Anastigmatic three-mirror telescope Dietrich Korsch A new configuration of a three-mirror telescope is introduced that combines high performance with practi- cality. A geometric spot size of less than 0.1 sec of arc in an easily accessible flat field of 1.50 and excellent stray light suppression are the outstanding features. A 1.5-m telescope of the concept to be presented here is being proposed by Marshall Space Flight Center for astronomical observations from Spacelab. The design is an all-reflective three-mirror telescope with excellent performance characteristics over a wide field and a broad spectral range, making it particularly suited for uv observations.' Several three-mirror telescopes have been proposed in the past, 2 - 9 none of which provides a real practical and useful solution. The main shortcomings are inac- cessibility of the image plane, a large central obscura- tion, practically invariable fast focal ratios, or largely asymmetric configurations. Two designs that are conceptually similar to the one presented here were introduced in a NASA report by the Itek Corporation' 0 and by Korsch.1 Both designs, however, have the disadvantage that, due to their geometric configuration, only less than half of the well-corrected field can be used. The elimination of this shortcoming and the advan- tage of a conveniently accessible focal plane are the outstanding characteristics of the new three-mirror design. While any practical two-mirror telescope configura- tion can only be corrected for maximally two aberra- tions, usually spherical aberration and coma, this three-mirror telescope is corrected for four aberrations: spherical aberration, coma, astigmatism, and field curvature. The primary-secondary configuration re- sembles the Cassegrainian, forming a real image closely behind the primary (Fig. 1). This secondary image is then reimaged by a tertiary mirror at approximately unit magnification. A small, flat mirror placed at the exit pupil, which is located between the primary mirror and the tertiary mirror, folds the light rectangularly away from the axis of the telescope where the final image is formed. The author is with Teledyne Brown Engineering, Huntsville, Ala- bama 35807. Received 20 December 1976. In an alternate configuration shown in Fig. 2, a flat perforated mirror is placed diagonally between primary and tertiary. This configuration minimizes obscuration by avoiding the spider that holds the small fold mirror and significantly improves the baffling of the system. The mathematical condition for correcting spherical aberration, coma, and astigmatism simultaneously can be written, according to Refs. 12 and 13, bibi + b 2 6 2 + b 3 h 3 = bo (vanishing spherical aberration); g 1 6 1 + g 2 6 2 + g 3 6 3 = go (vanishing coma); (1) cial + C26 2 + C36 3 = co (vanishing astigmatism). The 61 are the surface deformation constants, and bi, gi, c are functions of the individual mirror magnifica- tions with respect to the object mi and with respect to the pupil Pi. Since the system is free of astigmatism, the condition for a flat field is equivalent to the Petzval condition: (ml - Pl)m2m 3 P2P 3 + (l - p2)m3p3 + ( 3 - 3) = 0. (2) The primary magnification of a telescope is ml = 0, and p = -1 if the entrance pupil is at the first surface. The tertiary pupil magnification is made a dependent vari- able by solving Eq. (2) for p 3 , (3) -m2m 3 p2 - (M 2 - 2)m3 The third-order corrected system was subsequently further optimized by slightly varying the system pa- rameters to minimize higher order aberrations. A list of the final telescope parameters is given in Table I. This telescope provides a flat image field of 1.50 in diameter with a geometric rms spot size not larger than 0.07 sec of arc anywhere in the field. Only a central portion of 0.40 in diameter is partially vignetted, leaving an unvignetted area of 1.64 degree 2 (Fig. 3). The performance of the three-mirror telescope is demonstrated in Fig. 4, where it is compared with the performance of a Ritchey-Chretien telescope. The geometric spot size, i.e., the diameter of the smallest circle surrounding all rays traced through the system, is plotted as a function of the field angle. The superior 2074 APPLIED OPTICS / Vol. 16, No. 8 / August 1977 : - P =
Transcript
Anastigmatic three-mirror telescope
Dietrich Korsch
A new configuration of a three-mirror telescope is introduced that combines high performance with practi-cality. A geometric spot size of less than 0.1 sec of arc in an easily accessible flat field of 1.50 and excellentstray light suppression are the outstanding features.
A 1.5-m telescope of the concept to be presentedhere is being proposed by Marshall Space Flight Centerfor astronomical observations from Spacelab. Thedesign is an all-reflective three-mirror telescope withexcellent performance characteristics over a wide fieldand a broad spectral range, making it particularly suitedfor uv observations.'
Several three-mirror telescopes have been proposedin the past,2-9 none of which provides a real practicaland useful solution. The main shortcomings are inac-cessibility of the image plane, a large central obscura-tion, practically invariable fast focal ratios, or largelyasymmetric configurations. Two designs that areconceptually similar to the one presented here wereintroduced in a NASA report by the Itek Corporation' 0
and by Korsch.1 Both designs, however, have thedisadvantage that, due to their geometric configuration,only less than half of the well-corrected field can beused.
The elimination of this shortcoming and the advan-tage of a conveniently accessible focal plane are theoutstanding characteristics of the new three-mirrordesign.
While any practical two-mirror telescope configura-tion can only be corrected for maximally two aberra-tions, usually spherical aberration and coma, thisthree-mirror telescope is corrected for four aberrations:spherical aberration, coma, astigmatism, and fieldcurvature. The primary-secondary configuration re-sembles the Cassegrainian, forming a real image closelybehind the primary (Fig. 1). This secondary image isthen reimaged by a tertiary mirror at approximatelyunit magnification. A small, flat mirror placed at theexit pupil, which is located between the primary mirrorand the tertiary mirror, folds the light rectangularlyaway from the axis of the telescope where the finalimage is formed.
The author is with Teledyne Brown Engineering, Huntsville, Ala-bama 35807.
Received 20 December 1976.
In an alternate configuration shown in Fig. 2, a flatperforated mirror is placed diagonally between primaryand tertiary. This configuration minimizes obscurationby avoiding the spider that holds the small fold mirrorand significantly improves the baffling of the system.
The mathematical condition for correcting sphericalaberration, coma, and astigmatism simultaneously canbe written, according to Refs. 12 and 13,
bibi + b262 + b3h3 = bo (vanishing spherical aberration);
The 61 are the surface deformation constants, and bi,gi, c are functions of the individual mirror magnifica-tions with respect to the object mi and with respect tothe pupil Pi.
Since the system is free of astigmatism, the conditionfor a flat field is equivalent to the Petzval condition:
The primary magnification of a telescope is ml = 0, andp = -1 if the entrance pupil is at the first surface. Thetertiary pupil magnification is made a dependent vari-able by solving Eq. (2) for p3 ,
(3)-m2m 3 p2 - (M2 - 2)m3
The third-order corrected system was subsequentlyfurther optimized by slightly varying the system pa-rameters to minimize higher order aberrations. A listof the final telescope parameters is given in Table I.
This telescope provides a flat image field of 1.50 indiameter with a geometric rms spot size not larger than0.07 sec of arc anywhere in the field. Only a centralportion of 0.40 in diameter is partially vignetted, leavingan unvignetted area of 1.64 degree 2 (Fig. 3).
The performance of the three-mirror telescope isdemonstrated in Fig. 4, where it is compared with theperformance of a Ritchey-Chretien telescope. Thegeometric spot size, i.e., the diameter of the smallestcircle surrounding all rays traced through the system,is plotted as a function of the field angle. The superior
150 cm2.2121800 cm35 cm80 cm5.2 cm48.3 cm (1.50)47.1 cm (1.50)660.0000 cm126.9495 cm154.2855 cm-0.9702785 (ELLIPSOID)-1.7448287 (HYPERBOLOID)-0.5596906 (ELLIPSOID)-5.60.9740
277.8600 cm448.3266 cm92.0000 cm62.2817 cm
UNVIG NETTEDAREA
90arc min DIAMETER33 arc min
Fig. 3. Image area in telescope focal plane.
I-0cu
I- UJ
OwA.
<7 N
co
nIAMETER
1.0 -
0.5 -
0.0
RITCHEY CHRETIENCURVED FIELD
THREE-MIRROR TELESCOPEFLAT FIELD
30 40 51)
HALF FIELD ANGLE (arc min)
Fig. 4. Performance comparison.
performance of the three-mirror telescope is not onlyreflected in the significantly smaller spot size but alsoin the fact that the field is flat while the Richey-Chre-tien has a curved field.
The analysis of the misalignment sensitivities dispelsany apprehension concerning the possibility of a drasticincrease in complexity due to the addition of the thirdmirror. Table II gives the effects of secondary andtertiary misalignments on the performance in terms ofrms wavefront errors (optical path difference) and interms of induced aberrations (increase of spot size). Itshows that the tertiary is 15-200 times less sensitivethan the secondary.
To protect the secondary image in a Cassegrainiantelescope effectively from stray light requires a complexand elaborate baffling system. One major advantageof this three-mirror telescope is the natural bafflingproperty of its configuration. The final image plane isalready well protected from stray light without addingan extra baffling system. Because of the exit pupil infront of the final image, rays going through the secon-dary image in the hole of the primary mirror can onlyreach the final image if their extensions go through thevirtual pupil image behind the secondary.
In configuration I, Fig. 5, the only stray light that canreach the final image is that scattered off the structureholding the small fold mirror which, however, is locatedfar back in the system. An even more efficient bafflingeffect is achieved with configuration II, shown in Fig.6. No stray light can reach the image after only a singlescattering process. Even the light that is scattered offthe edges around the perforation of the fold mirror andthen reflected by the tertiary through the exit pupil willbe intercepted by the central vignetted portion ratherthan by the useful field. A further advantage is theaccessibility of the secondary spider image formed bythe tertiary. It is located immediately behind the exitpupil and can, at least in configuration II, easily bemasked off. An isometric view of the second configu-ration is shown in Fig. 7.
In conclusion, it is believed that the design as de-scribed here provides a feasible and very practical so-lution of a highly corrected all-reflective telescope. Theshape of the large image area makes it particularlysuitable for space applications where several instru-ments usually have to share the focal plane.
This work was done under NASA contract NAS8-21812 while the author was with Sperry Rand inHuntsville, Alabama.
IMAGE PLANE.
PRIMARY
FOLD MIRROR
ENTRANCE PUPILTERTIARY
STOP
Fig. 6. Stray light path in configuration II. Fig. 7. Isometric view of configuration II.
1. George C. Marshall Space Flight Center, "STARSAT-A SpaceAstronomy Facility," NASA TMX-73326 (1976).
2. M. Paul, Rev. Opt. 14, 13 (1935).3. J. G. Baker, IEEE Trans. Aerosp. Electron. Syst. AES-5, 261
(1969).4. J. Lagrula, Cah. Phys. 8,43 (1969).5. D. Korsch, Appl. Opt. 11, 2986 (1972).6. R. V. Shack and A. B. Meinel, J. Opt. Soc. Am. 56, 545 (1966).
7. N. J. Rumsey, in Proceedings, Optical Instrumentation andTechniques (Oriel, New York, 1969), p. 514.
8. R. A. Buchroeder and A. S. Leonard, Appl. Opt. 11, 1649(1972).
9. R. A. Buchroeder, Technical Report 68, Optical Science Center,U. Arizona (1971).
10. Itek Corporation, "Requirements and Concept Design for LargeEarth Survey Telescope for SEOS," Final Report, NASA CR-144796 (1975).
11. D. Korsch, Opt. Eng. 14, 533 (1973).12. D. Korsch, J. Opt. Soc. Am. 63, 667 (1973).13. D. Korsch, Appl. Opt. 13, 1967 (1974).
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