The blackbody radiation inversion problem: A numerical perspective utilizing Bernstein polynomials

摘要

The blackbody radiation inversion (BRI) problem can be formulated as a Fredholm integral equation of the first kind for which area as a function of temperature must be solved. This paper utilizes the Bernstein polynomials as a basis to approximate the solution of the BRI problem. By discretization, the BRI problem can be reduced to an ill-posed algebraic equation whose right-hand side is the measured power spectrum. The error in the right-hand side commonly causes a large variation in the solution of BRI. In order to eliminate the numerical instability, the truncated singular value decomposition regularization method is employed for solving the resulting linear system and an error analysis is made to estimate the upper bound between the recovered and the exact area temperature distribution. Numerical examples also shed light on the efficiency and accuracy of this method.