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Homework Help: Fourier Transform for Diffraction

  1. Nov 19, 2006 #1
    Hi all,

    I'm working in an exercise of advanced optics related to diffraction, in Fraunhoffer's aproximation.

    I need to calculate the FT of a gaussian multiplied by a rectangle function, i.e, FT(exp(-x^2)*rect(x/a)), and I cant obtain a result expressed using analytical common functions. I can only obtain one solution using Fresnel integrals.

    I think there could be a simpler way of expressing this result. Anyone can help me?

    Thanks.
     
  2. jcsd
  3. Nov 22, 2006 #2

    Dr Transport

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    Science Advisor
    Gold Member

    You can write the solution as

    [tex] F(e^{-x^2}) \otimes F(rect(x)) [/tex]

    where the [tex] \otimes [/tex] is the convolution operation. No need for Fresnel integrals because you integrate the exponential over all space and the rect funtion becomes a sinc funtion upon transform.
     
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