Surface topography and light scattering were measured on 15 samples ranging from those having smooth surfaces to others with ground surfaces. The measurement techniques included an atomic force microscope, mechanical and optical profilers, confocal laser scanning microscope, angle-resolved scattering, and total scattering. The samples included polished and ground fused silica, silicon carbide, sapphire, electroplated gold, and diamond-turned brass. The measurement instruments and techniques had different surface spatial wavelength band limits, so the measured roughnesses were not directly comparable. Two-dimensional power spectral density (PSD) functions were calculated from the digitized measurement data, and we obtained rms roughnesses by integrating areas under the PSD curves between fixed upper and lower band limits. In this way, roughnesses measured with different instruments and techniques could be directly compared. Although smaller differences between measurement techniques remained in the calculated roughnesses, these could be explained mostly by surface topographical features such as isolated particles that affected the instruments in different ways.

/pdf/surface-characterization-techniques-for-determining-the-root-1bn2vivtpm.pdf

Surface characterization techniques for determining the root-mean-square roughness and power spectral densities of optical components

The power spectral density (PSD), in its two-dimensional form, has been designated as the preferred quantity for specifying surface roughness on a draft international drawing standard for surface texture. The correct calculation of the one-dimensional PSD from discrete surface profile data is given, and problems in using fast Fourier-transform routines that are given in some of the standard reference books are flagged. The method given here contains the correct normalizing factors. Two ways to reduce the variance of the PSD estimate are suggested. Examples are shown of the variance reduction possible in the PSD's.

Calculation of the power spectral density from surface profile data

Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detecting and mitigating artifacts at the smallest scales, and computing upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography - however, this potential can only be achieved through the accurate, quantitative reconstruction of the power spectral density of real-world surfaces.

/pdf/quantitative-characterization-of-surface-topography-using-1di6n32wn5.pdf

Quantitative characterization of surface topography using spectral analysis

Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detecting and mitigating artifacts at the smallest scales, and computing upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography—however, this potential can only be achieved through the accurate, quantitative reconstruction of the PSDs of real-world surfaces.

/pdf/quantitative-characterization-of-surface-topography-using-45kh8tzr33.pdf

The paper tackles the theme of evaluating dynamic load increases that the vehicle transfers to the road pavement, due to the generation of vibration produced by surface irregularities. The study starts from the generation, according to the ISO 8608 Standard, of different road roughness profiles characterized by different damage levels. In particular, the first four classes provided by ISO 8608 were considered. Subsequently, the force exchanged between the pavement and three typologies of vehicles (car, bus and truck) has been assessed by implementing, in Matlab®, the QCM (Quarter Car Model) characterized by a quarter vehicle mass and variable speed from 20 to 100 km/h. The analysis allows determining the amount of dynamic overload that causes the vibrational stress. The paper shows how this dynamic overload may be predetermined as a function of the pavements surface degradation. This is a useful reference for the purposes of designing and maintaining road pavements.

https://link.springer.com/content/pdf/10.1007%2Fs12544-013-0127-8.pdf

The vibrations induced by surface irregularities in road pavements – a Matlab ® approach

The purpose of this study was (1) to measure angle-resolved scattering (ARS) and the wavelength dependence of scattering from polished and sputtered beryllium, (2) to measure surface-roughness parameters by profilometry, (3) to calculate the power spectral density (PSD) of the surface roughness and use it with ARS theory to compare with ARS measurements, and (4) to investigate a dual-source scattering theory and compare calculations from the theory with measured ARS. The wavelengths considered here were 0.633, 1.06, and 10.6 μm, the angle of incidence was 60°, and s and p polarization of the incident and scattered radiation were taken into account both in the theory and in the experiments. Two types of theoretical comparison were attempted. First, two-dimensional PSD functions were calculated from one-dimensional, mechanical-stylus-profile data, and these data were used in first-order roughness ARS theory to compare with ARS measurements. The calculated ARS curves were much too low at some wavelengths and showed incorrect wavelength scaling. Second, a dual-source (surface-roughness and dielectric inhomogeneity) ARS theory was used. In this model the surface-roughness PSD functions calculated from surface-profile data were used, and reasonable values for parameters characterizing the dielectric inhomogeneities were used in an analytic PSD function. This dual-source ARS theory can predict a significantly different angle and wavelength dependence of ARS than that predicted by roughness-only ARS theory. In contrast to ARS predicted by surface roughness alone, it was found that the dual-source theory was able to provide good agreement with measured ARS in angular and wavelength dependence. It is concluded that, for the two beryllium samples studied here, scattering caused by spatial variations in the near-surface dielectric response (variations in reflectance) is a significant and sometimes dominant source of scattering, especially at a 10.6-μm wavelength.

J. M. Elson

Papers

Calculation of the power spectral density from surface profile data

Wavelength and angular dependence of light scattering from beryllium: comparison of theory and experiment