Statistic and coherent properties of scattered light fields for different geometrical parameters of rough surfaces

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

“…In particular, for L с ≥20L s , C s =1 at the center of the receiving aperture and C s =e -0,12 at its edge. In this case, the interference pattern is analogous to the speckled structure of a field scattered by a rough surface under the condition that L с substantially exceeds the depth L s of the back-scattering domain of the surface [5,6]. The condition |ρ y |≤d ρ.h /2 also means that inside the domain with the size d ρ.h , the extremums (maximums and minimums) of the intensity distribution Ī(ρ y ) are approximately equal.…”

“…Then, r≈r c +R 2 /2ρ о , where R is the distance between the surface axis and the point with the radius vector r, ρ о is the curvature radius of the surface. In this case, one can show [6] that if |ρ 1 - 2 ]} and that the contrast of the scattered field speckle structure С=B a (ρ,ρ)/〈Ī(ρ)〉 ≈L с /2L s <1. This relatively low contrast can be explained by the fact that at each observation point, the field is formed by amplitude summation (interference) of waves scattered by separate points of the back-scattering domain of the surface.…”

“…It follows from Ref. [6] that under the condition L c ≥4λМ h 2 being the number of speckles in the domain, the contrast С(ρ) of the scattered field is practically constant within this domain. It means that the scattered field intensity distribution is uniform in this domain, and hence, the speckles, on the average, have approximately equal maximums and minimums, which shows that the probing radiation is coherent.…”

“…The fact that the functions ρ. t deviate from ρ 1 and ρ 2 demonstrates the deviation of the random process Ī(ρ) from uniformity, which is usually a very weak effect [6]. The contrast of the speckle structure of Ī(ρ) is given by the relation С(ρ)=B a (ρ, ρ)/〈 Ī(ρ)〉 2 .…”