Nondestructive Optical Depth Profiling in Thin Films through Robust Inversion of the Laser Photopyroelectric Effect Impulse Response

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Abstract
The laser photopyroelectric effect measures an optical absorption depth profile in a thin film through the spatial dependence of a heat flux source established below the film surface by light absorption from a short optical pulse. In this work, inverse depth profile reconstruction was achieved by means of an inverse method based on the expectation-minimum principle (as reported in a companion paper), applied in conjunction with a constrained least-squares minimization, to invert the photopyroelectric theory. This method and zero-order Tikhonov regularization were applied to the inversion of experimental photopyroelectric data obtained from samples with a variety of discrete and continuous depth dependences of optical absorption. While both methods were found to deliver stable and accurate performance under experimental conditions, the method based on the constrained expectation-minimum principle was found to exhibit improved resolution and robustness over zero-order Tikhonov regularization.