Patrick R. Kelly

Creation of photonic orbital angular momentum by distributed volume turbulence.

In previous work, we presented theory of how atmospheric turbulence can impart orbital angular momentum to propagating optical waves. In this paper we provide the first experimental demonstration of the detection of orbital angular momentum from distributed volume turbulence through the identification of well-defined, turbulence-induced, optical vortex trails in Shack-Hartmann wave front sensor measurements.

Aggregate behavior of branch points: characterization in wave optical simulation

Abstract. Atmospheric turbulence imparts phase distortions on propagating optical waves. These distortions couple into amplitude fluctuations at the pupil of a telescope, which, for strong enough phase distortions, produce zeros in the amplitude called branch points. In our earlier work, we presented the case that branch points can be utilized as a source of information on the turbulent atmosphere. Using our bench-top data, we have demonstrated several properties of branch points including motion, density, persistence and separation. We have shown that the pupil plane motion of subsets of branch points scales to the velocities of atmospheric turbulence layers and identifies the number of branch point producing layers. We have identified empirical relationships for density and separation as functions of the strength and altitude for a single layer. All of this work has been done using a bench-top adaptive optics system utilizing a two-layer atmospheric turbulence simulator. In this paper, we use simulations to verify these previous results by showing that all of these branch point properties follow similar behaviors in independently anchored wave optics simulations.

The aggregate behavior of branch points: theoretical calculation of branch point velocity

In our first work in this research thread, we demonstrated that turbulence-created optical vortices are created innitesimally close together in pairs of opposite helicity--call these creation pairs. In that rst work, we postu- lated that creation pairs separate as they propagate, and that they carry both the velocity of, and distance to, the turbulence layer that created them. Subsequent experimental papers have demonstrated this to be true. Our purpose here is to ll two gaps in our original theoretical results and demonstrate both how, in a mathematical treatment, turbulence-created optical vortices can have the velocity of the turbulence layer that created them, and also, present calculation of their separation velocity.

Experimental analysis of perspective elongation effects using a laser guide star in an adaptive-optics system

The use of a laser guidestar (LGS) for the purpose of a beacon in an adaptive-optics (AO) system is prone to perspective elongation effects on the spots of a Shack-Hartmann wavefront sensor. The elongated spots can vary in size over the subapertures and affect the gradient sensitivity of the sensor. The Air Force Research Laboratory (AFRL) has developed a LGS model that outputs gradient gains which represent the effects of an extended beacon on the spots for a Shack-Hartmann wavefront sensor. This paper investigates the application of these gains in an experimental setup in order to both analyze the effects of the variation in those gains due to spot size elongation and to measure the impact on the performance of an AO system.

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

We propose a sensor that measures the number, strength, altitude and velocity of atmospheric turbulence layers. Recent research has shown that pupil plane branch points contain four independent and measureable parameters and that these four parameters can be used to estimate four independent turbulence layer parameters--number, strength, altitude and velocity--for each atmospheric turbulence layer. Here, we summarized previous results and then demonstrate how these results allow for construction of a turbulence layer sensor.

The aggregate behavior of branch points: the use of branch point pairing to generate a hidden phase for closed-loop AO

Recent research has shown that branch points, as they appear in astronomical applications, have a rich collective behavior, showing, in particular, that branch point pairs have a well-defined, non-stoichastic velocity, and that once a branch point pairs location is measured, it can be tracked in open-loop adaptive optics operation. The research presented here uses this new information as a priori knowledge in closed-loop AO. Specifically, an algorithm was developed that measures branch point location and velocity at time tk and then uses this to estimate the phase contribution at time tk+n, giving it an effective memory of where branch points appear and allowing it to determine more accurately between real branch points and noise. The output of the new algorithm is used as a second input to the DM control law. Results of initial closed-loop AO tests will be presented.

Impact of realistic turbulence conditions on laser beam propagation

Methodology is presented using observations from a radar and new measurement system to address several fundamental turbulence issues related to laser beam propagation that impact high energy laser (HEL) and laser communication systems. The successful design and operation of these laser systems require high-fidelity realistic laser beam propagation models coupled with a thorough and comprehensive knowledge of the real turbulent atmosphere. To date, modeling and simulation of laser beam propagation through atmospheric turbulence have relied upon a traditional theoretical basis that assumes the existence of homogeneous, isotropic, stationary, and Kolmogorov turbulence. The approach and methodology is discussed to assess the impact of real atmospheric turbulence on laser beam propagation. Analysis will include effects of non-classical turbulence as well as inner (lo) and outer scale (Lo) effects. Data will be obtained from a new measurement platform using a free-flying balloon that lifts a ring with a boom upon which are mounted fine wire (1μm diameter) sensors to measure high-speed temperature and velocity fluctuations from which the turbulent quantities can be calculated including the refractive index structure parameter (C2n) and the eddy dissipation rate (ε). The “ring” is actually 8-sided with a diameter of 30 feet and trails the balloon with several risers. This design eliminates contamination of the balloon wake that plagues conventional systems.

Understanding the physics of optical deep turbulence at the Earth's boundary layer

The Air Force Research Laboratory (AFRL) is developing and extending a model of the boundary layer that takes, as input, common atmospheric measurements and ground condition parameters, and predicts key parameters of optical turbulence such as strength and inner scale. In order to anchor the model, a field campaign is also being conducted. The campaign will include co-located meteorological instruments and an open loop Hartmann wavefront sensor. Here, a portion of the boundary layer model is discussed: that relevant for the daytime surface layer. A sensitivity analysis of input parameters is presented.

Optical Vortex Density in Rytov Saturated Atmospheric Turbulence

We examine the optical vortex density in the regime where the Rytov parameter has saturated. The function breaks into three regions; a transitory region bounded by two empirical curves for turbulent optical vortex parameters.

The Aggregate Behavior of Branch Points - Modeling Parameters

This paper continues a series discussing branch points. In creating a wave optical model of our experiments, we found unexpected dependencies in the branch point distributions. This paper discusses these dependencies.