The formulation of a generalized expression for the thermal-wave field in an inhomogeneous finite-thickness solid on a homogeneous semi-infinite substrate is discussed. This is based on the Hamilton-Jacobi formulation of the thermal-wave problem ͓A. Mandelis, J. Math. Phys. 26, 2676 ͑1985͔͒. An algorithm to invert simulated photothermal frequency scan data in obtaining thermal diffusivity profiles using this expression is reported. The tolerance of this inversion procedure to noise in both simulated and experimental data is also discussed.
A capacitive photopyroelectric tomographic technique for obtaining spatial and depth-resolved photothermal scanning images of opaque solid samples is reported. Unlike the two-dimensional projection images obtained by conventional photothermal detection methods, tomographic reconstruction for depth-resolved imaging of subsurface defects is demonstrated to be possible with the assumption of raylike propagation of thermal waves.
An observed change in the photoacoustic signal frequency response of laser processed stainless-steel and carbon steel samples with respect to unprocessed reference samples is reported. A recently developed thermal wave theory for depth profiling of bulk inhomogeneities (where the surface thermal diffusivity is known and is the same as the homogeneous reference material) in condensed phases with arbitrary, continuously varying thermal diffusivity profiles [A. Mandelis, S. 3. Peralta, and J. Thoen, J. Appl. Phys. 70, 1761 (1991)] has been modified to obtain quantitative thermal diffusivity profiles extending from the surface into the bulk. Profiles obtained using this method, which is, in principle, of nondestructive nature, are consistent with the profiles obtained from destructive methods such as cross-sectional optical metallographic examination and microhardness testing.
Several applications will be presented using an inversion methodology based on the generalized theoretical formulation [J. Appl. Phys. 80, 5570 (1996)] of the Hamilton-Jacobi formulation of thermal-wave physics to the problem of photothermal radiometric depth profilometry of the thermal diffusivity of inhomogeneous solids. In the depth profile reconstruction algorithm three channels of information, namely, the amplitude, the phase, and the derivative of phase, of the photothermal signal are utilized to reduce multiple solutions to a single consistent and continuous solution. Wherever possible, diffusivity profiles are compared with those resulting from destructive microhardness testing.
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