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Resolution and Rayleigh's Criteria

  1. Mar 6, 2013 #1
    When working problems using Rayleigh's Criteria:

    θmin=1.22 [λ/D]

    Why do the answers come out in radians?
    I'm sure it has something to do with the aperture being circular but I don't understand why.

    Thanks!
     
  2. jcsd
  3. Mar 6, 2013 #2

    marcusl

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    You can change the units in the formula to degrees if you wish, in which case the constant 1.22 becomes 69.9°. Radians are the preferred unit in mathematics, however. The look direction in an optical system involves the quantity [itex]sin(\theta)[/itex], and [itex]\theta[/itex] is very small when determining resolution. We can use the approximation [tex]sin(\theta)≈\theta[/tex] in deriving the Rayleigh criterion. That approximation is valid as written only for [itex]\theta[/itex] in radians.
     
  4. Mar 7, 2013 #3

    Andy Resnick

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    The factor 1.22 is due to a circular aperture- for a square aperture, the numerical factor is 1.
     
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