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Is there a way to view the Airy Pattern as an infinite sum of Fraunhoffer diffraction patterns? I don't know where the 1.22 would come from then. Is there something inherently wrong with collapsing diffraction slits to infinitely small slits?

  • Do you mean slicing up a disk of radius $R$ into infinitely many parallel slits of variable length $2\sqrt{R^2-x^2}$? If that is the case, their Fraunhofer diffraction would be infinitely wide, and their superposition would be complicated to compute. – Emilio Pisanty Aug 26 '13 at 22:34
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    What is a "Fraunhofer diffraction pattern"? The Airy pattern is calculated from the equations of Fraunhofer diffraction. – fffred Aug 26 '13 at 23:38
  • I mean in the case of a rectangular slit, a linear diffraction pattern is created. From that, I figured that by summing together a lot of them, all centered on the same point, we would be able to create something akin to a circular aperture. But now that I think about it, this doesn't seem to make sense anymore... –  Aug 27 '13 at 01:15
  • Well, you could consider summing up slits together to get a larger slit, but I don't see how you get a disc. – fffred Aug 27 '13 at 02:27
  • Well, if the slits were collapsed to being lines, then those lines were all centered on the same central pivot point, that would be a disk of slits. –  Aug 28 '13 at 20:12
  • The Fraunhofer approximation is mathematically a Fourier transform. Since the Fourier transform is linear, yes, you can think of any diffraction pattern as the infinite sum of very small patterns (whatever shape), but that is in the electric field, before you square to get the intensity. Otherwise you would only add light, never subtract it (destructive interference) . – roadrunner66 Apr 30 '16 at 02:02

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