Cassegrainian Baffle Design

Rochelle Prescott

A straightforward graphical procedure for the design of light baffles for cassegrainian optical systems has

been developed. It is completely general and generates all of the paraxial parameters from a minimum

of input data.

I ntrod uctionThe problem of the optimum design of baffles for a

cassegrainian telescope is quite complex. Apparently themodern type of baffle which is necessary for wide aper-ture, wide field, short cassegrainian systems was not de-veloped until quite recently.' Sauer has evolved asolution to the problem of their design by a graphicalmethod using successive approximations, and this solu-tion has been reduced to a computer program byYoung.3 This solution has two shortcomings: it doesnot provide for baffling by the entrance window and itdoes not allow for the entrance pupil in any arbitraryposition. A new, general solution to this problem hasbeen devised. It, too, is graphical, and it also uses suc-cessive approximations but is extremely flexible as to in-put data and is rapid enough to allow examination of acomplete family of systems in a short time. It alsoprovides a graphical paraxial ray trace of the systems,which is of value in the early stages of design. Thissolution is amenable to computer programming and hasbeen reduced to a Telcomp* program.4

Light Baffling of a Cassegrainian SystemCriteria for the baffling of a cassegrainian telescope can

be determined on an objective basis by considering thepurpose and requirements of the design. If it is to beused as the objective of a radiometer, these criteriamight be: (1) minimum obscuration; (2) no straylight, i.e., no light passing directly from the object spaceto the image plane; and (3) no vignetting, i.e., theeffective aperture area constant over the entire field.

It appears that before World War II the baffling wasaccomplished by the secondary obscuration and a longenough extension of the telescope tube. Bouwers, andprobably others about this time, designed tubular

The author is with Aveo Everett Research Laboratory,Everett, Massachusetts 02149.

Received 20 October 1967.* A private line computation service.

baffles (extending from the edge of the secondary towardsthe primary and from the perforation of the primarytowards the secondary) which were more efficient or, atleast, did not require any extension of the telescopetube. It is the purpose of this paper to show how thesebaffles can be designed readily by graphical construc-tion.

ProcedureIn a cassegrainian system, six parameters are re-

quired to specify completely the first order design of thesystem. Four of these are associated with dimensionsalong the optical axis and two with dimensions perpen-dicular to it. The most basic of the first type are (1)focal length of the primary fa; (2) focal length of thesecondary fb; (3) separation of primary and secondaryd; (4) position of the stop; and the second type: (5)aperture diameter D; and (6) image field diameter.

For design purposes, other (derived) parameters areoften substituted for the first three. It is convenientfor most purposes of design to specify the focal length ofthe system f and the back working distance BWD, andthen to examine the properties of a family of systems ofa given aperture and field diameter as a function of avariable parameter. A convenient variable parameterin such a case is the ratio Q of the height of the intercepton the secondary of a ray from an axial point at infinityto the height of its intercept on the primary.

In Fig. 1, the focal length is scaled off on the opticalaxis and, as the back working distance is given, it is alsoscaled off, locating the primary. The half aperturediameter is scaled off at P', and the primary positionand ray 1' drawn parallel to the axis at this height.* Itshould be noted that, as this is a paraxial ray trace, thevertical and horizontal scales need not be the same. Asa matter of fact, it has proved most convenient andaccurate to have the vertical scale some four times the

* Primed numbers are used to label lines which are drawnparallel to lines of the same number unprimed.

March 1968 / Vol. 7, No. 3 / APPLIED OPTICS 479

Iw

fo

f ,I

Fig. 1. This figure identifies the various first-order parameters defined in the text. All primed umbers refer to lines which are parallelto the line with the same number unprimed. The line through a, a represents the limiting ray due to the baffles drawn in heavily along

rays 5 and 6. The shading represents the limits of the baffle cross section.

horizontal scale in the cases run. Of course, if the scalesare different, the field diameter is scaled by the samefactor as the aperture. A line is drawn from the ray 1'at P' to the focal point F'. This ray represents theaxial ray in image space. The path of the ray 2 (1' re-flected from the primary) can then be determined byconnecting it with Fa', if fa is given, or by having it crossthe line from P' to F' at the height Q, if Q is given. Theintercept of this ray with the ray from P' to F' deter-mines the position of the secondary. The field diameteris next scaled in and the edges of the field connectedwith the axis at the rear principal plane P' by lines 3 and4. The lines 3' and 4' drawn from the vertex of the pri-mary at corresponding angles with the axis intercept thefocal plane of the primary at the image points for ob-jects at the edge of the field. The ray from the edge ofthe field which just touches the stop is 3", and its inter-cept with the primary determines the minimum size ofthat element. The ray 5, connecting it with the cor-responding image point in the plane Fa', determines theminimum size of the secondary to eliminate vignettingby the secondary. The ratio of the height of this pointto the height of the semiaperture is defined as Q*. Theray 6 is the corresponding ray from the secondary to theedge of the field, and the lower edge of the baffles on thesecondary and primary must not go below the rays 5 and6, respectively.

The upper surface of the two baffles is determined bysuccessive approximations. A ray 4" parallel to 4 isdrawn through a point a on ray 5 to the primary, andthe ray 7 connects this ray with the image at Fa'.These rays determine the end of the baffles as indicatedby the heavy lines. A line drawn through the intersec-tions of 5 and 4" and 6 and 7, respectively, shows thepath of the ray a most nearly parallel to the axis whichwill get past such a baffle. (In the case shown, it wouldfall directly on the image surface which would be verydeleterious if this were a sensor surface.) In actualcase, only the intercepts a with the rays 5 and 6 need beshown until, by successive approximations, the corre-sponding ray, a, b, c, . . ., falls on or just above the en-trance window which, in this case, is also the stop for thesystem, or misses the sensor entirely. In some cases theprimary may be the stop, and one can use the point Iwto indicate the position of the end of a tube of conveni-ent length beyond the secondary, the entrance window.Often, regardless of the position, a relatively short ex-tension of the tube beyond its minimum length (along aray touching 1w to prevent vignetting) will appreciablyreduce the necessary obscuration ratio. In any case,the final choice determines the semidiameter of the ob-scuration; the ratio of this to the semidiameter of thestop is the quantity Q**.

It is probably worthwhile to point out that if a raygets through the entrance window and past the baffle it

480 APPLIED OPTICS / Vol. 7, No. 3 / March 1968

- I

does not necessarily harm the performance of the instru-ment. In some instruments, particularly visual andeven more so in those with erecting systems as well aseyepieces, the judicious placement of stops in this por-tion of the system will provide adequate control of thisstray light.' There are many variables in this problem,and each solution must be carefully and thoughtfullyexamined if it is to be correctly evaluated.

ConclusionsA rapid, general solution to the problem of the design

of baffles for a cassegrainian system has been devised.This solution requires only a minimum of input data andis of value in many other respects in the early stages ofdesign. While graphical solutions do not have a highdegree of accuracy, it is expected that, in general,

the actual ray paths will deviate considerably from thepredictions of paraxial theory, particularly in systemswith fast primaries. If the accuracy is not consideredsufficient in any particular case, the same approach canbe used after the design has been completed and a deter-mination of any desired degree of precision made.

The work reported in this paper was supported byBell Telephone Laboratories and Army Missile Com-mand contracts.

References1. A. Bouwers, Achievements in Optics (Elsevier Publishing

Company, Inc., New York, 1950).2. F. Sauer, Sterne u. Weltraum 4,141 (1966).3. A. T. Young, Appl. Opt. 6,1063 (1967).4. J. R. Golin, Avco Research Laboratory, in preparation.5. R. R. Willey, Jr., Sky and Telescope 25, 232 (1963).

Infrared Spectroscopy8th Annual Summer School14-26 July 1968Cambridge, U.K.

The 8th Annual Summer School will be held from 14 to 26 July in CambridgeU.K. The course has been designed for beginners in ir spectroscopy, andlecturers and demonstrators will include A. J. Baker, University of Glasgow,P. L. Carter, Fisons Pest Control Research Station, D. B. Powell, Universityof East Anglia, N. A. Puttnam, Colgate-Palmolive, Ltd., C. J. Timmons,University of Nottingham, and D. Welti, Unilever Research Laboratories.Topics covered will include introduction to ir spectroscopy and infraredinstruments; sample handling; quantitative analysis; interpretation ofspectra; inorganic applications; associated techniques (uv, nmr, massspectrometry); attenuated total reflectance; and combination of gaschromatography and ir spectroscopy. In addition, practical work willprovide opportunity for becoming familiar with most aspects of the tech-niques of rock salt polishing; use of liquid cells for samples and solutions;preparation of Nujol mulls, preparation of alkali halide disks, and quan-titative analysis. The fee, including accommodation at Gonville and CaiusCollege and tuition, is $192. Further information is available from J. E.Steward, Unicam Instruments, Ltd., York Street, Cambridge, U.K

March 1968 / Vol. 7, No. 3 / APPLIED OPTICS 481

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