In Chap. 2, Fig. 2.15, we showed that the limit case with m2 = —1 has practical significance as the folded Cassegrain, the secondary being a flat mirror; whereas the equivalent Gregory case with m2 = +1 is of no practical interest, as there is no real image. The same result applies to the 2-mirror aberration formulae of Eqs. (3.59) to (3.62). If we set m2 = —1 for the folded Cassegrain, then /' = —/1 and £ = 0 from (3.41). The 2-mirror formulae then reduce to the formulae of Eqs. (3.32) for the primary alone. The folded Gregory case with m2 = +1 gives the same result for the virtual image.

There is, however, a much more important limit case than the folded Cassegrain. This is the afocal case, whereby not only the object, but also the image is at infinity. Such a telescope is a 2-mirror beam compressor, as discussed in § 2.2.4 for conventional visual refractors. In the reflecting form as a Cassegrain or Gregory afocal system, it is a Mersenne telescope (Fig. 1.3). We shall see in §3.2.6 that this form has profound significance in the theory of 2-mirror telescopes. It is therefore important to express the aberration formulae in terms valid for this limit case. Eqs. (3.59) to (3.62) are convenient for the normal focal telescope but not for the afocal case because the parameters /L, m2, Z and £ become infinite and the forms are indeterminate. We therefore set up equivalent equations using only finite parameters such as /, y 1, and d1. The parameter m2 is also used but may have no power higher than zero in the numerator. It should be noted that the parameter /' in the numerator is automatically replaced by y 1 if we reduce the power n of the generalizing factor (f)n to (f )n- 1 and multiply through by (f). If Z and £ are expanded, /' is replaced by m2/{ and

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