Imaging through the diffusion equation

Meir Gershenson

doi:10.1117/12.235383

15 March 1996 Imaging through the diffusion equation

Meir Gershenson

Proceedings Volume 2766, Thermosense XVIII: An International Conference on Thermal Sensing and Imaging Diagnostic Applications; (1996) https://doi.org/10.1117/12.235383
Event: Aerospace/Defense Sensing and Controls, 1996, Orlando, FL, United States

Abstract

By using similarities between the diffusion equation and the wave equation it is shown that one can transform between solutions in one type of propagation to the other. The method is based on the similarities of the Laplace transform between the diffusive and the nondiffusive cases. In the diffusive case, the equation involves the Laplace variable s in the first power while for the nondiffusive cases, similar equations occur with s². Four alternative implementations are developed. The first implementation is based on substitution s² for the Laplace transform variable s using forward and inverse numerical Laplace transform. The second implementation is based on expanding the diffusive time response on exponential time base and replacing it with its image function in the wave case, namely sinusoidal function. The third implementation is based on direct transformation in the time domain using exponential time interval sampling. The fourth one which is optimized for thermal NDE is performed by singular value decomposition.

Citation Download Citation

Meir Gershenson "Imaging through the diffusion equation", Proc. SPIE 2766, Thermosense XVIII: An International Conference on Thermal Sensing and Imaging Diagnostic Applications, (15 March 1996); https://doi.org/10.1117/12.235383

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