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Re: convolution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38403] Re: convolution
  • From: "Mariusz Jankowski" <mjkcc at usm.maine.edu>
  • Date: Fri, 13 Dec 2002 04:18:58 -0500 (EST)
  • References: <at9e8r$q77$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"YourEmailId" <YourEmail at lmco.com> wrote in message
news:at9e8r$q77$1 at smc.vnet.net...
> I'm trying to do a 2 dimensional convolution of the Airy disk with the
> image of an extended source in an optical system, using the Digital
> Image Processing package.  Does anyone have an example routine for doing
> this?
>
> lanny.sterritt at lmco.com
>

Hi,

here is a suggestion. Assuming img is the image and ker is the Airy disk
shaped kernel calculate:

result = DiscreteConvolve[img, ker, Centered->True];

Display result using:

ListDensityPlot[ result, Mesh->False] ;

I understand that the Airy disk is defined BesselJ[1,x]^2/x^2, so a 2D disk
in rectangular coordinates can be obtained as follows (you may need to
change the limits and step size in Table to fit your needs):

ker = N[Table[If[x^2 + y^2 == 0, 1/2, BesselJ[1, Sqrt[x^2 + y^2]]^2/(x^2 +
y^2)], {x, -6, 6}, {y, -6, 6}]];

Hope this helps, Mariusz


===============================
Mariusz Jankowski
University of Southern Maine
mjkcc at usm.maine.edu
207-780-5580





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