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 χ → χ₀, 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

Power series of geometrical optics. II.

H. A. Buchdahl
J. Opt. Soc. Am. A 1(9) 958-964 (1984)

Power series of geometrical optics. III.

H. A. Buchdahl
J. Opt. Soc. Am. A 2(6) 847-851 (1985)

Power series of geometrical optics. IV

H. A. Buchdahl and G. W. Forbes
J. Opt. Soc. Am. A 3(8) 1142-1151 (1986)

Power series of geometrical optics. V. Characteristic coefficients of the refracting plane

H. A. Buchdahl
J. Opt. Soc. Am. A 3(10) 1620-1628 (1986)

Weighted truncation of power series and the computation of chromatic aberration coefficients

G. W. Forbes
J. Opt. Soc. Am. A 1(4) 350-355 (1984)