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Does a diffraction grating with a shape form fourier image

  1. Feb 6, 2015 #1
    i just wanted to get this cleared that a beam falling on a diffraction grating with a shape gives the fourier images of the grating object which can be reobtained by placing a biconvex lens that would converge the rays and form a focussed fourier image at its focal length and the image of the object at other points.
    please correct me if i have misunderstood any phenomenon above
    and is there any relation between the grating lines and the fourier image? how can i calculate the transfer function of the lens?
     
  2. jcsd
  3. Feb 6, 2015 #2

    blue_leaf77

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    FT relation between object and its image holds true only in far-field region and paraxial rays. The far-field image will give you the FT of the grating object if the used grating upstream was illuminated with plane wave, otherwise the far-field image will be the FT of the field just after the grating (i.e. product between incoming beam and grating transmission function). For the effect of placing a lens, I suggest this file: http://users.ece.utexas.edu/~becker/FOch5-6.pdf

    To obtain this relation you have to calculate the FT of the grating lines arrangement.
     
  4. Feb 6, 2015 #3
    any particular good book/reference where i can find how to mathematically? thanks for the help
     
  5. Feb 6, 2015 #4

    blue_leaf77

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    Fundamentals of Photonics by Saleh and Teich
     
  6. Feb 6, 2015 #5

    Andy Resnick

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    I'm a little confused by your question- do you mean that the diffraction grating was cut into a particular shape, like a circle or paper doll? Alternatively, by 'shape of the grating' do you mean the groove profile?
     
  7. Feb 7, 2015 #6
    groove profile, like a cartoon character on the squares, thats all.
     
  8. Feb 7, 2015 #7

    Andy Resnick

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    Thanks, that helps me understand. For example, you may have a laser pointer attachment that projects a square or cartoon character rather than the 'raw beam', right? That attachment is a 2-D phase grating, but if you want to suppress the undiffracted beam as well as undesired diffraction orders, then the grating is nonperiodic.

    In any case, the far-field diffraction pattern is the Fourier Transform of the grating transmission. Shining the diffracted beam onto a positive lens (it doesn't have to be biconvex, but it does have to be a positive lens) simply moves the far-field diffraction pattern from infinity to a user-defined plane that is closer and also converts the angular diffraction pattern into a linear diffraction pattern with a conversion factor that involves the focal length of the lens.

    Does this help?
     
  9. Feb 9, 2015 #8
    yes, thanks
     
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