The Aggregate behavior of branch points - measuring the number and velocity of atmospheric turbulence layers

Abstract

Optical waves propagating through atmospheric turbulence develop spatial and temporal variations in their phase. For sufficiently strong turbulence, these phase differences can lead to interference in the propagating wave and the formation of branch points; positions of zero amplitude. Under the assumption of a layered turbulence model, we show that these branch points can be used to estimate the number and velocities of atmospheric layers. We describe how to carry out this estimation process and demonstrate its robustness in the presence of sensor noise.

Photonic orbital angular momentum in starlight

“…Arranging the estimates into bins of increasing velocity creates a velocity distribution, D(v). In the velocity distribution, correlated measurements self-reinforce, and these lead to spikes at the location of optical vortex velocities (Oesch et al 2010). These velocities are the transverse velocities of the turbulence layers.…”

“…Therefore, detectors created for spatially distributed measurements, like WFSs used in AO, are better suited to the identification of turbulence-induced optical vortices. A number of laboratory experiments were conducted to understand the nature of optical vortices in the propagating wave (Oesch et al 2010. It is instructive to review the results of these experiments to understand POAM in traveling waves in the low-noise and high resolution measurements only achievable in a laboratory before moving to field experiments and astronomical observations where noise and time varying turbulence present additional difficulties.…”

“…The temporal evolution of the optical vortices in the WFS data is captured in the "projections" of the helicity spectrum (Oesch et al 2010). The projections of H are defined as…”

“…Figure 3 shows an example of Eq. (22) applied to data from a bench-top experiment (Oesch et al 2010). In the xt projection, the optical vortex trails form two sets with differing slopes, representing the two turbulence layer velocities of the ATS.…”

“…A&A 567, A114 (2014) A different technique for identifying POAM in propagating electromagnetic fields has been used by the Atmospheric Simulation and Adaptive-optics Laboratory Testbed (ASALT) research group at SOR. In earlier experiments (Oesch et al 2010, the spatial and temporal distribution of optical vortices has been used to profile threedimensional turbulence, providing information on the strength, distance and transverse velocities of turbulence layers encountered by a propagating wave. These estimations are based on the identification of optical vortex trails in the projections of the helicity spectrum of the WFS data .…”