Lin-xiang Cao, Theodore V. Vorburger, A. George Lieberman, and Thomas R. Lettieri, "Light-scattering measurement of the rms slopes of rough surfaces," Appl. Opt. 30, 3221-3227 (1991)
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.
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For all data, θi = −14° and −86° ≤ ϕs ≤ 86°. The Γ values are given in radians.
The point-to-point spacing in the Δq calculations [Eq. 1(c)] was ≈1.125 μm (three times the data-point spacing of 0.375 μm), except for nickel (3/100) and brass (1/800). For the nickel (3/100) specimen, both the Δq spacing and the data-point spacing were 0.95 μm; for brass (1/800), they were both 1.9 μm.
Γ8, Γ4, Γ2 and Γ1 indicate that the sampling increments are 8°, 4°, 2°, and 1°, respectively.
Nominal ratio of Ra and the wavelength of the sinusoidal surface.
These two specimens were measured with an instrument having a stylus tip width of 4 μm.
In order of increasing Δq; the Γ values are given in radians.
The angular sampling increment is 2°.
The point-to-point spacing in the Δq measurements was 1.0 μm (five times the data-point spacing of 0.2 μm).
Table III
Values of Γ (In Radians) for Different Values of θi
For all data, θi = −14° and −86° ≤ ϕs ≤ 86°. The Γ values are given in radians.
The point-to-point spacing in the Δq calculations [Eq. 1(c)] was ≈1.125 μm (three times the data-point spacing of 0.375 μm), except for nickel (3/100) and brass (1/800). For the nickel (3/100) specimen, both the Δq spacing and the data-point spacing were 0.95 μm; for brass (1/800), they were both 1.9 μm.
Γ8, Γ4, Γ2 and Γ1 indicate that the sampling increments are 8°, 4°, 2°, and 1°, respectively.
Nominal ratio of Ra and the wavelength of the sinusoidal surface.
These two specimens were measured with an instrument having a stylus tip width of 4 μm.
In order of increasing Δq; the Γ values are given in radians.
The angular sampling increment is 2°.
The point-to-point spacing in the Δq measurements was 1.0 μm (five times the data-point spacing of 0.2 μm).
Table III
Values of Γ (In Radians) for Different Values of θi