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

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.

Photothermal imaging of dehydrochlorination in poly(vinyl chloride) films

“…The reconstructions tolerate small experimental deviations from these assumptions (see Ref. 31). but larger variations require the solution of a more sophisticated inverse model, which is left to future work.…”

“…2(b) is assumed, A recovery of the flux profile, q ( 4 is seen from Eq 3 to require inversion of an integral equation. This expression may be simplified for the case of a sample with discretely varying properties as follows (25,31): (4) where q(x) is approximated by the discrete samples, q1 = (q(-(i-1)6xj, spaced at a uniform spacing 6x between samples.…”

“…For wideband data, the problem may be resolved either by attempting deconvolution of the data or by correction of the theory (29,31). The latter is achieved by measuring the electrical impulse response of the pyroelectric sensor, in the absence of thermal excita-tion, according to the procedure described in Ref.…”

“…If a low effusivity contact layer is present at the sample/pyroelectric interface, the heat flux profile from the sample is delayed and the flux contribution from the pyroelectric is broadened, over and above the broadening inherent to the inverse reconstruction (see discussion in the next section). A number of inverse reconstructions was made against a basis set that was computed for a more complete model of the pyroelectric effect response (31), including possible interface effects between the sample and the detector. The reconstructions, in all cases returned profiles of q(xj consistent with the results of Fg.…”

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

“…Unlike competitive techniques, phototherm al methods offer advantages of being potentially noncontact, single-ended, and robust in the presence of moderate light scattering levels. Previous phototherm al depth pro® ling studies include thin-® lm optical characterization 12,13 and depth pro® ling of humidity in starch m edia 15 using the laser photopyroelectric effect, and tissue absorption depth pro® ling using photothermal infrared radiometry. 16 W hile these techniques have their speci® c advantages, a primar y drawback in both cases is incompatibility with inspection at a solid/liquid interface, especially with aqueous media.…”