Ensemble-Averaged Coherence Function of Light Reflected from Rough Surface: Determination of Its Correlation Length

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Abstract
The ensemble-averaged coherence function of light reflected from the Gaussian rough surface having irregularities of gentle slope is derived on the basis of Kirchhoff's diffraction integral and with quasi-monochromatic approximation. The ensemble-averaged coherence function of light reflected at the rough surface depends on the roughness constants, σ andΔ, through the factorD(σ,Δ)=exp [-g2{1-ρ02(τ0)}], and the factor possesses spatial dependence through the Gaussian correlation function ρ0(τ0) of surface heights at two singular points of interval τ0. The ensemble-averaged coherence function takes the similar form to the averaged correlation between two geometrical beams reflected at the two points in specular direction referred to the mean surface of rough surface. The degree of coherence degradates on ensemble-averaging by the factorD(σ,Δ). This degradation factor is measured with the interferometer consisting of two diffracting apertures. The correlation lengthΔof the rough surface is estimated from measured values ofD(σ,Δ) by using rms roughness values σ obtained from reflectance for infrared light.

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