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 aberrations 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 the next page: