4.1 The Schmidt Concept
4.1.1 The Class of Two-Mirror Anastigmatic Telescopes
The basic principle of the wide-field telescope invented by the Estonian optician and astronomer Bernhard Schmidt in 1928 ([67-70], E. Schmidt ), is that a single concave and spherical mirror used with a pupil stop at its center of curvature has no unique axis and therefore yields equal size images at all points of its field of view. In the third-order theory, the mounting is free from Coma 3 and astigmatism Astm 3 ; all images have the same amount of spherical aberration, Sphe 3, coming from the spherical mirror. By using a refractive corrector plate at the mirror center of curvature, one therefore yields equally good images in the whole field of view. In the historical context in Europe, three scientists had previously developed the theoretical analysis on aplanatic telescopes in the two-mirror class, but none of them found or realized that the primary mirror could be used off-axis or could be replaced by an on-axis refractive element. Kellner who patented in 1910  several designs using a corrector lens, locates the plate in a wrong position for wide-field compensations. Schmidt placed the aspherical plate at the mirror center of curvature and emphasized the importance of this location for the entrance pupil of the telescope. The curved focal surface is a monocentric sphere with the mirror. In 1930-31, he succeeded in constructing the first wide-field telescope, 36cm clear aperture at f/1.75, with which he demonstrated the wide-field performance on 7.5 arc degrees during the two subsequent years. He obtained with Wachmann, about two hundred exposures onto curved films showing perfect images. Such astronomical object densities were never seen before. In 1932, Schmidt published his famous article "Em Lichtstarkes Komafreies Spiegelsystem"  and photographies . In fact, his coma-free i.e. aplanatic telescope is also free from third-order astigmatism: nowadays, this is called an anastigmatic telescope. Review papers on B. Schmidt's work were published by Schorr , Mayall , Wachmann [84, 85], Kross  and more recently by E. Schmidt , his nephew.
Within the class of two-mirror aplanats (Schwarzschild 1905 , Chretien 1922 ) satisfying the Abbe sine-condition, which has been reconsidered with
G.R. Lemaitre, Astronomical Optics and Elasticity Theory, Astronomy and Astrophysics Library, DOI 10.1007/978-3-540-68905-8.4, © Springer-Verlag Berlin Heidelberg 2009
parametric equation mirrors (Popov , Lynden-Bell ), the two-mirror anas-tigmats are particular solutions. Into this sub-class, the Schmidts possess the advantage, over the Schwarzschild or Couder designs (Couder 1926 ), of requiring only one aspherical surface (Linfoot , Wynne ). The Schwarzschild is flat fielded but requires a convex primary mirror which then is not convenient for moderate or large size instruments.
Let us briefly review the class of two-mirror anastigmats, as a function of a di-mensionless Petzval curvature factor p, and describe seven designs:
Primary mirror curvature: c\
Secondary mirror curvature: C2
System focal length [>0]: f
Mirror separation [<0]: d = M\M2 Anastigmatism condition: d = —2f' Power: \/f' = 2 (c2—c\ —2 dc\ C2)
Petzval: Cp = —2 (c\ — c2) = —p / f' Curvatures c\, c2 are solution of c\ —c2 = p /2f', c\c2 =(\+ p)/8f'2
c\ = [±V(\ + p)2 + \ + p] /4f' c2 = [±V(\ + p)2 + \ — p] /4f'
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