Phase structure function of random wave fields

Watson, Stephen M.; Subich, Christopher; Ridley, Kevin D.

doi:10.1016/j.optcom.2006.09.001

Cited by 2 publications

(2 citation statements)

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“…Results for three and more scatterers can be obtained using the numerical simulation techniques described in [11,12]. All graphical results presented in this paper were generated using a Gaussian phase shift correlation function ρ θ (τ ) = exp(−τ 2 /ξ 2 ), phase shift variance θ 2 = 100 and correlation length ξ = 200.…”

Section: Wrapped Phase Differencesmentioning

confidence: 99%

“…For example, the wrapped phase of a circular complex Gaussian field constitutes a stationary process, whereas the unwrapped phase is a non-stationary process with divergent variance. However, unwrapped phase fluctuations can be characterized by their mean square phase difference, or structure function, which can be obtained from (2) provided that the scattered field is once differentiable [10,11]. In this paper we therefore focus our attention on the mean square properties of wrapped and unwrapped phase differences returned from the two-dimensional random walk scattering model (1).…”

Section: Introductionmentioning

confidence: 99%

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Wrapped and unwrapped phase of radiation scattered by a discrete number of particles

Watson¹,

Ridley²

2007

J. Phys. A: Math. Theor.

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This paper investigates wrapped and unwrapped phase differences generated by a non-Gaussian scattering model: the two-dimensional random walk. Mean square values for these quantities are obtained for one and two scatterers, as well as the large scatterer limit when the field constitutes a circular complex Gaussian process. Numerical simulation is used to investigate the phase under more general fluctuation conditions, and reveals that the wrapped phase difference correlation converges rapidly to that result predicted for a Gaussian speckle field. Analytical results for the unwrapped phase indicate that this quantity transitions from a stationary process for one and two scatterers to a non-stationary process in the large scatterer limit. The nature of this transition is examined using numerical simulation for arbitrary scatterer number. Phase correlations are of consequence in various phase sensitive detection systems, and this paper examines both Gaussian and non-Gaussian fields.

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Section: Wrapped Phase Differencesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%