Page 122 - Modern Optical Engineering The Design of Optical Systems

Chapter
6

Third-Order Aberration Theory

and Calculation

6.1 Introduction
The previous chapter described the various aberrations and, in Eqs. 5.1
and 5.2, indicated the manner in which the various “orders” of aberra-
tions varied with the aperture and the field angle of the optical system.
For an axially symmetrical optical system only “odd” orders (1st, 3rd,
5th, 7th . . .) may exist. The aberrations of the first-order turn out to be
those which are eliminated by locating the reference point at the
paraxial image. The first-order aberrations are thus defects of focus or
of image size (or height) which vary linearly with aperture or obliquity,
such as simple defocusing or the paraxial chromatic aberrations (e.g.,
transverse axial chromatic or lateral color).
And so we come to the first “real” aberrations, the third-order
aberrations wherein the exponents of y (the aperture) and h (the field
angle) add up to three. And then we find the fifth-order aberrations,
followed by the seventh-, the ninth-, and so on. Limiting our attention
to the third- and fifth-order, we have the five third-order aberrations,
the five corresponding fifth-order aberrations, plus two new fifth-order
aberrations, oblique spherical and elliptical coma. The manner in
which the aberrations vary with aperture and field are tabulated on
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