Sampling theorems for two-dimensional isotropic random fields

Sampling theorems are developed for isotropic random fields and their associated Fourier coefficient processes. A wave-number-limited isotropic random field z(r) is considered whose spectral density function is zero outside a disk of radius B centered at the origin of the wavenumber plane. z(r) can be reconstructed in the mean-square sense from its observation on the countable number of circles with radius r_i=i π/B, i∈N, or of radius r_i=a_i,n/B, i∈N, where a_1,n denotes the ith zero of the nth-order Bessel function J _n(x), and n is arbitrary