title: Approximate scaling relationships of light diffraction by apertures with complicated shapes.
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 epsilon on ?, the fraction of the energy transmitted by the aperture within a given polar angle ? are similar in shape when ? is normalized by lambda/rho. Here rho is the size parameter of the aperture geometry (its shape and size) and of the light-amplitude profile. For a small ?, rho = rho(l,eff) = (Sigma(eff)/pi)((1/2)) depends on the effective aperture area Sigma(eff), which is calculated through the axial light intensity. For a large ?, rho = rho(2,eff) = 2Sigma(eff)/Rho(eff) depends on Sigma(eff) and the corresponding perimeter Rho(eff). In the case of a uniform light-amplitude distribution the normalization of rho(1) and rho(2) corresponds to the well-known expansion of epsilon(?) for small and large ?.
authors: I M
authors: IM
authors: Sizova