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

Area of Science:

• Optics and Photonics
• Materials Science
• Surface Metrology

Background:

• Sinusoidal surfaces are valuable as material standards for calibrating instruments measuring light scattering.
• The power in diffraction peaks of sinusoidal surfaces varies significantly, enabling calibration across orders of magnitude.
• Accurate calibration requires understanding the relationship between surface profiles and scattered light intensity.

Purpose of the Study:

• To investigate the discrepancy between calculated and measured diffraction peak intensities from sinusoidal surfaces.
• To analyze the influence of the illumination window size on the power distribution of scattered light.
• To assess the suitability of sinusoidal surfaces as standards for instrument calibration.

Main Methods:

• Theoretical calculation of diffraction peak power using Bessel functions.
• Analysis of measured or computed angular distributions from surface profiles.
• Modeling the effect of finite illumination area (rectangular window) on diffraction patterns.

Main Results:

• Calculated higher-order diffraction peak power from sinusoidal surfaces is significantly lower than measured or computed values.
• The harmonic content of the surface profile primarily determines measured distributions.
• A large background is introduced by the finite illumination window, obscuring higher-order peaks.
• Rectangular illumination windows result in minima near higher-order diffraction angles.

Conclusions:

• The theoretical model underestimates the power in higher-order diffraction peaks compared to experimental or computed data.
• The finite illumination window significantly affects the observed diffraction pattern, creating background noise.
• Careful consideration of illumination conditions is crucial when using sinusoidal surfaces for instrument calibration.