A unified solution of the inverse black-body radiation problem and some exact solutions.

The inverse black-body radiation problem is very interesting, especially in remote sensing, such as the remote detections of the surface temperature distributions of earth, sun, etc. In this field, Chen's solution with modified Möbius inversion formula has received much attention and was highly appreciated by Maddox in Nature (Maddox 1990 Nature 344 377). Dai's exact solution in a closed form has succeeded in obtaining a series of exact solutions. In this paper, it is shown that, by using a new representation of inverse Laplace transformations and a famous formula of the Riemann zeta-function, Chen's solution can be derived from Dai's formula, without using the modified Möbius inversion formula. The unique existence theorem and convergence of the series of Chen's series solution are also proven firstly. Some exact solutions are obtained by this new solution formula, which will be useful to test purely numerical inversions. [ABSTRACT FROM AUTHOR]