## Abstract

We describe a variation of the liquid-flat technique for
determining the absolute flatness of a 240-mm-diameter optical surface
to an accuracy better than 1/100λ in both its horizontal
(three-point support) and vertical orientations. Using the
appropriate mathematics to calculate the surface deformation of a disk
due to gravity, we achieved verification of the method by comparing
measurements carried out on a pair of optical flats and a liquid
reference surface.

© 1998 Optical Society of America

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### Equations (2)

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(1)
$$w=\frac{W}{\left(1+\mathrm{\nu}\right)8\mathrm{\pi}D}\left\{\begin{array}{l}\left({r}^{2}-r_{1}{}^{2}\right)\left[\frac{2D\left(1+\mathrm{\nu}\right)}{r_{2}{}^{2}}\left(\frac{1}{{C}_{s}}-\frac{2}{{C}_{n}}\right)+\left(1+\mathrm{\nu}\right)ln\left(\frac{{r}_{1}}{{r}_{2}}\right)+\frac{\left(1+3\mathrm{\nu}\right)}{4}\right]\\ +\frac{1}{8}\left[-\left(3-5\mathrm{\nu}\right)\frac{r_{1}{}^{4}}{r_{2}{}^{2}}+\frac{4\left(1-\mathrm{\nu}\right){r}^{2}r_{1}{}^{2}}{r_{1}{}^{2}}-\frac{\left(1+\mathrm{\nu}\right){r}^{4}}{r_{2}{}^{2}}\right]\end{array}\right\},$$
(2)
$${w}_{r=0}=0.0362\left(\mathit{Wr}_{1}{}^{2}/D\right).$$