Re: 2D Convolution
- To: mathgroup at smc.vnet.net
- Subject: [mg76005] Re: 2D Convolution
- From: Mathieu G <ellocomateo at free.fr>
- Date: Mon, 14 May 2007 05:51:05 -0400 (EDT)
- References: <f29389$m7p$1@smc.vnet.net>
Mathieu G a =E9crit :
> Hello,
> I need your help on this problem please!
> I would like to compute + plot a 2D convolution between a disk- or
> square shaped hole, and a 2D Gaussian.
> Here is where I am so far...
>
>
> HoleSize = 300*^-9; (*Radius or side length*)
> BeamRadius = 3.81*^-6;
>
> Gaussian2D[x_, y_] := Exp[-((x/BeamRadius)^2 + (y/BeamRadius)^2)/2];
>
> (*Disk-shape hole*)
> DHole = Disk[{0, 0}, HoleSize/2];
>
> (*Square-shape hole*)
> SHole = Rectangle[{-HoleSize/2, -HoleSize/2}, {HoleSize/2,
> HoleSize/2}];
>
> Plot3D[Gaussian2D[x, y], {x, -4 BeamRadius,
> 4 BeamRadius}, {y, -4 BeamRadius, 4 BeamRadius},
> ColorFunction -> "Rainbow", PlotRange -> Full]
>
> Beam = Gaussian2D[{x, -5 BeamRadius, 5 BeamRadius}, {y, -5 BeamRadius=
,
> 5 BeamRadius}];
>
> (*Graphics3D[Beam]
> Graphics[{Red,SHole,Orange,DHole},Frame->True]*)
>
>
> Every advice welcome!
> Thank you,
> Mat'
>
Am I going in the right direction???
It looks like the definition on the Hole functions are problem sources!?
HoleSize = 300*^-9;
BeamRadius = 3.81*^-6;
HoleSize = HoleSize/2;
DHole =.; SHole =.;
DHole[x_, y_] := If[Sqrt[x^2 + y^2] <= HoleSize, 1, 0];
SHole[x_, y_] := If[Abs[x] <= HoleSize && Abs[y] <= HoleSize, 1, 0]=
;
Gaussian2D[x_, y_] :=
Exp[-1/2 ((x/BeamRadius)^2 + (y/BeamRadius)^2)];
Convolve[f_, g_, x_, y_] :=
Integrate[
Function[{x, y}, f][xPrime, yPrime] Function[{x, y}, g][x - xPrime,
y - yPrime], {xPrime, -\[Infinity], \[Infinity]}, {yPrime, -\
\[Infinity], \[Infinity]}, GenerateConditions -> False]
Plot3D[DHole[x, y], {x, -2 HoleSize, 2 HoleSize}, {y, -2 HoleSize,
2 HoleSize}, Mesh -> All, PlotRange -> {0, 2}]
Convolve[DHole, Gaussian2D, x, y]