chapter 3, Optical Turbulence in the Atmosphere

In Part 1 Basic Theory from: Laser Beam Propagation through Random Media, Second

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

Published: 16 September 2005

Chapter DOI: http://dx.doi.org/10.1117/3.626196.ch3

Chapter Page Count: 26 pages

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Front Matter

Part 1 Basic Theory
1. Prologue

2. Random Processes and Random Fields

3. Optical Turbulence in the Atmosphere

4. Free-Space Propagation of Gaussian-Beam Waves

5. Classical Theory for Propagation Through Random Media

6. Second-Order Statistics: Weak Fluctuation Theory

7. Second-Order Statistics: Strong Fluctuation Theory

8. Fourth-Order Statistics: Weak Fluctuation Theory

9. Fourth-Order Statistics: Strong Fluctuation Theory

10. Propagation Through Complex Paraxial ABCD Optical Systems

Part II Applications
11. Free Space Optical Communication Systems

12. Laser Satellite Communication Systems

13. Double-Passage Problems: Laser Radar Systems

14. Imaging Systems Analysis

Part III Related Topics
15. Propagation Through Random Phase Screens

16. Partially Coherent Beams

17. Other Beam Shapes

18. Pulse Propagation

I. Special Functions

II. Integral Table

III. Tables of Beam Statistics

Back Matter

Preview

Chapter Contents

3.1 Introduction
3.2 Kolmogorov Theory of Turbulence
3.3 Power Spectrum Models for Refractive-Index Fluctuations
3.4 Atmospheric Temporal Statistics
3.5 Summary and Discussion
3.6 Worked Examples
Problems
References

Excerpt

Overview: In this chapter we present a brief treatment of atmospheric turbulence as it pertains to velocity fluctuations (classical turbulence), temperature fluctuations, and index of refraction fluctuations, the latter often referred to as optical turbulence. The primary objective here is to introduce various models of the power spectrum for optical turbulence that are commonly used in optical wave propagation studies. These models include the Kolmogorov power-law spectrum, Tatarskii spectrum (with inner scale parameter), von Kármán spectrum (with both inner scale and outer scale parameters), and the modified atmospheric spectrum (with both inner scale and outer scale parameters). However, only the modified atmospheric spectrum features a high wave number “bump” just prior to the onset of the dissipation range that has been observed in temperature data. It has been shown that the presence of this spectral bump in the temperature spectrum induces a corresponding bump in the refractive-index spectrum that can have important consequences on various aspects of optical wave propagation through the atmosphere, particularly in regards to scintillation.

In the last section of the chapter we discuss the notion of temporal statistics for the atmosphere. Here we rely on Taylor's hypothesis of frozen turbulence to convert spatial statistics to temporal statistics based on the transverse wind speed. We use this same idea in later chapters to convert spatial statistics concerning beam wave propagation to corresponding temporal statistics. In this latter case, the shape of the phase front radius of curvature of the optical wave must also be taken into account.

http://dx.doi.org/10.1117/3.626196.ch3

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