       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]

```

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