The surface integral that measures the solid angle subtended by a planar aperture at a point in space is transformed to a line integral over the boundary of the aperture. The problem is divided into three distinct cases, and in each case a transformation is established. The results have a direct application to the problem of converting the Kirchhoff integral of diffraction by an aperture on a plane screen to a line integral over the rim of the aperture.
© 1985 Optical Society of America
John S. Asvestas, "Line integrals and physical optics. Part I. The transformation of the solid-angle surface integral to a line integral," J. Opt. Soc. Am. A 2, 891-895 (1985)