## Intensity-weighted phase-derivative statistics

JOSA A, Vol. 18, Issue 9, pp. 2121-2131 (2001)

http://dx.doi.org/10.1364/JOSAA.18.002121

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### Abstract

It is shown that amplitude weighting can improve the accuracy of measurements of the frequency offset of a signal contaminated by multiplicative Gaussian noise. The more general non-Gaussian case is investigated through study of the statistics of a simple phase-screen scattering model. Formulas are derived for the low-order moments of the intensity-weighted phase derivative. Numerical simulation is tested against these results and is used to generate full probability densities that are analytically intractable and to determine the optimum weighting for the non-Gaussian regime of the model. The results are relevant to a variety of remote-sensing and signal-processing problems.

© 2001 Optical Society of America

**OCIS Codes**

(010.1300) Atmospheric and oceanic optics : Atmospheric propagation

(030.6600) Coherence and statistical optics : Statistical optics

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

(120.7280) Instrumentation, measurement, and metrology : Vibration analysis

(290.0290) Scattering : Scattering

**History**

Original Manuscript: November 16, 2000

Revised Manuscript: February 20, 2001

Manuscript Accepted: February 20, 2001

Published: September 1, 2001

**Citation**

Eric Jakeman, Stephen M. Watson, and Kevin D. Ridley, "Intensity-weighted phase-derivative statistics," J. Opt. Soc. Am. A **18**, 2121-2131 (2001)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-9-2121

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