Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Poisson's Spot

  1. Aug 24, 2005 #1
    Hi

    hoping someone can help me with this problem. If I block plane monochromatic light (wavelength lambda) with a circular disc of radius r, and then look at the diffraction pattern on a screen placed a distance x behind the disc, I get a bright spot in the centre of the shadow. All well and good. What I want to know is how do the intensity and radius of that central spot vary as a function of x. Specifically I want to know how small I need to make x in order to effectively eliminate the bright spot. Clearly at x=0 there is no bright spot - as x increases I don't know whether the spot appears with increasing radius or increasing intensity (presumably both) but I need to be able to put some numbers in to find at what point the spot becomes intolerably bright/large. For anyone interested the reasoning behind my problem is a botched photolith job that I'm trying to do an autopsy on and avoid repeating the same mistakes!!

    Thanks very much for any help anyone can give,

    Dan
     
  2. jcsd
  3. Aug 24, 2005 #2

    Doc Al

    User Avatar

    Staff: Mentor

  4. Aug 24, 2005 #3
    Hey Doc

    cheers for the reply. Yeah I've been looking through the textbooks (Fresnel diffraction rather than Fraunhoffer I think) but it's not as simple as I'd hoped. The Bessel functions from the standard analysis will never give you the dot disappearing, as the analysis is invalid for x approaching zero (which it's going to have to do.) The classic undergrad approach fails at the first hurdle. I've got a feeling it's going to involve a lot of unpleasant maths starting right from first principles of diffraction (doubtless quickly resulting in an analytically impossible integral) - just wondered/hoped whether anyone out there had already ploughed through this or had a better way in mind!
     
  5. Aug 24, 2005 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Oops, you're right. Obviously I haven't looked at this stuff in ages: I was thinking Airy disk (and far-field limits) while you were talking about the Poisson spot from a circular obstruction (a consequence of Fresnel diffraction).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Poisson's Spot
  1. Poisson brackets (Replies: 5)

Loading...