Circuits, Systems and Signal Processing

, Volume 19, Issue 4, pp 339–363

An adaptive multiscale inverse scattering approach to photothermal depth profilometry

  • Eric L. Miller
  • Ibrahim Yavuz
  • Lena Nicolaides
  • Andreas Mandelis
Article

DOI: 10.1007/BF01200892

Cite this article as:
Miller, E.L., Yavuz, I., Nicolaides, L. et al. Circuits Systems and Signal Process (2000) 19: 339. doi:10.1007/BF01200892

Abstract

Photothermal depth profilometry is formulated as a nonlinear inverse scattering problem. Starting with the one-dimensional heat diffusion equation, we derive a mathematical model relating arbitrary variation in the depth-dependent 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 ill-posed inverse problem. The algorithm is designed to produce an accurate, low-order 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 fine-scale 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.

Key Words

Adaptive signal representationmultiscale methodsB-splinesnonlinear inverse scatteringphotothermal depth profiling

Copyright information

© Birkhäuser 2000

Authors and Affiliations

  • Eric L. Miller
    • 1
  • Ibrahim Yavuz
    • 1
  • Lena Nicolaides
    • 2
  • Andreas Mandelis
    • 2
  1. 1.Department of Electrical and Computer EngineeringNortheastern UniversityBostonUSA
  2. 2.Photothermal and Optoelectronic Diagnostics Laboratories, Department of Mechanical EngineeringUniversity of TorontoTorontoCanada