An equation is derived that relates the emissivity of a spherical cavity to the temperature distribution along the axis normal to the opening. The mathematical formulation of the problem rests on De Vos’s method, and is carried out exactly, by means of a suitable serial development. The solution enables one to estimate the influence of the temperature gradient on the radiant emission of the reference spherical blackbody.
P. Campanaro and T. Ricolfi, "Radiant Emission Characteristics of a Nonisothermal Spherical Cavity," Appl. Opt. 5, 1271-1273 (1966)