Light scattering by sinusoidal surfaces: illumination windows and harmonics in standards.

Sinusoidal surfaces can be used as material standards to help calibrate instruments that measure the angular distribution of the intensity of light scattered by arbitrary surfaces, because the power in the diffraction peaks varies over several orders of magnitude. The calculated power in the higher-order diffraction peaks from sinusoidal surfaces expressed in terms of Bessel functions is much smaller than the values determined from angular distributions that are measured or computed from measured profiles, both of which are determined mainly by the harmonic contents of the profile. The finite size of the illuminated area, represented by an illumination window, gives rise to a background that is much larger than the calculated power in the higher-order peaks. For a rectangular window of a size equal to an even number of periods of the sinusoid, a computation of the power distribution produces minima at or near the location of the diffraction angles for higher-order diffraction angles.

Autocorrelation functions from optical scattering for one-dimensionally rough surfaces.

The relationship between the height autocorrelation function of a one-dimensionally rough surface and the Fourier transform of the intensity distribution of the light scattered by that surface is tested experimentally. The theory is derived by using the Fraunhofer approximation, without recourse to the inconsistent Kirchhoff boundary conditions. In spite of the limitations imposed by the approximations used, the results obtained from optical data agree well with those obtained from stylus data, even for an autocorrelation length as small as the optical wavelength. However, this method should be limited to surfaces with rms roughness smaller than approximately 0.14 times the wavelength of light.

Regimes of surface roughness measurable with light scattering.

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.

Light-scattering measurement of the rms slopes of rough surfaces.

Angle-resolved light scattering (ARLS) is used to estimate the root-mean-square (rms) slopes of rough surfaces having a well-defined lay, and the effect on slope measurements caused by changing the angles of incidence and scattering is investigated. The ARLS patterns are taken with the Detector Array for Laser Light Angular Scattering (Dallas) research instrument, and the rms slopes are obtained from the angular widths of these patterns. In general, it was found that the angular width, and thus the estimated rms slope, is surprisingly insensitive to relatively large changes in both the incident and scattering angles of light. These results are independent of surface material and are valid for both sinusoidal and random rough surfaces with lay. The principles, experiments, analyses, and conclusions involved in using ARLS to estimate rms surface slopes are described.

Light scattering from glossy coatings on paper.

The application of angle-resolved light scattering (ARLS) to the measurement of the surface roughness of glossy coatings on paper was investigated. To this end, ARLS patterns were measured for laser light scattered from several glossy paper samples, and these patterns were compared with those calculated using a theoretical model based on plane-wave scattering from an isotropic rough surface. Mechanical stylus profilometry data for the rms roughnesses and the autocorrelation functions of the coatings were used as input to calculate the patterns. For all the paper samples measured, as well as for all the incidence angles used, there was good agreement between the experimental and the calculated patterns when all the rms roughnesses measured by profilometry were reduced by 30%. The indication from these experiments is that ARLS may be used to determine the roughness parameters of the coatings. As a check on these results, measurements were also performed with a commercial optical surface probe; these data agreed well with both the ARLS and the stylus profilometry results.

Development of a One-Micrometer-Diameter Particle Size Standard Reference Material.

The average diameter of the first micrometer particle size standard (Standard Reference Material 1690), an aqueous suspension of monosized polystyrene spheres with a nominal 1 µm diameter, was accurately determined by three independent techniques. In one technique the intensity of light scattered by a diluted suspension of polystyrene spheres was measured as a function of scattering angle, using a He-Ne laser polarized in the vertical direction. The second technique consisted of measuring as a function of angle the intensity of light scattered from individual polystyrene spheres suspended in air, using a He-Cd laser with light polarized parallel and perpendicular to the scattering plane. The measurement of row length by optical microscopy for polystyrene spheres arranged in close-packed, two-dimensional hexagonal arrays was the basis of the third technique. The measurement errors for each technique were quantitatively assessed. For the light scattering experiments, this required simulation with numerical experiments. The average diameter determined by each technique agreed within 0.5% with the most accurate value being 0.895±0.007 µm based on light scattering by an aqueous suspension. Transmission electron microscopy, flow through electrical sensing zone counter measurements, and optical microscopy were also used to obtain more detailed information on the size distribution including the standard deviation (0.0095 µm), fraction of off-size particles, and the fraction of agglomerated doublets (1.5%).

Sizing of individual optically levitated evaporating droplets by measurement of resonances in the polarization ratio.

Resonances observed in the polarization ratio of light scattered at 90 degrees from single optically levitated evaporating droplets are shown to provide a means for continuous high-resolution monitoring of droplet size. Due to the distinctive character of the individual features in the polarization ratio, each experimentally measured feature could be clearly identified with a specific calculated one. For evaporating droplets of glycerol from 6.6 to 11.5 microm in diameter, the sharp features which appeared in the calculations at ~0.03-microm intervals allowed measurement of droplet diameter to a resolution of 0.003 microm.