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jinc function [Jun. 30th, 2013|02:37 pm]
Tobin Fricke's Lab Notebook
Reading: J. Goodman, "Intro to Fourier Optics", Ch 2-3

It turns out that the Fourier transform for a rotationally-symmetric function turns into:

G(rho) = 2 pi \int r g(r) J_0(2 pi r rho) dr

For the first time here I stumbled across the "jinc" or "besinc" functions. The fourier transform of the "rectangle" function is the sinc function. Well, the transform of the 2D analogue, the "circle" function, is the "jinc" function, bearing obvious similarity to its cousin the sinc:

sinc(x) = (sin pi x)/(pi x)

jinc(x) = J_1(2 pi x)/x

Naturally John D Cook has beaten me to the punch, but it seems I'm only 1.5 years behind!: