Optical design of two spectrographs for theCanada-France-Hawaii telescope

Christopher L. Morbey

Optical designs of two new spectrographs for the Canada-France-Hawaii telescope Cassegrain focus aredescribed. Also given is a summary of the design procedure using the Dominion Astrophysical Observatoryoptical design code OPTESA (optical system optimization by educated simulated annealing). The f/2.8multiobject spectrograph has a field of view of 10 min of-arc, whereas the f/10 subsecond of arc imagingspectrograph has a field of view of 3 armin. They are to be commissioned in 1991.

Key words: Focal reducer, multiobject spectrograph.

1. IntroductionFollowing a request from the Canada-France-HawaiiTelescope (CFHT) Corp. in early 1987 for a multiob-ject spectrograph, a cooperative effort of design andconstruction was initiated by Canadian and Frenchastronomers and engineers. Later that year reason-ably detailed but flexible design specifications weredrawn up. Finalized optical specifications were deter-mined by early 1988. This paper reports on the result-ing optical designs for two spectrographs: the f/2.8multiple-object spectrograph (MOS) and the f/10 sub-second of arc imaging spectrograph (SIS).

The primary aim of the MOS is to obtain the highestpossible efficiency for observations of numerous (>25)very faint (mu < 23) objects simultaneously at very low(>10-A) spectral resolution. Such an instrument isrequired by programs to observe complete surveys offaint galaxies or quasars. It is possible that such aspectrograph could also be used to observe brighterobjects (m, < 20) at higher spectral resolution (2-3 A).

High (FWHM -0.3 arcsec) spatial resolution spec-troscopy and imagery is the purpose of the secondspectrograph. Such an instrument would facilitateobservations of quasar host galaxies, nuclei of galaxies,or nebulas that require resolutions of >2 A on a singleextended object.

The author is with the National Research Council of Canada,Herzberg Institute of Astrophysics, Dominion Astrophysical Obser-vatory, 5071 West Saanich Road, RR#7, Victoria B.C., Canada.

Received 21 August 1990.0003-6935/92/132291-10$05.00/0.© 1992 Optical Society of America.

Earlier successes with focal reducer transmissionoptics at the CFHT and considerations of cost andgeometric constraints at the telescope dictated thedesign philosophy from the start. Such designs canprovide very good images over the full field of interestand can provide a high degree of spatial consistencybetween spectrographic and imaging modes. Essen-tially, a focal reducer' is made up of a collimator and acamera. The collimator at the telescope focus rendersthe light parallel again through a pupil and the cameraprovides an image at a new focal ratio. Resolution atthe image, the pixel size of the CCD detector, and theexpected seeing are all factors that influence the choiceof the focal ratio. Since the pupil is accessible there isan appropriate place for filters and dispersing ele-ments, and these can be contained in computer-con-trolled selectable modules. A combination transmis-sion grating-prism 2 (grism) is used for each of thedesired dispersions.

An analysis and design of the grisms to be used inthese instruments will not be given since their specifi-cations have not yet been finalized. A brief summaryof the Dominion Astrophysical Observatory opticaldesign code OPTESA (optical system optimization byeducated simulated annealing) will be followed by adescription of the two designs.

II. Optical System Optimization by Educated SimulatedAnnealingThe DAO optical design code OPTESA is a highlyevolved product originating with the IBM programPOSD that became available in the early 1960's. Sincethe days of the 8K IBM 1130 the code has run on aMOD COMP 11/25, an IBM 360 and 370, and a VAX11/780. For the last few years it has been used almostexclusively on an Alliant FX/1 and various Sun4s.During all this time the code has been greatly modified

1 May 1992 / Vol.31, No. 13 / APPLIED OPTICS 2291

to include many of the expectations of modern com-mercial programs, but it does lack much of the glitz.Additions of graphic laser printer output and an inter-active design facility have eased the burden of systemevaluation and setup. Because of the recent onslaughtof new and faster work stations and the difficultieswith each new FORTRAN compiler it was decided totranslate the FORTRAN code to C and C++ with thehelp of a commercial translation program. This en-deavor continues as the code establishes a permanenthome on a dual Motorola 88000 based work station(AViiON 402), which, for concurrently running jobs,provides an improvement in speed of -5 times over theSun4.

Although computer optimization was used through-out the design process, the final design was not reachedtotally automatically. It may be of some benefit tosummarize the more significant features of OPTESA inaddition to some methodology that would apply to anycode.

The optimization within OPTESA is based on thefamiliar damped least-squares method (DLSM), butthere is a built-in capability to deviate from the normalminimization of merit function route similar to thesimulated annealing method (SAM). The followingprocedures and code description are general in natureand not specific to the particular designs here.

(1) In an optical system many of the variables such ascurvature, axial separation, and aspheric coefficientsare not independent from one another. Solving inde-pendently for highly correlated variables with theDLSM can lead to erroneous results, and a good solu-tion can be completely missed. It is important to varyonly the variables that are least correlated at any trial.Covariances of the variables can be obtained directlyfrom the least-squares curvature matrix as the off-diagonal elements. In the SAM there is no worryabout dependencies between various variables. Thevariables are simply changed at random with the re-sulting new configurations accepted according to astatistical formula. A combination of the DLSM withthe SAM introduces some education into the SAMchoices, and most often computer time can be saved.

(2) Careful inspection of the direction and magni-tude of variable changes from iteration to iterationoften points to a new path. This is especially impor-tant if new glasses are to be tried. Allowing the refrac-tive index to vary at all wavelengths often shows whichglass might be better. Such a heuristic procedure isdifficult to implement totally in software, and often itis advantageous to choose a number of glass candidatesand try all the permutations. Procedures like theseare simple to implement in a Unix environment. Al-ternatively, the actual refractive indices of the glassescan be entered into the possible configurations to beevaluated by the SAM.

(3) Suppose a variable or image error makes an effortto exceed its defined boundary. An almost fail-safeprocedure to reverse this tendency is to fix the parame-ter at the boundary value and reiterate letting theparameter vary after the first iteration although the

merit function is larger at the start. The process hasan effect reminiscent of that used in the SAM, butagain the changes are somewhat educated rather thandetermined by a Boltzmann distribution.3 4 Becausethe OPTESA code defines the optimization route indi-cated by a combination of the DLSM and the SAM andso has the capability to deviate from the usual least-squares route, it is termed optical system optimizationby educated simulated annealing. The SAM is usuallyapplied to systems where there are always a large num-ber of similar close-by systems that can be evaluatedquickly (e.g., the traveling salesman problem and thephysical design of computer chips). Optical systemscomprise many fewer variables, and the evaluation ofconfigurations is much more computer intensive. In apure DLSM the iterations proceed only as long as themerit function decreases (in our formalism the smallerthe better), whereas in the SAM new configurationsmay be selected even though the merit function isgreater. Like the solution of the RUBIC cube, rela-tively disordered states occur within the progression ofincreasingly ordered states. In OPTESA the magni-tudes and directions of the parameter changes aredetermined by DLSM, and the SAM provides an op-portunity (of selectable degree) for the directions tochange. The application of sufficient and appropriateconstraints together with the invocation of the SAMensures that there is ample opportunity for the mini-mization route to ascend some of the tortuous terrainof hyperspace rather than continuously descendthrough one part of it. An absolute global minimumcannot be assured, but the chances of attaining it aremuch greater.

It is somewhat unclear how application of the SAMcan assist in many complex optimization problems. Inthe case of the optimization of optical parameters themethod essentially affords more opportunity for themerit function to increase within some region of hyper-space so that a lower value can be located beyond a hill.The question of whether there is some underlyingphysical (mathematical?) phenomenon that leads todeterministic or statistical preferences as a result ofmaking sufficiently small changes to the parameters isleft open, but it is an interesting problem.

(4) Constraints and glasses should be chosen so thatthe rays that traverse the system do not change direc-tion abruptly through lens elements. If a sufficientnumber of elements is involved, it is advantageous toencourage smooth bulges and constrictions in the com-plete bundle of rays through the system. This allowsthe overall system to have some power, whereas thesum of individual surface powers can approach zeroand a flat focal surface is more easily achieved. It alsofollows from the fact that aberrations on surfaces arebetter corrected on surfaces close by.

III. Optical Design for the MOS and SISAs in most optical design efforts, systems are rarelydesigned from scratch but instead start from somereasonably close configuration. An attempt was madeto use an earlier design of an /12.5 focal reducer5 as the

2292 APPLIED OPTICS / Vol.31, No. 13 / 1 May 1992

50

40

30

20

10

200

100

0

200

100

0 1 0 20 30 40 50

1 I I I I II I I i I I I I I I I 1

1 0 20 30 40 50 0 1 0 20 30 40 50

Fig. 1. Left diagrams show perspective and grey scale relative intensities in the detector plane of the MOS camera. Right diagrams show av-

erage relative intensities in the X and Y coordinates of the plane within a 50 X 50 grid (10 X 10 arcmin). Ordinate units are arbitrary relativeintensities.

starting point for the first series of trials. However, itsoon became obvious that the constraints demandedby the new specifications were severe enough that sig-nificant modifications would have to be made, and itwas decided to begin the designs from first principles.

IV. CollimatorsThe new design was started with a simple first-orderapproximation placing a field lens of sufficient clearaperture at the telescope focus (minimum aberrationsare introduced there) and a collimating lens farther on.Later on in the design some distance between thetelescope focus and the field lens was introduced notonly to allow compensating aberrations to balancethose of the collimating lens but also to comply withfabrication constraints imposed by the overall systemas it attaches to the CFHT bonnet.

It is possible to correct telescope coma by compensa-tion with the focal reducer collimator elements. How-ever, this is not desirable here because the specifica-tions require that the slit(s) at the telescope focus besharply imaged at the focal reducer focus.

The idea of the focal reducer collimator is to providean accessible pupil where a filter wheel and grism maybe placed. There are several constraints at the pupilthat must be maintained throughout the design of thecollimator. Not only should the light from any field

point be parallel there but also the beam from any fieldpoint should be the same size and cover the same area.In this way the grating affects all the light from eachfield point in the same way, assuming that the parallelbeams are dispersed in the same way although they areincident at different angles. These constraints can bemaintained within the computer optimization by fix-ing the necessary marginal and chief rays and bringingthem to a spherical focus with an appropriate sphericalmirror having a radius of curvature large enough sothat spherical aberration over the beam is not a prob-lem. In addition, other rays specifying a whole rangeof aberrations and colors can be fixed to provide anoverall optimization. Spot diagrams on the sphericalimage surface from all field points at all colors thenrepresent the quality of the pupil.

V. CamerasOnce the collimater (field and collimator lenses) isdesigned, the aperture stop of the system is fixed, andthe camera that is placed after this position providesthe image at the detector. If the grism is in place, wehave a spectrograph where the camera produces animage of the slits at the telescope focus together withthe dispersed light they contain. The design of thecamera is inherently much more difficult than thecollimator, the reasons being the geometric system

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80

50

40

30

20

10

60

40

20

0

80

60

40

20

0

0 1 0 20 30 40 50

1 0 20 30 40 50 0 1 0 20 30 40 50Fig. 2. Left diagrams show perspective and grey scale relative intensities in the detector plane of the SIS camera. Right diagrams showaverage relative intensities in the X and Ycoordinates of the plane within a 50 X 50 grid (3 X 3 arcmin). Ordinate units are arbitrary relativeintensities.

constraints in addition to rather severe optical expec-tations. Normal camera lenses make use of somewhatsymmetrical systems about the aperture stop, since itis much easier to balance aberrations in that configura-tion. In the case here, the stop lies in front of thecamera so that a grism may be placed there in theparallel light. Not only is the camera expected tooperate over a wide optical bandpass, but the imagesurface must be flat to a high degree and contain littledistortion over the field. Compounding the difficultyfor the MOS is the requirement for a resultant f/2.8beam, which is close to being telecentric. For theinitial configuration, three elements were chosen.The first (closest to the incoming parallel beam fromthe collimator) is the collecting element, the second, afield lens to assist with the field of view, and the third,an image flattener. The first attempts made use of amonochromatic approximation with all elementsweakly biconvex assuming borosilicate crown glass.Once a stable configuration was achieved, this becamethe starting point for later trials that involved rayscovering the complete wavelength range. All itera-tions after the first were made with a complete set ofimage errors that define all aberrations at all fieldangles, apertures, and colors. For each image errorand variable (radius, axial separation, etc.), there are

either equality or inequality constraints, and these aredefined by the system optical and geometric specifica-tions.

From this point on the design progressed by alteringglasses and adding to the number of components with-in the different elements as the minimization proce-dure and evaluations suggested. The designs of theMOS camera with the best spot sizes had either rela-tively thick glasses or at least two slightly ellipsoidalsurfaces. Requirements of telecentration and backfocal distance made it necessary to separate the secondelement into two for an added airspace and resultingcurvature variables. On the other hand, the collima-tor optics were much simpler and no aspherics werenecessary. Both the collimator and camera optics forthe 10 SIS were somewhat easier to design, the SIScamera resulting in two fewer air-glass surfaces.

Before the redesign of the final field lens of theEuropean Space Organization's Faint Object Spectro-graph and Camera there was a problem with the skyconcentration that manifested itself as a diffuse spoton the detector. Assuming that the detector surface isitself reflective, ray traces of the original design showthat a significant concentration of background lightdoes occur as a result of this reflected light beingreflected again at the final surface of the last optical

2294 APPLIED OPTICS / Vol.31, No. 13 / 1 May 1992

100

50

0

-50

-100

15000 15100 15200 15300 15400 15500 15600Fig. 3. MOS collimator. The first surface at the left is the telescope focus at 15030.0 mm from the telescope exit pupil, and the last element isa 5-mm filter plate.

50

0

-50

15600 15650 15700 15750 15800 15850 15900 15950Fig. 4. MOS camera. At the left is a 40-mm block of UBK7 glass, which replaces the thickest grism permitted. Before the detector plane atthe right is a 3-mm Dewar window. As in Fig. 3 the optical axis origin is at the telescope exit pupil.

50r

0r

-50

-100 _ I I I I I I I I I I I I I I I I I I I I I _15000 15100 15200 15300 15400 15500 15600

Fig. 5. SIS collimator. The first surface at the left is the telescope focus at 15030.0 mm from the telescope exit pupil, and the last element is a5-mm filter plate.

1 May 1992 / Vol.31, No. 13 / APPLIED OPTICS 2295

5 0 _n ch N u) Ne u) (n V)U

:=W~~~~~~ _ _ 0 00

-50

_ I I I I I l II I II15600 15700 15800 15900 16000 16100

Fig. 6. SIS camera. At the left is a 40-mm block of UBK7 glass, which replaces the thickest grism permitted. Before the detector plane atthe right is a 3-mm Dewar window. As in Fig. 5 the optical axis origin is at the telescope exit pupil.

MOS COLLIMATOR AND CAMERA

MERIDIONAL SAGITTALAXIS

1.00 FIELD

l - l Aj<2j---. -- I/

.70 FIELD

_ -- - FIEL

.50 FIELD

_ - - _NTzh~iiL. - -

DELZ DELY

RAY ABERRATIONS, VERTICAL AXES = .049 MM .3650 - -- .4861 - - 1.0140Fig. 7. Aberration plots for the MOS focal reducer as they are plotted from the Genii PC program. A conventional notation is used.

element in the camera. The spot is made up of out-of-focus images (ghosts) of object points. Diagrams com-paring the background illumination from-three focalreducers have been published.5 In all cases, the reflec-tion occurs at the last surface of the last optical ele-ment of the camera. In the MOS design the ghosts arenot as large and are more evenly distributed. Theproblem of central background concentration is, there-fore, reduced. Other reflective surfaces in the MOScamera appear not to contribute significantly to back-ground concentration.

Figures 1 and 2 show the results of up to 25,000 rays

emanating from a uniform projected sky at full fieldand incident randomly from the exit pupil of the tele-scope for the MOS and the SIS, respectively. Thelight is reflected at the detector forward to the lastcamera surface where it is again reflected back to thedetector surface. Each of the different diagrams inthe figures shows alternate representations of relativeintensity in the detector plane. On the left are aperspective view and a grey scale plot. The diagramson the right in each figure show a smoothed tangentialand sagittal sum of relative intensity columns. Theunits are such that the field of view lies within a grid of

2296 APPLIED OPTICS / Vol.31, No. 13 / 1 May 1992

.025

- .025

T _ S

LATERALCOLOR

.010

1.67PC DIST

.500FLDCV

I;: . /

SIS COLLIMATOR AND CAMERA

MERIDIONAL SAGITTAL AXIS

1.00 FIELD

l = . l

.71 FIELD

-~~~~~~~~~~ - -_---1 _1

- I I

.50 FIELD

I _jI I

DELZ DELY .022

- .022

LATERAL

COLORH T _S .013

\ \I

.500FLDCV

LI -1.40

PC DIST

RAY ABERRATIONS, VERTICAL AXES = .044 MM .4861 - -- .3650 - - 1.0140Fig. 8. Aberration plots for the SIS focal reducer as they are plotted from the Genii PC program. A conventional notation is used.

50 X 50 pixels, and the relative intensity ordinates arearbitrary. The plots show that the concentration ofcentral light arising from reflection at the last camerasurface amounts to about double the average light forMOS and is insignificant for the SIS. Perfect reflec-tion is assumed at the pertinent surfaces.

VI. Summary

The design progression of the MOS and SIS focalreducers using the DAO optical design program in-volved three stages, and these are listed below. Ateach step the image errors that represent definitions ofvarious aberrations were formulated with rays withinthe bandpass over a range of object and apertureheights. These image errors were then minimizedwith various constraints such as telecentration, paral-lelism at the pupil, f/number, thicknesses, and distor-tion.

(1) The collimator together with the 40-mm grismand 5-mm filter (assuming UBK7 glass) was optimizedto produce a pupil at the grism position. All colors ofrays at the edge, middle, and center of the field for aparticular aperture height were constrained to be coin-cident at the pupil. In addition, rays from each objectpoint were constrained to be effectively parallelthrough the grism so that the same region of the grismdisperses the light from any point of the field.

(2) The camera optics were optimized while main-taining the collimator optics constant except for posi-tion.

(3) Gratings (first-order 1666.667, 6666.667-nmspacing, e.g.) were applied to the grism glass, and thegrism angle and focus were adjusted while the collima-tor and camera optics were held constant.

Since the incident rays for the design emanate fromthe exit pupil of the CFHT, they are coma free. Theimaging and spectrographic modes, therefore, formconsistent images of the Cassegrain focus at the focusof the focal reducer.

The final optical design of both spectrographs as-sumes an optical bandpass of 365-1014 nm, a 30-mmdiam focal plane, and a 46-mm pupil between thecollimator and camera. Field sizes are 10 arcmin forthe MOS at f/2.8 and 3 arcmin for the SIS at f/10.Located after the collimator is a filter, and there isprovision for a grism at the pupil. For the MOS theback focal distance is 34 mm (vertex of final cameraelement surface to detector), and the exit pupil is 175mm from the focus. The same distances for the SISare 60 and 768 mm, respectively. Tolerances are notunduly severe for any of the surfaces, the least being aten-fringe power variation for four surfaces of theMOS camera. Deviations of this much result in a<20% increase in spot size.

Glass types PSK3 and FK54 are used for all the

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I _ ,

-

Table 1. Multlobject Spectrograph (f/8 Collimator and f/2.8 Camera Prescription)

Clear aperture radius

Cass focusCV 0.000(AS 158.75AIRFirst surface collimatorRAD 501.51AS 11.82PSK3Second surface collimatorRAD 131.64AS 25.00

41.89

52.40

52.47

FK54Third surface collimatorRAD -228.66AS 252.09AIRFourth surface collimatorRAD 1960.93

52.84

40.76

AS 15.02PSK3Fifth surface collimatorRAD 159.61AS 25.00FK54Sixth surface collimatorRAD -124.00AS 15.00PSK3Seventh surface collimatorRAD -183.54AS 55.26AIRFilter first surfaceCV 0.00000AS 5.0UBK7Filter second surfaceCV 0.

0

00000

40.09

39.83

40.01

32.92

32.55

25.97

23.00

30.45

27.12

26.64

AS 60.00AIRGrism block first surfaceCV 0.00000AS 40.0000UBK7Grism block second surfaceCV 0.00000AS 50.0000AIRFirst surface cameraRAD 50.000CC -0.156463AS 15.987PSK3Second surface cameraRAD 37.09AS 20.052FK54Third surface cameraRAD -84.56AS 15.000PSK3Fourth surface camera

RAD 44.92AS 35.923AIRFifth surface cameraRAD 105.26AS 15.000FK54Sixth surface camera

Doublet RAD -123.86AS 15.000PSK3Seventh surface cameraRAD -310.74AS 0.2AIREighth surface cameraRAD 237.72AS 15.000FK54Ninth surface cameraRAD -87.39AS 1.000

Triplet AIRTenth surface cameraRAD 45.07CC -0.1400AS 8.000PSK3Eleventh surface cameraRAD 31.18AS 23.370FK54Twelfth surface cameraRAD -89.72AS 15.000PSK3Thirteenth surface cameraRAD 29.68AS 24.000AIRFirst surface Dewar windowCV 0.00000AS 3.00000FSSecond surface Dewar windowCV 0.00000AS 7.00000AIRImage

Clear aperture radius

33.41

33.73

35.20

35.52

35.51

31.02

26.42

24.46

17.21

15.47

15.28

14.62

Triplet

24.39 )

optical elements excluding the grism (UBK7) and theDewar window (FS). Excluding the 40-mm UBK7grism block the total internal transmittances at 365,400, 500, and 700 nm are, respectively, 72, 87, 96, and98%.

Tables I and II summarize the designs for the MOS

and the SIS, respectively. The input to these designsis an aberration-free f/8 beam. Figures 3-6 show theoptical layout for the f/2.8 and f/to reducers. Incidentrays are at zero and full object heights and full aper-ture. The units are in millimeters, and the abscissasrepresent actual distances from the exit pupil of the

2298 APPLIED OPTICS / Vol. 31, No. 13 / 1 May 1992

Doublet

Singlet

Triplet

Detector

100

Table I. Subsecond of Arc Imaging Spectrograph (f/8 Collimator and /10 Camera Prescription)

Cass focusCV 0.00000AS 159.57AIRFirst surface collimatorRAD 1955.8AS 17.82PSK3Second surface collimatorRAD 121.54AS 8.14FK54Third surface collimatorRAD -153.97AS 271.63AIRFourth surface collimatorRAD -1930.60AS 5.7PSK3Fifth surface collimatorRAD 225.8AS 15.00FK54Sixth surface collimatorRAD -107.95AS 15.00PSK3Seventh surface collimatorRAD -160.02AS 57.52AIRFirst surface filterCV 0.00000AS 5.00000UBK7Second surface filterCV 0.00000AS 57.48AIRFirst surface grism blockCV 0.00000AS 40.0000UBK7Second surface grism blockCV 0.00000AS 82.31AIR

Clear aperture radius

12.6

22.7

23.5

23.7

27.1

27.2

27.4

28.1

26.0

25.9

23.9

23.0

First surface cameraRAD 107.95AS 15.00PSK3Second surface cameraRAD 72.39AS 15.00FK54

Doublet Third surface cameraRAD -168.66AS 15.00PSK3Fourth surface cameraRAD -1358.1AS 100.60AIRFifth surface cameraRAD 65.99AS 15.00FK54Sixth surface cameraRAD -132.72

Triplet AS 15.00PSK3Seventh surface cameraRAD 59.43AS 90.72AIREighth surface cameraRAD -45.34AS 20.00PSK3Ninth surface cameraRAD -37.084AS 15.00FK54Tenth surface cameraRAD 107.95AS 15.00PSK3Eleventh surface cameraRAD -88.29AS 50.56AIRFirst surface Dewar windowAS 3.0FSSecond surface Dewar windowCV 0.00000AS 7.00000Image

Clear aperture radiusI 1

26.1

25.0

24.6

24.1

18.5

17.1

15.2

13.6

15.5

16.9

17.6

16.0

15.9

15.7

telescope. Note that the maximum field is 3 arcminfor the /10 reducer and 10 arcmin for the f/2.8 reducer.Since the original specifications called for a maximumthickness of 40 mm for the grism this thickness ofUBK7 glass at the pupil was introduced for designpurposes. Thinner grisms will result in a displace-ment of the pupil, but the resultant additional aberra-tion is insignificant. The 3-mm FS glass plate is theDewar window. Figures 7 and 8 are aberration plotsfor the spectrographs with the 40-mm UBK7 blocks inplace instead of grisms. The vertical aberration forthe MOS and SIS reducers is 0.049 mm or 1.0 arcsec

and 0.044 mm or 0.25 arcsec, respectively. Encircledenergy levels of 80% are well within these limits even atfull field and from 365 to 1014 nm.

Figures 7 and 8 showing aberration plots were con-structed with the Genii PC and Optics Analyst pro-grams from Genesee Optics Software, Inc. The authorgratefully acknowledges the helpful insights, encour-agement, and enthusiasm from E. Harvey Richardson.

References1. D. J. Schroeder, Astronomical Optics (Academic, San Diego,

Calif, 1987), pp. 173-178.

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Triplet

Doublet

Triplet

Detector

2. B. Nelles and E. H. Geyer, "Distortion of grating prisms and theiruse in radial velocity determinations of astronomical objects withslitless field spectrographs," Appl. Opt. 20, 660-664 (1981).

3. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization bysimulated annealing," Science 220, 671-680 (1983).

4. Various papers presented at the 1990 Lens Design Conference, inLens Design, Vol. 10 of OSA 1990 Technical Digest Series (Opti-cal Society of America, Washington, D.C., 1990).

5. W. A. Grundmann, C. L. Morbey, and E. H. Richardson, "The fi2.5 focal reducer lens and multiobject spectrograph for the Casse-grain focus of the CFHT," presented at the European SpaceOrganization Conference on Very Large Telescopes and TheirInstrumentation, 1988.

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