Photothermal study of subsurface cylindrical structures. I. Theory

A study of the photothermal signal generated by subsurface cylindrical structures is presented in two parts: theoretical modelization (Part I), and experimental measurements on calibrated samples (Part II). In this first part we develop a theoretical study of the scattering of planar and spherical thermal waves by a buried single infinite cylinder, parallel to the sample surface, as a function of its size and depth, and the thermal characteristics (thermal conductivity and diffusivity) of both the sample and cylinder. Temperature field solutions to the heat conduction equation are explored in two ways: by means of the Green’s function method and by a series expansion. We discuss the limits and accuracy provided by both types of calculations, and we compare the resulting temperature field for extended and pointlike illumination. Our study shows that photothermal methods allow one to locate and characterize the geometrical and thermal properties of the buried cylinder.