## Abstract

Comprehensive measurements in the vacuum uv range of 1200–3000 Å of efficiency, polarization, and scattering of classically ruled and photoresist gratings are reported. The results show that the art of ruling gratings for vacuum uv use has reached a high level of sophistication and that careful analysis of grating properties can lead to useful improvement of the ruling art.

© 1978 Optical Society of America

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### Equations (7)

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(1)
$${E}_{g}=\left(D{R}_{m}\right)/M$$
(2)
$${R}_{m}\frac{{I}_{G}\left(\theta ,\mathrm{\lambda}\right)}{{I}_{m}\left(\theta ,\mathrm{\lambda}\right)}={R}_{\theta ,\mathrm{\lambda}}$$
(3)
$${p}_{\mathrm{\lambda}}=\frac{{R}_{\perp}-{R}_{\parallel ,\mathrm{\lambda}}}{{R}_{\perp}{}_{\mathrm{\lambda}}+{R}_{\parallel ,\mathrm{\lambda}}}$$
(4)
$$\frac{{I}_{s}\left(\mathrm{\lambda}\right)}{I\left({\mathrm{\lambda}}_{0}\right)}=S\left({\mathrm{\lambda}}_{0}-\mathrm{\lambda}\right)W{R}_{g}\left({\mathrm{\lambda}}_{0}\right),$$
(5)
$$\begin{array}{ll}{f}_{s}\left(\mathrm{\lambda}\right)=\hfill & \frac{{\displaystyle {\int}_{{\mathrm{\lambda}}_{1}}^{\mathrm{\lambda}-W}I\left({\mathrm{\lambda}}^{\prime}\right){R}_{g}\phantom{\rule{0.2em}{0ex}}\left({\mathrm{\lambda}}^{\prime}\right)\left[WS\left({\mathrm{\lambda}}^{\prime}-\mathrm{\lambda}\right)\right]d{\mathrm{\lambda}}^{\prime}}}{{\displaystyle {\int}_{{\mathrm{\lambda}}_{1}}^{\mathrm{\lambda}-W}I\left({\mathrm{\lambda}}^{\prime}\right)d{\mathrm{\lambda}}^{\prime}}}\hfill \\ \hfill & +\frac{{\displaystyle {\int}_{\mathrm{\lambda}-W}^{{\mathrm{\lambda}}_{2}}I\left({\mathrm{\lambda}}^{\prime}\right){R}_{g}\phantom{\rule{0.2em}{0ex}}\left({\mathrm{\lambda}}^{\prime}\right)\left[WS\left({\mathrm{\lambda}}^{\prime}-\mathrm{\lambda}\right)\right]d{\mathrm{\lambda}}^{\prime}}}{{\displaystyle {\int}_{\mathrm{\lambda}-W}^{{\mathrm{\lambda}}_{2}}I\left({\mathrm{\lambda}}^{\prime}\right)d{\mathrm{\lambda}}^{\prime}}}.\hfill \end{array}$$
(6)
$$\Delta \beta =\mathrm{\lambda}/\left(a\phantom{\rule{0.2em}{0ex}}\text{cos}\beta \right),$$
(7)
$$\text{cos}2\varphi =1+\frac{\left[2I\left(I-{I}_{\parallel}-{I}_{\perp}\right)\right]}{{I}_{\parallel}{I}_{\perp}},$$