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GENERAL INFORMATION
chapter 12, Beam Shape
Chapter Contents
- 12.1 General Formula for Beam Shape
- 12.2 Beam Shape for Uncorrected Turbulence
- 12.3 Beam Shape with Tilt Jitter
- 12.4 Beam Shape with Anisoplanatism
Excerpt
Propagating a wave through turbulence not only reduces the Strehl ratio, but also changes the beam shape. Mellin transform techniques can be used to calculate the beam shape using the same technique as previously applied. Determining the beam shape simply adds another parameter to an integral. The beam profile after propagating through uncorrected turbulence, or through a medium with turbulence-induced beam jitter present, or with anisoplanatic effects can all be represented as special cases of a general integral. Results from evaluating the general integral are used to find the average beam profiles for the three specific cases.
12.1 General Formula for Beam Shape
A framework for finding the beam profile for any ratio of coherence diameter to aperture diameter is developed here. The starting point for obtaining the beam profile with uncorrected turbulence is the general expression for the normalized beam shape with isotropic turbulence in eq. 2.162 and the structure function for uncorrected turbulence given in eq. 7.7. This gives
©2007 Society of Photo-Optical Instrumentation Engineers
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