Introduction

In Chapter 10, we discussed the effects on high-data-rate FSOC systems from atmospheric turbulence, which are dominated by scintillation / channel fading and beam wander, how they are modeled and how they are mitigated to yield high communications link / network performance. From some of the figures there, one can see channel dynamics on a very fast scale. When clouds insert themselves in the link, we suggested that RF communications (a hybrid system) could provide a means for keeping the link connected at a reasonably high, but much lower, data rate. This works well in the atmosphere in those climates where clouds are infrequent or sparse. This strategy does not work in the optical scatter channel where particulate absorption and scattering significantly degrade the incoming signal to the point that the original diffraction-limited beam becomes lost in the system noise floor. Alternate strategies must be employed to facilitate high communications link / network availability because of the significant degradation of the original signal by the atmospheric and maritime optical scatter channels. The signal structures that result from each channel are quite different from each other, as well as significantly different from the turbulence channel. Kennedy was one of the first to recognize that these significant differences in structure from the former relative to the latter could not be easily mitigated; he suggested that optical system designers exploit their new structures in order to close the communications link as typical mitigation techniques were useless in the diffusive scattering regime that defines high link availability [1]. Chapters 5 and 9 showed that it could be used for target imaging. This chapter will discuss how this approach can be used for communications in the optical scattering channel, highlighting the models and techniques used by today’s researchers and engineers.

Optical scatter channel models

Chapter 5 introduced the optical scatter channel by describing Mie scattering and its effect on optical signals. This introduced the inherent properties of the optical channel. In this section, we will expand this discussion, focusing on the detailed effects on laser communications created by the atmospheric and maritime scatter channels, and their modeling. Each has its own unique characteristics.

When we decided to write this book about the design of electro-optic systems, we agreed to make it as fundamental as possible. To do this in detail would most probably make the book unwieldy. Rather, we will try to motivate all aspects of the design from fundamental principles, stating the important results, and leaving the derivations to references. We will take as our starting point the first two Laws of Thermodynamics [1]. The Three Laws of Thermodynamics are the basic foundation of our understanding of how the Universe works. Everything, no matter how large or small, is subject to the Three Laws. The Laws of Thermodynamics dictate the specifics for the movement of heat and work, both natural and man-made. The First Law of Thermodynamics is a statement of the conservation of energy – the Second Law is a statement about the nature of that conservation – and the Third Law is a statement about reaching Absolute Zero (0° K). These laws and Maxwell’s equations were developed in the nineteenth century, and are the foundation upon which twentieth-century physics was founded.

Preface

The authors have been active participants in the area of electro-optic systems for over four decades, covering the introduction of laser systems and low loss optical fibers and the institutionalizing of photonic systems into everyday life. Yet for all the literature that exists, and all the work that has been accomplished, we felt that no single book existed that integrated the entire field of electro-optics, reaching back to all the fundamental building blocks and providing enough examples to be useful to practicing engineers. After much discussion and a slow start, we decided first to reference as much material as possible, bringing forth only the highlights necessary to guide researchers in the field. Then we decided to minimize mathematical developments by relegating them, as much as possible, to explanatory examples. What has evolved in our development is a clear statement of the duality of time and space in electro-optic systems. This had been touched upon in our earlier work, but has been brought forth clearly in this book in the duality of modulation index in time, and contrast in space. In doing so, and in other areas, we feel that this book contains new material with regard to the processing of spatial images which have propagated through deleterious channels. We feel that this book contains much new material in the areas of communications and imaging through deleterious channels.

In Chapter 1, we reach back to the true foundations of modern physics, the establishment of the first two laws of thermodynamics. While taken for granted, it is the first law that explains why we can see stars at the edge of the universe, and governs the radiant properties of propagating systems. The second law and the insight of Claude Shannon have created the modern field of Information Theory. Using his fundamental definitions of channel capacity we are able to establish the duality of time and space in electro-optics. This requires one basic mathematical development that is included in Appendix A, and is developed in Chapters 3 and 4.

Introduction

This chapter discusses some of the key aspects of the signal modulation and coding schemes used in FOC and FSOC systems today. Most notably, we will review the use of return-to-zero (RZ) and non-return-to-zero (NRZ) in coding the information streams and see their effect on systems performance, as well as receiver sensitivity.

Modern signal modulation schemes

Let us begin with some definitions.

Return-to-zero (RZ)

RZ describes a signal modulation technique where the signal drops (returns) to zero between each incoming pulse. The signal is said to be “self-clocking”. This means that a separate clock signal does not need to be sent alongside the information signal to synchronize the data stream. The penalty is the system uses twice the bandwidth to achieve the same data-rate as compared to non-return-to-zero format (see next definition).

Although any RZ scheme contains a provision for synchronization, it still has a DC component, resulting in “baseline wander” during long strings of “0” or “1” bits, just like the line code non-return-to-zero. This wander is also known as a “DC droop”, resulting from the AC coupling of such signals

Introduction

Since lasers were invented in 1964, optical communications has been investigated for both military and commercial application because of its wavelength and spectrum availability advantages over radio frequency (RF) communications. Unfortunately, only fiber optic communications (FOC) systems have achieved wide implementation since then because of their ability to maximize power transfer from point to point while also minimizing negative channel effects. Recently, free-space optical communications (FSOC) has reemerged after three decades of dormancy due to the availability of new FOC technologies to the FSOC community, such as low-cost sensitive receivers and more power-efficient laser sources. Applications of FSOC, however, have been limited to local area (short range) networking because optical systems have been unable to effectively compensate for two atmospheric phenomena; cloud obscuration and atmospheric turbulence. Making a hybrid FSOC/RF communications system will compensate for cloud obscuration by using the RF capability when “clouds get in the way”. For this chapter, we will discuss how to mitigate the atmospheric turbulence for incoherent communications systems. In particular, we will discuss a new statistical link budget approach for characterizing FSOC link performance, and compare experimental results with statistical predictions. We also will comment at the end of the chapter on progress in coherent communications through turbulence. For those readers interested in science and modeling of laser propagation through atmospheric turbulence, we refer them to several excellent books on the topics for the details [1–5].

When a digital communications system experiences a very noisy/fading channel, the electrical signal-to-noise ratio may never be strong enough to obtain a low probability of detection error. Shannon proved in 1948 that a coding scheme could exist to provide error-free communications under those conditions. In particular, he showed it was possible to achieve reliable communications, i.e., error-free communications, over an unreliable, i.e., noisy, discrete memory-less channel (DMC), using block codes at a rate less than the channel capacity if the number of letters per code word, and consequently, the number of code words, are made arbitrarily large [1]. This result motivated a lot of research to find the optimum code, i.e., one that minimizes the number of letters and code words, to create reliable communications. The various approaches that have emerged from this research form a class of coding best known as forward error correction (FEC) coding (also called channel coding) [2–4]. Richard Hamming is credited with pioneering this field in the 1940s and invented the first FEC code, the Hamming (7,4) code, in 1950. He, and most others, basically has the originator systematically add generated redundant data to its message. These redundant data allows the receiver to detect and correct a limited number of errors occurring anywhere in the message stream without that person requesting the originator to resend part, or all, of the original message. In other words, the FEC provides a very effective means to correct errors without needing a “reverse channel” to request retransmission of data. This advantage is at the cost of a higher channel data rate if one wants to keep the information data rate the same. These techniques are typically applied in communications systems where retransmissions are relatively costly, or impossible, such as in mobile ad hoc networking when broadcasting to multiple receivers (multicast) [5–7], HF communications and optical communications. For the interested reader, Zhu and Kahn provide a detailed summary of FEC coding applied to the turbulence channel [8, Ch. 7, pp. 303–346].

Lidar (light detection and ranging) is an optical remote sensing technology that measures properties of scattered and reflected light to find range and/or other information about a distant target. The common method to determine distance to an object or surface is to use laser pulses, although as in radar it is possible to use more complex forms of modulation. Also as in radar technology, which uses radio waves instead of light, the range to an object is determined by measuring the two-way time delay between transmission of a pulse and detection of the reflected signal. In the military, the acronym Ladar (laser detection and ranging) is often used. Lidar has also expanded its utility to the detection of constituents of the atmosphere. It is not the intention of this book to expand on all the applications for which this technology has been applied, they are too numerous. Rather we will try to group applications by the technology needed. Thus, for example, a laser speed gun used for traffic monitoring uses the same basic technology as those used for surveying and mapping; i.e., bursts of nanosecond pulses. The wavelengths may vary due to eye safety requirements (>1.5 μm), and the pulse energies may vary because of the distances involved, but both use time of flight measurements. Also the scanning requirements can vary because of the areas to be covered, and the scanning equipment that is available can vary because of the pulse energies involved. For high-energy pulses reflective mirrors are needed, whereas for low-energy pulses electronic scanning with a CCD or CMOS shutter can be used. Most applications use incoherent optics. In some cases, where the additional cost warrants it, coherent (optical heterodyne) detection is used. Such an example is the measurement of clear air turbulence where coherent 10 μm laser ranging systems have been employed. Another class of incoherent applications use backscatter signatures to investigate chemical constituents, primarily in the atmosphere. Such systems use Raman, Brillouin, Rayleigh, and Mie scattering, as well as various types of fluorescence. As we discussed in Chapter 5, Mie theory covers most particulate scattering, ranging from the Rayleigh range ~1/λ4 for smaller particles (molecules) to the larger particles (aerosols). Raman and Brillouin scattering both induce wavelength shifts, requiring multiple wavelength generation and discrimination. The selection of interference filters, prisms, gratings or spectrascopic machines is determined by the resolution and costs associated with the specific application.

This paper serves as a survey of enclosure-type methods used to determine the obstacles or inclusions embedded in the background medium from the near-field measurements of propagating waves. A type of complex geometric optics waves that exhibits exponential decay with distance from some critical level surfaces (hyperplanes, spheres or other types of level sets of phase functions) are sent to probe the medium. One can easily manipulate the speed of decay such that the waves can only detect the material feature that is close enough to the level surfaces. As a result of sending such waves with level surfaces moving along each direction, one should be able to pick out those that enclose the inclusion.

Let (M, g) be a compact oriented Riemannian manifold with smooth boundary, and let SM = {(x, v) ∈ TM : |v| =1} be the unit tangent bundle with canonical projection π : SM → M. The geodesics going from ∂M into M can be parametrized by the set ∂+(SM) = {(x, v) 2 SM : x ∈ ∂M, (u, v) ≤ 0}, where is the outer unit normal vector to ∂M. For any (x, v) ∈ SM we let t →γ(t, x, v) be the geodesic starting from x in direction v. We assume that (M, g) is nontrapping, which means that the time τ( x; v) when the geodesic γ(t, x, v) exits M is finite for each (x, v) ∈ SM. The scattering relation