Image Processing Reference
In-Depth Information
Chapter 2
Effects of Turbulence on a
Wavefront
2.1 Introduction
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 di-
rection 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 rip-
ples 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 road-
way 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 re-
fractive indices. When looking up through the atmosphere at the stars, this turbu-
lence 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 associ-
ated with stars, it has a detrimental effect on “free 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.
2.2 Effect of the Atmosphere
Earth's atmosphere is a thick gas layer that surrounds the planet. Its main constituents
are nitrogen and oxygen, along with a number of trace compounds. While the atmo-
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