Photoacoustic frequency-domain depth profiling of continuously inhomogeneous condensed phases: Theory and simulations for the inverse problem

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Abstract
An application is presented of the Hamilton–Jacobi formulation of thermal‐wave physics [A. Mandelis, J. Math. Phys. 26, 2676 (1985)] to the problem of photoacoustic depth profiling of inhomogeneous solids with arbitrary, continuously varying thermal diffusivity profiles. Simple expressions for the modulation frequency dependence of the photoacoustic signal in the case of exponential thermal diffusivity profiles are obtained, and a working general method for solving the inverse problem and obtaining arbitrary diffusivity depth profiles is demonstrated through computer simulations. The method was found to possess excellent profile reconstruction fidelity.