Harold Hopkins


a great physicist, teacher and friend, who revealed to me the beauty and power of aberration theory

Karl Schwarzschild ca. 1908 (courtesy Martin Schwarzschild)

Preface to the 2nd edition

A corrected reprint of the first 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 (y2 to y4), 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 (first 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 first edition, unchanged apart from some further corrections, but with 25 pages more of additional explanations or new material, including 5 new figures (2 in Chap. 4, 2 in Chap. 5 and 1 following the Portrait Gallery). Significant text additions are on pages 1-2, 22, 43-46, 63, 85-86, 86-87, 117, 120-122, 126, 129-130, 131-132, 214, 222-223, 232-233, 262, 269, 278-279, 281, 324, 328, 370-372, 402-404, 426-429, 433-435, 500-501. The most important of these are the following: pages 43-46 with the correction to Eq. (2.53) and the extensive justification of the definition of m2 in Eq. (2.55) - due to a most fruitful correspondence with Dr. Dan Schroeder, for which I express here my grateful thanks; pages 120-122 where the mathematical argument has been completely reformulated; pages 232-233 and 278-279 where the remarkable new analytical procedure of Rakich and Rumsey for setting up 3- or 4-mirror telescope solutions is briefly discussed; pages 370-372 with the new prime-focus corrector due to Bernard Delabre of ESO including a new "Spot-Diagram" in the same standard format used in the first edition; pages 402-404 with a description of the new Linear ADC-corrector used in the ESO VLT; pages 426-429 with the historical print of the casting of the blank of the Melbourne reflector - kindly supplied by Peter Hingley, librarian of the RAS, to whom my grateful thanks; pages 435-436 with a historic photo of Ritchey at his

60 cm telescope and pages 500-501 with the historic group photo of the ISU Meeting at Mt. Wilson in 1910. The latter two photos, previously unknown in the astronomical community, were kindly supplied by Dr. Don Osterbrock, to whom I express my grateful thanks. I consider the above three historic print/photos to be a major enrichment of the book.

A change hopefully made correctly throughout the book is the spelling of the name "Abbe" without an acute accent on the "e". This error was pointed out by a reviewer in an Irish journal and has been confirmed by a former colleague of mine at Carl Zeiss. Abbe himself pronounced his name in later life (as virtually everyone does today, also in Germany) as though there were an accent, but he apparently never wrote it that way!

Apart from the valuable help from outside sources, acknowledged above or in the text, I also owe a great debt of gratitude to a number of ESO colleagues: Uta Grothkopf and Angelika Treumann of the ESO library, for their admirable service in literature procurement, particularly concerning historical aspects of Petzval's work; Bernard Delabre for information on his P.F. corrector; Gero Rupprecht for information on the ESO Linear ADC system; Philippe Dierickx for help with the setting-up of the new Spot Diagram (Fig. 4.18); Ed Janssen for completing this Spot Diagram, for the new figure of the LADC (Fig. 4.36) and corrections to two existing figures (see above); Stephane Guisard for pointing out two errors; and, above all, Lothar Noethe for many discussions and suggestions arising from his detailed knowledge of the book - I sometimes think he knows parts of it better than I know them myself! My deep thanks are again due to my wife Anne, who always serves as my "Delphic Oracle" on the English language; to Springer-Verlag for the admirable cooperation in all respects, also to Uwe Matrisch of the firm LE-TeX in Leipzig for excellent work in setting up the final form of this edition; and to the management of ESO for their invaluable general support.

I hope, of course, that this second edition will be often reprinted. Minor corrections, hopefully few, can then be made. But I am virtually certain that I shall not produce a third edition. Unlike the matter of RTO II, the theory of RTO I is, I believe, largely complete. Innovations may be made with minor modifications of known solutions for centered systems or with new "Schiefspiegler" with several mirrors. But radically new optical design solutions seem unlikely. Revolutionary progress is more likely in the domain of RTO II or in aspects not treated there, such as interferometry.

July 2003

Ray N. Wilson


The development of telescope optics is a fascinating story. Until this century, the optical theory of reflecting telescopes was essentially limited to the Cartesian treatment of axial imagery. In 1905, Karl Schwarzschild initiated a revolution by applying third order (Seidel) theory to the field imagery of 2-mirror telescopes. Since then, the whole gamut of possible telescope systems has been invented, analysed and, in many cases, tried out in practice.

Over all its history, the optical development of the telescope has also depended on technical inventions, above all in mirror materials, glasses, support systems and means of achieving high reflectivity. Over the last 30 years, developments have been particularly spectacular, above all in manufacture and test techniques and generally in enhancing the image quality available.

When I started this work in 1988 there was little literature in book form available on telescope optics. Two of the best were in German: "Die Fernrohre und Entfernungsmesser" by Konig-Kohler (1959) and the monograph on "Teleskope" by K. Bahner in "Handbuch der Physik", Vol. XXIX, which appeared in 1967. A major part of this latter work was devoted to a condensed, but excellent exposition of the theory of telescope optics. Inevitably, more modern technical developments which have since assumed great importance could not be included; furthermore, the fact that it was written in German has reduced its impact and dissemination to a limited section of the interested community.

In 1987, "Astronomical Optics" by D. J. Schroeder appeared. Harland Epps kindly drew my attention to this excellent book in 1988 and I reflected then whether scope for a further work on the subject still existed. I finally concluded that it did: Schroeder's book covers a much wider field, since "astronomical" optics includes the broad subject of astronomical instruments, whereas my intention was (and remains) only the comprehensive coverage of the optics of the reflecting telescope, in the broadest interpretation of that term. Furthermore, Schroeder's work emerged more from the university orbit and includes much basic optical theory addressed to graduate students who need, and can profit from, the whole physics background.

The aim of the present book is different from Schroeder's. It is addressed primarily to specialists in the field, both in the astronomical community itself and in the industries concerned, although I hope it may also be useful to stu dents. Consequently, subjects such as practical alignment and test techniques, as well as maintenance aspects, occupy a significant part. Nevertheless, there are inevitably major overlap areas with both Bahner's and Schroeder's books which the informed reader will recognise. This overlap, involving repetitions in a somewhat different context, is unavoidable for a complete presentation.

Bahner's book included sections on achromatic objectives for refracting telescopes, astrographic objectives and oculars. No such material is included in this book. The refractor as such and the optical design of oculars are only of historical interest in large telescope optics and are only mentioned in this context. Of course, refracting elements still play an important role in wide-field telescopes, field correctors and focal reducers, and these are dealt with in Chapters 3 and 4. In general, mirrors supply the optical power while refracting elements have only the subordinate but important role of improving the imagery.

I favour the morphological approach with a strong emphasis on the historical background of the subject. In this sense, Chapter 5 is to be seen as essential background for understanding the current situation in telescope optics. For the background of the general theory of optical aberrations and diffraction, the reader is referred to specialist books in the field of optics. Only the essential consequences of Gaussian optics, third order theory and diffraction theory are given: the emphasis is on a complete treatment of the application to reflecting telescope optics.

At the suggestion of the publisher, the work has been split into two volumes. The first volume deals with the historical development (but there is no claim to completeness as a history of telescope optics - that would be a separate work) and the theory of reflecting telescope optics, including that of the refracting corrector elements. The second volume deals with technical aspects and modern developments in general. Although there is considerable cross-referencing between the volumes, the split is a logical one, since each volume has its own entity.

Every attempt has been made to give complete references to the international literature. It is hoped that the work will be useful, apart from its own content, as a "source book" of the subject.

While I was writing the book, three further works on the subject were published: "Telescope Optics" by Rutten and van Venrooij (1988), "Astrooptik" by Laux (1993) and "Reflective Optics" by Korsch (1991). The first two are primarily destined for amateurs, but have equally great value for professionals. As with the works of Bahner and Schroeder, there is considerable overlap with my material and I have referred to them liberally in my text. I only became aware of Korsch's work when my own text was finished, but again there is inevitably considerable overlap of treatment. However, not only the content and aim of these five works, all admirable, are very different, but also their styles. In this sense, I feel confirmed in my own enterprise.

Chapter 3 of Vol. I, dealing with the aberration theory of reflecting telescopes, is the longest and certainly one of the most important in the whole work. It is in this area that there is the greatest overlap with the above books. However, an illustration of the major, and legitimate, differences in presentation is the data given on the optical quality of systems discussed. Spot-diagrams are the commonest way of representing the quality according to geometrical optics. Rutten-van Venrooij and Laux give virtually complete spot-diagram analyses of the systems they discuss, a very valuable feature. To keep Vol. I within reasonable bounds, I have preferred to limit myself to chosen examples, intended to illustrate with spot-diagrams the key points of the development. Some of these are taken from the literature; but most of those in Chapter 3 (and a few in Chapter 4) have been optimized by Bernard Delabre of ESO from starting systems I set up from the basic theory, or with minor modifications emerging from the calculations. I am deeply grateful for this major contribution to the work.

I owe a great debt of gratitude to many specialist members of the astronomical community and associated industrial concerns, particularly Carl Zeiss (Oberkochen) and REOSC (Paris), who have generously supplied information. This debt extends, too, to many ESO colleagues. Above all, I am grateful to the ESO management for supporting the project and for extensive help in establishing the final text. In the detailed work, I wish to thank specifically, as well as Bernard Delabre mentioned above, Marion Beelen, Samantha Milligan, Baxter Aitken (who has not only played a major role in the text-processing but also kindly read through the entire work), Ed Janssen (who drew and formatted the figures) and Hans-Hermann Heyer for much hard work and enthusiastic support. My gratitude is also due to Richard West for general encouragement and support. Finally, I thank the publisher, SpringerVerlag, for excellent cooperation, and, last but by no means least, my wife Anne, for much help with the text and, above all, for patience throughout the whole task.

D-85296 Rohrbach January 1996

Ray N. Wilson


1 Historical introduction 1

1.1 Period 1608-1672 1

1.2 Period 1672-1840 11

1.3 William Herschel's telescopes 15

2 Basic (Gaussian) optical theory of telescopes 21

2.1 Basic function of a telescope 21

2.2 The ideal optical system, geometrical optics and Gaussian optics 23

2.2.1 The ideal optical system and Gaussian concept 23

2.2.2 Geometrical optics and geometrical wavefronts 26

2.2.3 The Gaussian optics approximation 27

2.2.4 The conventional telescope with an ocular 36

2.2.5 Basic forms of reflecting telescope 40

2.2.6 The scale of astronomical telescopes and the magnification in afocal use of compound telescopes ... 54

2.2.7 "Wide-field" telescopes and multi-element forms 55

3 Aberration theory of telescopes 57

3.1 Definition of the third order approximation 57

3.2 Characteristic Function and Seidel (3rd order) aberrations: aberration theory of basic telescope forms 59

3.2.1 The Characteristic Function of Hamilton 59

3.2.2 The Seidel approximation:

third order aberration coefficients 63

3.2.3 Seidel coefficients of some basic reflecting telescope systems 65

3.2.4 Analytical (third order) theory for 1-mirror and 2-mirror telescopes 69

3.2.5 Higher order aberrations and system evaluation 82

3.2.6 Analytical expressions for a 1-mirror telescope and various forms of 2-mirror telescopes (Classical, Ritchey-Chretien, Dall-Kirkham, Spherical Primary) . . 88

3.2.7 Other forms of aplanatic 2-mirror telescopes (Schwarzschild, Couder) 111

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

3.3 Nature of third order aberrations and conversion formulae from wavefront aberration to other forms 128

3.3.1 Spherical aberration (Sj) 128

3.3.3 Astigmatism (Sjjj) and field curvature (Sjv) 135

3.3.5 Examples of conversions 139

3.3.6 Conversions for Gaussian aberrations 139

3.4 The theory of aspheric plates 140

3.5 The role of refracting elements in modern telescopes: chromatic variations of first order and third order aberrations 146

3.6 Wide-field telescopes 148

3.6.1 The symmetrical stop position: the Bouwers telescope . 148

3.6.2 The Schmidt telescope 151

3.6.3 The Maksutov telescope 165

3.6.4 More complex variants of telescopes derived from the principles of the Schmidt,

Bouwers and Maksutov systems 174

3.6.5 Three- or multi-mirror telescopes (centered) 223

3.7 Off-axis (Schiefspiegler) and decentered telescopes 255

3.7.1 Two- and three-mirror Schiefspiegler 255

3.7.2 The significance of Schiefspiegler theory in the centering of normal telescopes:

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

3.8 Despace effects in 2-mirror telescopes 279

3.8.1 Axial despace effects 279

3.8.2 Transverse despace effects 287

3.9 Zernike polynomials 288

3.10 Diffraction theory and its relation to aberrations 293

3.10.1 The Point Spread Function (PSF) due to diffraction at a rectangular aperture 293

3.10.2 Coherence 297

3.10.3 The Point Spread Function (PSF) due to diffraction at a circular aperture 298

3.10.4 The Point Spread Function (PSF) due to diffraction at an annular aperture 302

3.10.5 The diffraction PSF in the presence of small aberrations 304

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

3.10.7 The diffraction PSF in the presence of larger aberrations: the Optical Transfer Function (OTF) 312

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

4 Field correctors and focal reducers or extenders 325

4.1 Introduction 325

4.2 Aspheric plate correctors 327

4.2.1 Prime focus (PF) correctors using aspheric plates 327

4.2.2 Cassegrain or Gregory focus correctors using aspheric plates 340

4.3 Correctors using lenses 348

4.3.1 Prime focus (PF) correctors using lenses 348

4.3.2 Secondary focus correctors using lenses 372

4.4 Atmospheric Dispersion Correctors (ADC) 392

4.5 Focal reducers and extenders 404

4.5.1 Simple reducers and extenders in front of the image.. . 404

4.5.2 Wide-field focal reducers (FR) as a substitute for a prime focus 406

4.5.3 Other Cassegrain focal reducers 414

5 Major telescopes from Lord Rosse to about 1980 419

5.1 Major telescopes in the speculum mirror epoch to 1865 419

5.2 Glass optics telescopes up to the Palomar 200-inch 431

5.3 Reflectors after the 200-inch Palomar Telescope up to about 1980 449

Appendices 465

A. List of mathematical symbols 467

B. Portrait gallery 487

References 502

List of Figures 513

List of Tables 527

Name Index 531

Subject Index 536

1 Historical introduction

The history of the telescope for astronomical purposes is certainly one of the most inspiring aspects of the development of science and technology. Many excellent accounts exist as chapters in more general works, in biographies or accounts of specific projects, but only a few books are devoted solely to the historical development. The works of King (1955) [1.1] and Riekher (1957, 1990) [1.2] are notable. The recent second edition of Riekher has been heavily modified and includes excellent new material which partially displaces interesting older material of the first edition. An updating of the work of King would be an enrichment of the subject but, failing that, the author hopes the present work will, with this chapter and with Chap. 5, to some extent fill this gap, at least on the optics side.

1.1 Period 1608-1672

The purpose of this introduction, as well as the content of Chap. 5, is to illustrate the course of development of telescope optics as a consistent logical process, an understanding of which is essential to a clear appreciation of the current situation and the way to the future. Precisely the early history, from 1608 up to 1672, is particularly instructive, since not only the basic theory of the reflecting telescope was completely and correctly expounded, but also all its basic forms. The theory of the refractor evolved more slowly but it remained for at least 100 years the more powerful practical tool purely for manufacturing reasons which will be considered in detail in RTO II, Chap. 1. This early history is treated particularly well in the classic work on telescopes by Danjon and Couder [1.3]. Another interesting account from an earlier epoch was given by Grant [1.4].

Above all in the Anglo-Saxon literature, Isaac Newton is often represented as the inventor of the reflecting telescope. But this is far from the truth: Newton's great merit was that he was the first person who made a reflecting telescope which could rival the refractors of the time. But the idea of a reflecting telescope goes right back to the origins of the refractor which emerged in a practical form between 1608 and 1610 in Holland and Italy. The first genuinely scientific analysis of the optical function of the refractor was given by Kepler in 1611 [1.2]. However, Galileo understood the basic imaging properties of his first telescope (1610) far better than most of his contemporaries and recognised immediately that the convex lens objective could, in principle, be replaced by a concave mirror. This was clear from his contact with Sagredo, Marsili and Caravaggi,1 in which not only concepts but also attempts to make a reflecting telescope were documented [1.3]. One of the first serious attempts at manufacture was by Zucchi in 1616 [1.1] [1.3]. He states he procured a bronze concave mirror "executed by an experienced and careful artist of the trade" and used it directly with a negative Galilean eyepiece. This implies a "front-view" reflector of the type later introduced by William Herschel. Since a "front-view" telescope must necessarily have used an inclined beam to avoid obstruction by the observer's head (Fig. 1.1), it may be that field coma and astigmatism were also a significant factor in the poor image produced (see Chap. 3). But, in all probability, the manufacturing

Fig. 1.1. Zucchi's attempt at a Herschel-type front-view reflecting telescope, 1616

1 Cesare Caravaggi of Bologna should not be confused with the well-known painter Michelangelo Merisi da Caravaggio who lived in Lombardy and died in 1610. (According to Hockney [1.10], Caravaggio was one of the first painters who most successfully used a concave mirror to project the visual scene on to a screen and thereby achieve amazingly accurate perspective effects). I am most grateful to Dr. S. D'Odorico of ESO and Prof. F. Bertola of Padua University for copies of original letters of B. Imperiali to Galileo (21 March, 1626), C. Marsili to Galileo (7 July, 1626) and Galileo to Marsili (17 July, 1626), referring to the construction of a reflecting telescope by Caravaggi. These make it clear that Caravaggi, named Caravagio (sic) by Imperiali, was certainly already dead in 1626 when the letters were written. Riekher [1.2] states that he died in that year, but this is not clear from the above letters. Marsili refers to an attached drawing of the telescope, but this was subsequently lost. The comments in the letters do not make its construction clear, nor when it was made. Probably it had the same form as the Zucchi telescope of 1616. Unless further evidence emerges, which seems unlikely, we must conclude that Zucchi was the first person actually to construct a reflecting telescope.

quality of the mirror was too poor to produce a useful image on axis. Mirrors are more critical than lenses: the reason why surface accuracy requirements for mirrors are higher than for lens surfaces is given below and in RTO II, Chap. 1.

Not long after, soon after 1630, Descartes invented analytical geometry, a tool which enabled him to confirm not only the paraboloid as the necessary form for a concave telescope mirror, which was already well-known, but also the aspheric forms necessary for theoretically perfect imagery on the axis of a lens system. (Kepler had anticipated this work to a limited extent with his pioneer views on vision and the correction of aberration in the human eye in "Dioptrice", 1611 [1.1]). With this brilliant analysis, Descartes already laid down in his works "Traite du monde ou de la lumiere" (1634) and "Diop-trique" (1637) the complete theory for the elimination of spherical aberration (Fig. 1.2) by suitable aspheric surfaces on mirrors or lenses. Descartes' theory

Fig. 1.2. Spherical aberration of a spherical concave telescope mirror. "Paraxial" rays are nominally at a negligible height from the axis

recognized the fundamental role of the conic sections in general as defined by second degree equations. For lenses free of spherical aberration, he even established the curve of fourth degree (Cartesian oval) required for imagery with two finite conjugates [1.5]. A spherical mirror (or single lens surface) has no axis, but an aspheric mirror has an axis uniquely defined by its equation. Thus Descartes' theory enabled a complete theoretical prescription for perfect axial imagery of mirror and lens systems in the sense that each element was itself free from spherical aberration. It is remarkable that no further advance was made in the basic theory of mirror forms of reflecting telescopes until Schwarzschild [1.6] in 1905, 270 years later! Schwarzschild was concerned to optimize imagery in the field as well as on axis (see Chap. 3), whereas at the time of Descartes the problem was far more fundamental: how to make the form prescribed by Descartes to get adequate axial imagery. Improvement of field imagery relative to axial imagery would have been a problem of no practical meaning at that time.

The significance of Descartes' work for reflecting surfaces was well understood by another contemporary Frenchman, Mersenne [1.1] [1.3], with whom Descartes was in close contact. Mersenne proposed the forms shown in Fig. 1.3, published in his work "L'Harmonie Universelle" in 1636. Although Mersenne's work is often referred to, its full significance is rarely appreciated - and certainly could not be appreciated by Mersenne or his contemporaries. His proposals had the following novel and remarkable features:

a) The invention of the compound reflecting telescope comprising two curved mirrors, in both the Gregory and Cassegrain forms.

b) The use of the second mirror as ocular.

c) As a consequence of b), Mersenne was the first to propose the afocal reflecting telescope with a parallel beam entering and leaving the mirror system, i.e. a beam compressor consisting of two mirrors in the same sense that the refracting telescopes of the time were beam compressors consisting of a large positive and small negative (eyepiece) lens (see Fig. 1.3).

a) Mersenne reflecting afocal b) Mersenne reflecting afocal

Cassegrain form Gregory form

Fig. 1.3. Two of Mersenne's designs for reflecting telescopes, adapted from "L'Harmonie Universelle", 1636, and King [1.1], compared with Galileo-type and Kepler-type refracting telescopes

Fig. 1.3. Two of Mersenne's designs for reflecting telescopes, adapted from "L'Harmonie Universelle", 1636, and King [1.1], compared with Galileo-type and Kepler-type refracting telescopes d) Because of his acquaintance with Cartesian theory, Mersenne was fully aware that the correction of spherical aberration for each mirror required confocal paraboloids for their forms.

e) Without knowing it, Mersenne invented, above all with his Cassegrain2 form using a convex secondary, the basis of the first mirror telephoto system with strong telephoto effect. The properties of the lens telephoto system were first recognized by Kepler in 1611 but it was forgotten and re-invented by Barlow in 1834, then as a photographic objective by Dallmeyer in 1891 [1.7]. This property was of central importance for the future development of the reflecting telescope (see Chap. 2).

f) Also without knowing it, Mersenne invented the aplanatic (and anastig-matic) reflecting telescope in a limit case where the "aplanatic" and "classical" forms converge. This will be discussed in detail in Chap. 3. An "aplanatic" solution also corrects field coma for modest field angles, a property which would have been too sophisticated for Mersenne, or even Descartes, to understand. Its significance would only have become clear after the work of Fraunhofer, or of Petzval and Seidel in aberration theory (see Chap. 3). In fact, it was only with Schwarzschild's work in 1905 [1.6] that it would have been possible to fully understand this property of the Mersenne telescopes; and much later still that the clear recognition took place with the Wolter telescopes for X-ray astronomy [1.8] which are simply extreme forms of Mersenne telescopes with small modifications.

Ironically, Descartes himself completely failed to recognize the interest of Mersenne's proposals. He raised a number of objections [1.3], of which only one had real validity: that the exit pupil of the Mersenne forms using the smaller mirror as an eyepiece was inaccessible to the eye pupil giving severe field limitation. In fact, the Galileo-type refracting telescope current at the time had the same disadvantage, although to a lesser extent (see Fig. 1.3 and Chap. 2). Descartes also raised the interesting objection that the Mersenne telescopes "should not be less long than equivalent refractors if one wished for the same effect, so the construction would be no easier", a remark which showed he had failed to grasp the potential telephoto property. In the Mersenne afocal form, Descartes was right that there was little effective gain in compactness over the equivalent Galileo- or Kepler-type refracting telescopes. Only with the work of Gregory (see below), with his proposal to form a real image with a 2-mirror system, was the enormous telephoto advantage compared with a primary image telescope revealed. However, this was not generally understood until much later.

In fact, Descartes wished only to apply his theory to lens forms, not to mirrors, since he believed the failure or inability to produce the theoreti

2 The term "Cassegrain form" is used here because it is normal terminology. However, a further 36 years were to pass before the proposal of Cassegrain was made

- see also footnote on p. 324 concerning Mersenne.

cal aspheric required to eliminate spherical aberration was responsible for the image defects of the refracting telescopes of the time. This major error came from Descartes' theory of the nature of light and colour and hence of chromatic aberration [1.1] which was completely inadequate to explain scientifically the real nature of the problem of the colour aberration of refracting telescopes. With the authority of Descartes behind it, this erroneous interpretation led to a major effort by the opticians of the time to manufacture aspheric forms on objective lenses, a problem which was not only completely insoluble with the technical means available but also futile, since spherical aberration was negligible with the low relative apertures which makers of refractors were forced to use because of chromatic aberration. In general, the manufacturing problem, also for primary mirrors for reflectors, was not the inability to produce the correct aspheric but the inability to produce an adequate sphere (see Chapters 2, 3, 5 and RTO II, Chap. 1).

No doubt discouraged by the negative reaction of Descartes, Mersenne apparently abandoned any attempts to actually make an afocal reflector. In any event, as we shall see, the manufacture of a relatively steep secondary operating as an eyepiece would, indeed, have required an aspheric form as Descartes insisted, and this would anyway have failed at that time. Nevertheless, Mersenne must be accorded the credit for inventing, on paper, the definitive basic geometrical form of the modern telescope. One of the principal motivations for Mersenne was certainly to solve the problem of the observer head obstruction in Zucchi's earlier direct front-view (Herschel) arrangement of Fig. 1.1. This problem was clearly seen as a fundamental disadvantage of the concave mirror as a replacement for the refracting convex objective.

While the simple refractor made progress - mainly through Huygens - by increased length to minimize chromatic (and also spherical) aberration and produced notable astronomical discoveries, the reflector had still not been realized in practice when Gregory made a further major advance in its theoretical form. In 1663, he proposed the Gregory form [1.3], apparently without knowledge of the work of Mersenne [1.7], as shown in Fig. 1.4.

Gregory analysed three possibilities with considerable scientific rigour: a telescope comprising only lenses (refractors as then used); a telescope comprising only mirrors (one of the Mersenne telescopes, Fig. 1.3(b)), and a telescope combining mirrors and a lens or lenses. He recommended the last, an important step from the basic afocal Mersenne concept to a modern form in which a compound (2-mirror) reflecting telescope forms a real image. He also showed a positive eyepiece (Kepler, 1611, in "Dioptrice"). This had two advantages: the exit pupil of the telescope was accessible to the eye, thereby markedly increasing the field over that of the Galilean telescope; a real intermediate image was provided enabling the use of a reticle. But Kepler's work was not realized in practice, and little known till about 1650. Thus, the Gregory proposal was the first reflecting telescope form that had, in principle, all the advantages: back view (no obstruction by the observer's head),

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