Equivalence of Normalized Thermal-Wave Fields Between Curved and Flat Surfaces and Its Application in the Characterization of Curved Samples

Equivalence of the normalized thermal-wave fields between curved and flat surfaces under certain conditions is investigated based on theoretical models of cylindrical, spherical, and flat solids with multilayer structures. The principle and the physical mechanism of the elimination of the surface curvature effect from the overall photothermal signal of the curvilinear solid are suggested. The effects of the relative values of radii of curvature of the curvilinear solid, the thickness of the inhomogeneous surface layer, and the measurement azimuthal angle on the validity of the equivalence principle are discussed. Consistent experimental reconstructions of thermophysical depth profiles of hardened cylindrical steel rods of various diameters are performed and obtained based on both the curvilinear theory and the equivalent flat surface theory.