On the van Cittert - Zernike theorem for intensity correlations and its applications

摘要

A reciprocal relationship between the autocovariance of the light intensityin the source plane and in the far-field detector plane is presented in a formanalogous to the classical van Cittert - Zernike theorem, but involvingintensity correlation functions. A "classical" version of the reciprocityrelationship is considered first, based on the assumption of circular Gaussianstatistics of the complex amplitudes in the source plane. The result isconsistent with the theory of Hanbury Brown - Twiss interferometry, but it isshown to be also applicable to estimation of the source size or the spatialresolution of the detector from the noise power spectrum of flat-field images.An alternative version of the van Cittert - Zernike theorem for intensitycorrelations is then derived for a quantized electromagnetic beam in a coherentstate, which leads to Poisson statistics for the intrinsic intensity of thebeam.