as the Couder telescope (§ 3.2.7.2). It is a remarkable demonstration of the law of nature that you never get something for nothing, that both the Schmidt and Couder telescopes achieve this monochromatic correction at the cost of a physical tube length = 2f', about three times the length of a Cassegrain telescope using a primary with the same geometry. However, the Schmidt telescope has a more convenient image position and does not suffer from baffling problems which, in practice, increase the length of the Couder telescope further. From the point of view of stray light from the sky, the Schmidt telescope is as good as the classical refractor.

The Schmidt telescope has a major monochromatic advantage over the Bouwers telescope (§ 3.6.1): the corrector plate does not introduce its own zonal error (fifth order spherical aberration), whereas the concentric Bouw-ers meniscus in combination with its spherical primary does. Furthermore, since the aspheric form is theoretically free, it can compensate fifth and even seventh order spherical aberration of very steep primaries, so very steep primaries of the order of f/1 can be compensated, if the correctors can be made to sufficient accuracy.

Unlike the Bouwers telescope, the Schmidt telescope does possess an axis, albeit only weakly defined by the axis of symmetry of the aspheric form on the plate. This leads to asymmetries in the angles of incidence of oblique beams on the aspheric surface of the plate at points a and b in Fig. 3.27. These asymmetries lead to higher order field aberrations. This limits the theoretical field, the limitation being more severe the higher the relative aperture of the system, but the chromatic limitations are usually more serious in practice.

The corrector plate introduces uncorrected chromatic aberrations, the most important of which is (SSI)c of Eq. (3.223): spherochromatism. There are also chromatic differences of the monochromatic higher order field effects. Since, from Eq. (3.214), the plate produces no third order Sjj or Sjjj, there are also no chromatic differences: spherochromatism is the only third order chromatic aberration.

3.6.2.2 Corrector plate profile and spherochromatism. As we saw from Eqs. (3.219) or (3.220), the required correction is achieved by

in our normalized system with f' = — y 1 = — 1, where Si is the third order spherical aberration of the primary and 5Sj the compensating aberration of the plate. From (3.184), the spherical aberration of the spherical mirror, expressed as wavefront aberration at the Gaussian focus, is given by:

From Table 3.4 we have, setting ym = y for the edge of the aperture,

1 y4

referred to the Gaussian focus. In § 3.3.6 we gave in Eq. (3.211) the conversion formula for longitudinal focus shift 5z to equivalent wavefront aberration as

Since n' = — 1 after reflection at the mirror, the total wavefront aberration to be corrected by the plate is y4 y2

whereby the second term introduces a wavefront compensation by a focus shift produced by the plate. If Wym = 0 for the edge of the pupil ym, then (3.233) gives, for example, y2

a negative distance since f ' is negative. From (3.187), the longitudinal spherical aberration is (with sign reversal because n' = —1)

a positive distance since f' is negative. The focus shift Az0 from (3.234) is therefore half the longitudinal aberration 5s' and of opposite sign.

For the figured plate of thickness dpi, we can generalise (3.221) to give the general plate form for compensation

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