## Abstract

A sensitive interferometric sensor scheme that is based on coherent imaging of a first phase grating onto a second phase grating, their periods accurately matched, is suggested. Experimental data, obtained with a setup based on the suggested scheme, are presented. The sensor was found capable of measuring an angular tilt of a mirror less than 0.5 µrad. Compared with a previously suggested measuring scheme, the novelty of the one presented here is the inclusion of a second set of gratings, which eliminates measurement ambiguity. Some characteristics of the sensor scheme are discussed.

© 2003 Optical Society of America

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### Equations (8)

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(1)
$${P}_{1}\left(\mathrm{\delta}\right)=K\left[1+0.906cos\left(2\mathrm{\pi}\mathrm{\delta}/{\mathrm{\lambda}}_{0}+\mathrm{\theta}\right)\right],$$
(2)
$${P}_{2}\left(\mathrm{\delta}\right)=K\left[1-0.906cos\left(2\mathrm{\pi}\mathrm{\delta}/{\mathrm{\lambda}}_{0}+\mathrm{\theta}\right)\right],$$
(3)
$${P}_{1}\prime \left(\mathrm{\delta}\right)=K\prime \left[1+0.906sin\left(2\mathrm{\pi}\mathrm{\delta}/{\mathrm{\lambda}}_{0}+\mathrm{\theta}\right)\right],$$
(4)
$${P}_{2}\prime \left(\mathrm{\delta}\right)=K\prime \left[1-0.906sin\left(2\mathrm{\pi}\mathrm{\delta}/{\mathrm{\lambda}}_{0}+\mathrm{\theta}\right)\right],$$
(5)
$$S\left(\mathrm{\delta}\right)=cos\left(2\mathrm{\pi}\mathrm{\delta}/{\mathrm{\lambda}}_{0}+\mathrm{\theta}\right),$$
(6)
$$S\prime \left(\mathrm{\delta}\right)=sin\left(2\mathrm{\pi}\mathrm{\delta}/{\mathrm{\lambda}}_{0}+\mathrm{\theta}\right),$$
(7)
$$\mathrm{\Delta}\mathrm{\phi}=\frac{{\mathit{FL}}^{2}}{16{\mathit{EI}}_{s}},$$
(8)
$$\mathrm{\Delta}\mathrm{\delta}/{B}^{1/2}\ge 0.25{\mathrm{\lambda}}_{0}{\left(\frac{e}{{I}_{o}}\right)}^{1/2}=0.25{\left(\frac{\mathit{hc}{\mathrm{\lambda}}_{0}}{P\mathrm{\eta}}\right)}^{1/2},$$