# Preface

This book is intended for any scientist, practical engineer, and designer who is concerned with the operation and service of optical wireless (atmospheric) communication links, laser beam systems, and LIDAR applications. It can be useful for graduate and postgraduate students who study such topics in courses related to the operation and service of atmospheric communication links, lasers, and LIDAR applications in atmospheric optical communications.

It briefly examines the fundamentals of the atmosphere, its structure, and the content, including the effects of atmospheric turbulence and different kinds of hydrometeors, such as aerosols, rain, clouds, and snow, on optical wave propagation in the atmospheric links. The main task of this book is to explain these effects deeply for each specific situation occurring in the irregular atmosphere and for specific natural phenomena accompanying the corresponding features (e.g., t urbulences and hydrometeors) that fully affect the propagation of optical rays and laser beams through the atmosphere. The book also emphasizes how to use LIDAR to investigate atmospheric phenomena and predict primary parameters of the irregular turbulent atmosphere, and to suggest what kinds of optical devices can be operated in different atmospheric situations to minimize the deleterious effects of natural atmospheric phenomena. Finally, such investigations allow prediction of imaging of various phenomena via solution of inverse problems related to irregular atmospheric communication channel.

Generally speaking, the book introduces the reader of any scientific level to the main relevant topics of optical wave propagation in the irregular turbulent atmosphere and their relations to laser beam and LIDAR applications, both for communications and for optical location.

The organization of the book is as follows. Chapter 1 illuminates the fundamental aspects of the atmosphere as an inhomogeneous gaseous structure and briefly describes the main parameters of the atmosphere. The content of the atmosphere is presented briefly to reflect on the problems. Particularly, the structures of aerosols and their dimensions, concentration, and the spatial distribution of aerosol sizes, their spectral extinction, and altitude localization are briefly presented in the chapter. Then, the existence of various water and ice particles in the inhomogeneous atmosphere, called hydrometeors, such as rain and clouds, their

Vii spatial and altitudinal distribution, and size distribution and their effects on optical wave propagation are briefly discussed in this chapter. Finally, the atmospheric turbulent structures caused by the temperature and humidity fluctuations combined with turbulent mixing by wind and convection-induced random changes in the air density of the atmosphere, as an irregular gaseous medium, is briefly discussed in this chapter.

In Chapter 2, a general presentation of optical waves, as a part of a wide electromagnetic waveband spectrum, is done. Fundamentals of optical wave propagation based on deterministic approach of Maxwell equation in the time-harmonic and phasors forms and the propagation of optical waves in free space and through the intersection between two material media are briefly presented based on the deterministic presentation of wave equations. Then, the subject of optical wave propagation, through the irregular atmosphere as a random medium is discussed briefly based on the methods of statistical physics by introducing the main random equations and functions that describe stochastic processes in the random medium. Finally, we describe the main random equations, based on Feynman’s diagram theory, via the expansion of Green’s functions.

In Chapter 3, the results of long-term experimental studies of properties of atmospheric turbulence in the anisotropic boundary layer are stated. It is shown that the correct assignment of turbulent characteristics of the atmosphere is an important premise for the exact forecast of the results of distribution of optical radiation in the atmosphere. It is established that the similarity theory of turbulent flows can be extended to any anisotropic boundary layer. With the use of semiempirical hypotheses of the turbulence theory, it is shown theoretically and experimentally that any anisotropic boundary layer can be considered locally weakly anisotropic, in which the weakly anisotropic similarity theory of Monin—Obukhov is applied locally (in some vicinity of each point in the layer). It is established that at the known characteristic scales of temperature and velocity, the anisotropic boundary layer can be replaced with the isotropic layer. It provides an opportunity to use the optical models of turbulence developed for the isotropic boundary layer.

Processes of origination and disintegration of the Benard’s cell in air are experimentally studied. It is established that disintegration of the Benard’s cell is realized according to Feigenbaum’s scenario. It is shown in the chapter that the turbulence resulting from the disintegration of Benard’s cell meets all the criteria characterizing the appearance of chaos in typical dynamic systems. We define the coherent structure as the compact formation including the long-living space hydrodynamic vortex cell (resulting from the long action of thermodynamic gradients) and products of its discrete coherent cascade disintegration.

It is shown in this chapter that the known processes of transition of laminar flows in turbulent (Rayleigh—Benard convection, the flow fluid around obstacles, etc.) can be considered as coherent structures (or the sums of such structures). In this case, the real atmospheric turbulence can be considered as an incoherent mix of different coherent structures with incommensurable frequencies of the main energy vortices.

Chapter 4 describes the most typical situations occurring in the irregular turbulent atmosphere, where nonlinear optical effects during laser radiation propagation should be taken into account. The stimulated Raman scattering (SRS) effect in airborne liquid droplets, as typical hydrometeors, is considered, which is connected with the excitation and amplification of Stokes waves in the whispering gallery zones in cavity droplets. Equations for the SRS excitation threshold in microparticles are given. The most attention is paid to the pump depletion case. The threshold conditions are found for the incident light intensity resulted in steady-state generation of Stokes radiation of a preset strength. The computational framework of light field intensity for thermal nonlinear effects, where the medium is heated due to the light energy dissipation or kinetically cooled, is presented here. The corresponding calculations are carried out on the basis of original algorithms based on the radiation transfer equation. The results presented in the chapter, which are based on this equation, allow to calculate the wide-aperture laser beams, which can be strongly distorted in the region of geometric shadow of a beam. The calculations of high-power laser radiation propagation along the far stratospheric paths under the SRS effect are also described in this chapter. Additionally, the diffraction effect on the nonlinear distortions of wide-aperture laser beams is discussed. Special attention is paid to the pump depletion effect under light field transformation into the Stokes components.

In Chapter 5, a brief historic insight into the development of femtosecond LIDAR technology and femtosecond lasers, as well as perspectives on the application of white-light LIDAR and fiber optic devices, is provided. In addition, this chapter describes the main mechanisms of generation of supercontinuum radiation in optic fiber and in atmospheric air. Most attention in this chapter is paid to the LIDAR’s equation for the problems of atmospheric sensing by ultrashort (femtosecond) pulses with allowance made for the formation of conical emission and the use of supercontinuum radiation as a main effect for the study of gas—aerosol composition of the atmosphere. Here, we provide the basic equations and describe the Monte Carlo simulation of transport of conical broadband emission radiation in the atmosphere. We prove the proposed approach by introducing some numerical and field experiments aimed at the evaluation of possibilities of applying white-light LIDAR for the determination of the gas—aerosol composition of the atmosphere as well as on the development of the solution of inverse problems. Particularly, the possibilities of water vapor sensing with application of LIDAR based on femtosecond sources of radiation is analyzed.

Finally, we analyze the possibility to utilize the white-light LIDAR for aerosol sensing and present an iterative method for the solution of LIDAR’s equation to determine the optical interaction coefficients, as well as the microphysical characteristics of clouds based on methods of neural networks and genetic algorithms. The conducted LIDAR experiment on the study of microphysical characteristics of artificial aerosol at short paths is described finally, and possibilities of reconstructing the microphysical characteristics of thin mists with the use of white-light LIDAR are evaluated and examined.

Chapter 6 introduces the development of modern theory of vision in scattering media. It reflects the mechanisms of imaging and special features of influencing scattering media on the quality of image of objects, for example, problems of correction of hyperspectral satellite images for the distorting effect of the atmosphere. It is shown that despite the fact that until recently there are number of general theoretical problems demanding unambiguous interpretation, the present framework is devoted exactly to this subject. The main problems are formulated here via the possibility to determine the optical transfer function (pulse response, point spread function, or influence function) of a scattering medium or an imaging channel in the scattering medium, or via the possibility to determine the general transfer properties inherent in a concrete scattering medium (by analogy to its optical characteristics) that can subsequently be used for imaging of objects with arbitrary optical properties and any characteristics. In this chapter, we illuminate these problems and present the corresponding models giving comprehensive answers to the imaginary problems that could take place in the irregular atmosphere. The chapter presents an additional problem that arises due to the fact that the pulsed response or the point spread function (PSF) used in vision theory is not an image of a point object, as in the theory of optical systems (though in the literature devoted to vision theory they are sometimes identified). Having solved this problem, we simultaneously answer the question on how many optical transfer functions or PSFs are required to be determined in order to restore or filter out wide-angle images of objects observed through the scattering media. The answers to these questions and problems of constructing the PSF connected with them for spherical models of the system atmosphere—Earth’s surface—are the main topics of this chapter.

We can emphasize that this book is a synthesis of different backgrounds in order to present a broad and unified approach to the propagation of optical waves and laser beams in various scenarios occurring in the irregular ionosphere, consisting of turbulences, aerosols, and hydrometeors, with applications to LIDAR utilization in direct problems (communication) and in inverse problems (imaging of objects and location), based on novel technologies and numerical frameworks that have been recently proved experimentally.