## Reflecting Telescope Optics I: Basic Design Theory and its Historical DevelopmentA corrected reprint of the ?rst edition appeared in 2000. It was a requirement that the pagination remain unaltered, but nevertheless, apart from minor and format corrections on 17 pages, a number of corrections or additions of substance could be incorporated. These included minor corrections to Figs. 1. 3 b) and 2. 8 and to the text of Fig. 5. 18. The most important change of all was probably the complete revision of the historical treatment of Cassegrain in the Portrait Gallery, due to the superb research of Baranne and Launay on his identity, published in 1997. Additions of substance were text on pages 21, 323 and 487 (Portrait Gallery – Mersenne) and corrections on pages 117 2 4 (y to y ), 174 (concerning the scale of Fig. 3. 37), 263 (Fig. 3. 96 instead of 3. 97 in the text), 341 (sign in the text equation below Eq. (4. 36)), Table 5. 2 (concerning UKIRT), Table A. 15 (?rst symbol), pages 505 (Ref. 3. 71) and 531 (Brown and Cassegrain). Several of these errors were pointed out by readers, to whom I express my gratitude. The present 2nd edition contains all the material of the ?rst edition, - changed apart from some further corrections, but with 25 pages more of - ditional explanations or new material, including 5 new ?gures (2 in Chap. 4, 2 in Chap. 5 and 1 following the Portrait Gallery). |

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Lurie's configurations (1975) do not have astigmatism. They are anastigmatic and involve only aspheric mirrors. Mr. Wilson is confusing Lurie with the Houghton design (1940s), which uses only spherical mirrors.

### Contents

1 | |

11 | |

15 | |

Basic Gaussian optical theory of telescopes | 21 |

22 The ideal optical system geometrical optics and Gaussian optics | 23 |

222 Geometrical optics and geometrical wavefronts | 26 |

223 The Gaussian optics approximation | 27 |

224 The conventional telescope with an ocular | 36 |

formulae for the effects of decentering of 2mirror telescopes | 261 |

38 Despace effects in 2mirror telescopes | 279 |

382 Transverse despace eﬀects | 287 |

39 Zernike polynomials | 288 |

310 Diffraction theory and its relation to aberrations | 293 |

3102 Coherence | 297 |

3103 The Point Spread Function PSF due to diffraction at a circular aperture | 298 |

3104 The Point Spread Function PSF due to diffraction at an annular aperture | 302 |

225 Basic forms of reﬂecting telescope | 40 |

226 The scale of astronomical telescopes and the magniﬁcation in afocal use of compound telescopes | 54 |

227 Wideﬁeld telescopes and multielement forms | 55 |

Aberration theory of telescopes 31 Deﬁnition of the third order approximation | 56 |

aberration theory of basic telescope forms | 59 |

third order aberration coefficients | 63 |

323 Seidel coefficients of some basic reﬂecting telescope systems | 65 |

324 Analytical third order theory for 1mirror and 2mirror telescopes | 69 |

325 Higher order aberrations and system evaluation | 82 |

and various forms of 2mirror telescopes Classical RitcheyChrétien DallKirkham Spherical Primary | 88 |

327 Other forms of aplanatic 2mirror telescopes Schwarzschild Couder | 111 |

328 Scaling laws from normalized systems to real apertures and focal lengths | 126 |

and conversion formulae from wavefront aberration to other forms | 128 |

332 Coma SII | 131 |

333 Astigmatism SIII and ﬁeld curvature SIV | 135 |

334 Distortion SV | 138 |

335 Examples of conversions | 139 |

34 The theory of aspheric plates | 140 |

chromatic variations of ﬁrst order and third order aberrations | 146 |

36 Wideﬁeld telescopes | 148 |

362 The Schmidt telescope | 151 |

363 The Maksutov telescope | 165 |

364 More complex variants of telescopes derived from the principles of the Schmidt Bouwers and Maksutov systems | 174 |

365 Three or multimirror telescopes centered | 223 |

37 Offaxis Schiefspiegler and decentered telescopes | 255 |

3105 The diffraction PSF in the presence of small aberrations | 304 |

3106 The diffraction PSF in the presence of small aberrations and an annular aperture | 310 |

the Optical Transfer Function OTF | 312 |

3108 Diffraction effects at obstructions in the pupil other than axial central obstruction | 322 |

Field correctors and focal reducers or extenders | 325 |

42 Aspheric plate correctors | 327 |

422 Cassegrain or Gregory focus correctors using aspheric plates | 340 |

43 Correctors using lenses | 348 |

432 Secondary focus correctors using lenses | 372 |

44 Atmospheric Dispersion Correctors ADC | 392 |

45 Focal reducers and extenders | 404 |

452 Wideﬁeld focal reducers FR as a substitute for a prime focus | 406 |

453 Other Cassegrain focal reducers | 414 |

Major telescopes from Lord Rosse to about 1980 | 419 |

52 Glass optics telescopes up to the Palomar 200inch | 431 |

53 Reﬂectors after the 200inch Palomar Telescope up to about 1980 | 449 |

Appendices | 464 |

A List of mathematical symbols | 467 |

B Portrait gallery | 487 |

References | 502 |

List of Figures | 513 |

List of Tables | 526 |

Name Index | 531 |

536 | |

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### Common terms and phrases

2-mirror telescope afocal anastigmatic angle angular aplanatic arcmin arcsec aspheric plate astigmatism axial axis basic beam Bouwers Cassegrain form Cassegrain telescope chromatic aberration classical Cassegrain coeﬃcients correction Couder decentering coma deﬁned deﬁnition diﬀerent diﬀraction dispersion eﬀect entrance pupil equations exit pupil f/no ﬁeld coma ﬁeld curvature ﬁnal image ﬁnite ﬁrst ﬂat focal length formulae function Gaussian Gaussian optics geometry given gives glass Gregory Korsch Lagrange Invariant lens lenses magniﬁcation Maksutov Maksutov telescope meniscus Mersenne mirror negative normal object obstruction optical system order spherical aberration parabolic primary paraboloid parameters paraxial plane position prime focus principal ray radius ray trace RC telescope reduced reﬂecting telescope reﬂector refracting refractor relative aperture Schiefspiegler Schmidt telescope Schmidt-Cassegrain Schwarzschild signiﬁcant SIII solution spherical aberration spherical primary spot-diagrams suﬃx surface Table telescope optics term theory third order aberrations upr1 wavefront wavefront aberration wavelength Wynne zero