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Chapter 2:
Effects of Turbulence on a Wavefront
The earth's atmosphere has an index of refraction that varies with both temperature and pressure. The air is also constantly mixed by winds that change in speed and direction with height. As a result, the atmosphere is an inhomogeneous mixture of small air cells that, to a wavefront passing through, consists of a dynamically changing index of refraction (Sarazin and Roddier 1990; Tokavinin 2002). Thus, a plane optical wavefront traveling through an atmosphere loses its well-defined shape. On small spatial scales, a wavefront passing through the atmosphere shows ripples or local angular variations. Over the whole of the wavefront a global angle can be measured, and each subsequent wavefront arrives with a different angle to the optical axis of the receiver (Hardy 1998). Human eyes cannot see these changes in angle or phase variations because they are not sensitive to phase changes. However, the effect of phase variations on intensity is visible nearly every day. A common example of phase change is the effect of heat distortion caused by sunlight heating an asphalt roadway. The thermal currents that arise from the roadway distort the view of everything that lies on the other side of the road. Similarly, light projected over a long distance encounters temperature fluctuations in the air and, just as it does when passing over a hot roadway, passes through differing refractive indices. When looking up through the atmosphere at the stars, this turbulence is one of the main contributors to the familiar phenomenon that makes stars appear to twinkle. While the twinkling effect is perceived as beautiful when associated with stars, it has a detrimental effect on €œfree space€ optical communications, astronomical imaging and other beam-propagation applications. This chapter explores how the atmosphere affects wavefront transmission and develops a model of a wavefront passing through the atmosphere.
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