An adaptive multiscale inverse scattering approach to photothermal depth profilometry
 Eric L. Miller,
 Ibrahim Yavuz,
 Lena Nicolaides,
 Andreas Mandelis
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Photothermal depth profilometry is formulated as a nonlinear inverse scattering problem. Starting with the onedimensional heat diffusion equation, we derive a mathematical model relating arbitrary variation in the depthdependent thermal conductivity to observed thermal wavefields at the surface of a material sample. The form of the model is particularly convenient for incorporation into a nonlinear optimization framework for is particularly convenient for incorporation into a nonlinear optimization framework for recovering the conductivity based on thermal wave data obtained at multiple frequencies. We develop an adaptive, multiscale algorithm for solving this highly illposed inverse problem. The algorithm is designed to produce an accurate, loworder representation of the thermal conductivity by automatically controlling the level of detail in the reconstruction. This control is designed to reflect both (1) the nature of the underlying physics, which says that scale should decrease with depth, and (2) the particular structure of the conductivity profile, which may require a sparse collection of finescale components to adequately represent significant features such as a layering structure. The approach is demonstrated in a variety of synthetic examples representative of nondestructive evaluation problems seen in the steel industry.
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 Title
 An adaptive multiscale inverse scattering approach to photothermal depth profilometry
 Journal

Circuits, Systems and Signal Processing
Volume 19, Issue 4 , pp 339363
 Cover Date
 20000701
 DOI
 10.1007/BF01200892
 Print ISSN
 0278081X
 Online ISSN
 15315878
 Publisher
 BirkhäuserVerlag
 Additional Links
 Topics
 Keywords

 Adaptive signal representation
 multiscale methods
 Bsplines
 nonlinear inverse scattering
 photothermal depth profiling
 Industry Sectors
 Authors

 Eric L. Miller ^{(1)}
 Ibrahim Yavuz ^{(1)}
 Lena Nicolaides ^{(2)}
 Andreas Mandelis ^{(2)}
 Author Affiliations

 1. Department of Electrical and Computer Engineering, Northeastern University, 235 Forsyth Building, 02115, Boston, Massachusetts, USA
 2. Photothermal and Optoelectronic Diagnostics Laboratories, Department of Mechanical Engineering, University of Toronto, 5 King's College Road, M5S 3G8, Toronto, Canada