The irradiance produced at image points in any lossless optical system by an extended diffuse radiator of given radiant emittance is determined by the final pencil of rays and the indices of refraction of object and image space, and can easily be calculated using thermodynamic reciprocity. Graphs and formulas are given to show the degree to which parabolic and spherical reflectors depart from the usual paraxial irradiance formulas when an extended source or a small source is placed near the aperture. An expression is derived for the off-axis irradiance in systems having circular symmetry and no vignetting.
H. F. Gilmore, "The Determination of Image Irradiance in Optical Systems," Appl. Opt. 5, 1812-1817 (1966)