chapter 3, Theory of Scintillation: Plane Wave Model

In Part I Scintillation Models from: Laser Beam Scintillation with Applications

Author(s): Larry C. Andrews, Ronald L. Phillips, Cynthia Y. Hopen

Published: 20 July 2001

Chapter DOI: http://dx.doi.org/10.1117/3.412858.ch3

Chapter Page Count: 29 pages

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Front Matter

Part I Scintillation Models
1. Optical Wave Propagation in Random Media: Background Review

2. Modeling Optical Scintillation

3. Theory of Scintillation: Plane Wave Model

4. Theory of Scintillation: Spherical Wave Model

5. Theory of Scintillation: Gaussian-Beam Wave Model

6. Aperture Averaging

Part II Applications
7. Laser Communication Systems

8. Fade Statistics for Lasercom Systems

9. Laser Radar Systems: Scintillation of Return Waves

10. Laser Radar Systems: Imaging through Turbulence

Back Matter

Preview

Chapter Contents

3.1 Introduction
3.2 Zero Inner Scale Model
3.2.1 Effective Kolmogorov Spectrum
3.3 Nonzero Inner Scale Model
3.3.1 Effective Atmospheric Spectrum
3.3.2 Outer-Scale Effects
3.4 Covariance Function of Irradiance
3.4.1 Zero Inner Scale Model
3.4.2 Nonzero Inner Scale Model
3.5 Temporal Spectrum
3.5.1 Zero Inner Scale Model
3.5.2 Nonzero Inner Scale Model
3.6 Gamma-Gamma Distribution
3.6.1 Comparison with Simulation Data
References

Excerpt

3.1 Introduction

Most theoretical treatments of optical wave propagation have concentrated on simple models like an unbounded plane wave or spherical wave. The first optical wave model to be extensively studied was the plane wave, defined as one in which the equiphase surfaces (phase fronts) form parallel planes [1]. In a transverse plane at distance L from the transmitter, this model is described by

where r is a transverse vector, k is the optical wave number, A₀ is the initial amplitude, and φ₀ is the initial phase. Although this model is relatively simple, it provides a great deal of insight into the behavior of more realistic optical wave models.

In this chapter we examine the irradiance fluctuations of a plane wave that has propagated a distance L through optical turbulence. For simplicity, we assume that the index of refraction structure parameter Cn2 is constant, characteristic of a horizontal path. Our greatest emphasis is on the scintillation index, but we also discuss the covariance function of irradiance and related temporal spectrum. Under weak fluctuation theory, the scintillation index can be expressed as [1]