Sherman Karp

Radiation models using discrete radiator ensembles

In recent literature radiation emitted or reflected from a body or surface has been modeled as equivalent radiation from a collection of individual discrete radiators. This model has application to the analysis of forward and backscatter from rough surfaces, clutter and chaff models for radar, and cavity emissions at optical frequencies. In this paper we investigate radiation using a generalization of the above radiator ensemble. We allow some degree of coupling to exist between individual radiators, and we assume each radiator emits random energy bursts as a Poisson process. Analysis is confined to power spectral densities and first-order statistics of the resulting scalar radiation fieid. The results indicate that the pulsed radiator model can account for many properties of radiation. A by-product of the analysis is a filter model for dispersive channels, applicable to radar design problems. Theoretical results are compared with previously reported experimental results wherever possible. Some consideration is given to a relativistic interpretation of the radiator ensemble.

Progress in Laser Communications

Two major military applications have been heavily investigated over the last 40 years: Free Space Optical Communication (FSOC) and Submarine Laser Communication (SLC). This paper will highlight progress made in these two important applications.

The Optical Scatter Channel and Its Properties

With the introduction of ultraviolet, visible, and infrared technologies in the areas of communications and surveillance, it has become necessary to account for the atmospheric and oceanic influences on such systems—in specific terms, the effects of particulate multiple scattering on optical radiation transfer. This is because the haze, fog, rain, and clouds comprising most of the atmospheric channel, and the yellow substance and small “sea animals” in the marine channel, cause the majority of the degradation suffered by the information-containing signal traversing that channel. Recall from the previous chapter that atmospheric and marine turbulence can generate significant wavefront distortions of a signal when optical paths of 50 meters or more are involved. However, the total angular and spatial spreading which can be experienced by an initially collimated pencil beam rarely exceeds 100 microradians and a meter or two, respectively.(1) Also, coherence distances are still on the order of centimeters (requiring only modest diversity of a coherent receiver), and no experimental evidence of pulse broadening exists, even down to picosecond lengths.(2,3) In contrast, particulate multiple scatter can induce dispersion in angle of arrival the order of tens of degrees, beam spreading in the hundreds of meters, degradation of spatial coherence down to lengths of microns or less, and multipath time spreading in the tens of microseconds.(4) Because of the magnitude of these larger effects, the mutual coherence function approach to channel characterization cannot be universally applied (we will shortly find it to be valid only over a finite range of scattering thicknesses), and additional mathematical techniques must be used to model optical propagation through these individual channels. In this chapter, we shall review the inherent and characterizing properties of the three basic components of the optical scatter channel: the atmosphere, the ocean, and the air/sea interface. A clear understanding of these building blocks must be possessed if one is to model satisfactorily the transfer of optical radiation through their individual and/or combined parts. Chapter 7 will describe how this information has been, and is currently, used to quantify energy propagation through the invididual and combined structures of this channel. Whenever possible, we have compared measured characteristics of the channel and its components with predictions from pertinent analytical or empirically devised models.

Mathematical Models for Energy Propagation in the Optical Scatter Channel

With the basic composition of the optical scatter channel defined in Chapter 6, we can now turn to how this information is used to quantify radiance and irradiance propagation in that medium. Unfortunately, the extensive amount of material currently available on the subject prohibits our being complete and all-inclusive in one chapter of a book. Therefore, we shall limit our discussions to those mathematical approaches and results which have found, and still find, great utility in optical communication systems analysis. We will begin the chapter with a formulation of the mutual coherence function for multiple-forward-scatter media, as derived by Lutomirski.(1) This development will be discussed in terms of its physical implications and also its validity in predicting real-life phenomena. The discussion will then move into a radiative transfer analysis of energy transport in particulate media, and the basic limitations of the closed-formed solutions derived by the small-angle scattering/Huygens-Fresnel approximations will be considered. The conclusion one draws at this point is that the aforementioned techniques can provide insight and answers to optical propagation problems if used properly, but can give misleading results if not. Other mathematical techniques can then be employed if one expects channel characterizations outside the validity range of these closed-form solution sets. Some of the more useful analytical methods of this type will be highlighted and discussed. The result of this discussion will be an in-depth look at two Monte Carlo-based analyses which provide function sets of engineering equations for general atmospheric and marine communication system performance assessments. The next section of this chapter will describe three mathematical techniques which can be applied to energy transfer through the air/sea interface. The final section of this chapter will illustrate how these propagation models can be integrated to yield a total picture of radiation transport in the optical scatter channel. Throughout the chapter, comparisons between model predictions and experimental data will be made whenever possible.

The Fiber-Optic Channel

Perhaps the most important optical communication channel is the optical fiber. The fiber is a thin “pipe” of glass through which one can shine an optical beam to transmit optical energy from one point to another. The fiber is the optical equivalent of a coaxial cable or waveguide commonly used for microwave transmission. Decades ago attempts to communicate by fiber over long distances were hampered by the severe attenuation of this channel. However, in the early 1970s the demonstration of a fiber with 20 dB/km of loss indicated the potential of this link, coupling the high data rates of the optical carriers with the small spatial occupancy of the fiber. Fiber losses have now been reduced to about 0.1 dB/km, and the technological development of solid-state sources and detectors has further advanced the fiber communication channel. In this chapter we attempt to outline the basic communication characteristics of this type of channel.

Coherence Theory and Random Channels

In this chapter we will introduce the concept of field coherence, which is necessary to describe fully the propagation of electromagnetic fields in both free space and nonvacuous channels. In particular, the ideas of temporal and spatial coherence will be presented together with the concept of the mutual coherence function. We will derive the equations which govern the propagation of both the field and the mutual coherence function in free space. In doing so, we will quantify the notions of monochromaticity and narrowbandedness. Finally, we will show how the presence of both nonvacuous channels and receiver optics affects the quantities defined above. Since the concepts discussed in this chapter do not relate strongly to problems in fiber transmission, those readers primarily interested in fibers can skip this chapter and proceed to Chapter 3. The concepts in this chapter lay the groundwork for subsequent introduction of generalized radiometry, which describes power flow for partially coherent fields. However, because of the specialized nature of this topic, it will be pursued in Appendix A.

The Turbulence Channel

In Chapter 4 we examined the guided optical channel or fiber link. In this chapter we consider the turbulent atmosphere as an unguided optical channel. It is well known that turbulence-induced random fluctuations in the atmosphere’s temperature generate corresponding random irregularities in the index of refraction. Upon passing through these irregularities, the wavefronts associated with an optical beam become distorted, the magnitude of the distortions depending on the strength of the turbulence and the length of the atmospheric optical path. Among the effects which are attributable to wavefront distortion and which can seriously degrade the performance of an optical communication system are (1) spreading of the beam beyond that normally caused by diffraction, (2) scintillation of the received intensity, (3) a decrease in the spatial and temporal coherence, and (4) wander of the beam from position to position. Quantification of these effects requires a theoretical understanding of the relationship between the properties of the medium and the transmitted optical radiation.