Dependence of the probability density function of laser radiation power on the scintillation index and the size of a receiver aperture.

Power scintillations of a Gaussian laser beam propagated through a 7 km long horizontal atmospheric path for a wide range of turbulence strengths and different sizes of the receiver aperture were studied experimentally. The probability density function (PDF) and its properties were analyzed for a wide range of scintillation conditions. It was shown that the PDF can be described by the fractional exponential distribution in the strong scintillation regime (scintillation index of power measured on aperture σPIB2>1) for apertures with diameter d < a, where a is the size of the isoplanatic region, and by the gamma distribution in the weak scintillation regime (σPIB2<1), as well as by the lognormal distribution for σPIB2≪1. More than one distribution can be considered as a good approximation for experimental data for some ranges of d/a and σPIB2, but the transition from one distribution to another as the best approximation occurs at certain characteristic values of these parameters. In the strong scintillation regime, the aperture averaging effect resulted in the transition from the fractional exponential distribution to the fractional gamma (FG) distribution when the aperture diameter is about the size of the isoplanatic region (d/a∼1). The FG distribution better approximates the experimental PDF because it accounts for the fact that the probability of zero power values becomes zero due to the averaging effect of the aperture. The fractional gamma distribution is the best approximation of the PDF for a finite aperture when σPIB2>σPIB,crit2=[0.7-0.8], while the gamma distribution is the best approximation for σPIB2<σPIB,crit2.

Comparative efficiency analysis of fiber-array and conventional beam director systems in volume turbulence.

The performance of two prominent laser beam projection system types is analyzed through wave-optics numerical simulations for various atmospheric turbulence conditions, propagation distances, and adaptive optics (AO) mitigation techniques. Comparisons are made between different configurations of both a conventional beam director (BD) using a monolithic-optics-based Cassegrain telescope and a fiber-array BD that uses an array of densely packed fiber collimators. The BD systems considered have equal input power and aperture diameters. The projected laser beam power inside the Airy size disk at the target plane is used as the performance metric. For the fiber-array system, both incoherent and coherent beam combining regimes are considered. We also present preliminary results of side-by-side atmospheric beam projection experiments over a 7-km propagation path using both the AO-enhanced beam projection system with a Cassegrain telescope and the coherent fiber-array BD composed of 21 densely packed fiber collimators. Both wave-optics numerical simulation and experimental results demonstrate that, for similar system architectures and turbulence conditions, coherent fiber-array systems are more efficient in mitigation of atmospheric turbulence effects and generation of a hit spot of the smallest possible size on a remotely located target.

Deep turbulence effects mitigation with coherent combining of 21 laser beams over 7 km.

We demonstrate coherent beam combining and adaptive mitigation of atmospheric turbulence effects over 7 km under strong scintillation conditions using a coherent fiber array laser transmitter operating in a target-in-the-loop setting. The transmitter system is composed of a densely packed array of 21 fiber collimators with integrated capabilities for piston, tip, and tilt control of the outgoing beams wavefront phases. A small cat's-eye retro reflector was used for evaluation of beam combining and turbulence compensation performance at the target plane, and to provide the feedback signal for control of piston and tip/tilt phases of the transmitted beams using the stochastic parallel gradient descent maximization of the power-in-the-bucket metric.

Experimental demonstration of coherent beam combining over a 7 km propagation path.

We demonstrate coherent combining (phase locking) of seven laser beams emerging from an adaptive fiber-collimator array over a 7 km atmospheric propagation path using a target-in-the-loop (TIL) setting. Adaptive control of the piston and the tip and tilt wavefront phase at each fiber-collimator subaperture resulted in automatic focusing of the combined beam onto an unresolved retroreflector target (corner cube) with precompensation of quasi-static and atmospheric turbulence-induced phase aberrations. Both phase locking (piston) and tip-tilt control were performed by maximizing the target-return optical power using iterative stochastic parallel gradient descent (SPGD) techniques. The performance of TIL coherent beam combining and atmospheric mitigation was significantly increased by using an SPGD control variation that accounts for the round-trip propagation delay (delayed SPGD).

Target-in-the-loop wavefront sensing and control with a Collett-Wolf beacon: speckle-average phase conjugation.

Adaptive optical systems for laser beam projection onto an extended target embedded in an optically inhomogeneous medium are considered. A new adaptive optics wavefront control technique--speckle-average (SA) phase conjugation--is introduced. In this technique mitigation of speckle effects related to laser beam scattering off the rough target surface is achieved by measuring the SA wavefront slopes of the target return wave using a conventional Shack-Hartmann wavefront sensor. For statistically representative speckle averaging we consider the generation of an incoherent light source, referred to here as a Collett-Wolf beacon, directly on the target surface using a rapid steering (scanning) auxiliary laser beam. Our numerical simulations and experiment show that control of the outgoing beam phase using SA phase conjugation can lead to efficient compensation of turbulence effects and results in an increase of the projected laser beam power density on a remote extended target. The impact of both target anisoplanatism and the Collett-Wolf beacon size on adaptive system performance is studied.