Solid Angle Calculation for a Circular Disk

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Abstract
A general expression for the solid angle subtended by a circular disk is derived in terms of complete elliptic integrals of the first and third kind. The elliptic integral of the third kind is reduced in terms of Heuman's lambda function, which has been tabulated. By transformation of the double integral Ω = ∫ ∫ sinθdθdβ into a single line integral, the solid angle can be conveniently determined. Since the solution involves only tabulated functions, it is well suited for desk calculation.

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