## Abstract

The effects introduced by a plane diffraction grating on the diffracted wave front when a quasi-plane beam incides on it are calculated. These effects are evaluated by ray tracing and by analytical expressions.

© 1985 Optical Society of America

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### Equations (5)

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(1)
$$\begin{array}{cc}E\left({x}^{\prime},{y}^{\prime},{z}^{\prime}\right)=& A{\displaystyle {\int}_{-a}^{a}{\displaystyle {\int}_{-b}^{b}\text{exp}\{i\frac{2\pi}{\lambda}[\left(\frac{m\lambda}{d\sqrt{1-{\delta}^{2}}}-\text{sin}\varphi \right)\sqrt{1-{\delta}^{2}}x}}\\ & +\delta y+\phi \left(x,y\right)+l\left(x,y,{x}^{\prime},{y}^{\prime},{z}^{\prime}\right)\}dxdy,\end{array}$$
(2)
$$\begin{array}{ll}{z}_{2}\left({x}_{2},{y}_{2}\right)=& {z}_{1}\left({x}_{1},{y}_{1}\right)\\ & +O\left[{\left(\partial {z}_{1}/\partial {x}_{1}\right)}^{2},{\left(\partial {z}_{1}/\partial {y}_{1}\right)}^{2},\left(\partial {z}_{1}/\partial {x}_{1}\right)\left(\partial {z}_{2}/\partial {x}_{2}\right)\right],\end{array}$$
(3)
$$\begin{array}{l}{x}_{1}={x}_{2}\frac{\text{cos}\varphi}{\text{cos}{\varphi}^{\prime}},\\ {y}_{1}={y}_{2}+\frac{\delta \left(\text{sin}\varphi +\text{sin}{\varphi}^{\prime}\right)}{\text{cos}{\varphi}^{\prime}}{x}_{2}.\end{array}$$
(4)
$$\begin{array}{ll}\delta {x}_{2}=\hfill & \partial {z}_{2}/\partial {x}_{2}=\left(\partial {z}_{1}/\partial {x}_{1}\right)\frac{\text{cos}\varphi}{\text{cos}{\varphi}^{\prime}}\hfill \\ \hfill & +\left(\partial {z}_{1}/\partial {y}_{1}\right)\phantom{\rule{0.2em}{0ex}}\left[\delta \frac{\left(\text{sin}\varphi +\text{sin}{\varphi}^{\prime}\right)}{\text{cos}{\varphi}^{\prime}}\right],\hfill \\ \delta {y}_{2}=\hfill & \partial {z}_{2}/\partial {y}_{2}=\partial {z}_{1}/\partial {y}_{1},\hfill \end{array}$$
(5)
$${z}_{1}\left({x}_{1},{y}_{1}\right)=\frac{\theta}{4{f}^{2}}{y}_{1}\left({x}_{1}^{2}+{y}_{1}^{2}\right),$$