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Reconstruction of surface profiles from scattering data is considered in the Kirchhoff aproximation. For reconstruction of the profile phase information is required. For surfaces with Gaussian height variation, the autocorrelation function can be determined from intensity data.
C. J. R. Sheppard
"Inverse scattering for rough surfaces", Proc. SPIE 2778, 17th Congress of the International Commission for Optics: Optics for Science and New Technology, 27783X (1 September 1996); https://doi.org/10.1117/12.2299023
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C. J. R. Sheppard, "Inverse scattering for rough surfaces," Proc. SPIE 2778, 17th Congress of the International Commission for Optics: Optics for Science and New Technology, 27783X (1 September 1996); https://doi.org/10.1117/12.2299023