A two-phase parameter estimation method for radiative transfer problems in paper industry applications

A two-phase method for estimation of the scattering and absorption coefficients and the asymmetry factor (σ s , σ a and g) in the radiative transfer problem is presented. The first phase parameterizes σ s and σ a through g via a simplified model and performs–at a relatively low cost–a scalar optimization over g. It is shown that this gives such a good starting point that the second phase can be accurately performed by a simple Gauss-Newton method. It is also shown that as a part of the first phase can be used on its own when only σ s and σ a are wanted, and it is noted that this gives higher accuracy than the commonly used Kubelka–Munk method when using standardized paper industry reflectance factor measurements. The parameter estimation problem is shown to be non-trivial and ill-conditioned, and its character is analysed. It is discussed that as standard optimization methods are so sensitive to the choice of starting point for this problem that it is hard to find a starting point that gives convergence a...