## Info

The Gaussian focus shift by adding the constant term which shifts the origin to minimize the rms the term R0 (No. 8) balances the third order spherical aberration against focus and a constant. Such balancing is, of course, well known from optical design using classical Hamilton terms. Another excellent treatment of Zernike polynomials is given by Malacara 3.124 . He tabulates some comparative properties of a number of one-dimensional orthogonal polynomials Legendre, Tschebyscheff, Jacobi,...

## V

Where Sq is the total aberration for one of the five monochromatic Seidel aberrations and (Sq)v the contribution of surface v. Because the physical interpretation is the most direct, and because wave-front aberration (in general, not just for third order) can be added up algebraically through an optical system, we have given the formulation of the Characteristic Function above in terms of wavefront aberration. In telescope optics, both wavefront and lateral (angular) aberration (see Fig. 3.1)...

## Id

Fig. 1.4. (a) Facsimile of the Gregory telescope from Optica Promota, 1663 (after Danjon and Couder 1.3 ). (b) Raypath of the Gregory form (after King 1.1 ) Fig. 1.4. (a) Facsimile of the Gregory telescope from Optica Promota, 1663 (after Danjon and Couder 1.3 ). (b) Raypath of the Gregory form (after King 1.1 ) moderate telephoto effect (reduced length - see Chap. 2), a reasonable field, and an upright image, a useful advantage at that time. Gregory not only gave the correct geometrical forms...

## M2 M3 M3

Putting si 0 and applying these formulae to the paraxial principal ray, the quantities ypr and Av can be checked for any of the systems given in Tables 3.2 and 3.3. With the normalization used there, we set up upri +1. The above general form is, in practice, of more direct use for the principal ray for which spri is normally finite, often zero. For astronomical telescopes, of course, the normal case is si ro, and si ro has little practical significance. Because of the singularity introduced...

## CEO m

Basic design (schematic) for an FR with intermediate image for a field of 0.9 diameter at the Cassegrain (RC) focus of the 3.5 m MPIA f 3 to f 8 telescope 4.15 . mpR 1 2.67 in Fig. 4.40. The monochromatic image suffers from appreciable coma which may be correctable with some design modification. Fundamental, however, is the large chromatic difference of coma. The elements of the FR must be disposed over a large axial distance, so that some of them are still a long way from the pupil....

## 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) Karl Schwarzschild ca. 1908 (courtesy Martin Schwarzschild) 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...

## Hpj

Fig. 4.15. 3-lens prime focus corrector designed by Richardson et al. 4.34 for the then proposed 7.6 m, f 2 primary of University of Texas. (After Richardson et al.) The front meniscus lens of Fig. 4.15 is about the same size as the same authors' design for the 3.9 m AAT, i.e. the size relative to the primary (g value above) is much larger in the latter case. The AAT primary has f 3.25 compared with f 2.0 proposed for Texas. As a result, while the first two lenses of the AAT design are...

## Mathematical Symbols In Aberration Chaptr

3 The original blank of the Isaac Newton Telescope (INT) primary was made by Corning in 1936 for the Michigan Observatory in the course of work initiated for the Palomar 200-inch telescope, but the proposed telescope was never built. The blank was presented to the INT project in 1949 5.33 . I am extremely grateful to Dr. R. Bingham for information about this blank and confirmation that it was massive. He also kindly drew my attention to the publication 5.34 , the most complete on the original...

## References

Bahner, K., 1967, Teleskope in Handbuch der Physik, Vol. XXIX, Springer Verlag, Heidelberg, 227-342 2. Born, M., Wolf, E., 1987, Principles of Optics, 6th ed., Pergamon Press, Oxford 3. Czapski, S., Eppenstein, O., 1924, Grundz ge der Theorie der optischen Instrumente, 3. Aufl., J.A. Barth, Leipzig 4. Danjon, A., Couder, A., 1935, Lunettes et Telescopes, reissued 1983, Blanchard, Paris 5. Gascoigne, S.C.B., 1968, Some Recent Advances in the Optics of Large Telescopes, Quart. J. Roy. Astron....

## William Lassell

Born 1799, Bolton, England Died 1880, Maidenhead Lassell was above all a great maker of telescopes. His greatest contribution to the advance of the reflector was his invention of the astatic lever for mirror supports, a principle fundamental to improved image quality in large telescopes. He was the first to apply the equatorial mount to a large reflecting telescope. (Courtesy National Museums and Galleries on Merseyside from an original Daguerreotype of 1845 owned by the Liverpool Astronomical...

## James Gregory

Born 1638, Aberdeen, Scotland Died 1675, Edinburgh Gregory is rightly considered the inventor of the 2-mirror telescope in focal (Gregory) form. Mersenne had already invented the equivalent afocal form. (Courtesy Royal Astronomical Society, through Peter Hingley) * A. Baranne, F. Launay, 1997, Cassegrain un celebre inconnu de l'astronomie instrumental ', J. Opt. 28, 158-172. I am delighted and proud that questions I addressed to my French colleagues, above all Andre Baranne, concerning the...

## E ciySiy2K2 22iko 3315

It is easily shown that the secondary spectrum is also reduced compared with a classical full-size achromat because the individual powers of such an achromat are higher than that of the Dialyte singlet. This is true of normal glasses if special glasses are used, the secondary spectrum can be further reduced. The medial systems of Schupmann took up these principles but used cata-dioptric compensation elements. The first such system was already proposed by Hamilton 3.68...

## Chapter

2.1 The ideal optical system the principal planes and unit magnification between them 23 2.2 Geometrical construction of ideal image 2.3 Geometrical wavefronts and rays 2.4 The relationship between the focal 2.5 Derivation of the Lagrange 2.6 Aperture stop, entrance and exit pupils 2.7 Telecentric aperture 2.8 Gaussian optics of a conventional refracting telescope with ocular (afocal in both object and image 2.9 Image principal plane in the defocused telescope of Fig. 2.8, producing a real...

## Ev ypryv

As given in the definitions for (3.20). The remaining parameter is the aspheric parameter tv given in the definitions for (3.20) as For our purely catoptric system with reflexions only, this becomes Finally, we have for the field curvature This completes the formulae enabling the calculation of third order aberrations for any system consisting only of mirrors in a quite general way, with or without normalization of aperture and field, without the need of numerical ray tracing. They provide a...

## F1 f2 d1

3.8.1.2 Change in spherical aberration S . A very important despace effect is the change of spherical aberration in the axial image (and therefore uniformly over the whole field) when d1 is varied and the image shifts according to (3.398). The third order contribution (Sj )2 of the secondary is easily derived from the recursion formulae (3.336) and (3.337) or directly from (3.39) and (2.72) as

## M

Three-element corrector for an f 2.00 to f 5.28 classical Cassegrain designed by Epps et al. 4.36 for a 300-inch telescope, giving f 6.00 with the corrector Fig. 4.21. Spot-diagrams for the design of Fig. 4.20 for a field of 1 diameter (Epps et al. 4.36 ) Fig. 4.21. Spot-diagrams for the design of Fig. 4.20 for a field of 1 diameter (Epps et al. 4.36 ) 1014.00 6S6.30 587.60 546-10 486.10 435-80 404.70 365-00 - - - - - - - - - - - - - - - - - - o.38 - - - - - - - - - i0-27 - - - - -...

## Fl f2 di

Eliminating f from (2.75) and (2.76) Eliminating s2 and f1 from (2.71), (2.72) and (2.76) Eliminating L from (2.74) and (2.79) gives f2 dl(b - dl) (2.80) 2 f - b + 2dl () We now introduce a further important constructional parameter P in Figs. 2.11 and 2.12, representing the distance between the primary and secondary images. This is a positive quantity in both the Gregory and Cassegrain forms and is defined by P L - s2 b - fl b - s2 - dl , (2.81) from (2.71). Now we can write, using (2.55)

## Karl Schwarzschild

In 1905 Schwarzschild formulated the complete third order aberration theory of 1- and 2-mirror telescopes. Furthermore, his formulation can be extended to any system and forms the basis of all modern reflecting telescope optics. He also developed a practical Eikonal theory giving the total aberration at a given field point. (Courtesy Martin Schwarzschild)

## F Z S L

Taking again the data of Table 3.2 and f g 35, the values are d1 -0.19375 ', L +0.225 ' U -0.5 ', V +3.583 333 ', E +31.4167 giving S -0.00418133 ' Z +0.729 015 +3.258 650 From Table 3.5 with m2 -4 bs1 -1.045 563 bs2 -3.260 541 Comparing with the values for the RC system of Table 3.2, we see that bs1 has increased by 0.89 which is negligible from a manufacturing viewpoint. However, the increase in (1 + bs1) is 25.6 which is very advantageous for prime focus correctors. The increase in bs2 is...

## 1

2.1 Gaussian optics of a prime focus reflecting telescope with a single powered mirror sign of the paraxial parameters 41 2.2 Gregory and Cassegrain telescope forms sign of paraxial ray trace quantities (*denotes sign inversion between Gregory and Cassegrain) 44 2.3 Signs of derived quantities from the paraxial ray trace for the Gregory and Cassegrain forms 53 3.1 Aberration types from the Characteristic Function 61 3.2 Paraxial values for deriving the Seidel coefficients (Table 3.3) for some...

## F gif g2

This should be compared with Eq. (4.9), the equivalent expression for the single (Gascoigne) plate correcting a hyperboloid for spherical aberration and coma. Eq. (4.21) for the 2-plate corrector gives with g1 f' 10, g2 f' 20. The Gascoigne plate with g f' 10 gives from (4.9) The 2-plate corrector correcting Si, Sii and Siii therefore requires a much stronger hyperbola for the spherical aberration correction than the Gascoigne plate and this places it normally outside the useful range of RC or...

## M2 m2 1 m2 1m2

The numerator has the same form as Eq. (3.129), derived in connection with the form of the primary in a certain simple limiting geometry of the DK telescope. The roots of this numerator are the magic number t +1.618034 in the case of m2 positive (Gregory), or 1 t (t 1) 0.618034 in the case of m2 negative (Cassegrain). With m2 t or 1 t in the Gregory or Cassegrain cases respectively, Eq. (3.382) gives (Ra)p 0, corresponding to a telescope in which the secondary has shrunk to a point at the prime...

## H0

Spot-diagrams for the aplanatic Schmidt-Cassegrain system of Fig. 3.45 with 400 mm, f 2 - f 10, and an achromatic corrector plate 3.6.4.2 Further developments of meniscus-type systems. The first obvious extension of the Bouwers-Maksutov concepts discussed in 3.6.1 and 3.6.3 is the Bouwers-Cassegrain or the Maksutov-Cassegrain. The basic principles of the layout of such a system are essentially the same as those of the Schmidt-Cassegrain, the role of the corrector plate being replaced...

## Chief Rry

Spot-diagrams for the Schwarzschild telescope 1905 3.1 for an aperture of 1 m with f 3.0 3.23(a) , two such telescopes of significant size with 24-inch and 12-inch apertures were made between the world wars in the United States. It seems unlikely this system will be manufactured again today, except perhaps in the Couder modification discussed below. But the precise form of the original Schwarzschild proposal is completely unimportant. His aims were later satisfied by Schmidt...

## Oo

Within 0.4 arcsec in the range 330 nm to 1000 nm. The spot-diagrams of Fig. 4.18 may be compared with those shown in Fig. 4.14(b) for the original Wynne-type corrector, for which the field performance in the blue part of the spectrum is much inferior to the 1 arcsec specification. It should be emphasized that the new corrector, like its predecessor, only uses spherical surfaces. The circular field covered is marginally smaller, 0.9 diameter instead of 1.0 . However, this field size is solely...

## S

The same equations, in a slightly different form and adapted to his sign convention, are given by Bahner 3.5 . Other treatments have been given by Conrady 3.109 , Marechal 3.110 , Slevogt 3.111 , Baranne 3.112 and Schroeder 3.22(d) . In the thirties, Ritchey built the first major RC telescope, with an aperture of 1 m, for the US Naval Observatory in Washington. A short account is given by Riekher 3.39(h) and the basic data by Bahner 3.5 . This important telescope is discussed further in Chap....