## Abstract

In a recent paper [J. Opt. Soc. Am. A **16**, 113 (1999)] a thin-element approximation of diffractive optical elements was used to describe diffraction of oblique incident wave fronts. This expression motivated by a ray optical analysis is shown to be incorrect. I discuss how the thin-element approximation can be generalized to arbitrary diffraction geometries. This includes an intuitive interpretation of the results.

© 2000 Optical Society of America

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### Equations (5)

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(1)
$$\varphi (\mathbf{x})=\frac{2\pi}{\mathrm{\lambda}}h(\mathbf{x})\mathrm{\Lambda},$$
(2)
$$\tilde{u}(\nu )=C[{\beta}^{(i)},\beta ]{\int}_{-\infty}^{\infty}exp\mathbf{(}-i2\pi \{[\beta -{\beta}^{(i)}]h(x,y)+[\nu -{\nu}^{(i)}]x\}\mathbf{)}\mathrm{d}x,$$
(3)
$$\mathrm{\Lambda}=-2cos\alpha ,$$
(4)
$$\mathrm{\Lambda}=-(cos{\alpha}^{\prime}+cos\alpha ).$$
(5)
$$\mathrm{\Lambda}={n}_{1}cos\alpha -{n}_{2}cos{\alpha}^{\prime}.$$