ultraviolet spectrometer and polarimeter for the solar maximum mission

Ultraviolet spectrometer and polarimeter for the SolarMaximum Mission

M. S. Miller, A. J. Caruso, B. E. Woodgate, and A. A. Sterk

The detailed optical design of the Solar Maximum Mission-Ultraviolet Spectrometer and Polarimeter is dis-cussed in conjunction with the scientific objectives that led to the design. The instrument consists of a1.8-m effective focal length aplanatic Gregorian telescope followed by a 1-m Ebert spectrometer. The de-

sign of the Stokes polarimeter is also discussed.

1. Introduction

The general scientific objectives and design of theSolar Maximum Mission-Ultraviolet Spectrometer andPolarimeter (SMM-UVSP) have been described byWoodgate et al.' The instrument was based on thedesign of the UV spectrometer on the Orbiting SolarObservatory (OSO-8) described by Bruner.2 We nowdescribe the detailed optical design of the UVSP afteroutlining the objectives and instrument modes that ledto the design.

A full understanding of the buildup and energeticsof a solar flare require measurement of the spatial andtime development of the plasma as characterized by thetemperature, density, velocity, and magnetic field.Thus, the UVSP instrument operates in a number ofdifferent modes that will allow determination of thesefour essential parameters, primarily at chromosphericand transition region temperatures. These modesare:

(1) Integrated Line Intensities. The integrated lineintensity mode allows simultaneous measurement ofseveral spectral lines formed at different temperatures.These line measurements can be used to determine thetemperature and density structure of a specific featurein the solar atmosphere.

(2) High Resolution Spectroscopy. The highspectral resolution allows the measurement of closelyspaced lines and Stokes profiles.

(3) Velocity Measurements. The use of a doubleexit slit allows measurement of the Doppler shifting ofa spectral line by splitting a line profile into long andshort wavelength halves via a sharp-edged beam split-ter. Each half is then imaged to a separate detector,and the difference in signal is used to determine thevelocity.

The velocity measurements can be used to determinemass motions that are essential in any flare model bothfor studying the dynamics of the flare itself and for in-formation on the flare-triggering mechanism.

(4) Polarimetry. In conjunction with the spec-trometer's grating, which serves as analyzer, the waveplate retarder allows determination of the four Stokesparameters. The Stokes parameters can be used todetermine solar magnetic fields. The measurement ofchromospheric and transition region longitudinalmagnetic fields could provide valuable insight into thelocation of the reservoir for flare energies in the solaratmosphere.

Linear polarization from resonance scattering andfrom atoms that have been excited by anisotropichigh-energy electron streams will also be measured withthe polarimeter.

Finally, as well as solar measurements, the instru-ment can measure various earth upper atmosphericconstituents in the 1150-3000-A range during orbitalsunrise and sunset. Some of the constituents are:

ozonenitric oxidemolecular oxygen

2000-3000 A2049 A1000-2000 A

A. A. Sterk is with General Electric Company, P.O. Box 85555,Philadelphia, Pennsylvania 19101; the other authors are with NASAGoddard Space Flight Center, Greenbelt, Maryland 20771.

Received 9 April 1981.

11. Instrument Description

The UVSP is shown in Fig. 1, and the overall instru-ment properties are summarized in Table I. The in-strument consists of a 1.8-m focal length aplanaticGregorian telescope with a geometric aperture of 66.4cm2 followed by a 1-m Ebert spectrometer. The spec-

1 November 1981 / Vol. 20, No. 21 / APPLIED OPTICS 3805

/ / / 7 . .. . ..

Fig. 1. Layout of SMM-Ultraviolet Spectrometer and Polarimeter.

Table 1. UVSP Instrument Properties

Telescope effective focal lengthTelescope collecting areaSecondary magnificationField-of-viewEntrance slit sizes

Minimum raster stepEbert mirror focal lengthGrating frequencySpectral range

Spectral resolution

Exit slit widths

System efficiency at 1215 A(without polarimeter)

1.8m66.4 cm2

6.0256 X 256 arcsec 2

1 X 1, 3 X 3, 10 X 10, 30 X 301 X 10, 4 X 4, 15 X 286,1 X 180 arcsec 2

1 arcsecl m3600 gr/mm1150-1800-A second order;

1750-3600-A first order0.02-A FWHM second order,

0.04-A FWHM first order0.01, 0.03, 0.05, 0.2, 0.3,

0.5, 0.6, 0.8, 2.3, 3.0 A0.004

trometer employs a holographic diffraction grating witha ruling frequency of 3600 gr/mm. The angle of inci-dence is variable from 18 to 430, corresponding towavelength ranges of 1150-1800 A in the second orderand 1750-3600 A in the first order. A retarder can beinserted into the beam behind the entrance slit of thespectrometer, which acts with the spectrometer'sgrating as an analyzer to form a Stokes polarimeter. Avariety of exit slits can be used with any entrance slitdepending on the observational mode. The exit slitoptics include two micron-edge beam splitters and de-flectors that direct the diffracted radiation to the ap-propriate detector(s).

The detectors consist of five photomultipliers thatoperate in the pulse counting mode. Four of the pho-tomultipliers have CsI photocathodes and LiF windowsfor wavelengths below 1900 A, and the fifth has a CsTephotocathode with a LiF window for wavelengths below3600 A.

Ill. Telescope

The design of the telescope is driven by a number offactors. To fill the grating of the spectrometer properlythe f number of the telescope must match the spec-trometer aperture ratio. The experiment housing de-termines the maximum clear primary aperture, and thescientific requirements of the Mission, primary aper-ture, and spacecraft pointing stability determine theultimate angular resolution.

An experiment housing from the OSO-8 spectrometerwas available so it was used for the SMM-UVSP ex-periment housing. The primary aperture width (120

mm) and the telescope's effective focal length (1.8 m)would, therefore, be the same for the UVSP telescopeand the OSO-8 spectrometer's telescope.

The OSO-8 telescope employed a Cassegrain designwith a secondary magnification of six. The OSO in-strument, however, experienced a large loss of UVsensitivity shortly after launch, which was believed tobe due to the effects of surface contamination of thesecondary mirror. The Cassegrain secondary mirrorof OSO-8 was exposed with up to 30 solar constants ofsolar radiation. If the secondary became contaminatedwith hydrocarbons, polymerization would be likelyunder such high solar fluxes, and the resultant UV ab-sorbing substance would reduce the mirror reflectivities.The SMM-UVSP telescope design was therefore drivenby the need to minimize irradiance on the secondarymirror. This is most readily accomplished by a Gre-gorian design with a field stop at prime focus.3 Thefield stop reduces the field of view to -470 sec of arcsquare, which in turn reduces the secondary irradianceto 1.5 solar constants. Telescope baffling and field stopsize were designed to produce no vignetting of the sec-ondary beam. The stop is made of copper and is ren-dered highly absorbing by a black oxide coating. Theabsorbed solar radiation is conducted away to a radia-tion plate by supporting struts and two heat pipes.4Other measures have been taken to avoid possiblecontamination problems, including:

(1) Switchable primary and secondary mirrorheaters.

(2) A telescope door, which remained closed duringthe first few days of flight to prevent solar radiationfrom reaching the mirror until most of the contaminantshad evaporated.

(3) Care during assembly and test to avoid depositionof hydrocarbons.

To focus off-axis object points on the axial spec-trometer entrance slit it is necessary to raster the sec-ondary mirror. The resulting image growths for aGregorian telescope are listed in Table II, which datawere obtained by optical ray trace analysis to determinethe degradation in spatial resolution resulting fromsecondary mirror motions that occur in changing thepointing direction of the telescope. The secondarymirror was tilted about a number of points to bring in-cident off-axis collimated light to a focus at the normalentrance slit of the spectrometer. Image size for TableII is taken to be the smallest spacing between two par-allel slit jaws that will pass 80% of the rays. The sourceangle of 169.7 sec of arc corresponds to the diagonal ofa 2-min of arc square raster pattern.

The results of this analysis is a confirmation of thewell-known rule, that the secondary mirror has to tiltaround the common focal point of the primary andsecondary mirrors. The distance between the secon-dary mirror and the common focal point is 70 mm,which results in a moment of inertia of 9.8 X 10-5 kg-M 2

for the mirror. This high inertia is a problem becauseof the dynamic requirements and the limited torquemotor driving power available. The mirror rasters ina step-and-stare-mode, with measurements being made

3806 APPLIED OPTICS / Vol. 20, No. 21 / 1 November 1981

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Table II. Image Growth as a Function of Point of Rotation of the Secondary Mirror for the Gregorian Telescope

Source Secondary mirror 80% width image growthangle Displacement Along scan Cross scan(sec) (sec) About (arcsec) (arcsec)

169.68 869 Common focal point 0.2 0.1169.68 468 40 mm to sunward side of 1.6 1.3

common focal point169.68 398 60 mm to sunward side of 1.8 1.5

common focal point169.68 366 Secondary mirror vertex 2.0 1.6169.68 338 10 mm to sunward side of 2.1 1.7

secondary mirror vertex

Table Ill. Image Growth as a Function of Point of Rotation of the Secondary Mirror for the Aplanatic Telescope

Source Secondary mirror 80% width image growthangle Displacement Along scan Cross scan(see) (sec) About (arcsec) (arcsec)

169.68 852 Common focal point 3.9 3.1169.68 480 40 mm to secondary side of 1.0 0.8

common focal point169.68 394 60 mm to secondary side of 0.3 0.3

common focal point169.68 362 Secondary mirror vertex 0.1 0.1169.68 335 10 mm to sunward side of 0.2 0.2

secondary mirror vertex

during the stare period only when the mirror is at rest.The step period should be short to minimize total ras-tering time. It was specified at <30 msec. The currentto energize the torque motor for driving the mirrorgimbal was limited to 0.160 A. Another practical lim-itation is that only a very small motor can be accom-modated without interfering with the telescope opticalpath. With all these limitations a design could not berealized without a radical change in concept.

The approach taken was to tilt the secondary mirroraround an axis passing through the center of gravity ofthe mirror. The moment of inertia decreased now to1.56 X 10-6 kg-M 2 or by a factor of 62 compared with theprevious case. With this configuration the dynamicresponse was 20 msec for a 1-sec of arc step, the motorcurrent was limited to 0.155 A, and the motor diameterwas only 2.54 cm.

To avoid the severe degradation in optical perfor-mance, as shown in Table II under secondary mirrorvertex, the optical design had to be modified.

Bottema and Woodruff5 have investigated the opticalproperties of two-mirror telescopes with the secondarymirror tilted around an axis passing through its vertex.They arrived at a design, the "tilted aplanatic," thateliminates coma by changing the eccentricities of theprimary and secondary of the Gregorian system to

|11+ S(m 2 + 1)11/2, (1)

4m(m - 1) + ( 2 + 1)(m + S) 1/2eS = 1 + (m- [1)3' (2)

where

S (image distance from secondary) (3)

intervertex distance

and m is the secondary magnification.

The intervertex distance (370.32 mm) and secondarymagnification (6), as well as the vertex radii for eachmirror of the original Gregorian design, remain the samefor the aplanatic system. The image distance from thesecondary (421.9 mm) also remains unchanged. Thenusing this information with Eqs. (1) and (2), the primarybecomes an ellipse with eccentricity ep = 0.89713, whilethe secondary in the aplanatic system is a hyperbolawith eccentricity e = 1.01446.

Another optical ray trace analysis was performed forthis optical design for various locations of the point ofmirror rotation and the results are summarized in TableIII. It can be seen that the optimum performance,equaling the best result of Table II, occurs with thepoint of rotation at the secondary mirror vertex, whichis very close to the center of gravity of the mirror.

Having thus established that the secondary mirrorcan be rotated about a point near its vertex withoutdegrading the image quality at the spectrometer's en-trance slit, the design was implemented by mountingthe telescope's secondary mirror on two gimbals con-nected to torque motors and controlled by linear dif-ferential voltage transformers (LDVTs) in a servo loop.The scan range produced is 256 X 256 sec of arc, with aminimum step of 1 sec of arc and a maximum step of 30sec of arc.

The telescope was fabricated and tested at theGoddard Space Flight Center. Figure 2 shows theimage quality as a function of source angle for the ap-lanatic flight telescope. No change from the on-axiscase was observed in the image quality at the spec-trometer entrance slit as the source was moved off to onecorner of the square raster pattern. The telescoperesolution was measured at 2570 A with a frequency-doubled visible laser and found to be <1.7 sec of arc by1.1 sec of arc FWHM. The asymmetry was caused by


Finally, coma can be corrected by moving the centerof rotation of the grating from its plane along the axisof dispersion toward the entrance slit to reduce theoff-axis angle and the wave front curvature introducedduring collimation.

Bruner8 has studied in detail coma correction for anEbert spectrometer. The grating offset for coma cor-rection can be derived as a function of the angles of in-cidence of the chief ray on the Ebert mirror duringcollimation (a) and after diffraction from the grating (b).These angles are related to the angles of incidence anddiffraction by (see Fig. 3)

On axis Off axis maximum

Fig. 2. Image quality at spectrometer's entrance slit as a functionof source angle for aplanatic telescope.

a small lateral displacement of the secondary and therectangular masking of the primary.

IV. Spectrometer

The Ebert spectrometer consists of a 1-m focal lengthspherical Ebert mirror that collimates light from theentrance slit onto a plane holographic grating with afrequency of 3600 gr/mm. The light diffracted from thegrating is then focused by the Ebert mirror into the exitslit. Following Harrison,6 the light diffracted from agrating of width W in a Ebert spectrometer of focallength F may be characterized by

nX = d(sina + sin), (4)

da3 n 2 tan:3

dX d coso X

dx nF 2F tan3dX d cos3 (

nW 2Wsin:3d A, ' 7

where n is the order of diffraction, R the spectral reso-lution, X the wavelength, d the grating spacing, a theangle of incidence, and : the angle of diffraction. Theexpressions on the extreme right-hand side have em-ployed a - , which is appropriate for a Ebert-Fastiemounting.

The simplicity of the Ebert spectrometer, coupledwith its adaptability to the long focal lengths necessaryfor high spectral resolution, make it ideal for use in theUVSP instrument. The 1-m system with a 75 X 75 mmgrating provides a theoretical resolution of 540,000 withEq. (7). This resolution is more than adequate to meetthe system bandpass goal of 0.01 A. In practice theresolution is limited by aberrations. The aberrations,principally spherical aberration, astigmatism, and coma,must therefore be limited.

The f/19 beam used in the spectrometer reduces thespherical aberration [(F/W)- 3] to an acceptableamount. Fastie7 has shown that the astigmatism maybe minimized by placing the entrance and exit slits asclose to each other as possible without producing vi-gnetting of the input and output beams.

a cos3 flb -a - K.

The grating offset e for coma correction in an Ebertspectrometer of focal length F is then

e h (1 K) (I + , (9)

where

h Kb - - (10)F 2F (0

and h is defined in Fig. 3.The grating offset will depend on the grating wave-

length, and so it was necessary to place the axis ofrotation behind the grating, thereby allowing the offsetto vary with wavelength. By employing these designconsiderations to reduce system aberrations it waspossible to produce an instrument with a measuredspectral resolution of 0.02-A FWHM in the secondorder.

The 75 X 76-mm plane 3600-gr/mm gratings wereholographically ruled by Caruso. These gratings werecoated with 70 nm of Al plus 25 nm MgF2 and specifi-cally designed to produce maximum polarization withan acceptable absolute unpolarized efficiency (>10%)for the negative second order in the wavelength range1200-1800 A.

Experimental measurements of the absolute effi-ciency for S plane (electric vector perpendicular to thegrating grooves) and P plane (electric vector parallel tothe grating grooves) polarization of high frequencyblazed holographic gratings reveal that the higher theunpolarized efficiency, the lower the polarization in thewavelength region 1200-1800 A in the second order. 9

Fig. 3. Geometry of coma correction.


(8)

24 I I

3600 1/-!22 75 x 76..'

I20 AD = 18.5

1- I /

12 _/ _

4 _

2 ,

12 13 14 15 16 17

4 IN 6XI

Fig. 4. Absolute unpolarized efficiency of flightnegative second order.

grating for the

From this observation three 3600-gr/mm plane gratingswere ruled so that an acceptable absolute unpolarizedefficiency was produced while simultaneously producinghigh polarization.

Experimental evaluation of the gratings was per-formed at Johns Hopkins U. using a test chamber thathas an angle of deviation of 18.50 (Ref. 10). Figure 4shows the absolute unpolarized efficiency of the flightgrating for the negative second order. A maximumunpolarized absolute efficiency of 18.5% occurs at 1540A. The structure in the curve is caused by anomaliesat the indicated wavelengths. Figure 5 shows the po-larization for the flight grating in the negative secondorder. A maximum negative polarization of 0.75 occursat 1219 A and maximum positive polarization of 0.62occurs at 1385 A. The negative polarization is the resultof the P plane efficiency being higher than the S planeefficiency as a function of wavelength, and positivepolarization occurs when the S plane efficiency is higherthan the P plane efficiency. It is well-known that ifefficiency measurements are made at different anglesof deviation, the anomalies will shift in wavelength re-sulting in a shift in the polarization peaks. This wasobserved when the grating was again evaluated for po-larization in the flight spectrometer that has an angleof deviation of 7.160 and the peak polarization shiftedto 150 nm.

The groove frequency of the grating was also deter-mined. A laser beam of 4579-A wavelength passedthrough a 5.0-mm diam aperture and impinged on thesurface of the plane grating mounted on a turntable(2.0-sec of arc accuracy). The beam was reflected backon itself in the zero order so that it passed through theaperture. There was a distance of 2.5 m between ap-erture and grating surface. The grating was then ro-tated via the turntable so that the first-order diffractedimage passed through the aperture where a = (Lit-trow configuration), and the corresponding angle wasread from the turntable scale. The grating groove fre-quency was then calculated to an accuracy of 0.5 gr/mmusing the grating equation with the known wavelengthand measured incident and diffracted angles.

The significant advantage of using holographicgratings is the low scattered light and absence of ghosts.Experimental evaluation of the gratings showed noghosts and extremely low scattered radiation about theparent lines. For example, the scattered radiation inthe negative second order was only 0.003% at -50 Afrom the 1219-A line. The measured scattered light at2572 A is 10-5 of first-order efficiency at 0.3 A from theparent line as determined using a frequency-doubledvisible laser.'1

V. Entrance and Exit Slits

The entrance and exit slits are mounted on a singleplate that can be rotated by a slit-changing mechanismso that various combinations of exit and entrance slitscan be used. This plate is tilted by 0.6 with respectto the Ebert normal to compensate for the curvature inthe spectrometer focal plane. Multiple exit slits allowobservations at several wavelengths simultaneously, andin turn place a severe constraint on the grating rulingfrequency. This constraint comes from the fact thatthe relative separation between two lines in the spec-trometer's focal plane must be maintained to within 2Aum of the design for some slit sets for balanced simul-taneous observations of the lines to be made. Thegrating, therefore, was measured to an accuracy of 0.5gr/mm.

There are five different types of slit set used in theexperiment: spectroscopy, velocity and polarization,intensity, aeronomy, and coronal slits. Narrow en-trance and exit slits are required for high resolutionspectroscopy. The corona slits have large entrance slitsto allow lines above the solar limb to be measured. Theaeronomy entrance slit is long and narrow to increasethe signal for the measurement while maintaining highspectral resolution. Many of the exit slits require relayoptics to deflect the beam to the appropriate detector.

3600 g,',

03 /

0.7 /

Fig-5.Polriztio1 fr.figh0grtin inth neatie scon orer

Fig. 5. Polarization for flight grating in the negative second order.


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3810 APPLIED OPTICS I Vol. 20, No. 211/1 November 1981

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The slit set choice is shown in Table IV, where specificwavelengths are identified for simultaneous observationusing a specific grating angle. Any wavelength can beobtained individually using any slit set by selecting thatslit and the grating angle.

The absolute intensity of the signal as measured incounts by the detector is

= Asq(X,n) SIx(X:x,y)dXdQ, (11)

where A = telescope aperture,-q(X,n) = efficiency of telescope-spec-

trometer-detector system as afunction of wavelength X andspectral order n,

Q = solid angle, andIx(X:x,y) = specific intensity or spectral ra-

diance of the sun or other source(in photons per unit time, perunit area, per unit solid angle,per unit wavelength interval) asa function of wavelength X, andthe position x ,y on the sun or inthe sky.

The integral over source angle is taken over the en-trance slit while the wavelength integral is over the exitslit width. The efficiency is assumed constant over anarrow exit slit width (<3 A) and was taken out of thewavelength integral. The spectral distribution will alsobe slightly affected by the grating and width of the en-trance slit. For the case of the intensity slits where awide exit slit is used,

4 = Ain(X,n)(I1x(x,y)) (12)

Fig. 6. Sharp-edged beam splitter.

Fig. 7. Exit slit plane.

Fla Fat(M F2 Crystal)

1or (

FitR~~whg -.pl- ~~~~~T-rid BR, 2.42

where (Ix(x,y)) is the intensity or radiance integratedover the profile of a spectral line.

The velocity slits employ a 2-gtm edge beam splitterthat separates the spectral line into a long (red) andshort (blue) wavelength half. This is illustrated in Figs.6 and 7. The velocity slits also employ two wide exitslits, thereby yielding two spectral lines that are thenfurther split into long and short wavelength halves.The use of two lines formed at different heights canallow wave velocities and relative phases for transientor other wave motions to be determined. The resultingimbalance in signals between the long and short wave-length halves of each line will then be used to measurevelocity via the Doppler shift. The velocity signal isgiven by

S = I j ' (13)1) + C (13

where I and 44 are the observed detector signals in thered and blue halves of the line, respectively. A correc-tion to one of the signals will be needed to compensatefor the difference in sensitivity between the two detec-tors. The exit slits employed in the velocity measure-ments are wide compared with the line width, so thedenominator 44 + 4I will be proportional to IL, theintegrated line intensity, and S, will be independent ofintensity. However, So, will still depend on the line-width. To calibrate the dependence on linewidth, the

Fig. 8. Optical layout of polarimeter.

wavelength drive will be used to deliberately offset theline by a known wavelength shift. The polarimeter willalso employ the velocity slits to measure longitudinalmagnetic fields.

VI. Polarimeter

The geometry of the polarimeter is illustrated in Fig.8. It consists of a dual-channel rotating wave platesystem followed by a four-mirror polarizer. One waveplate will only be used in conjunction with the gratingfor those spectral regions where the grating has highpolarization. The other wave plate will be used inconjunction with the four-mirror polarizer for all otherspectral regions of interest.

Both wave plates are made of magnesium fluoridesince it is the only birefringent material known totransmit wavelengths as short as Lyman-oa. The re-tardation 3 of a birefringent plate of thickness d is

6 = 360'And/X, (14)

where An is the difference between ordinary and ex-traordinary refractive index, and X is the wavelengthexpressed in the same units as the thickness. The bi-refrin ence of magnesium fluoride is a maximum at1400 and decreases rapidly at shorter wavelengths so


R = 122m)

t

that a/4 retardation at Lyman-a would require an8-gim thick plate. It is impossible to manufacture sucha thin plate, but what is commonly done is to use twomagnesium fluoride plates with crossed optical axes thatdiffer in thickness by 8 gim. The off-axis retardationR of two crossed plates of thickness D + E and D - e isgiven by12

[2eAn 4b2An Ino + n ' 2eAn ine - no 6R = _ - I cos2a - 11 x 3600°

X 2 noX t- nonI 2

noX '~none J

(15)

where q = angle between incident ray andnormal,

a = azimuth of incident ray with respect tobirefringent optical axis,

no = ordinary refractive index, andne = extraordinary refractive index.

The first term of Eq. (15) corresponds to the 6 of Eq.(14). The last term is very small and can be neglectedwhile the middle term represents the principal off-axiseffect.

Each wave plate is made of two magnesium fluoridedisks, each -0.3 mm thick, which are optically contactedtogether. The wave plate used in conjunction with onlythe grating has a maximum retardance of 2860, whichmeans in the region from 1300 to 1600 A it is ap-proximately a three-quarters wave retarder, and at 1240A, it is a halfwave retarder. The wave plate used withthe four-mirror polarizer and the grating has a maxi-mum retardance of 122°, and can be used as a quarter-wave retarder in the region 1,250-2,500 A. For a po-larization measurement either one of the two waveplates may be inserted into the light path and then ro-tated. Rotation will occur in steps of 22.5° so thatsixteen steps are required for one full rotation.

The four-mirror polarizer has been described in greatdetail by Hass and Hunter.' 3 It consists of two pairsof parallel mirrors symmetrically placed and tilted atan angle of 60° to the normal. The first three mirrorsare flat while the fourth mirror is a convex toroid. Thetoroid allows the beam to be focused at the normalspectrometer exit slit and also allows some control ofastigmatism at the exit slit. One mirror is a MgF2crystal, while the others are Al overcoated with MgF2.The four-mirror polarizer provides a measured polar-ization in excess of 80% at all wavelengths and exceeds90% at the wavelength where the mirror angles nearlyequal the Brewster angle. However, the four-mirrorpolarizer provides a throughput of only 5% or less. Thedesign of the polarimeter is discussed in greater detailby Calvert et al. 14

The theory underlying the operation of the polar-imeter can most easily be understood by employing theStokes parameters. These parameters can uniquelydefine any arbitrary polarized state of light. Considertwo orthogonal plane waves propagating in the Z di-rection, with amplitudes Eo, and Eoy:

E = Eo. exp[i(wt + x)] E = Eoy exp[i(cot + by)]. (16)

The Stokes parameters can be written as a columnmatrix (Perrin)15 :

II1nO2 +E Q I Eo -E2S = Q O O

U | 2EoxEoy cos6

L VJL2Eo.Eo, sinbj

(17)

where 6 - by - xDefine S - (I,Q,U,V) as the Stokes vector of the light

beam incident on the polarimeter, and let S' (I',Q',U',V') be the Stokes vector of the beam that has beenmodified by passing through the polarimeter. Orrall16has expressed the transformation from S to S' as

S' = [MP][MR]S. (18)

Here [Mp] and [MR] are the Mueller matrices of thepolarizer and retarder, respectively. Orrall found theintensity reaching the detector (IO) to be given by

Io = I + p(a + b cos4wt)Q + pbU sin4wt + pV sinb sin2wt,(19)

where p = polarization of linear polarizer,6= retardance of wave plate,a= /2(1 + cosb),b= 1/2(1 - cos6), and

wt= rotation angle of the fast axis of the waveplate. -

One can see immediately from Eq. (19) the need for ahigh degree of linear polarization to measure the Stokesparameters.

The wave plate retardance varies with wavelength,and for those wavelengths where approaches 180° Eq.(19) shows that V becomes indeterminate. For thisreason the two wave plates employed in the polarimeterhave different retardances, which in turn require anextensive calibration of the polarimeter as a functionof wavelength (see Calvert et al. 17). Since the Stokesparameters vary with wavelength, Eq. (19) must be in-tegrated over the exit slit width.

To determine the Stokes parameters the expressionfor I can be written in terms of a Fourier series:

7I, = co + E (c. cosnO + Sn sinnO) + c8 cos8O.

n=1(20)

Berry' 8 has shown how to use Fourier analysis to eval-uate the coefficients and solve for the Stokes parame-ters.

Longitudinal magnetic fields may be determined byobservation of the circularly polarized components ofa Zeeman triplet. Beckers'9 has shown that the StokesV parameter, which is proportional to the intensity ofthe circularly polarized state, may be used to determinethe longitudinal field via

Vx = cos-y[p(X + AXB) - p(X - AXB)I/2. (21)

In the above equation y is the angle between B and theline of sight, p (X) is the line profile, AXB is the Zeemansplitting of the spectral line with wavelength X0, and theazimuth of the magnetic field coincides with the refer-ence direction for the Q Stokes parameter. For smallsplittings (AXB small) one can use a Taylor expansionfor Vx:


400

0 1302.17

0 1 1304.86 011306.02

100 200 300 400 500

Fig. 9. In-orbit spectral resolution for the 1304.86 and 1306.02 A 0-Ilines. The wavelength scale is 0.01 A/data point.

Fig. 10. Dopplergram at CIV 1548 A of the loop prominences of 27 Mar 1980. Picture at left shows intensity, while right frame shows velocity.In the velocity frame material moving towards the observer is shown in blue, while material moving away is displayed as red. Assuming theright-hand leg of the loops is nearer to the observer than the left-hand leg, the change of color at top shows that material is draining down each

leg from the top.


V = AXB COS dp (22)dX

where AXB - XgB.For weak fields (<2000 Gauss) it is necessary to use

the velocity slits in conjunction with the polarimetersince the two i; components of the Zeeman triplet willnot be completely separated. The magnetic field isthen determined by integrating Eq. (22) over the twohalves of the line profile and averaging for the two de-tectors:

B cosy - /2 b (23)

In Eq. (23) we have used Beckers' result, b _ Wfor small splittings, and Iu(44) is defined as the StokesV(I) parameter for the red (blue) half of the line ex-pressed in counts. One must also take into account thedifference in detector efficiency for the red and bluehalves as a correction to one of the signals. By mea-suring the direction and amount of linear polarization,which is related to the Stokes Q and U parameter, onecan also determine the square of the transverse mag-netic field.

VII. Conclusion

The instrument was launched in February 1980, andafter an initial checkout period was pronounced fit foroperation. The instrument observed a number of solarevents during its ten months of operation. Figure 9shows the 1304.86- and 1306.02-A 0-I lines and is rep-resentative of the in-orbit spectral resolution. TheZeeman effect has been measured in the transition re-gion above a sunspot in the CIV 1548-A line showing alongitudinal magnetic field of 1100 300 Gauss(Tandberg-Hanssen20 ).

An image of a set pf loop prominences above the limbof the sun in the spectrum line of CIV at 1548 A is shownin Fig. 10. The picture at the left shows intensity whilethe right frame shows velocity. The velocity picture isformed by using the Doppler shift. Light from theshort wavelength side of the spectrum line is split off toone detector via a sharp-edged beam splitter in the ve-locity slits, while the long wavelength side of the splitline is reflected to another detector. The differencebetween the images formed by the two detectors is usedto form the velocity image.

Instrumental efficiency was monitored continuouslyas a function of wavelength during the ten-monthMission lifetime. The efficiency at Lyman-a degradedby two orders of magnitude during the first threemonths of operation and then stabilized for the re-

mainder of the Mission. At 1300 A the efficiency de-creased by a factor of 4, while the efficiency decreasedonly 8% at 1550 A during the ten months of operation.The degradation in instrumental efficiency was believeddue to the contamination of the optical UV coatings. Afew possible contamination sources are2l oil leakagefrom wavelength drive mechanism, contamination fromother instruments, and contamination experiencedduring thermal vacuum testing of the spacecraft.

The authors would like to acknowledge the dedicatedefforts of several groups in bringing together the opticalsubsystem of the UVSP.

The polarimeter was designed and built at the Mar-shall Space Flight Center by F. Rutledge, D. B. Griner,J. A. Calvert, F. J. Nola, and J. Montenegro. The op-tical integration was carried out by E. D. Knox and G.W. Bethke of General Electric, Valley Forge. Primaryoptical parts fabrication was by the Goddard SpaceFlight Center Optics Branch, including J. D. Mangus,J. F. Osantowski, G. J. Bergen, R. S. Spencer, C. M.Fleetwood, and S. H. Rice.

References1. B. E. Woodgate et al., Sol. Phys. 65, 73 (1980).2. E. C. Bruner, Space Sci. Instrum. 3, 369 (1977).3. Technical Report, General Electric Space Division, Valley Forge,

Penn., unpublished.4. P. S. Caruso and E. Stipandic, AIAA Thermophysics Conference,

Orlando, Florida (1979).5. M. Bottema and R. A. Woodruff, Appl. Opt. 10, 300 (1971).6. G. R. Harrison, J. Opt. Soc. Am. 39, 522 (1949).7. W. G. Fastie, J. Opt. Soc. Am. 42, 647 (1952).8. E. C. Bruner, Space Sci. Instrum. 3, 369 (1977).9. A. J. Caruso, G. M. Mount, and B. E. Woodgate, Appl. Opt. 20,

1764 (1981).10. G. H. Mount and W. G. Fastie, Appl. Opt. 17, 3108 (1978).11. B. E. Woodgate et al., Sol. Phys. 65, 73 (1980).12. E. A. Tandberg-Hanssen et al., A High-Resolution Ultraviolet

Spectrometer and Polarimeter for the Solar Maximum Mission,NASA Technical Proposal (1975).

13. G. Hass and W. R. Hunter, Appl. Opt. 17, 76 (1978).14. J. Calvert et al., Opt. Eng. 18, 287 (1979).15. F. Perrin, J. Chem. Phys. 10, 415 (1942).16. F. Q. Orrall, in Solar Magnetic Fields, R. Howard, Ed. (D. Reidel,

New York, 1971), Part I.17. J. Calvert et al., Opt. Eng. 18, 287 (1979).18. H. G. Berry, G. Gabrielse, and A. E. Livingston, Appl. Opt. 16,

3200 (1977).19. J. M. Beckers, in Solar Magnetic Fields, R. Howard, Ed. (D.

Reidel, New York, 1971), Part I.20. E. Tandberg-Hanssen et al., Astrophysical J. (Letters) 244, L127

(1980).21. B. E. Woodgate et al., (1981) in preparation.

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ultraviolet spectrometer and polarimeter for the solar maximum mission

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