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Calibration of numerical aperture effects in double beam interferometers

The numerical aperture (NA) of the double beam interferometers (DBI) can affect the accurate measurement of surface profiles. Based on the double beam interference microscope imaging theory, the fringe spacing will vary wide nonlinearly with the increasing of numerical aperture. The double beam interferometers require oblique incidence illumination, including Michelson, Mirau and Linnik types. The intensity distribution of the illumination across its stop is constant so the correction factor depends mainly on the NA in the Michelson and Linnik interferometers. The correction factor expression is derived in the Michelson interferometer. The reference surface is a central obscuration in the beam, which will reduce the effective numerical aperture in the Mirau interferometer. At the same numerical aperture, larger central obscuration has a much effect on the correction factor. The correction factor expression is determined by considering the influence of central obscuration and oblique incidence in the Mirau interferometer.