the first term being the contribution of the primary mirror and the second that of the plate. For the RC primary of Table 3.2 with bs1 = -1.03629, we have E Siii = f'(1 + 27.56), so the astigmatism of the primary is increased by a factor about 29 times. In terms of g, (4.9) gives

Clearly, the larger the negative value of (1 + bs1) and, as a result g, the more favourable the correction of the Gascoigne plate at the PF.

For RC telescopes with a lower value of |m2| than that in Table 3.2 (|m2| = 4), the primary is more eccentric and thus more favourable. We shall see later that certain correctors at the Cassegrain focus favour quasi-RC solutions for which the eccentricity of the primary is of the order of 30% higher than for the strict RC solution. This favours the Gascoigne plate corrector for the PF. Such a telescope is the ESO 3.6 m at La Silla. The Gascoigne plate corrector is provided with an additional field-flattening lens which flattens the mean astigmatic field. For an angular aberration of 1 arcsec at the mean astigmatic focus for the edge of the field, a field diameter of 16 arcmin is possible in this case. Such a Gascoigne plate corrector with field flattener is an excellent solution for modern telescopes equipped with a CCD detector at the PF: it is robust, favourable for ghost images as we saw above, and also for chromatic effects as we shall show below. Let us consider first the field lens required. The mean field curvature is given as in Table 3.3 and from Eq. (3.206) as

Now Siv = -f' for the mirror and is zero for the plate. From (4.12)

g from (3.20), where H is the Lagrange Invariant and Pc the Petzval curvature. Now H = n'u'rf and, with our normalization and the fictitious plane secondary, n' = 1, u' = -1, and r/' = f' in image space, so that H = -f'. The wavefront aberration MFC of the mirror-plate combination is positive according to (4.13), with Pc negative, so that the mean field curvature is concave towards the primary, i.e. the sign is reversed compared with the much weaker field curvature of the primary alone. Then (4.13) gives

From the definitions for Eqs. (3.20), we have for a surface v of the field flattener (FF)

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