Sombrero function
A sombrero function 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. It can be defined through the Bessel function of the first kind where.
The normalization factor makes. Sometimes the 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:
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.