Aggregate behavior of branch points - persistent pairs

Abstract

Light propagating through atmospheric turbulence acquires spatial and temporal phase variations. For strong enough turbulence conditions, interference from these phase variations within the optical wave can produce branch points; positions of zero amplitude. Under the assumption of a layered turbulence model, our previous work has shown that these branch points can be used to estimate the number and velocities of atmospheric layers. Key to this previous demonstration was the property of branch point persistence. Branch points from a single turbulence layer persist in time and through additional layers. In this paper we extend persistence to include branch point pairs. We develop an algorithm for isolating persistent pairs and show that through experimental data that they exist through time and through additional turbulence.

Least-squares phase estimation with wrapped measurements and branch points

“…∇ yc x; y cx; y ux; (19) with u· the unit step function and the "star" operations indicating 2D convolution with uxuy and 1D convolutions with ux and uy, respectively. For clarity, we note that the first line of Eq.…”

“…Atmospheric branch points have been shown to create in pairs and evolve smoothly in time [16]. The gradient measurements have been used to estimate the turbulence layers' altitude and strength [17][18][19][20]. Sanchez and Oesch have proposed that branch points indicate the presence of photons with nonzero orbital angular momentum [21,22].…”

The aggregate behavior of branch points: a proposal for an atmospheric turbulence layer sensor

“…The fifth algorithm finds the velocity classes of the polarity array (see 16 ). The sixth algorithm equates a velocity with each unique subset of p(x, y, t) and the creation pairs are assigned to a unique subset (see 7,8 ). Once these six algorithms have completed, we have in-hand the polarity array, and the velocity distribution for this polarity array.…”

“…In particular, we demonstrated that the ensemble of pupil-plane branch points carry four independent parameters. [5][6][7][8][9] These four independent parameters can be used to estimate four independent atmospheric turbulence layer parameters--number, strength, altitude and velocity. 8 In this work, we describe a sensor that estimates those four parameters, describing how it can be built and implemented at an observatory.…”

The aggregate behavior of branch points: verification in wave optical simulation II

“…5 Included in the measurement of turbulence layer velocity through pupil plane branch points, is the concept of persistence. 5,6 Persistence is the property that branch points endure both in time and through additional turbulence. The first is a byproduct of our atmospheric turbulence simulator (ATS) 4 obeying Taylor's frozen flow hypothesis, though this has also been demonstrated in atmospheric measurements.…”