Abstract
The yybar diagram for Gaussian beam optics is employed to model the behavior of an interferometer system testing very small radius parts. The model was developed to overcome the limitations and known inconsistencies of a paraxial optics representation used to evaluate a calibration method for testing cylindrical wave optics using a fiber reference test. Gaussian beam analysis inherently contains physical optics conditions, and the yybar diagram method provides both an intuitive and powerful framework to generate analytical solutions. Particularly, we show how to model an interferometric test from a Fizeau transmission sphere (TS), to a small test ball and back to the TS, and yield test ball radius limits as a function of the test wavelength and TS F / # . A computation of error estimates for measuring the radius of curvature of the test balls is also presented.
Highlights
The fiber reference test employs a specially prepared reflective coated optical fiber as the reference surface for an interferometric test that employs or results in a cylindrical wave.[1,2,3,4,5] A previous paper presented the experimental results of the alignment sensitivities of the fiber reference test when employing a proposed new method for absolute calibration of cylindrical wave metrology.[6]
In the analysis, paraxial optics methods were employed, which, when investigating the behavior of the converging cylindrical beam very near focus and interacting with a reflecting surface of a small radius (
The analysis, presented here assuming rotational symmetry, yields a relationship that defines the boundary between conditions where the fiber test may yield one or two separate positions where the small radius reference surface will produce null fringes depending on the test wavelength, the convergence of the test beam, which defines the size of the waist it would form, and the radius of the test surface
Summary
The fiber reference test employs a specially prepared reflective coated optical fiber as the reference surface for an interferometric test that employs or results in a cylindrical wave.[1,2,3,4,5] A previous paper presented the experimental results of the alignment sensitivities of the fiber reference test when employing a proposed new method for absolute calibration of cylindrical wave metrology.[6] in the analysis, paraxial optics methods were employed, which, when investigating the behavior of the converging cylindrical beam very near focus and interacting with a reflecting surface of a small radius (
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