Thomas R. Lettieri

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.

Observation of sharp resonances in the spontaneous Raman spectrum of a single optically levitated microdroplet

Abstract Sharp resonances have been observed in the spontaneous Raman spectra of single, optically levitated microdroplets. The droplets, 10 to 35 μm in diameter, were suspended by a CW argon laser beam which also served as the Raman excitation source. Experiments with dioctyl phthalate (DOP) and silicone oil confirmed that all Raman bands present in the bulk liquid spectra were also observable in the levitated droplet spectra, in agreement with previous micro-Raman studies of droplets on substrates. However, superimposed on the spectra of the levitated droplets was a series of sharp features not present in the bulk liquid spectra. Time-resolved experiments with growing DOP droplets showed that the sharp Raman features have the same origin as the elastic light scattering and flourescence resonances observed in previous studies of microspheres and fibers.

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.

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.

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.

Dimensional calibration of the NBS 0.3-μm-diameter particle-sizing standard☆

Abstract This article summarizes the procedures used at the National Bureau of Standards (NBS) in the certification of SRM 1691, a new submicrometer particle-sizing Standard Reference Material. The mean diameter of the SRM 1691 polystyrene microspheres was accurately measured using two independent micrometrology techniques. One technique, transmission electron microscopy, measured the particles dried and in a vacuum and gave a result of 0.269 ± 0.007 μm for the certified mean diameter. The supporting method, quasi-elastic light scattering, yielded a value of 0.276 ± 0.007 μm for the diameter of the microspheres in liquid suspension. Descriptions of the experimental techniques, data analyses, and sources of error are discussed in the paper. The calibrated microspheres are now available from NBS for use as a primary length standard in the submicrometer size range. Applications include microcontamination measurement in semiconductor processing, atmospheric sampling, and electron-microscope calibration.

Resonance light scattering from a liquid suspension of microspheres

Resonance light scattering (RLS) spectra have been obtained from a liquid suspension of dielectric microspheres a narrow size distribution to find the mean diameter and standard deviation of the size spheres with Comparison with single-particle spectra shows that most peaks in the size-distributed spectra are due to several resonances in the an or bn Mie scattering coefficients. A good estimate of the mean diameter, obtained by matching experimental peak wavelengths with those calculated from Mie scattering formulas, agrees, well with optical microscopy and scanning electron microscopy results. However, the RLS-measured standard deviation of the size distribution is less than half of that from optical microscopy and transmission electron microscopy. Several sources of experimental error which affect the RLS spectra, including scattering angle uncertainty and oversized acceptance aperture, are discussed.

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.

Sinusoidal surfaces as standards for BRDF instruments

This study of light scattered by sinusoidal surfaces shows that such a configuration can be used as a material standard to help calibrate instruments that measure the BRDF of arbitrary surfaces. Measured and computed values of the power scattered into the diffraction peaks show good agreement, and such calculations can be further improved and used to verify the standards.