A New Look at Fundamentals of the Photometric Light Transport and Scattering Theory. Part 1: One-Dimensional Pure Scattering Problems

ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 5

DOI: 10.18698/1812-3368-2017-5-78-94

A NEW LOOK AT FUNDAMENTALS OF THE PHOTOMETRIC LIGHT

TRANSPORT AND SCATTERING THEORY.

PART 1: ONE-DIMENSIONAL PURE SCATTERING PROBLEMS

S. Persheyev

sp95@st-andrews.ac.uk

D.A. Rogatkin

School of Physics and Astronomy, St Andrews University, St Andrews,

The United Kingdom of Great Britain and Northern Ireland

Moscow Regional Research and Clinical Institute named after M.F. Vladimirsky,

Moscow, Russian Federation

Abstract

Keywords

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 pheno-

menological 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 prob-

lems 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 ap-

proximations, which can be a source of errors in calculations

Scattering, absorption, light transport,

radiative transport equation, one-

dimensional problems, pure scatte-

ring, single scattering approximation,

multiple scattering

Received 29.06.2017

Introduction.

The light transport and scattering theory (LT&ST) is widely used today

in biomedical optics, ocean optics, optics of atmosphere, etc. However, it is well-

known; there are difficulties with the analytical and closed-form solution of the classic

radiative transport equation (RTE). In the general case, it does not have the analytical

solution. Only a number of simplified approximations exist which have it. As we have

reported in our previous publications, we think the problem follows from the not

quite correct formulation of main equations in LT&ST for different applications.

In our opinion, for example, there is an error in description of the scattering