Solid Angle Contour Integrals, Series, and Tables

Abstract

The solid angle subtended at a point by any object is determined by the closed contour which outlines the ``visible'' boundary of the object from the point. By transformation of the double integral Ω=∫ ∫ sinθdθd[open phi] into a single integral over θ or [open phi] with limits determined by the contour and choice of axes, the solid angle may be simply represented in the important cases discussed as a contour integral. The integration has been carried out on the high‐speed digital computer ORACLE at Oak Ridge National Laboratory. Solid angle tables have been prepared for the case of the circular disk and the entire finite right circular cylinder in terms of cylindrical coordinates. Each table contains in excess of 12 000 entries to six significant figures.