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Sombrero function information


Sombrero function 3D

A sombrero function (sometimes called besinc function or jinc function[1]) is the 2-dimensional polar coordinate analog of the sinc function, and is so-called because it is shaped like a sombrero hat. This function is frequently used in image processing.[2] It can be defined through the Bessel function of the first kind () where ρ2 = x2 + y2.

The normalization factor 2 makes somb(0) = 1. Sometimes the π factor is omitted, giving the following alternative definition:

The factor of 2 is also often omitted, giving yet another definition and causing the function maximum to be 0.5:[3]

The Fourier transform of the 2D circle function () is a sombrero function. Thus a sombrero function also appears in the intensity profile of far-field diffraction through a circular aperture, known as an Airy disk.

  1. ^ Cite error: The named reference Blahut was invoked but never defined (see the help page).
  2. ^ Cite error: The named reference Hendee was invoked but never defined (see the help page).
  3. ^ Cite error: The named reference Wolfram was invoked but never defined (see the help page).

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