Classical photometry of prefractal surfaces

Using the scale invariance of classical photometry, we develop an approach to finding the photometric function of prefractal structures that form a random topography. The photometric function of the prefractal surfaces is found as the general solution of the resulting differential equation in partial derivatives. The function depends on two parameters: the number of hierarchical levels of the prefractal structures and the roughness parameter of the single-level generation. As a limiting case, the approach includes our previous theory that considered fractoids.