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Mathematical Modeling of the Solid Angle Function, Part II: Transmission Through Refractive Media
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Previously, we developed a classical solid angle function that is valid only when the light is traveling within a homogeneous medium. As soon as the light path contains a refractive interface, the direct solid angle formula is invalid. A different approach must be used if one is to include refraction effects in the solid angle formulation. The variables of integration are given more of a physical interpretation than a geometrical one: by using the emitting point instead of the detection aperture as the basis for the coordinates system, we are thus able to obtain an expression for the solid angle subtended by a circular aperture from a point source situated in a different optical medium. The final refracted solid angle formula also includes the expression of Fresnel's transmission coefficient. Key words: solid angle; refraction; integration; Fresnel's coefficients
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