Depth Profiling of Optical Absorption in Thin Films via the Mirage Effect and a New Inverse Scattering Theory. Part I: Principles and Methodology

Abstract

Impulse mirage effect spectroscopy is developed in this work as a nondestructive method for depth profiling the optical properties of samples which are nearly thermally homogeneous with depth. Both a theory and an experimental methodology are presented. An inverse scattering theory of the experimental photothermal deflection signal is derived, based on a previous theory of the impulse mirage effect, which takes into account the effect of Fresnel diffraction on the probe beam. To reconstruct the depth profile of heat source density generated by light absorption in an unknown sample, we have applied our inverse theory to the experimental impulse response, using a regularized minimum square error reconstruction algorithm based on our previously published expectation minimum principle. Because this reconstruction problem is ill posed, it was necessary to identify and compensate for all experimental bias errors significantly affecting the fidelity of the depth profiles. A procedure for obtaining the overall best-fit model of the depth profile given the minimum prior experimental information is presented. These procedures have produced an agreement between the experimental and theoretically predicted mirage effect response to within typical root-mean-square error levels of 0.5% or less.