4 V™2 + 1/ The first equation of (3.220) requires

for correction of £ Si by the plate, giving

This is an important practical result to be compared with the value —0.25 for the classical Schmidt from Eq. (3.229) and —0.621 for the Baker Schmidt-Cassegrain Type B of Table 3.13. The monocentric Schmidt-Cassegrain thus requires a plate asphericity five times that of a classical Schmidt of the same equivalent focal length, and about twice that of the Baker Type B system. It is instructive to see from (3.306) why this is so: the first term Z dominates and depends on (m2)3. Now m2 is —1 for the classical Schmidt (effectively a plane mirror as secondary), —1.538 for the Baker Type B and —2.0 for the monocentric Schmidt-Cassegrain. Here we see that the advantages of increase in |m2| (reduction in effective length and reduction in obstruction ratio from the theoretical value of 0.5 for the classical Schmidt with a fictitious plane mirror to 0.333 for the monocentric Schmidt-Cassegrain) have to be paid for by a marked increase in asphericity on the plate. Of course, these effects are completely analogous to the higher aberration of a Cassegrain primary compared with a Newtonian of the same focal length because of the telephoto effect and the steeper primary (see Table 3.3). The very strong plate is the weakness of the monocentric system. It is highly desirable to achromatise it; but this produces much larger individual plate strengths unless highly absorbing flint glass is chosen to give a big difference in Abbe number. A further weakness is the length of the system compared with the mirror separation.

It is left to the reader to confirm from the second and third equations of (3.220) that si - = 53 sI - - =0

The analysis above of the required asphericity on the corrector plate reveals the main reason why Schmidt-Cassegrain solutions have only been realized in sizes up to barely about 1 m effective aperture: the chromatic effects of a simple plate become unacceptably large. The classical Schmidt may be long but the plate manufacture is far easier and a single plate may be adequate, although large Schmidts are now often equipped with an achromatic plate. An achromatic plate of 1 m diameter for a monocentric Schmidt-Cassegrain is a major technical undertaking. Spot-diagrams showing the correction of such a system with a singlet (non-achromatic) plate are given in Fig. 3.44 and should be compared with those of the achromatic concentric meniscus system disussed in § 3.6.4.2. Apart from the field curvature, the spot-diagrams show that the spherochromatism is the only significant error giving absolutely uniform quality over the ±1° field.

If some astigmatism and a smaller field of the order of 1° are acceptable, then a wide variety of aplanatic solutions are possible. Such solutions are widely offered by professional suppliers for the amateur market for modest sizes and are also realized by amateurs. The advantages of compactness usually drive the plate position parameter sp down towards +f', giving lengths about half that of the classical Schmidt. A primary of f/2 and Cassegrain focus of f/10 (m2 = -5) is a common layout, typical apertures being 200 to 400 mm. Slevogt types [3.44] with both mirrors spherical are available from about f/4 to f/12. Excellent accounts of these possibilities are given by Rutten and van Venrooij [3.12(b)] and by Schroeder [3.22]. Usually, at least one mirror is spherical, most frequently the primary. Eqs. (3.220) provide the basis for rapidly analysing any such system to third order accuracy. The starting geometry for amateur use will be strongly dependent on whether visual observation is intended, where low central obstruction ratio Ra is important (see Sections 3.10.4 and 3.10.7 on physical optical aspects), or only photographic (flat field and anastigmatism for larger fields more important). Such aspects are discussed in detail in [3.12].

It is instructive to set up a typical modern aplanatic Schmidt-Cassegrain for amateur use to illustrate the ease and rapidity with which the paraxial and aberration formulae can be applied.

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