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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

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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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