Depth profiling of optical absorption in thin films via the mirage effect and a new inverse scattering theory. Part I: Principles and methodology

Impulse mirage effect spectroscopy is developed in this work as a nondestru ctive method for depth profiling the optical properties of samples which ar e nearly thermally homogeneous with depth. Both a theory and an experimenta l methodology are presented. An inverse scattering theory of the experiment al 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 sou rce density generated by light absorption in an unknown sample, we have app lied our inverse theory to the experimental impulse response, using a regul arized minimum square error reconstruction algorithm based on our previousl y published expectation minimum principle. Because this reconstruction prob lem is ill posed, it was necessary to identify and compensate for all exper imental bias errors significantly affecting the fidelity of the depth profi les. A procedure for obtaining the overall best-fit model of the depth prof ile given the minimum prior experimental information is presented. These pr ocedures have produced an agreement between the experimental and theoretica lly predicted mirage effect response to within typical root-mean-square err or levels of 0.5% or less.