Intensity Distribution near the Focus of a Large Aperture Optical System

Abstract

A general expression for the light disturbance near the focus of a large aperture optical system is obtained from the Kirchhoff integration. On reversal of the sign of the aberration function, the light intensity at a point symmetrical to an original point about an axis (y-axis), perpendicular to the meridian plane and passing through the Gaussian image point, is the same as that of the original one. The intensity distribution on the y-axis is expressed in a form, I=I(γ_1^cγ_3^d…,γ_2^eγ_4^f…), c+d+…=even, e+f+…=even, where γ1, γ3,… are comatic aberration terms and γ2, γ4,… are astigmatic terms. This equation holds at the Gaussian image point, too. Aberrations of the same type, comatic or astigmatic, must be corrected one another in order to minimize the decrement of the intensity at the Gaussian image point.