## F di sprl

upr1

Inserting spr1 = — 2f' = 2fi, since f' = — f'1 because of the folding flat, and L = f' — m2di = f' + with m2 = — 1, Eq. (3.227) reduces to the same result as (3.226).

The above two results (3.226) and (3.227) show that Schwarzschild's own formulation implicitly gave the Schmidt solution for freedom from field aberrations.

Of course, some solution must be found to correct the spherical aberration. In fact, the most general way of doing this, following the symmetry concept, was not the Schmidt method with an aspheric corrector but the concentric meniscus proposed by Bouwers in 1941 [3.32]. The Bouwers telescope is shown in Fig. 3.26. As with the basic, stop-shifted form without spherical aberration correction of Fig. 3.25, it is completely symmetrical and without axis, again giving a field of 180° of identical performance apart from vignetting effects. However, the system has a fundamental problem: the concentric meniscus corrects the third order spherical aberration but introduces primary longitudinal chromatic aberration defined by C1 of (3.223). In its pure form, therefore, the system is only useful for narrow spectral band-widths. It also exhibits spherochromatism, (SSj)c in (3.223). Furthermore, the relative aperture is limited to about f/4 by fifth order spherical aberration (zonal error). For these reasons, the Bouwers form has rarely found application. But as a generic type leading to other modified "meniscus-type" solutions, it is of great significance. The most important of these is the Mak-sutov telescope. The basic theory of the Bouwers form leading to the Mak-sutov modification is given in § 3.6.3. An important modification, proposed by Bouwers to produce chromatic correction while preserving concentricity, is dealt with in § 3.6.4.2.

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