Theory of photothermal wave diffraction tomography via spatial Laplace spectral decomposition

Laser-generated thermal wave diffraction theory is presented as a perturbative Born (or Rytav) approximation in a two-dimensional spatial domain for use with tomographic image reconstruction methodologies. The ranges of validity of the pertinent twodimensional spatial-frequencylthermal wavenumber domain complex plane contours are investigated in terms of the existence af inverse spatial Laplace transforms in the meansquare sense. The spectral decomposition of the Laplace transforms according to a Laplace diffraction theorem is shown to involve regular complex-valued propagation functions, which represent the two-dimensional Laplace transform afa scattering abject alongsemicirculm arcs comprising the objcct’s thermal wavenumber domain. A discussion ofthe complex thermal-wave spatial frequency domain content is also presented, with a view to tomographic recovery of the scattering abject field.