The problem of estimating the thickness and the optical constants of thin Alms using transmission data only is very challenging from the mathematical point of view and has a technological and an economic importance, In many cases it represents a very ill-conditioned inverse problem with many local-nonglobal solutions. In a recent publication we proposed nonlinear programming models for solving this problem, Well-known software for linearly constrained optimization was used with success for this purpose, Ln this paper we introduce an unconstrained formulation of the nonlinear programming model and we solve the estimation problem using a method based on repeated calls to a recently introduced unconstrained minimization algorithm, Numerical experiments on computer-generated Alms show that the new procedure is reliable, (C) 1999 Academic Press.1512862880