A problem is considered of transmission of radiation from a point source through a plane layer of absorbing medium with smooth random inhomogeneities of its permittivity for the case when the source and the detector are at different distances from the layer boundary. The correlation function and spatial spectrum of the light power are calculated by the method of the complex geometric optics. It is shown that, for sufficiently strong attenuation of the waves in the layer, the width of the spectrum increases with increasing absorption and with increasing distance between the source and the layer. As the distance between the detector and the boundary of the scattering medium increases, the width of the spectrum first increases but then tends to zero. In addition, the maximum of the spectrum shows a noticeable shift with respect to the direction to the source. The magnitude and sign of the shift also depend on the positions of the source and the detector.
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