Coherence solution for bidirectional reflectance distributions of surfaces with wavelength-scale statistics

Area of Science:

• Optics and Photonics
• Surface Science
• Electromagnetism

Background:

• Understanding light interaction with rough surfaces is crucial for remote sensing and material science.
• Existing models for bidirectional reflectance distribution function (BRDF) have limitations for surfaces with roughness comparable to illumination wavelengths.

Purpose of the Study:

• To derive a general scalar bidirectional reflectance distribution function (BRDF) applicable to conducting surfaces with roughness comparable to the illumination wavelength.
• To develop a model that smoothly interpolates between linear and parabolic approximations for surface autocorrelation functions.

Main Methods:

• Utilizing coherence theory and assuming a random reflective phase screen.
• Applying an expansion valid for large effective roughness.
• Employing a general quadratic expansion of the two-dimensional isotropic surface autocorrelation function.

Main Results:

• A general BRDF solution is derived, comprising incoherent and nonspecular coherent components.
• Representative Cauchy and Gaussian BRDF solutions are obtained as special cases.
• The derived solution shows good agreement with experimental bistatic BRDF data from a machined aluminum surface.

Conclusions:

• The general quadratic autocorrelation expansion provides a versatile BRDF solution.
• The model accurately describes light scattering from rough surfaces across various geometries and parameters.
• This work offers a more comprehensive understanding of surface reflectance properties.