for the CFP. Again with f 'Ra = m2s2 from (2.72), this reduces to

In the Gregory case, the bracket term is always positive and less than unity because Ra is negative. For the Cassegrain, with Ra positive, the bracket term is negative in all practical cases: it can only be positive if Ra is high (>0.5) with a fairly large |m2|, giving an image position far behind M1. This means that, in practical Cassegrain cases, the CFP lies in front of the secondary. This sign reversal, compared with the other cases, arises because of the large positive value of bs2 (oblate spheroid) in (3.377) as distinct from the negative values in the classical and RC cases. In the afocal Cassegrain case, the CFP moves to ro if Ra = 0.5 and is behind the secondary if Ra > 0.5. With our standard values of Table3.2 (m2 = -4, Ra = 0.225), we have (zcfp)sP,cass = -0.730s2, i.e. in front of the secondary.

The above specific cases show a general trend in the position of the CFP. Since the rotation decentering coma of M2 is independent of the mirror form, the position of the CFP reflects the value of the lateral (translation) decenter-ing coma of (3.362). The general case for the CFP is given by setting (3.377) to zero, which leads with simple reduction to zCFP = s2

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