circular beams with a diameter
of 9 cm, the downward movement of the ring when the telescope is
horizontal is 35|4. Thus the total displacement of the secondary with
the telescope in this position is 57|UL, which is just inside the
tolerance of 70̂ JL. When the telescope is vertical there is a safety
factor of about 20, over the Euler buckling load. The total weight
of 8 such beams forming the four conventional serrurier trusses is 66 5 kg.
The primary mirror analysed in Chapter 5 weighs only ^500 kg, and
is stiff enough to maintain its figure when mounted on nine back
supports with two radial supports. A cell for such a mirror must,
at the most, be as stiff as the mirror itself. It could therefore be
expected to weigh about the same as the mirror. For example, a cell
could be constructed which was of a similar honeycomb structure to the
mirror. In this case, since an optical quality surface is not required,
the ribs could be thickened and their spacings increased so that the
overall bending and total weight remains the same while providing strong 166
plates to link to the elevation axis. A lighter cell could probably
be designed by taking this idea to its extreme and building an open
framework of light tubing, similar to Leighton's design (section 3.7).
A weight of 500 kg therefore seems a reasonable upper limit to the
weight required for the cell.
Using the weight estimates of the preceeding paragraphs the
total telescope weight is about 1800 kg. Since the weight budget for
a dynamic launch is 3000 - 4000 kg for the whole payload and this
telescope weighs approximately half the limit, we can conclude that
a 3 m balloon telescope can be built within the design criteria set
out in Chapter 2. In the following section some suggestions for
further weight reductions are made.
6.2 Suggestions for further work
The work in section 6.1 is not a complete, or optimised design
for a 3 m balloon telescope but is intended to illustrate some of the
structural strengths required for a telescope of this size. Since
the minimum possible weight is desired it would be worth considering
ways of further lightening the weight of the primary mirror and its
cell.
The primary mirror chosen for the 3 m telescope (Chapter 5) is
stiff enough to maintain its figure under self-weight deflections
against its supports. If the construction of the nine pads on the
back of the mirror follows the standard practice, they will be self-
aligning and grouped in threes. A minimum requirement for the primary
cell is therefore that it provides three points of contact to define
the position of the mirror relative to the yoke which carries the
elevation bearing. The sag of the cell is essentially decoupled from
the behaviour of the primary by the use of self-aligning pads, and
167
will not therefore distort the mirror. Tolerable sags for the cell
are determined by the tolerance on primary-secondary separation and
primary decenter. Thus a cell weighing considerably less than 500 kg
can probably be designed, because of the structural stiffness of the
primary mirror. An investigation of several lightweight cell
configurations is therefore the next step in the design study.
Further optimisation of the telescope could possibly be
achieved by considering the primary and its cell together. For
example, the weight of the primary could probably be reduced by
thinning the edge of the mirror, and deepening the center as shown
in figure 6.3. A primary with this construction would be mounted in
its cell via the thick central ring, and the only requirement on the
edge of the mirror is that it does not sag excessively. This technique
was employed successfully in the Nanjing telescope study (Meinel 1980)
to achieve a weight reduction of a factor of three. Prevenslick (1968)
has proposed the use of solid mirrors of linearly-varying thickness, as
a lightweight alternative to a honeycomb construction. For the 3 m
telescope, a honeycomb mirror with linearly varying thickness may be a
very light solution. However the support constraints on the cell will
be different for a mirror mounted in this manner and so a trade-off
analysis between weight and stiffness of primary mirror and weight
and stiffness of the cell is needed to determine the best solution.
The design of the rest of the telescope has not been fully
considered in section 6.1. Here the most important part of the
structure for further weight reduction is the secondary and its ring.
The secondary mirror, chosen for optical performance in Chapter 4, is
quite large and so using a lightweighted secondary (perhaps by drilling
out the back) should be considered. A careful analysis of the stresses
in the secondary ring is needed so that it, too, can have the minimum
168
Figure 6.3
A primary of varying thickness
169
possible weight. If the buckling and strength requirements are very
high, it would be worth investigating a space frame design. Reducing
the weight of the secondary and its ring could lead to a substantially
lower weight for the trusses. A spaceframe structure, perhaps using
carbon—fibre rods seems the most attractive to use for a baseline
design of the gondola, which has not been considered in this thesis.
A further problem in the design of such a lightweight telescope
and gondola which is not considered at all in this thesis is thermal
distortion. This can occur both from the change in ambient temperature
when the telescope is at float altitude and from warm radiation from
the earth on the back of the primary during the flight. A detailed .
finite element model could be set up and used to check firstly the
thermal distortion of the primary, since this seems to be the most
important thermal effect, and then the differential expansion of the
various telescope components.
In conclusion this thesis explores the next stage of development
of balloon-borne telescopes for far-infrared astronomy. The scientific
case for a 3 m telescope rests on its increased sensitivity and angular
resolution when compared to the current range of airplane, balloon and
space infrared telescopes. The scientific objectives of 3 m balloon
telescopes could include the entire span of far infrared astronomy.
High spectral resolution line astronomy of galactic sources, photometry
of faint sources and cosmological observations are among the studies
which would benefit from the capabilities of a 3 m balloon telescope.
Since the scientific case for a 3 m far-infrared telescope is compelling,
the optical and mechanical problems posed by such an instrument were
addressed. The central technological problem is to manufacture a 3 m
primary mirror which is sufficiently lightweight that the telescope can
be launched and flown using conventional dynamic launching techniques,
170
and sufficiently stiff that it provides diffraction-limited images
in the far-infrared. A survey of lightweight mirror technology
suggested that a (welded) aluminium honeycomb construction was the
most promising. Manufacturing problems are reduced by chocsing a
Cassegrain configuration with a sperical primary and an aspheric
secondary for the optical design.
A study of the flexure of the honeycomb mirror was undertaken
using finite element analysis. The aim was to investigate whether
such a mirror would be stiff enough to maintain the optical figure
and light enough to permit the construction of a telescope to fly
from a balloon. The proposed mirror will weight about 500 kg, and
its supporting cell and the remainder of the telescope were shown to
weigh at most another 1300 kg. A balloon telescope satisfying the
optical requirements is therefore possible for a weight of less than
2000 kg.
171
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