Comment on “Simultaneous density and thermal conductivity depth profile reconstructions from noised thermal-wave amplitude and phase data using a combined integral-equation and imperialist competitive algorithm method” [J. Appl. Phys. 133, 055102 (2023)]

Abstract

In a recent paper, Mandelis et al. [J. Appl. Phys. 133, 055102 (2023)] describe a photothermal methodology and a new inversion technique which, when applied to a heterogeneous material, is claimed to allow a simultaneous reconstruction of the depth profiles of thermal conductivity and density (assuming that the specific heat is a known constant). In this Comment we recall that, for the thermophysical configuration considered, the thermal conductivity and volumetric heat capacity profiles cannot be identified simultaneously because they are fully correlated. The exposed problem exhibits unconditional non-identifiability leading to the non-uniqueness of the solution. The apparent success of the inversion tests does not preclude the fact that, for any (apparently) optimal solution, an infinite multiplicity of equally satisfactory pairs of conjugate profiles can be built. The simultaneous identification of the density and thermal conductivity profiles is here an unsolvable inverse problem.