Abstract

It seems that virtually nothing is to be found in the literature about the generic behavior of the power series of geometrical optics. As a first step toward remedying this state of affairs, I examine what kinds of singularities the spherical-aberration function ′ of symmetric systems of spherical refracting surfaces can possess and present a detailed classification of them. If χ is a suitable variable that specifies rays, and the first singularity of ′ is encountered at χ = χ0(′ not being defined in the real domain for χ > χ0), then it turns out that as χχ0, the asymptotic behavior of ′ is always of the kind given by the relation ′ ~ a + b(1 − χ/χ0)W. a and b are constants and W a number the possible values of which can be enumerated. As a partial check on the theoretical conclusions, the spherical-aberration function of a realistic optical system is studied numerically.

© 1984 Optical Society of America

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