Closed form approximations to the inverse black body radiation problem

The inverse black body radiation problem is the problem of determining the unknown area-temperature distribution of a black body from its radiated electromagnetic power spectrum. An exact iterative solution to this problem (the inverse Planck problem) was derived by this author in 1982. Recently Hamid and Ragheb derived a closed form approximation to this problem claimed to be valid for the Rayleigh-Jeans regime (the inverse Rayleigh-Jeans problems). It is shown that this Hamid-Ragheb solution is actually far superior to an inverse Rayleigh-Jeans approximation. A closed form approximation to the inverse black body radiation problem valid for the Wien regime (the inverse Wien problem) is presented, and shown to be equivalent to the leading term of the exact iterative solution of this author.