Optimisation of wavelengths selection used for the multi-spectral temperature measurement by ordinary least squares method of surfaces exhibiting non-uniform emissivity

Abstract

In this paper, a method based on the ordinary least squares method for optimising the wavelength selection used for the multi-spectral temperature measurement of surfaces exhibiting non-uniform temperature-depending emissivity is presented. The goal consists of minimising the standard deviation of the estimated temperature (optimal design experiment). Two methods for wavelengths selection are presented – sequential and global with or without constraints – on the spectral range. Then, the estimated temperature results obtained by two different models taking into account a second-order polynomial transfer function including the emissivity and for different number of parameters and wavelengths are compared. The first model is based on Wien’s approximation and fluxes ratio (as done in the bicolour temperature technique) and the other is based on the fluxes (Planck’s law but without fluxes ratio). Different selection criteria are presented. These points are treated from theoretical, numerical and experimental points of view.