Development of a linearized model for determining the temperature of thermal objects on the basis of radiation data

Abstract

A piecewise linearized model has been developed for determining the temperature of thermal objects using their radiation characteristics in the IR range. The task of calculating the temperature of a thermal object is formulated as an optimization problem of a variational type, in which the task is to find such a dependence of the considered wavelength interval ∆λ = λ_2-λ_1 on the central wavelength λ_с =(λ_2-λ_1)/2, at which the value of the objective functional, equivalent to the calculated temperature reaches a minimum when a certain restrictive condition is imposed on the function ∆λ = ψ(λ_с). It is shown that the minimum of the objective functional is possible if the inverse dependence of ∆λ on λ_с is ensured, i.e. with increasing λ_с, ∆λ should decrease, which in turn leads to a decrease in the linearization error.