If a rough surface is illuminated by a coherent light wave of wavelength λ1 it is not possible to determine the surface profile from the phases of the speckle field formed by the scattered light. If the rough surface is illuminated, however, by an additional coherent wave of wavelength λ2, the phase differences between the two speckle fields do contain information about the macroscopic surface profile even if subject to a statistical error. We present the pertinent statistical properties of dichromatic speckle fields and show (1) that the macroscopic surface profile may be determined from the phase differences if the effective wavelength Δ = λ1λ2/|λ1-λ2| sufficiently larger than the standard deviation of the microscopic profile of the illuminated surface and (2), that the statistical error is reasonably small if the phase measurements are obtained from speckles with sufficient intensity.
A. F. Fercher,
"Statistical Properties And Application Of Two-Wavelength Speckles", Proc. SPIE 0556, Intl Conf on Speckle, (25 November 1985); doi: 10.1117/12.949558; https://doi.org/10.1117/12.949558