Regimes of surface roughness measurable with light scattering

Abstract

In this paper we summarize a number of previous experiments on the measurement of the roughness of metallic surfaces by light scattering. We identify several regimes that permit measurement of different surface parameters and functions, and we establish approximate limits for each regime. Using a straightforward criterion, we calculate that the smooth-surface regime, in which the angular distribution of scattered light is closely related to the power spectral density of the roughness, ranges over 0 < σ/λ ≲ 0.05, where σ is the rms roughness and λ is the opitcal wavelength. Above that the surfaceautocorrelation function may be calculated from a Fourier transform of the angular distribution over 0 < σ/λ ≲ 0.14. Then comes the specular regime where the specular beam can still be identified andmeasured over 0 < σ/λ ≲ 0.3. For all these regimes and for rougher surfaces too, the rms width of thescatter distribution is proportional to the rms slope of the surface.

Episcopic coaxial illumination device for the simultaneous recording of the speckle signature in the spectrum and in the image of scattering reflective surfaces

“…10, p. 418) V is the complex amplitude of the field just before reaching the object, k = 2π/λ the wavenumber, B L a lens transmission coefficient that accounts for the optical thickness of the lens at its center and any losses, p L the lens aperture function, and R o the complex amplitude reflection coefficient of the object, which comprises the effect of different factors including 1,7 (Ref. 11, p. 93) the object pupil function (which can also specify a limited illumination field), the illumination and observation directions, the surface microtopography -i.e., the height h(x o , y o ) of the surface points with respect to a reference plane-, multiple scattering, and shadowing.…”

“…Since the invention of laser, many attempts have been made to extract surface roughness and defect features by exploiting different optical configurations, usually contrived to render the spectrum of the scattered radiation [1][2][3][4][5][6][7][8] . In most cases, speckle is present in the whole space downstream from the scatterer, and it sometimes constitutes a kind of noise which must be filtered, but other times speckle is precisely the desired signal.…”

A high-speed particle-detection in a large area using line-laser light scattering

“…Several surface scattering models have been developed to relate the light scattering characteristics to the surface power spectral density (PSD) and surface statistics such as root-meansquare (RMS) roughness [8,12e16]. Among them, BeckmannKirchhoff, Rayleigh-Rice (Vector Perturbation) and Harvey-Shake scattering theories are most popular and well summarized in references [8,16].…”

Episcopic coaxial illumination instrument for the simultaneous recording of the speckle signature in the energy spectrum and in the image of scattering reflective surfaces

“…Since the invention of laser, many attempts have been made to decode the information present in the light scattered from a given surface for identifying and extracting the defect features and for measuring surface roughness statistics using a parametric approach as an alternative to the profiling techniques. 1,2 Generally speaking, the different approaches described in the literature are based on analyzing some kind of angular distribution of the scattered light under well controlled coherent illumination (Approach A) or statistical properties of the speckle such as its contrast or correlation (Approach B) (Refs. 3, p. 305, 4, 5).…”