Classical photometry of prefractal surfaces

Area of Science:

• * Photometry and surface analysis
• * Fractal geometry and random topography

Background:

• * Understanding the photometric properties of complex surfaces is crucial for applications in remote sensing and computer graphics.
• * Previous theories often focused on idealized fractals, limiting their applicability to more general prefractal structures with random topographies.

Purpose of the Study:

• * To develop a general method for deriving the photometric function of prefractal surfaces with random topography.
• * To extend existing theories on fractoids to a broader class of prefractal structures.

Main Methods:

• * Utilizing the principle of scale invariance inherent in classical photometry.
• * Formulating and solving a partial differential equation to find the photometric function.
• * Analyzing prefractal structures characterized by hierarchical levels and a roughness parameter.

Main Results:

• * The photometric function is derived as the general solution to the established differential equation.
• * The function's dependence on the number of hierarchical levels and the single-level roughness parameter is identified.
• * The approach is shown to encompass previous theories concerning fractoids as a limiting case.

Conclusions:

• * The developed approach provides a robust framework for analyzing the photometric properties of random prefractal surfaces.
• * This method offers a more generalized understanding of light interaction with complex, naturally occurring topographies.
• * The findings contribute to advancements in modeling and simulating light scattering from rough surfaces.