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Title: Phase-factor spectra of turbulent phase screens

The optical phaseϕ<#comment/>is a key quantity in the physics of light propagating through a turbulent medium. In certain respects, however, the statistics of the phasefactor,ψ<#comment/>=exp⁡<#comment/>(iϕ<#comment/>), are more relevant than the statistics of the phase itself. Here, we present a theoretical analysis of the 2D phase-factor spectrumFψ<#comment/>(κ<#comment/>)of a random phase screen. We apply the theory to four types of phase screens, each characterized by a power-law phase structure function,Dϕ<#comment/>(r)=(r/rc)γ<#comment/>(wherercis the phase coherence length defined byDϕ<#comment/>(rc)=1rad2), and a probability density functionpα<#comment/>(α<#comment/>)of the phase increments for a given spatial lag. We analyze phase screens with turbulent (γ<#comment/>=5/3) and quadratic (γ<#comment/>=2) phase structure functions and with normally distributed (i.e., Gaussian) versus Laplacian phase increments. We find that there is a pronounced bump in each of the four phase-factor spectraFψ<#comment/>(κ<#comment/>). The precise location and shape of the bump are different for the four phase-screen types, but in each case it occurs atκ<#comment/>∼<#comment/>1/rc. The bump is unrelated to the well-known more » “Hill bump” and is not caused by diffraction effects. It is solely a characteristic of the refractive-index statistics represented by the respective phase screen. We show that the second-orderψ<#comment/>statistics (covariance function, structure function, and spectrum) characterize a random phase screen more completely than the second-orderϕ<#comment/>counterparts.

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Publication Date:
Journal Name:
Journal of the Optical Society of America A
Page Range or eLocation-ID:
Article No. 1339
1084-7529; JOAOD6
Optical Society of America
Sponsoring Org:
National Science Foundation
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