A model has been developed that predicts the effective optical path through a thick, refractive specimen on a reflective substrate, as measured with a scanning confocal interference microscope equipped with a high-numerical-aperture objective. Assuming that the effective pinhole of the confocal microscope has an infinitesimal diameter, only one ray in the illumination bundle (the magic ray) contributes to the differential optical path length (OPL). A pinhole with finite diameter, however, allows rays within a small angular cone centered on the magic ray to contribute to the OPL. The model was incorporated into an iterative algorithm that allows the measured phase to be corrected for refractive errors by use of an a priori estimate of the sample profile. The algorithm was validated with a reflected-light microscope equipped with a phase-shifting laser-feedback interferometer to measure the interface shape and the 68° contact angle of a silicone-oil drop on a coated silicon wafer.
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