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/sub i/=i pi /B, i in N, or of radius r/sub i/=a/sub i,n//B, i in N, where a/sub 1,n/ denotes the ith zero of the nth-order Bessel function J/sub n/(x), and n is arbitrary.<
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