using fourier transforms in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg103773] using fourier transforms in mathematica*From*: tcarsten <tschmid.creol at gmail.com>*Date*: Mon, 5 Oct 2009 13:16:45 -0400 (EDT)

Hi guys I'm new to mathematica and I wrote the following code to compute the diffraction pattern of a rectangular aperture on a screen at some distance behind. Even though this simple case works great, more complicated aperture shapes don't have an analytical solution, and consequently my approach won't work. What could I try instead? Any help is highly appreciated. Carsten x0 =. ; y0 =. ; z = 25; lamda = 630/10^6; g6[x1_, y1_] := Boole[x1^2 <= 0.005]*Boole[y1^2 <= 0.005]; F = Integrate[g6[x1, y1]*Exp[(-I)*2*Pi*(x1*xs + y1*ys)], {x1, - Infinity, Infinity}, {y1, -Infinity, Infinity}] /. {xs -> x0/ (lamda*z), ys -> y0/(lamda*z)} FF = (1/(lambda^2*z^2))*FullSimplify[F*Conjugate[F]] /. {xs -> x0/ (lamda*z), ys -> y0/(lamda*z)} Plot3D[FF, {x0, -0.125, 0.125}, {y0, -0.125, 0.125}, PlotPoints -> 150]