Characterisation of surface roughness by laser light scattering: diffusely scattered intensity measurement

Abstract

This paper aims to describe a method which would allow us to gain some statistical information about a rough random surface, from the measurement of light diffusely scattered at this surface. At first, we give a short description of a theory which quantitatively relates surface roughness to incoherent intensities backscattered at this surface. The scattered light can be expressed as the product of a structure factor by an angular factor. The structure factor, which is the Fourier transform (FT) of the two-point height distribution function, only depends on the surface roughness. The angular factor depends on the dielectric properties of the surface. If the root mean square of height s is small at the scale of the light wavelength λ, the structure factor can be developed in a power series in σ/ λ. The first term of this series is proportional to the FT of the autocorrelation function of surface heights. This quantity is nothing else than the power spectral density of the surface height function considered as a stationary random function. The higher order terms are the FT of non-classical autocorrelation functions. Particularly, the third order one cancels every time both senses of each direction of the surface are statistically equivalent. Using the expression of the diffusely scattered intensity, we develop a method for determining the power spectral density of a rough surface. This method is tested in the case of a steel sample surface presenting a system of grooves oriented along only one direction. The power spectral density is determined for both directions parallel and perpendicular to grooves. In this particular case of surface roughness, we give an evaluation of the autocorrelation function and of the correlation length of the surface, in direction parallel and perpendicular to grooves. We observe that, contrarily to the assumption made in many previous works, the autocorrelation function and the power spectral density are not Gaussian. For instance, in the direction perpendicular to grooves, the power spectral density is rather exponential and then the autocorrelation function is Lorentzian.