  In this paper we study the asymptotic theory for spectral analysis of
stationary random fields, including linear and nonlinear fields. Asymptotic
properties of Fourier coefficients and periodograms, including limiting
distributions of Fourier coefficients, and the uniform consistency of kernel
spectral density estimators are obtained under various mild conditions on
moments and dependence structures. The validity of the aforementioned
asymptotic results for estimated spatial fields is also established.
