Abstract

We present a technique to correct interferometry for the material-dependent phase shift that accompanies reflection. Such corrections are needed for nanometer accuracy of surfaces that are not of homogeneous composition. We adapt the general theory of reflection from surfaces in which there are irregular and unresolved areas of several materials to treat the specific case in which only two materials are present, as is the case for many practical applications. We show, for the approximation of a large numerical aperture that collects all reflected light, how measurements of three quantities, together with known values of the optical constants, allow determination of the material-dependent phase shift at each position on the surface. We demonstrate with numerical simulation, appropriate to measuring a surface of alumina in which optically unresolved titanium carbide granules are embedded, that our approach also succeeds, with nanometer accuracy, when the numerical aperture is small. The method is discussed for use with a miniature interferometric phase sensor, but it has application to any interferometer.

© 2004 Optical Society of America

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