Abstract

The behavior of the spherical aberration function ∊′(χ) of symmetric systems was investigated in two previous papers in which all refracting surfaces were assumed to be spherical [ J. Opt. Soc. Am. A 1, 952, 958 ( 1984)]. This restriction is now abandoned: Any particular surface may be a member of a certain rather general class of aspherics. The various ways in which particular singularities of ∊′(χ) can be caused are elaborated in detail. The asymptotic behavior of ∊′(χ) is again given by the general relation ∊′(χ) ∼ a + b(1 − χ/χ0)W; but W can now take more general values than previously, namely, it can be any rational number other than a positive integer. This result is very much one of principle: Given a realistic system in practice, one is unlikely to encounter any value of W other than 1/2.

© 1985 Optical Society of America

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