Abstract

The ideal mapping geometry in a Fizeau interferometer is to map equal height increments on a flat object and equal angle increments on a spherical surface to equal heights on the detector. So the initial intent of the optical design of Fizeau transmission spheres (TSs) is to provide $R\text{‐}\theta$ mapping geometry for equal angle increments. The corresponding unequal heights mapping will introduce retrace error as coma when linear carrier fringes exist. On the contrary, equal heights mapping with $R\text{‐}\sin \theta$ mapping geometry will avoid linear carrier fringes induced coma error. These two different mapping geometries conflict especially for the TS with a small $f$-number. In this paper, we will first explore the design and the performance of the $f/0.75\mathrm{TS}$ according to the two different mapping geometries, and then evaluate the mapping geometry for the commercial ZYGO $f/0.75\mathrm{TS}$, and give some engineering notes for the designers, the metrologists, and the fabricators in the optical laboratory.

© 2018 Optical Society of America

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