Optical wave propagation through random media is a fairly mature subject area, having been studied extensively since the 1950s. Consequently, a number of research monographs and textbooks on optical wave propagation have emerged over the years, including Laser Beam Propagation through Random Media, by two of the current authors (Andrews and Phillips). Thus far, the general theory is well developed for weak fluctuation regimes using the Rytov methodâi.e., tractable expressions have been derived for most of the statistical quantities of interest, including those for a simple Gaussian-beam wave. Theory for strong fluctuations has also produced tractable results for certain second-order field statistics, based on the extended Huygens-Fresnel principle, the parabolic equation method, or other methods. Still, there are problems of great interest where adequate theory and useful analytic expressions have not evolved in a satisfactory way. This is the case, for example, for optical scintillationâa fourth-order field statistic that describes the irradiance fluctuations of an optical wave. Optical scintillation is considered one of the most crucial atmospheric effects that must be fully understood because it ultimately determines the performance limitation of an optical system.
In most applications the irradiance fluctuations usually range from weak fluctuations (generally associated with shorter path lengths) up to the point where scintillation attains its peak values, the so-called focusing regime. Because of the potential for large values of scintillation, the focusing regime can be considered the most hostile to optical systems; unfortunately, the rigorously developed scintillation theory is not applicable in this regime. Applications that involve very long propagation paths may cause the irradiance fluctuations to extend beyond the focusing regime into the saturation regime where scintillation begins to decrease toward a limiting value of unity. Asymptotic expressions (including inner scale effects) have been derived for the saturation regime, but recent findings show that these results do not compare well with either experimental or simulation data.
The purpose of this book on laser beam scintillation is twofoldâfirst, to present a tractable theory of optical scintillation in the atmosphere that is applicable under all irradiance fluctuation conditions, and second, to investigate the impact of optical scintillation on system performance in the application areas of free-space laser communication (i.e., lasercom) and laser radar. Renewed interest in laser communications, laser radar, and other application areas involving beam wave propagation through atmospheric turbulence has provided the impetus in recent years for developing several new and useful analytic models of scintillation behavior that extend from weak-to-strong irradiance fluctuations. This book is an attempt to connect these new models with other well-known theoretical expressions, and with experimental and simulation data. Although the new models arise from a heuristic theory of scintillation, the theory is based on sound principles of physics embraced over the years by many researchers. Moreover, the ensuing analytic scintillation models are simple and can be used for most propagation circumstances. Perhaps one of the more interesting aspects of this theory is the fact that it predicts significant effects from the presence of a finite outer scale under moderate-to-strong irradiance fluctuations, causing a steeper drop in scintillation beyond the focusing regime than that predicted by the conventional asymptotic theory. Outer scale effects on scintillation are contrary to traditional beliefs that are fostered primarily by weak fluctuation theories. Where possible, we make quantitative and qualitative comparisons of scintillation results with published experimental and simulation data in order to lend support to the scintillation models developed here.
We have broadly divided the book into two partsâbackground and general scintillation models are developed in Part I (Chapters 1â6) and applications of optical wave propagation are discussed in Part II (Chapters 7â10). The intended audience for this text includes practicing engineers and scientists who are interested in a sound understanding of propagation phenomena and the role of scintillation on optical system behavior. In that regard the material contained within should aid design engineers in identifying some of the limitations on system performance imposed by the atmosphere.
In Chapter 1 we provide a brief review of basic optical wave propagation issues and provide many well-known theoretical results, most of which are based on weak fluctuation theory. Derivations of the analytic results are generally not given in this first chapter, but appropriate references are cited for more detailed discussions and derivations. Chapter 2 presents the physical concepts upon which the heuristic theory of scintillation is based. Specifically, we introduce the modified Rytov theory which invokes the premise that, within the distribution of turbulent scale sizes (inhomogeneities) in the atmosphere, those with dimensions between the spatial coherence radius and the scattering disk of the optical wave do not contribute significantly to scintillation in moderate-to-strong fluctuation regimes. Therefore, to eliminate such scale size effects from the analysis, we formally introduce appropriate filter functions into the spatial power spectrum of refractive-index fluctuations. Current probability distribution models proposed for optical wave propagation are also reviewed in this second chapter. A systematic development of the heuristic theory is then presented in Chapters 3 through 5 for infinite plane waves, spherical waves, and Gaussian-beam waves, respectively. Because of their inherent simplicity over Gaussian-beam waves, we use the plane wave and spherical wave developments in Chapters 3 and 4 as âstepping stonesâ to the more useful results in Chapter 5 concerning Gaussian-beam waves. Our analysis in all cases leads to tractable models for large-scale and small-scale scintillations, based only on knowledge of the atmospheric refractive-index structure parameter , propagation path length L, inner scale of turbulence , and outer scale of turbulence , in addition to various beam characteristics like wavelength, beam spot size, and phase front radius of curvature. Each type of optical wave leads to different cutoff spatial frequencies (or wave number) for the large-scale and small-scale filters for the turbulent eddy cell distribution. The scintillation theory is then extended in Chapter 6 to large aperture receiving systems that reduce the scintillation through a process known as aperture averaging.
Part II on applications starts with Chapter 7 and a review of optical communication systems, analyzing the distinctions between direct detection and coherent detection receiving systems. In particular, we include an analysis of scintillation effects on system performance in regards to signal-to-noise ratio (SNR) and bit error rate (BER). Mitigating techniques for optical scintillation are discussed in terms of spatial diversity architectures. The treatment of optical communication systems is followed in Chapter 8 by an analysis of fade statistics associated with various optical channels. The optical channels of interest involve line-of-sight terrestrial links as well as uplink/downlink channels for satellite communication. Fade probabilities predicted by both the gamma-gamma distribution and lognormal distribution are presented and compared for these channels. We consider the gamma-gamma distribution a general irradiance model for both weak and strong fluctuations.
In Chapter 9, the double-pass propagation phenomenon associated with laser radar systems is analyzed primarily in terms of scintillation statistics under general conditions of irradiance fluctuations. The increase in mean irradiance along the optical axis of a monostatic system, often referred to as the enhanced backscatter effect, is also discussed. Target models examined in this analysis are a small unresolved target (also called a âpoint targetâ) and a finite diffuse target. Models for threshold detection are presented, and experimental data collected for an eight-element equal-gain coherent detection array are compared with the double-pass theoretical models developed here. Lastly, in Chapter 10 we examine some of the impact of scintillation on incoherent imaging systems. Linear system theory is briefly reviewed for both coherent and incoherent systems, the latter presented in the context of a laser imaging radar. We end this chapter with a discussion of the role of optical scintillation and target speckle on performance characteristics like target resolution and single pixel signal-to-noise ratio.
Finally, we wish to extend our appreciation to M. Ammar Al-Habash, who participated as a coauthor on several key papers providing the mathematical foundation for this textbook. His physical insights and useful suggestions were most helpful to us during many long discussions at the blackboard.
Larry C. Andrews
Ronald L. Phillips
Cynthia Y. Hopen
© 2001 Society of Photo-Optical Instrumentation Engineers