MATHEMATICAL-MODELING OF THE SOLID ANGLE FUNCTION .2. TRANSMISSION THROUGH REFRACTIVE MEDIA

Previously, we developed a classical solid angle function that is vali d only when the light is traveling within a homogeneous medium. As soo n 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 vari ables of integration are given more of a physical interpretation than a geometrical one: by using the emitting point instead of the detectio n aperture as the basis for the coordinates system, we are able to use the symmetry of the light distribution to simplify the bounds of inte gration. With carefully chosen coordinate changes, we are thus able to obtain an expression for the solid angle subtended by a circular aper ture from a point source situated in a different optical medium. The f inal refracted solid angle formula also includes the expression of Fre snel's transmission coefficient.