Slope distribution of a rough surface measured by transmission scattering and polarization

Measurement of roughness based on the Talbot effect in reflection from rough surfaces

In the present work, the Talbot effect of a square grating is analyzed when light is reflected from a rough surface. It is shown theoretically that the scattered light intensity in the Fresnel diffraction limit depends on statistical properties of the rough surface, the angle of incidence of the light, the grating period, and a geometric coefficient, related to the ratio of distance of the rough surface and the observation plane from the grating. At Talbot distances of the grating, the surface height difference function, in terms of multiplication of the Talbot number, the grating period, and the geometric coefficient is the modulation transfer function (MTF) of the scattering in reflection from the rough surface. If the argument of the height difference function is larger than twice the surface correlation length, the height difference function is constant for different spatial frequencies. Therefore, the square wave is reproduced with smaller contrast. The surface roughness can be obtained by measuring the contrast at different incident angles. It is also shown that the contrast measurements in both reflection and transmission, provide the refractive index of transparent samples with a rough surface. In experimental studies, the roughness of three metal standard rough surfaces are determined at different angles of incidence. Also, the refractive index of a sheet glass with a rough surface is obtained. The results are quite consistent.

Determination of the rough interface parameters using the self-imaging effect

In this work, a linear grating is used to project a periodic light intensity distribution on a rough interface, and the near field transmitted light scattering is studied. It is shown theoretically that the intensity in the Fresnel regime depends on statistical properties of the rough interface and the light intensity period. The self-image contrast exponentially depends on the interface height-height correlation function. The correlation is obtained in terms of multiplication of the self-image number and the period of the light intensity distribution. Therefore, the roughness and the correlation length of the interface can be obtained by determining the contrast of the self-images when the light intensity period is smaller than the interface correlation length. For periods longer than twice the correlation length, the contrast measurements only provide the interface roughness. In experimental studies, the roughness of interfaces is determined by square gratings with periods much longer than the correlation lengths. The rough interfaces are prepared by roughening sheet glass by powders of different grit numbers. The results for different gratings and light wavelengths are quite consistent.

Determination of height distribution on a rough interface by measuring the coherently transmitted or reflected light intensity

In this work it is shown theoretically and examined experimentally that the measurement of coherently transmitted or reflected monochromatic light intensity from a randomly rough interface as a function of incident angle provides the height distribution on the interface. It is also shown that the spectrum of coherently transmitted or reflected light from a rough interface is modified and the modified spectrum yields the height distribution. The experimental results obtained by applying both methods, in transmission and reflection, on rough surfaces prepared by roughening the sheet glasses by powders of different grain sizes are quite consistent. In addition, the effect of the surrounding medium's refractive index on the roughness measurement is studied by immersing the samples into liquids of different refractive indices. Also, the application range and limitations of the introduced methods are discussed.

Determination of the correlation between physical measurements of roughness, optical properties, and perception of frosted glass surfaces

Chemical frosting is used as a surface decorating method by many glass package producers. After immersion in an acid frosting bath, glass items present the desired frosted effect. The perception of this particular effect is due to the formation of a microscopic crystalline pattern on the glass surface, which scatters light passing through the glass surface. The chemical composition of the frosting bath influences these properties by modifying the surface roughness, the depth, and the average slopes of the crystalline pattern. Perception of the final aspect can be modified according to the chemical composition of the frosting bath. Different correlations between all these parameters exist and have been quantified.

Polarization of transmission scattering simulated by using a multiple-facets model

A Mueller matrix for scattering by a rough plane surface of a glass hemisphere was simulated by using a micro-facet model. The algorithms are formulated in vector representation in terms of the input and output directions. The single-facet scattering simulation used the results of the Kirchhoff integral for medium rough surfaces with exponential height distribution. Scatterings by two or more facets were also simulated. For a fixed angle between the incident and the detection directions, the transmission scattering and its polarization properties were symmetric when plotted against the off-specular incident angle. The single-facet model generated no depolarization or polarization change. When double-facet scattering was included, polarizations were changed appreciably while depolarization was still very small. Depolarization increased appreciably when scattering by higher orders was included. The simulated results that include all orders of scattering fit excellently to the measured scattering transmittance and its polarization and depolarization.