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16.684 Space Systems Product DevelopmentChart: 1February 13, 2001 MIT Space Systems Laboratory
Introduction to Optics part II
Overview Lecture
Space Systems Engineering
presented by: Prof. David Millerprepared by: Olivier de Weck
Revised and augmented by: Soon-Jo Chung
16.684 Space Systems Product DevelopmentChart: 2February 13, 2001 MIT Space Systems Laboratory
Interferometer Types (NASA, AirForce)
Space Technology 3-2005 Air Force UltraLITESIM-2006Michelson Interferometer
Precision AstrometryMichelson Interferometer Fizeau Interferometer
Earth Observing Telescope
TPF - 2011NGST - 2007
Michelson Interferometer A Common Secondary Mirror (MMT, Fizeau)Primary Mirror = 8 m diameter
16.684 Space Systems Product DevelopmentChart: 3February 13, 2001 MIT Space Systems Laboratory
Interferometer Types (Ground)
Michelson Interferometer (Visible)
Keck Interferometer-2006Michelson Interferometer (Infrared)
Twin 10 m Keck Telescopes and four 1.8 m outriggersBaseline 85m
Palomar Testbed InterferometerMichelson Interferometer (Infrared)
Testbed for Keck and SIM
Mark III Interferometer
Keck Observatory: Multiple Mirror Telescope (MMT)
Fizeau Interferometer (Visible, Infrared)36 hexagonal segments => 10 m overall aperture
16.684 Space Systems Product DevelopmentChart: 4February 13, 2001 MIT Space Systems Laboratory
Michelson Interferometer
Independent Light Collectors feed light to a common beam combiner. Get interfered fringes => Inverse Fourier Transform (CLEAN,MEM)
Suitable for Astronomical Objects:Unchanged over a long period of time
BeamsplitterCollector
Collector
Michelson Interferometer
Stellar wavefront
Detector
DetectorOptical delay line
Object
Imaging with Michelson Interferometer
FT "FT-1"
Baseline orientations:
+y
x
yvvv
uu u x
u-v (Fourier plane) Reconstructed image
16.684 Space Systems Product DevelopmentChart: 5February 13, 2001 MIT Space Systems Laboratory
Fizeau Interferometer
Gives a direct image of a target from a large combined primary mirror, and a wide field of view (Imaging applications in space and MMT)
Suitable for Wide Angle Astrometry And for rapidly changing targets (Terrestrial, Earth Objects)
1 2 3
Telescope
Telescopes
Fizeau Interferometer
Fizeau Interferometer
DetectorDetector
Sparse aperture Telescope
"Beam combiner"
16.684 Space Systems Product DevelopmentChart: 6February 13, 2001 MIT Space Systems Laboratory
Comparison (Fizeau, Michelson)
Fi zea uInt erfer omet er
Miche lson Inte rfe romete r
Pro duce a dir ec t im age o f itstarg et ( Ful l Instan t u- v c over agepr ov ided)
Takes a sub se t o f u- v po intsobtaine d a peri od o f tim e.
W ide ang le(f ield) of viewim aging app lications
Ast rome try,Null ing Inter ferom etry
Rapidly Cha nging t arge ts(Terre st rial, Ea rth Objects)
Targ et u nc han ged(Ast ron omi cal Objects)
Takes t he comb ine d sci en celigh t from all the ap erture s an dfocuses it i nto C CD
Me as ure s po ints in Fouriertran sform of ima ges => Inver seFFT ne eded
U- V re so lu tion dep end s on b oththe separa tion and the s ize ofaper ture s
Angula r re so lu tion de pend ssolel y on the separa tion ofaper ture s
Optima l Con figura tion:Golay (m inim um aper ture s ize )
The angul ar res olution im pro vesas t he sep ara tion incre as es
16.684 Space Systems Product DevelopmentChart: 7February 13, 2001 MIT Space Systems Laboratory
CCDBeamCombiner
Common Secondary vs Sub Telescope
Phased Sub-Telescope Arrays
Common Primary Sub Telescope FizeauPrecise Off Axis ConfigurationOff Axis Optical Aberration
Need Combiner + Phase sensing andcompensater mechanism (complex)
Less Central Obstruction(Off Axis) On Axis Suffers Central ObstructionHard to change the Configuration Can employ Off-the-shelf telescopes
Common Secondary Mirror Array
AirForce is studying two options for UltraLITE(Golay 6)
16.684 Space Systems Product DevelopmentChart: 8February 13, 2001 MIT Space Systems Laboratory
Optical Arrays
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
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Optical Array Configuration
X - Distance [m]
Y -D
ista
nce
[m]
Instead of using a single aperture use several and combine their light to form a single image
Aperture positions (uv) are critical -look at combined PSF / Transmissivity
of the Optical Array
Transmissivity Function:
Derivation see separatehandout (Mennesson)
16.684 Space Systems Product DevelopmentChart: 9February 13, 2001 MIT Space Systems Laboratory
CDIO: Breaking the Paradigm
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Optical Array Configuration
X - Distance [m]
Y -
Dist
ance
[m]
GolayGolay--3 0.6 m telescope3 0.6 m telescope-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
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Optical Array Configuration
X - Distance [m]
Y -
Dist
ance
[m]
Physical Physical ApertureApertureLayoutLayout
Monolithic 0.6 m telescopeMonolithic 0.6 m telescope
CompareArchitectures
withQuantitative
Metrics
PSFPSF
16.684 Space Systems Product DevelopmentChart: 10February 13, 2001 MIT Space Systems Laboratory
Effective Radius of Optical Array
How to find the effective radius(Reff) of the array?
• =the radius of the arraythought as that of a monolithicaperture.• UV coverage plot
x,y is any point within aperture• : the maximum radius ofuv plot without any holes •
• Fill Factor: the array’s total collecting area over the area of a filled aperture with the same uvcoverage(the same Reff)
u = ± x2 − x1
λv = ± y2 − y1
λ
Ruv
Reff
Reff = 0.5Ruv
16.684 Space Systems Product DevelopmentChart: 11February 13, 2001 MIT Space Systems Laboratory
Golay Configurations• Optimum Golay is
Deff-dependent• Labor moves
Golay benefits to larger Deff
• Golay’s sacrifice Encircled Energy
EE=83.5% EE=26.4% EE=9.3% EE=3.6% EE=2.2%
16.684 Space Systems Product DevelopmentChart: 12February 13, 2001 MIT Space Systems Laboratory
Technological Trends
• Lightweight (Low-Area-Density) Optics - 15kg/m2
• Deployable Optics• Adaptive and Active Optics• Membrane Mirrors and Inflatables• Ultra-Large Arrays (CCD Mosaics)• Distributed Optical Arrays• Space Based Astronomy• White light interferometry
16.684 Space Systems Product DevelopmentChart: 13February 13, 2001 MIT Space Systems Laboratory
Optical Performance Criteria
• Sensitivity(Effective Collecting Area)• Point Spread Function(PSF): Frequency used merit
function(Irradiance distribution),Can measure Phase difference, can derive Resolution,EE, MTF(OTF)
• Encircled Energy: particularly relevant merit function of the optic performance of an optical system whose purpose is to collect light and direct it thru the entrance slit of a spectrometer
• Modulation Transfer Function(MTF): For many imaging applications involving extended objects containing fine structure, the MTF is a more appropriate performance criterion than PSF. Practical Cutoff Frequency(Fr) -> Cutoff Frequency(Fc)
16.684 Space Systems Product DevelopmentChart: 14February 13, 2001 MIT Space Systems Laboratory
Optical Sensitivity
0.65 0.7 0.75 0.8 0.85 0.9 0.95 10
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N=8
N=6
N=2
Phase SubTelescope
Common Secondary
Effe
ctiv
e C
olle
ctin
g A
rea
REFLECTANCE R
• Sensitivity of Phased Telescope Array (Effective Collecting Area)R: the reflectanceN: the number of reflections
•
Ngeoeff RAA =
2 types may be viable conceptfor quasi-monochromatic applications; however, phased telescope arrays will suffersubstantial sensitivity losses forbroadband spectral applications
A Region: UVB Region: Visible (Color)C Region: Quasi-Monochromatic
A B C
16.684 Space Systems Product DevelopmentChart: 15February 13, 2001 MIT Space Systems Laboratory
PSF,EE (Golay Array –3)Preliminary Calculation(0.3m GR) => D=2.0m,approx needed !!For Reff=1m, r=0.5m and Array Radius(L)= 1.m (Golay 3,monochrome)
r=0.3685m and Array Radius(L)= 1.1m (Golay 6,monochrome)
Using Analysis Tool:Evaluate Configuration Using •PSF(Point Spread Function)•Encircled Energy•MTF(ModulationTransfer Function)•FF(Fill Factor)
16.684 Space Systems Product DevelopmentChart: 16February 13, 2001 MIT Space Systems Laboratory
Modulation Transfer Function• An image of an extended object is far more complex thant point source(e.g) astrometry. PSF is not enough! -> MTF of each configuration is necessary• Both Resolution and Contrast (Modulation) Transfer IMPORTANT
0 5 10 15 20 25 30 35 40 45 50-1
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TextEnd
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IntensityOf Object
Image
Object
Optical Array
PSF of Optical Array
IntensityOf Image
Modulation= Imax − I min
Imax + I minFFT(I object)
OTF=FFT(PSF)
FFT(I image)
*
Real ImageInvFFT
MTF=abs(OTF)
16.684 Space Systems Product DevelopmentChart: 17February 13, 2001 MIT Space Systems Laboratory
Optical Control and Beam Combining
Optics ControlActuators
Piezoelectric translators (PZTs)Fast steering mirrors (Tilt and Tip)Optical delay lines (or inchworm positioners)Alignment mirrors
SensorsLaser interferometersQuad cellsCharge Coupled Device (CCDs) camerasAvalanche Photo Diodes (APDs)
16.684 Space Systems Product DevelopmentChart: 18February 13, 2001 MIT Space Systems Laboratory
Fine Optical Pointing and Phasing:Single Aperture
• Light path– Light enters spacecraft by reflecting off
primary and then secondary, after which it is collimated (not converging or diverging except for diffraction effects)
– Reflects off two-axis (tip and tilt) Fast Steering Mirror (FSM)
• FSM controls out the low level line-of-sight (LOS) jitter in the deadband of the attitude control
– Lens focuses light onto camera• LOS jitter control using FSM
– Feedforward attitude sensors to command FSM
– If bright point source in FOV, measure motion on camera and command FSM to minimize its motion
PrimaryMirror
SecondaryMirror
FastSteeringMirror
LightRays
CameraLens
16.684 Space Systems Product DevelopmentChart: 19February 13, 2001 MIT Space Systems Laboratory
CC
D
Fig.10, Cassegrain Type beam combiner (above) and refractive lense combiner
Beam Combining Goal:1. maintain the optical phase difference of each beam to a fraction of a
wavelength 2. align images from telescopes to within a fraction of a resolution
element over the whole field of view(Additionally) Field of curvatures on the order of wavelength, finer than
required for conventional telescopes
Beam CombinerPhase(Piston Error) Contributor:1. Lateral Pupil Geometry Error (Pupil Mapping
Error)=>the elimination of this error : golden rule of separated telescope ( significant in wide field of view telescope)
2. Piston Error: part of piston error is induced by pupil geometry e
3. Tilt Error : Measured separately from piston error. X-Tilt Error, Y-Tilt Error
16.684 Space Systems Product DevelopmentChart: 20February 13, 2001 MIT Space Systems Laboratory
Lateral Pupil Geometry Error
Physical Meaning:If the subapertures of the entrance pupilhave a D, and separated by S, with magnification M, the exit pupil must havedimensions for D/M and separation S/M
a a
)sin(aMP ε=pCorrect Pupil Geometry
Incorrect Pupil GeometryDifficult to measure lateral pupil geometry =>abstract optical quantity
Use the relationship and Kalman filter to estimate ε
Pg
ψ
)sin(M
Pgψε=
ε :lateral pupilgeometry error
16.684 Space Systems Product DevelopmentChart: 21February 13, 2001 MIT Space Systems Laboratory
Optical Tolerance
p
γ
r
Tilt induced piston error
)sin(γrPt =])sin([)sin(
)(
pM
r
pppm gtp
++=
++=
ψεγ
FOV=4km,h=500km,piston error55nm =>1µm
Lateral pupil Geometry Error
<1/10 of Airy Disk Diameter=> 33
µrad
Alignment Error(Image Rotation)
1/10 of λ, r=0.5m => 110 nradTilt1/10 of wavelength = 55 nmPiston
Total Piston Error
P :the opticalpath differencebetween beams
ToleranceErrors
DFOVHalfAngle
)44.2)(1.0( λ<∆Φ
16.684 Space Systems Product DevelopmentChart: 22February 13, 2001 MIT Space Systems Laboratory
Beam Combining Layout
OPDA(Optical Path Difference Adjuster) :is driven by
•Piezoelectric translator(PZT) = Fine Control Translation Range (-12 µm),Resolution(5nm), SlewRate(4.5 µm/s)Angular Tilt Range(700 µrad),Resolution (200 nrad)
•Burleigh inchworm positioners = Coarse ControlTranslation Range(5mm) with a resolution of 0.1 µm
CCDRetro Mirror
Sensor System (Interferometer)
Scraper(Scan) Mirror
OPDA
16.684 Space Systems Product DevelopmentChart: 23February 13, 2001 MIT Space Systems Laboratory
Sensor System Optics(Example from AFRL)
PolarizingBeam Splitter
FilterBeam Splitter
Direction to Scraper Mirror
Line ScanCamera
Line ScanCamera
Beam Expander Argon Laser
Motor
Field Scan Mirror (ψ)
Piston Sensing
: Lateral Effective Photo detector(LEP)
: Split PolarizerTilt
Sensing : Microscope Lens
16.684 Space Systems Product DevelopmentChart: 24February 13, 2001 MIT Space Systems Laboratory
Fine Optical Pointing and Phasing:Multiple Aperture
• Now need to stabilize both absolute and relative LOS jitter (Differential Wavefront Tilt)
• Also need to interfere same wavefront of light at combiner– Use Optical Delay Lines (ODLs)
• ODLs add and subtract optical pathlength from the companion telescope to the combiner.
• Used to control small positional mis-alignment and S/C attitude error
• Typically a multi-stage device with voice coils and piezoelectrics
PrimaryMirror
SecondaryMirror
FastSteeringMirror
LightRays
CameraLens
SecondaryMirror
LightRays
FastSteeringMirror
OpticalDelayLine
FoldMirrors
BeamCombiner
16.684 Space Systems Product DevelopmentChart: 25February 13, 2001 MIT Space Systems Laboratory
References
[1] Larson, W.J., Wertz, J.R., “Space Mission Analysis and Design”, Second Edition, 9.5 Designing Visual and IR Payloads, pp.. 249-274, Microcosm, Inc,1992
[2] Born Max, Wolf Emil, “Principles of Optics”, Electromagnetic Theory of propagation interference and diffraction of light, Sixth Edition, Cambridge University Press, 1998
[3] Hecht E. “Optics”, Addison-Wesley, 1987
[4] Günter Diethmar Roth, “Compendium of Practical Astronomy”, Volume 1, Instrumentation and Reduction Techniques, Springer Verlag, Berlin, New York, ISBN 3-540-56273-7, 1994
16.684 Space Systems Product DevelopmentChart: 26February 13, 2001 MIT Space Systems Laboratory
Optical System Design Process
From SMAD Chapter 9
1. Determine Instrument Requirements2. Choose preliminary aperture3. Determine target radiance4. Select detector candidates5. “Optical Link Budget”, SNR considerations6. Determine Focal Plane architecture and scanning schemes7. Select F# and telescope/optical train design8. Complete preliminary design and check MTF9. Estimate weight, power and ACS requirements10. Iterate and document - code optics software module