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Inversion of optical scattered field data

The technique of computed tomography uses projection data which measure the line integral of an object parameter along straight lines, enabling the Fourier slice theorem to be used. When object inhomogeneities, such as refractive index fluctuations in a semi-transparent object, are comparable in size to the interrogating wavelength, scattering or diffraction effects become significant. Fourier data on the object are still obtainable in this situation provided the Born or Rytov approximations are valid. The authors describe these approximations which allow inversion algorithms to be formulated and discuss the criteria for their validity. When inverting Fourier data there is the question of how to make best use of the limited set of noisy samples available. At optical frequencies, there is an additional problem, that the phase of the scattered field may only be measured with difficulty. Some methods for phase retrieval are assessed.