Phase-factor spectra of turbulent phase screens
Abstract
The optical phase ϕ is a key quantity in the physics of light propagating through a turbulent medium. In certain respects, however, the statistics of the phase factor, ψ = exp ( i ϕ ) , are more relevant than the statistics of the phase itself. Here, we present a theoretical analysis of the 2D phase-factor spectrum F ψ ( κ ) of a random phase screen. We apply the theory to four types of phase screens, each characterized by a power-law phase structure function, D ϕ ( r ) = ( r / r c ) γ (where r c is the phase coherence length defined by D ϕ ( r c ) = 1 r a d 2 ), and a probability density function p α ( α ) of the phase increments for a given spatial lag. We analyze phase screens with turbulent ( γ = 5 / 3 ) and quadratic ( γ = 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 spectra F ψ ( κ ) . The precise location and shape of the bump are different for the four phase-screen types, but in each case it occurs at κ ∼ 1 / r c . The bump is unrelated to the well-known “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-order ψ statistics (covariance function, structure function, and spectrum) characterize a random phase screen more completely than the second-order ϕ counterparts.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 20, 2021
- Source ID
- 10.1364/josaa.429928
Entities
People
- Andreas Muschinski
Organizations
- Air Force Office of Scientific Research
- National Science Foundation
- Northwest Research Associates
- University of Colorado Boulder