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Approximate scaling relationships of light diffraction by apertures with complicated shapes

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Abstract

Numerical and analytical simulations of Fraunhofer diffraction by oddly shaped apertures and exponential light amplitudes show that within an accuracy of 20–40%, the dependencies of the normalized encircled energy ∊ on ϑ, the fraction of the energy transmitted by the aperture within a given polar angle ϑ are similar in shape when ϑ is normalized by λ/ρ. Here ρ is the size parameter of the aperture geometry (its shape and size) and of the light-amplitude profile. For a small ϑ, ρ = ρ1,eff = (∑eff/π)1/2 depends on the effective aperture area ∑eff, which is calculated through the axial light intensity. For a large ϑ, ρ = ρ2,eff = 2∑eff/Peff depends on ∑eff and the corresponding perimeter Peff. In the case of a uniform light-amplitude distribution the normalization of ρ1 and ρ2 corresponds to the well-known expansion of ∊(ϑ) for small and large ϑ.

© 1992 Optical Society of America

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