Fraunhofer's diffraction at a circular aperture It has more practical value, because most of the optical instruments have circular stops. The intensity distribution in case of circular aperture looks the same as that of the rectangular slit but the dimensions of the pattern are different. The maxima and minima take the form of concentric circles. The bright central maximum is called `Airy's disc'. The angular position of minima of the diffraction pattern are given by,
D sin q = J l (d13)
where D is the diameter of the slit and J is the Bessel's function of the first kind. The first few values of J are,
1.220, 2.233, 3.238, 4.241, 5.243 etc.
As the angles q ‘s are small, sin q » q . This gives,
q
1 = 1.22 l /Dfor the first minimum. The linear radius of the Airy’s disc is given by the product of q 1 and focal length of the lens used. See also Rayleigh’s criterion.