Theory of photothermal wave diffraction tomography via spatial Laplace spectral decomposition

Laser-generated thermal wave diffraction theory is presented as a perturbative Born (or Rytov) approximation in a two-dimensional spatial domain for use with tomographic image reconstruction methodologies. The ranges of validity of the pertinent two-dimensional spatial-frequency/thermal wavenumber domain complex plane contours are investigated in terms of the existence of inverse spatial Laplace transforms in the mean-square 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 of a scattering object along semicircular arcs comprising the object's thermal wavenumber domain. A discussion of the complex thermal-wave spatial frequency domain content is also presented, with a view to tomographic recovery of the scattering object field.