Scattered-wave integral-transform method of holographic-image reconstruction from forward-scattering diffraction patterns

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Abstract
Forward-scattering holography has advantages for the study of the structure of subsurface atoms, but early results reveal the need for image-correction techniques to compensate for the angular dependence of the scattered waves which are the object waves of the photoelectron hologram. We have developed a generalized integral transform for image reconstruction, with a kernel derived from the single-scattering wave functions, that includes the effects of the angular variation of the atomic-scattering-factor amplitude and phase, as well as matrix-element effects that appear in the scattered object waves. This method for scattering-factor corrections preserves the direct-inversion principle of holographic transforms and does not require a priori knowledge of atomic positions. In the limit of pure s-wave scattering, the scattered-wave-included Fourier transform reduces to a simple phased Fourier transform. It can also be approximately described as a generalized deconvolution which uses a function with six degrees of freedom (momentum and position) derived from the scattered wave functions.