## Abstract

A simple visual test for the evaluation of concave diffraction gratings is described. It is twice as sensitive as the Foucault knife edge test, from which it is derived, and has the advantage that the images are straight and free of astigmatism. It is particularly useful for gratings with high ruling frequency where the above image faults limit the utility of the Foucault test. The test can be interpreted quantitatively and can detect zonal grating space errors of as little as 0.1 Å.

© 1972 Optical Society of America

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### Equations (10)

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(1)
$$n\mathrm{\lambda}=d\left(\text{sin}\theta +\text{sin}i\right)=d\phantom{\rule{0.2em}{0ex}}\text{sin}\theta ,$$
(2)
$$n\mathrm{\lambda}=d\left(\text{sin}{\theta}^{\prime}+\text{sin}{i}^{\prime}\right)=d\left(\text{sin}{\theta}^{\prime}+\text{sin}\theta \right).$$
(3)
$$n\mathrm{\lambda}=\left(d+\delta d\right)\phantom{\rule{0.2em}{0ex}}\text{sin}\left(\theta -\delta \theta \right),$$
(4)
$$n\mathrm{\lambda}=d\phantom{\rule{0.2em}{0ex}}\text{sin}\theta -d\phantom{\rule{0.2em}{0ex}}\text{cos}\theta \delta \theta +\delta d\phantom{\rule{0.2em}{0ex}}\text{sin}\theta $$
(5)
$$\delta d\phantom{\rule{0.2em}{0ex}}\text{sin}\theta =d\phantom{\rule{0.2em}{0ex}}\text{cos}\theta \delta \theta .$$
(6)
$$n\mathrm{\lambda}=\left(d+\delta d\right)\left[\text{sin}{\theta}^{\u2033}+\text{sin}\left(\theta +\delta \theta \right)\right]$$
(7)
$$n\mathrm{\lambda}={\theta}^{\u2033}d+d\phantom{\rule{0.2em}{0ex}}\text{sin}\theta +d\phantom{\rule{0.2em}{0ex}}\text{cos}\theta \delta \theta +\delta d\phantom{\rule{0.2em}{0ex}}\text{sin}\theta .$$
(8)
$${\theta}^{\u2033}=-2\left(\delta d/d\right)\phantom{\rule{0.2em}{0ex}}\text{sin}\theta .$$
(9)
$$\delta S=-\left[2R/\left(1+\text{cos}\theta \right)\right]\left(\delta d/d\right)\phantom{\rule{0.2em}{0ex}}\text{sin}\theta $$
(10)
$$\delta d=1.1\times {10}^{-6}\delta S.$$