Anatomy of the slope discrepancy structure function: characterization of turbulence

Terry J. Brennan

doi:10.1117/12.487749

21 August 2003 Anatomy of the slope discrepancy structure function: characterization of turbulence

Terry J. Brennan

Proceedings Volume 5087, Laser Systems Technology; (2003) https://doi.org/10.1117/12.487749
Event: AeroSense 2003, 2003, Orlando, Florida, United States

Abstract

A new approach, for estimating r₀ and the Greenwood frequency from wavefront sensor measurements, is introduced. Unlike other techniques, which use phase statistics calculated from reconstructed wavefront sensor measurements, this approach makes use of the slope discrepancy, the component of the measurement that is not reconstructed by a least squares reconstructor. It is shown that the r₀ estimator based on the slope discrepancy is a high degree-of-freedom estimator with a much smaller estimation variance than estimates based on the phase variance. An new temporal atmospheric sample rate, f₀(ε²), is introduced in this work. This quantity is calculated from the slope discrepancy structure function and sets the minimum required sampling rate to maintain the residual wavefront error below ε²/K for a system dependent gain, K. For Kolmogorov turbulence statistics it is shown that the Greenwood frequency is related to f₀ by f_G=f₀(K(2π/20)²)/40. In non-Kolmogorov turbulence, f₀ continues to be a legitimate specification of sampling requirements. These results are all illustrated with wave optics simulations.

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Terry J. Brennan "Anatomy of the slope discrepancy structure function: characterization of turbulence", Proc. SPIE 5087, Laser Systems Technology, (21 August 2003); https://doi.org/10.1117/12.487749

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