A new look at fundamentals of the photometric light transport and scattering theory. Part 1: One-dimensional pure scattering problems

In the majority of practical cases there exist difficulties with deriving an analytical closed-form solution of the classic radiative transport equation (RTE) in the light transport and scattering theory, which is widely used today in biomedical optics, ocean optics, atmospheric optics, etc. In our opinion, certain problems stem from the fact that the mathematical formulation of main physical processes at scattering in turbid media is not quite accurate. To study the problem in more detail, this paper once again describes and analyzes the photometric transport theory from the ''first phenomenological principles''. We show that this approach assists to clarify the problem in depth, as well as to obtain certain new, accurate and unexpected results. In this part 1 of the article, we consider in detail one-dimensional (1D) pure scattering problems featuring no absorption. We discuss and solve every main typical 1D pure scattering problem using various approaches. It allows us to prove that the scattering coefficient is not so much a real optical property of a turbid medium, but a parameter of the mathematical description of the problem. In the general case, the scattering coefficient depends on both optical properties of the medium and the mathematical approach selected. Therefore, it can vary with different approximations, which can be a source of errors in calculations.