If a rough surface is illuminated by a coherent lightwave 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 λ1, the phase differences between the two speckle fields do contain information about the macroscopic surface profile even if subject to a statistical error. It is shown that (1) the macroscopic surface profile may be determined from the phase differences if the effective wavelength Λ = λ1λ2/|λ1−λ2| is sufficiently larger than the standard deviation of the microscopic profile of the illuminated surface, and (2) the statistical error is reasonably small if the phase measurements are obtained from speckles of sufficient intensity. Using a heterodyne interferometer we demonstrate the feasibility of this technique. In the first experiment we determine the radius of curvature of a rough spherical surface. In the second experiment the macroscopic surface contour on two ophthalmic lenses of the same power variation, one with a grounded surface and the other with a polished surface, was determined.
© 1985 Optical Society of America
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