Inverse black body radiation

Abstract

The total power spectrum radiated by a black body with a given area-temperature distribution is given by Planck's law. The inverse black body radiation problem is thus the problem of determining the area-temperature distribution of a black body, given its (measured) total radiated power spectrum. The concept of a normalized absolute coldness as the (proportional to the) reciprocal of the absolute temperature is introduced, yielding an integral equation for the inverse black body radiation problem. This integral equation is solved analytically with the aid of the (inverse) Laplace transform and a very simple iterative process (the method of successive approximations) that converges in two iterations. Numerico-experimental results for the reconstruction of a Gaussian area-coldness distribution are presented.