## Abstract

A simple interferometric test setup for measuring thermal expansion coefficients as low as 1 × 10^{−8}/°C is described. The sample to be tested is polished optically flat, interference fringes are formed between the front surface of the sample and a reference surface, and their movement, as boiling water is applied to the back side of the test piece, is observed. When this process was applied to Zerodur, approximate agreement with expected values was achieved. A small permanent change in the Zerodur optical figure occurred as a result of this test procedure, suggesting that Zerodur should not be exposed to strong thermal shock during use.

© 1984 Optical Society of America

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### Equations (8)

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(1)
$$w=-\frac{6\alpha ({a}^{2}-{\rho}^{2})}{{l}^{3}}{\int}_{-l/2}^{l/2}T(z,t)zdz+\frac{1}{1-\nu}\left[(1+\nu )\alpha {\int}_{0}^{z}Tdz-\frac{\nu \alpha z}{l/2}\hspace{0.17em}{\int}_{-l/2}^{l/2}Tdz-\frac{3\nu \alpha {z}^{2}}{2{(l/2)}^{3}}\hspace{0.17em}{\int}_{-l/2}^{l/2}Tzdz\right],$$
(2)
$$w=-\frac{6\alpha {a}^{2}}{{l}^{3}}{\int}_{\gamma /2}^{l/2}{T}_{0}zdz$$
(3)
$$=\frac{3}{4}\frac{\alpha {a}^{2}}{l}{T}_{0}\left[1-{\left(\frac{\gamma}{l}\right)}^{2}\right].$$
(4)
$$T={T}_{0}\hspace{0.17em}\text{erfc}\frac{{z}^{\prime}}{2\sqrt{\kappa t}},$$
(5)
$$\text{erfc}x\equiv \frac{2}{\sqrt{\pi}}{\int}_{x}^{\infty}\text{exp}(-{\xi}^{2})d\xi ,$$
(6)
$$\text{erfc}x\cong 1-\frac{2}{\sqrt{\pi}}\left(x-\frac{{x}^{3}}{3}+\frac{{x}^{5}}{10}+\dots \right).$$
(7)
$$t={l}^{2}/\pi \kappa .$$
(8)
$$\alpha =\frac{4wl}{3{a}^{2}{T}_{0}}.$$