Boundary Conditions for Algebraic Solution of Few View Fiber-Optical Tomographic Problem

General mathematical definition of two layouts of the fiber-optical measuring lines on distributed fiber-optical measuring network in three directions with diagonal lines removal and zigzag method are given. The results on advantages of new layouts as opposed to traditional are presented. The development of distributed fiber-optical measuring networks based on extended interferometric-type sensing elements for synograms formation of external physical fields is substantiated. The applicability of few view fiber-optical tomography for solving problems of distributed fields monitoring on extended perimeters has been proven. The description of useful signal allocation from the general flow of incoming data, composition and features of interference and noise is given. The boundary conditions for operation of such monitoring system are presented in terms of external conditions, criteria for considered fiber-optical interferometric sensing elements and the signal-to-noise ratio. The results of modeling for two extreme cases of considered external physical influences on a distributed measuring network are presented. The possibilities of isolating and processing useful signals that have values almost at the noise level, as well as the operation of the monitoring system with low noise level, are demonstrated. The purpose of this work is mathematically justification of two new layouts of fiber-optical measuring lines for transition to tomographic implementation of security system for extended areas with hidden fiber-optical interferometric sensitive elements, to describe the boundary conditions of physical fields monitoring system.