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15 March 1996 Imaging through the diffusion equation
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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.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
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);


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