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Determine the focal length of a Fresnel Zone Plate

  1. Nov 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Derive an expression for the Fresnel Zone Plate's focal length



    2. Relevant equations
    The fresnel zone plate has a transmittance function
    1/2 (1+cos (ar^2)circ(r/2l)


    3. The attempt at a solution
    Using Eulers formula. this splits into e^(iar^2)+e^(-iar^2) Since the transmittance funciton of a lens is e^(i[itex]\pi[/itex]r^2/[itex]\lambda[/itex]f) The fresnel zone transmittance function is pretty much equivalent to a lens which satisfies
    a=[itex]\pi[/itex]/[itex]\lambda[/itex]f
    Hence; the focal length is f= [itex]\pi/[/itex]/[itex]\lambda[/itex]a
    Is this right?
     
  2. jcsd
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