Extended averaging phase-shift schemes for Fizeau interferometry on high-numerical-aperture spherical surfaces

Jan Burke

doi:10.1117/12.860914

2 August 2010 Extended averaging phase-shift schemes for Fizeau interferometry on high-numerical-aperture spherical surfaces

Jan Burke

Author Affiliations +

Proceedings Volume 7790, Interferometry XV: Techniques and Analysis; 779006 (2010) https://doi.org/10.1117/12.860914
Event: SPIE Optical Engineering + Applications, 2010, San Diego, California, United States

Abstract

Phase-shifting Fizeau interferometry on spherical surfaces is impaired by phase-shift errors increasing with the numerical aperture, unless a custom optical set-up or wavelength shifting is used. This poses a problem especially for larger numerical apertures, and requires good error tolerance of the phase-shift method used; but it also constitutes a useful testing facility for phase-shift formulae, because a vast range of phase-shift intervals can be tested in a single measurement. In this paper I show how the "characteristic polynomials" method can be used to generate a phase-shifting method for the actual numerical aperture, and analyse residual cyclical phase errors by comparing a phase map from an interferogram with a few fringes to a phase mpa from a nulled fringe. Unrelated to the phase-shift miscalibration, thirdharmonic error fringes are found. These can be dealt with by changing the nominal phase shift from 90°/step to 60°/step and re-tailoring the evaluation formula for third-harmonic rejection. The residual error has the same frequency as the phase-shift signal itself, and can be removed by averaging measurements. Some interesting features of the characteristic polynomials for the averaged formulae emerge, which also shed some light on the mechanism that generates cyclical phase errors.

Citation Download Citation

Jan Burke "Extended averaging phase-shift schemes for Fizeau interferometry on high-numerical-aperture spherical surfaces", Proc. SPIE 7790, Interferometry XV: Techniques and Analysis, 779006 (2 August 2010); https://doi.org/10.1117/12.860914

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