Fig. 4.5. Conjugate virtual plate in object space for a real aspheric plate at distance g in front of the Cassegrain focus

with f2 defined as negative for a Cassegrain telescope. Therefore

This expression in terms of f is the same as that given by Burch [4.10] and Gascoigne [4.9]. Eq. (4.34) is valid for both Cassegrain and Gregory forms: since f is positive for Cassegrain and negative for Gregory, E also has these signs. Strict aplanatic telescope. If such a plate is applied to a strict aplanatic (normally RC) focus, corrected for E S/ = E S// = 0, then the first equation of (4.31) requires S = 0 if E S/ = 0 with the plate. Since S = 0 if g > 0, it follows that such a plate changes all three aberrations. Clearly, it can correct the astigmatism of an RC telescope at the cost of introducing spherical aberration and coma. From Eq. (3.108) or (4.31), the RC condition for the secondary is

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