Correlation and coherence properties of time-averaged speckle patterns for light fields scattered by rough surfaces.

We analyze the relation between the coherence properties of scattered light fields and various geometric parameters of the scattering objects. It is shown that if the coherence time tau(c) of the probing radiation exceeds 3/omega(0), with omega(0) being the central frequency of the radiation spectrum, then the correlation properties of the scattered, field speckle pattern averaged over a time T > 10 tau(c) determine the homogeneity domains and the coherence properties of the scattered fields. These domains and coherence properties are determined by the following parameters: the coherence length of the probing radiation L-c =tau(c)c, where c is the speed of light; the transverse size d and the depth L-s of the backscattering domain; the distance r(c) between the receiving aperture and the scattering surface, the size d(p) of the receiving aperture, the central wavelength of the probing radiation lambda=c/omega(0), and the mean square deviation sigma of the surface roughness height distribution. The obtained results enable one to find the relations between the parameters L-s, L-c, and sigma corresponding to various intervals of the coherence length variation, where the scattered field manifests itself as coherent, partially coherent, and incoherent. The smallest possible coherence length of the probing optical radiation is estimated to be 8 lambda.