Radiometry and Coherence for Quasi-homogeneous Scalar Wavefields

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Abstract
On the basis of Wolf's wave equations for the propagation of coherence a new, explicit representation of the cross-spectral density function is obtained in terms of a generalized radiance function which is constant along geometrical rays. By means of a series development of this representation it is shown that the laws of classical radiometry and free space radiative transfer are valid provided the radiance function (the specific intensity) may be considered constant over distances comparable to the transverse coherence length. The corresponding expression for the cross-spectral density function is identical to a result previously obtained by Ovchinnikov and Tatarskii and implies that, for quasi-homogeneous wavefields, the radiance function is everywhere uniquely related to the field coherence by a generalized van Cittert-Zernike theorem. Furthermore, by use of the central limit theorem, the field statistics are shown to be gaussian, so that a complete statistical description is provided in terms of the phenomenological radiance function. The analogy of this statistical model with kinetic descriptions of transfer phenomena in other fields of physics is discussed.

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