The image-quality degradation as a result of propagation through a turbid medium is analyzed within the small-angle approximation to the equation of transfer. By using the well-known correspondence between the radiance distribution and the mutual-coherence function, we formulate a factorization assumption for the mutual coherence in order to restrict the class of radiance distributions in the object plane. Depending on the contrast factor, this is, in general, the class of partially coherent light beams. The general formula for the irradiance distribution in the image plane contains the classic result of Hufnagel and Stanley [ J. Opt. Soc. Am. 54, 52 ( 1964)] as a special case. We study the limits of an infinite lens and a Gaussian aperture and investigate in detail the case of a Gaussian beam with a cosinusoidally superimposed signal. The solution in the form of a multiple-scattering series enables us to discuss the significance of scattering events of higher order.
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