# Why is the diffraction pattern for an annular aperture the difference of the two Bessel functions?

Inspired by this question, the pattern for the annular intensity is given by the square of the difference of the two Bessel functions. I would have thought the sum was more appropriate, could someone explain why not?

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Because you can think of it as two circular apertures, the middle one being a "negative" aperture. –  genneth Dec 20 '11 at 18:32
because its obscuring, of course! –  Nic Dec 20 '11 at 23:16
@genneth, if you want an 'accept' just make that the answer... –  Nic Jan 7 '12 at 16:13

As per Genneth above:

The equation given represents the electric field at the image surface, by superposition this is the sum of the two apertures, one term positive and one negative.

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