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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.

Simplified physical model of interferometric radius of curvature test using the yybar diagram