![]() And another question is the rules for recognizing the recorded beam profile. The main question when choosing a set of spatial codes is the range of distortions during propagation in a complexly disturbed environment. Spatial signal-code structures for open optical data transmission channels can be created based on a set of orthogonal spatial field distributions using the own functions of open optical cavities of symmetry various types. The differential method for recording structurally stable profiles of wave beams makes it possible to increase the information capacity of codes set in optical communication systems with space-time modulation of the signal beam. This equation makes it possible to estimate the phase increment pattern for regular and chaotic structures in the absence of intensity zero. The possibility of writing a second-order elliptic differential equation for the wave beam phase with the right-hand side depending only on the intensity distribution is discussed. Distortions of the profile arising from the earlier described deformations of the wave beam (transverse shear, astigmatic effect) are also presented. The profiles of the first and second spatial derivatives for the lowest modes of free space smoothed by a special Ritz filter are analyzed in detail. The cut profile along the time axis allows to set the rate of change of this structure. In the non-stationary case, a profile stack is considered. The described method is equally suitable for the analysis of stationary processes and non-stationary. It is determined through the consistency parameters of the distortion structure and the effective energy intensity of the distortion structure. Based on the analysis of second-rank tensors array constructed for each pixel of the recorded intensity distribution (margin or projection of the Wigner distribution of complex amplitude), quantitative characteristics of the intensity profile deformation are obtained. Application of the developed method is promising for a wide class of study problems of non-stationary spatial structures. It allows constructing the local and averaged over the aperture of the analyzed image, the orientation statistical characteristics and distribution profiles. The tensor of structure is determined based on the first spatial derivatives. Such characteristics are in demand in problems of statistical topography of random and regular fields. ![]() In addition to the tensor of structure based on the first spatial derivatives, it is advisable to determine the structure matrix based on the second spatial derivatives, which details the discrete properties of the intensity profiles set. The tensor of structure matrix method formed for the intensity distribution frame is applicable for both regular and random spatial distributions. It's possible to associate the observed spatial parameters with the meteorological conditions on the path and in the first approximation, restore the main directions of phase modulation in the observation plane. Differential characteristics of the spatial structure make it possible to classify distortions of the beam profile by types of symmetry and direction of deformations. It can be used as a basis for describing the of the initial intensity distribution. The matrix of local orientation values determined on the basis of the first spatial differentials is unique for the image. The characteristic values for such approaches are based on the geometry analysis of constant level curves, directions of steepest descent from a given point on the surface and quadratic combinations describing the deformation of the analyzed surface. The amplitude distribution complex structure of the optical beam profile at the end of a long atmospheric path can be considered in terms typical of surface profile descriptions used in solid state physics or geophysics.
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