High-power lasers for directed-energy applications: comment.

Sprangle et al. [Appl. Opt.54, F201 (2015)APOPAI0003-693510.1364/AO.54.00F201] recently concluded that our experiments on coherent combining of laser beams over an atmospheric path [Opt. Lett.36, 4455 (2011)OPLEDP0146-959210.1364/OL.36.004455] were "effective only because at these low-power levels the linewidth of the lasers was very narrow… and the level of atmospheric turbulence was low…." These conclusions are inaccurate, not relevant to practical high-power coherently combined laser systems, and contradict our most recent experiments with coherent combining of 21 laser beams with a linewidth of about 1 GHz over 7 km distance. In this comment we also challenge the major conclusion of Sprangle et al. [Appl. Opt.54, F201 (2015)APOPAI0003-693510.1364/AO.54.00F201] and the more recently published paper by Nelson et al. [Appl. Opt.55, 1757 (2016)APOPAI0003-693510.1364/AO.55.001757] regarding inefficiency of coherent beam combining under typical atmospheric conditions.

Target-in-the-loop remote sensing of laser beam and atmospheric turbulence characteristics.

A new target-in-the-loop (TIL) atmospheric sensing concept for in situ remote measurements of major laser beam characteristics and atmospheric turbulence parameters is proposed and analyzed numerically. The technique is based on utilization of an integral relationship between complex amplitudes of the counterpropagating optical waves known as overlapping integral or interference metric, whose value is preserved along the propagation path. It is shown that the interference metric can be directly measured using the proposed TIL sensing system composed of a single-mode fiber-based optical transceiver and a remotely located retro-target. The measured signal allows retrieval of key beam and atmospheric turbulence characteristics including scintillation index and the path-integrated refractive index structure parameter.

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.

Scintillation resistant wavefront sensing based on multi-aperture phase reconstruction technique.

A scintillation resistant sensor that allows retrieval of an input optical wave phase using a multi-aperture phase reconstruction (MAPR) technique is introduced and analyzed. The MAPR sensor is based on a low-resolution lenslet array in the classical Shack-Hartmann arrangement and two high-resolution photo-arrays for simultaneous measurements of pupil- and focal-plane intensity distributions, which are used for retrieval of the wavefront phase in a two stage process: (a) phase reconstruction inside the sensor pupil subregions corresponding to lenslet subapertures and (b) recovery of subaperture averaged phase components (piston phases). Numerical simulations demonstrate the efficiency of the MAPR technique in conditions of strong intensity scintillations and the presence of wavefront branch points.

Speckle-metric-optimization-based adaptive optics for laser beam projection and coherent beam combining.

Maximization of a projected laser beam's power density at a remotely located extended object (speckle target) can be achieved by using an adaptive optics (AO) technique based on sensing and optimization of the target-return speckle field's statistical characteristics, referred to here as speckle metrics (SM). SM AO was demonstrated in a target-in-the-loop coherent beam combining experiment using a bistatic laser beam projection system composed of a coherent fiber-array transmitter and a power-in-the-bucket receiver. SM sensing utilized a 50 MHz rate dithering of the projected beam that provided a stair-mode approximation of the outgoing combined beam's wavefront tip and tilt with subaperture piston phases. Fiber-integrated phase shifters were used for both the dithering and SM optimization with stochastic parallel gradient descent control.

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).

Obscuration-free pupil-plane phase locking of a coherent array of fiber collimators.

Control methods and system architectures that can be used for locking in phase of multiple laser beams that are generated at the transmitter aperture plane of a coherent fiber-collimator array system (pupil-plane phase locking) are considered. In the proposed and analyzed phase-locking techniques, sensing of the piston phase differences is performed using interference of periphery (tail) sections of the laser beams prior to their clipping by the fiber-collimator transmitter apertures. This obscuration-free sensing technique eliminates the need for a beam splitter being directly located inside the optical train of the transmitted beams--one of the major drawbacks of large-aperture and/or high-power fiber-array systems. Numerical simulation results demonstrate efficiency of the proposed phase-locking methods.

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.

Deep turbulence effects compensation experiments with a cascaded adaptive optics system using a 3.63 m telescope.

Compensation of extended (deep) turbulence effects is one of the most challenging problems in adaptive optics (AO). In the AO approach described, the deep turbulence wave propagation regime was achieved by imaging stars at low elevation angles when image quality improvement with conventional AO was poor. These experiments were conducted at the U.S. Air Force Maui Optical and Supercomputing Site (AMOS) by using the 3.63 m telescope located on Haleakala, Maui. To enhance compensation performance we used a cascaded AO system composed of a conventional AO system based on a Shack-Hartmann wavefront sensor and a deformable mirror with 941 actuators, and an AO system based on stochastic parallel gradient descent optimization with four deformable mirrors (75 control channels). This first-time field demonstration of a cascaded AO system achieved considerably improved performance of wavefront phase aberration compensation. Image quality was improved in a repeatable way in the presence of stressing atmospheric conditions obtained by using stars at elevation angles as low as 15 degrees.

Laser beam projection with adaptive array of fiber collimators. I. Basic considerations for analysis.

We present a mathematical model and provide an analysis of optical beam director systems composed of adaptive arrays of fiber collimators (subapertures), referred to here as conformal optical systems. Performances of the following two system architectures are compared: A conformal-beam director with mutually incoherent output laser beams transmitted through fiber collimators (beamlets), and a corresponding coherent system whose beamlets can be coherently combined (phase locked) at a remote target plane. The effect of the major characteristics of the conformal systems on the efficiency of laser beam projection is evaluated both analytically and through numerical simulations. The characteristics considered here are the number of fiber collimators and the subaperture and conformal aperture fill factors, as well as the accuracy of beamlet pointing.

Laser beam projection with adaptive array of fiber collimators. II. Analysis of atmospheric compensation efficiency.

We analyze the potential efficiency of laser beam projection onto a remote object in atmosphere with incoherent and coherent phase-locked conformal-beam director systems composed of an adaptive array of fiber collimators. Adaptive optics compensation of turbulence-induced phase aberrations in these systems is performed at each fiber collimator. Our analysis is based on a derived expression for the atmospheric-averaged value of the mean square residual phase error as well as direct numerical simulations. Operation of both conformal-beam projection systems is compared for various adaptive system configurations characterized by the number of fiber collimators, the adaptive compensation resolution, and atmospheric turbulence conditions.

Imaging with an array of adaptive subapertures.

An imaging system composed of an array of adaptive optics subapertures referred to as a conformal imaging system is considered. A conformal image of an object viewed through atmospheric turbulence is obtained using the following sequential steps: adaptive compensation of phase distortions through optimization of image quality metrics at each subaperture, measurements of the phase and intensity distributions corresponding to the compensated subaperture images, digital combining and processing of the obtained data, computation of a conformal image using arbitrary phase shifts between subapertures, and correction of these phase shifts through conformal image quality optimization using the stochastic parallel gradient descent algorithm. Numerical simulation results of a dual-star conformal image through atmospheric turbulence are presented.

Adaptive laser beam projection on an extended target: phase- and field-conjugate precompensation.

The problem of adaptive laser beam projection onto an extended object (target) having a randomly rough surface in an optically inhomogeneous medium (atmosphere) is analyzed. Outgoing beam precompensation is considered through conjugation of either the target-return wave phase or the complex field. It is shown that in the presence of "frozen" turbulence, both phase-conjugate (PC) and field-conjugate (FC) precompensation can result in a superfocusing effect, which suggests the possibility of achieving a brighter target hit spot in volume turbulence than in vacuum. This superfocusing effect is significantly more distinct for FC precompensation. In the quasi-stationary case (slowly moving turbulence or target), PC and FC beam control lead to enhanced intensity fluctuations at the target surface associated with intermittent formation and disintegration of bright target hit spots that sporadically attach to the extended target surface. This intensity fluctuation level exceeds intensity fluctuations in the absence of beam control and is higher for FC precompensation. In the nonstationary case, both PC and FC lead to an increase of beam width and centroid wander at the extended target surface compared with conventional projection of a collimated or focused beam.

Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters.

A scalable adaptive optics (AO) control system architecture composed of asynchronous control clusters based on the stochastic parallel gradient descent (SPGD) optimization technique is discussed. It is shown that subdivision of the control channels into asynchronous SPGD clusters improves the AO system performance by better utilizing individual and/or group characteristics of adaptive system components. Results of numerical simulations are presented for two different adaptive receiver systems based on asynchronous SPGD clusters-one with a single deformable mirror with Zernike response functions and a second with tip-tilt and segmented wavefront correctors. We also discuss adaptive wavefront control based on asynchronous parallel optimization of several local performance metrics-a control architecture referred to as distributed adaptive optics (DAO). Analysis of the DAO system architecture demonstrated the potential for significant increase of the adaptation process convergence rate that occurs due to partial decoupling of the system control clusters optimizing individual performance metrics.

Speckle-field propagation in 'frozen' turbulence: brightness function approach.

Speckle-field long- and short-exposure spatial correlation characteristics for target-in-the-loop (TIL) laser beam propagation and scattering in atmospheric turbulence are analyzed through the use of two different approaches: the conventional Monte Carlo (MC) technique and the recently developed brightness function (BF) method. Both the MC and the BF methods are applied to analysis of speckle-field characteristics averaged over target surface roughness realizations under conditions of 'frozen' turbulence. This corresponds to TIL applications where speckle-field fluctuations associated with target surface roughness realization updates occur within a time scale that can be significantly shorter than the characteristic atmospheric turbulence time. Computational efficiency and accuracy of both methods are compared on the basis of a known analytical solution for the long-exposure mutual correlation function. It is shown that in the TIL propagation scenarios considered the BF method provides improved accuracy and requires significantly less computational time than the conventional MC technique. For TIL geometry with a Gaussian outgoing beam and Lambertian target surface, both analytical and numerical estimations for the speckle-field long-exposure correlation length are obtained. Short-exposure speckle-field correlation characteristics corresponding to propagation in 'frozen' turbulence are estimated using the BF method. It is shown that atmospheric turbulence-induced static refractive index inhomogeneities do not significantly affect the characteristic correlation length of the speckle field, whereas long-exposure spatial correlation characteristics are strongly dependent on turbulence strength.

Atmospheric compensation with a speckle beacon in strong scintillation conditions: directed energy and laser communication applications.

Wavefront control experiments in strong scintillation conditions (scintillation index, approximately equal to 1) over a 2.33 km, near-horizontal, atmospheric propagation path are presented. The adaptive-optics system used comprises a tracking and a fast-beam-steering mirror as well as a 132-actuator, microelectromechanical-system, piston-type deformable mirror with a VLSI controller that implements stochastic parallel gradient descent control optimization of a system performance metric. The experiments demonstrate mitigation of atmospheric distortions with a speckle beacon typical for directed energy and free-space laser communication applications.

Multiframe selective information fusion from robust error estimation theory.

A dynamic procedure for selective information fusion from multiple image frames is derived from robust error estimation theory. The fusion rate is driven by the anisotropic gain function, defined to be the difference between the Gaussian smoothed-edge maps of a given input frame and of an evolving synthetic output frame. The gain function achieves both selection and rapid fusion of relatively sharper features from each input frame compared to the synthetic frame. Effective applications are demonstrated for image sharpening in imaging through atmospheric turbulence, for multispectral fusion of the RGB spectral components of a scene, for removal of blurred visual obstructions from in front of a distant focused scene, and for high-resolution two-dimensional display of three-dimensional objects in microscopy.

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing.

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.

Compensation of distant phase-distorting layers. II. Extended-field-of-view adaptive receiver system.

We analyze the anisoplanatic adaptive receiver system field of view (FOV) and the possibility of controlling the system FOV by using an adaptive optics system with multiple wave-front sensors that sense wave-front phase aberrations of reference waves with different arrival angles. The conventional decoupled stochastic parallel gradient descent (D-SPGD) technique is generalized to include output signals from multiple wave-front sensors. The multiple-reference D-SPGD control algorithm introduced here is applied to obtain an anisotropic FOV in adaptive receiver systems by using two and three reference waves.