Fourier diffraction theorem for diffusion-based thermal tomography. (English) Zbl 1112.80003

The Fourier diffraction theorem for thermal waves is presented for the case of a three-dimensional infinite-space domain, in parallel with traditional development of the standard Fourier diffraction theorem for fields satisfying the wave equation. It is shown that the values of the 3D Fourier transform of an object (multiplied by an attenuating exponential), which are contained in the Fourier transform of the image on the detection plane, are located on the plane of zero vertical frequences for low temporal frequences and on a curved surface for higher temporal frequences. Because these are subsurfaces of the full 3D Fourier transform, data at different angles and/or different frequences are necessary to uniquely reconstruct the object.


80A20 Heat and mass transfer, heat flow (MSC2010)
80A23 Inverse problems in thermodynamics and heat transfer
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