Abstract

The Kirchhoff-Huygens equation is used to investigate wave propagation in optical systems, with large propagation Fresnel numbers <i>N</i><sub><i>F</i></sub> and aperture-to-length ratios (<i>a</i> /<i>L</i>) which are not small. The limit of applicability of the Fresnel approximation is analytically established for a thin rectangular aperture. It is shown that the error introduced by the Fresnel approximation to the Kirchhoff integral is comparable to the effects of diffraction, computed by the approximation, times the dimensionless parameter π<i>N</i><sub><i>F</i></sub> (<i>a</i> /2<i>L</i>)<sup>2</sup>.

© 1978 Optical Society of America

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