Indirect measurement of a laser communications bit-error-rate reduction with low-order adaptive optics

In experimental measurements of the bit-error rate for a laser communication system, we show improved performance with the implementation of low-order (tip/tilt) adaptive optics in a free-space link. With simulated atmospheric tilt injected by a conventional piezoelectric tilt mirror, an adaptive optics system with a Xinetics tilt mirror was used in a closed loop. The laboratory experiment replicated a monostatic propagation with a cooperative wave front beacon at the receiver. Owing to constraints in the speed of the processing hardware, the data is scaled to represent an actual propagation of a few kilometers under moderate scintillation conditions. We compare the experimental data and indirect measurement of the bit-error rate before correction and after correction, with a theoretical prediction.     

Bootstrap beacon creation for overcoming the effects of beacon anisoplanatism in a laser beam projection system

We address the problem of using adaptive optics to deliver power from an airborne laser platform to a ground target through atmospheric turbulence under conditions of strong scintillation and anisoplanatism. We explore three options for creating a beacon for use in adaptive optics beam control: scattering laser energy from the target, using a single uncompensated Rayleigh beacon, and using a series of compensated Rayleigh beacons. We demonstrate that using a series of compensated Rayleigh beacons distributed along the path provides the best beam compensation.     

Atmospheric-compensation experiments in strong-scintillation conditions

Most atmospheric-turbulence-compensation experiments have been performed under weak-scintillation conditions; conventional phase-conjugate adaptive-optics systems usually provide good correction for these conditions. We have performed an experiment over a 5.5-km horizontal propagation path to explore the efficacy of conventional adaptive optics in strong-scintillation conditions. The experimental results showed a significant degradation in correction as the scintillation increased. The presence of branch points in the phase appears to be the primary reason for the degradation in correction as the scintillation increases.     

Measurement of seeing and the atmospheric time constant by differential scintillations

A simple differential analysis of stellar scintillations measured simultaneously with two apertures opens the possibility to estimate seeing. Moreover, some information on the vertical turbulence distribution can be obtained. A general expression for the differential scintillation index for apertures of arbitrary shape and for finite exposure time is derived, and its applications are studied. Correction for exposure time bias by use of the ratio of scintillation indices with and without time binning is studied. A bandpass-filtered scintillation in a small aperture (computed as the differential-exposure index) provides a reasonably good estimate of the atmospheric time constant for adaptive optics.     

Pupil-plane imager for scintillometry over long horizontal paths

A pupil plane imaging (PPI) system has been designed and implemented to measure scintillation induced by atmospheric turbulence and to estimate key parameters of atmospheric turbulence. A high-speed, high-resolution camera images the pupil of a telescope. The process of estimating normalized intensity variance and the underlying rationale is discussed. Experimental results are presented for data taken at North Oscura Peak in southern New Mexico from light originating at Salinas Peak or an aircraft, over near-horizontal paths of approximately 50 km. Strong scintillation is often observed. The results are compared to those of other instruments operating in parallel, and systematic and random errors are discussed. The primary goal is to accurately estimate scintillation strength using PPI in order to assess adaptive optics performance as a function of such scintillation.     

Decoupled stochastic parallel gradient descent optimization for adaptive optics: integrated approach for wave-front sensor information fusion

A new adaptive wave-front control technique and system architectures that offer fast adaptation convergence even for high-resolution adaptive optics is described. This technique is referred to as decoupled stochastic parallel gradient descent (D-SPGD). D-SPGD is based on stochastic parallel gradient descent optimization of performance metrics that depend on wave-front sensor data. The fast convergence rate is achieved through partial decoupling of the adaptive system's control channels by incorporating spatially distributed information from a wave-front sensor into the model-free optimization technique. D-SPGD wave-front phase control can be applied to a general class of adaptive optical systems. The efficiency of this approach is analyzed numerically by considering compensation of atmospheric-turbulence-induced phase distortions with use of both low-resolution (127 control channels) and high-resolution (256 x 256 control channels) adaptive systems. Results demonstrate that phase distortion compensation can be achieved during only 10-20 iterations. The efficiency of adaptive wave-front correction with D-SPGD is practically independent of system resolution.     

Effects of different beacon wavelengths on atmospheric compensation in strong scintillation

During strong scintillation, the number and location of branch points in a distorted optical field induced by atmospheric turbulence are closely related to the characteristic parameters of the turbulence effect, propagation distance, and wavelength. It is necessary to consider the effect of the beacon's wavelength on the adaptive optics system that is used to compensate for atmospheric turbulence. Our analytical results show that the performance of adaptive optics can be improved by nearly a factor of 2 when the beacon's wavelength is chosen slightly longer than the wavelength of the main laser in the branch points considered.     

Horizontal Line-of-Sight Turbulence Over Near-Ground Paths and Implications for Adaptive Optics Corrections in Laser Communications

Atmospheric turbulence over long horizontal paths perturbs phase and can also cause severe intensity scintillation in the pupil of an optical communications receiver, which limits the data rate over which intensity-based modulation schemes can operate. The feasibility of using low-order adaptive optics by applying phase-only corrections over horizontal propagation paths is investigated. A Shack-Hartmann wave-front sensor was built and data were gathered on paths 1 m above ground and between a 1- and 2.5-km range. Both intensity fluctuations and optical path fluctuation statistics were gathered within a single frame, and the wave-front reconstructor was modified to allow for scintillated data. The temporal power spectral density for various Zernike polynomial modes was used to determine the effects of the expected corrections by adaptive optics. The slopes of the inertial subrange of turbulence were found to be less than predicted by Kolmogorov theory with an infinite outer scale, and the distribution of variance explained by increasing order was also found to be different. Statistical analysis of these data in the 1-km range indicates that at communications wavelengths of 1.3 mum, a significant improvement in transmitted beam quality could be expected most of the time, to a performance of 10% Strehl ratio or better.     

Including outer scale effects in zonal adaptive optics calculations

Mellin transform techniques are applied to evaluate the covariance of the integrated turbulence-induced phase distortions along a pair of ray paths through the atmosphere from two points in a telescope aperture to a pair of sources at finite or infinite range. The derivation is for the case of a finite outer scale and a von Karman turbulence spectrum. The Taylor hypothesis is assumed if the two phase distortions are evaluated at two different times and amplitude scintillation effects are neglected. The resulting formula for the covariance is a power series in one variable for the case of a fixed atmospheric wind velocity profile and a power series in two variables for a fixed wind-speed profile with a random and uniformly distributed wind direction. These formulas are computationally efficient and can be easily integrated into computer codes for the numerical evaluation of adaptive optics system performance. Sample numerical results are presented to illustrate the effect of a finite outer scale on the performance of natural and laser guide star adaptive optics systems for an 8-m astronomical telescope. A hypothetical outer scale of 10 m significantly reduces the magnitude of tilt anisoplanatism, thereby improving the performance of a laser guide star adaptive optics system if the auxiliary natural star used for full-aperture tip/tilt sensing is offset from the science field. The reduction in higher-order anisoplanatism that is due to a 10-m outer scale is smaller, and the off-axis performance of a natural guide star adaptive optics system is not significantly improved.     

Adaptive optics compensation for propagation through deep turbulence: initial investigation of gradient descent tomography

To implement adaptive optics compensation for propagation through deep turbulence, the concept of gradient descent tomography has been developed. Here two or more deformable mirrors are controlled by an efficient iterative algorithm that optimizes the integral I(2) image-sharpening metric. In this work a difficult case involving imaging over a 2 km path with a C(n)(2) of 2 x 10(-13)m(-2/3) is considered. For a wavelength of 1.06 microm and a 10-cm-diameter aperture, lambda/D is seven times the isoplanatic angle (theta(0)=1.54 microrad), and the Rytov number is 5.5. For three points placed along a line spanning approximately 70 isoplanatic patch sizes all three points are compensated somewhat, illustrating that anisoplanatism is addressed. The fact that the corresponding performance improvement ratios are 1.20, 1.34, and 3.26 in the presence of such strong scintillation and anisoplanatism is quite significant.     

Correctability limitations imposed by plane-wave scintillation in multiconjugate adaptive optics

Plane-wave scintillation is shown to impose multiconjugate adaptive optics (MCAO) correctability limitations that are independent of wavefront sensing and reconstruction. Residual phase and log-amplitude variances induced by scintillation in weak turbulence are derived using linear (diffraction-based) diffractive MCAO spatial filters or (diffraction-ignorant) geometric MCAO proportional gains as open-loop control parameters. In the case of Kolmogorov turbulence, expressions involving the Rytov variance and/or weighted C(2)(n) integrals apply. Differences in performance between diffractive MCAO and geometric MCAO resemble chromatic errors. Optimal corrections based on least squares imply irreducible performance limits that are validated by wave-optic simulations.     

A new two-code keying scheme for SAC-OCDMA systems enabling bipolar encoding

In this paper, we propose a new two-code keying scheme for enabling bipolar encoding in a high-rate spectral-amplitude coding optical code-division multiple-access (SAC-OCDMA) system. The mathematical formulations are derived for the signal-to-noise ratio and bit-error rate (BER) of SAC-OCDMA system based on the suggested scheme using multi-diagonal (MD) code. Performance analyses are assessed considering the effects of phase-induced intensity noise, as well as shot and thermal noises in photodetectors. The numerical results demonstrated that the proposed scheme exhibits an enhanced BER performance compared to the existing unipolar encoding with direct detection technique. Furthermore, the performance improvement afforded by this scheme is verified using simulation experiments.     

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.     

Residual phase variance in partial correction: application to the estimate of the light intensity statistics

Although the wave-front correction provided by an adaptive optics system should be as complete as possible, only a partial compensation is attainable in the visible. An estimate of the residual phase variance in the compensated wave front can be used to calibrate system performance, but it is not a simple task when errors affect the compensation process. We propose a simple method for estimation of the residual phase variance that requires only the measurement of the Strehl ratio value. It provides good results over the whole range of compensation degrees. The estimate of the effective residual phase variance is useful not only for system calibration but also for determining the light intensity statistics to be expected in the image as a function of the degree of compensation introduced.     

Image compensation in the presence of thermal blooming

The effect of image compensation in viewing extended targets through thermal blooming is discussed. A wave-optics propagation code simulating multiple point sources and a low-bandwidth return-wave adaptive optics system is used to determine the steady-state thermally induced phase distortions and wave-front correction through various Zernike modes. Incoherent point spread functions for the isoplanatic regions are generated and convolved with the appropriate object field to reconstruct the extended target image. Image distortion, degradation in peak irradiance, and adaptive optics loop stability are discussed with respect to degree of correction and wavelength sensitivity.     

Performance study of Kalman filter controller for multiconjugate adaptive optics

We compare the performance of the Kalman filter (KF)-based and the minimum variance (MV) control algorithms for a zonal adaptive optics with a phase temporal prediction step included for effective compensation of the errors attributable to latencies in the system. The main goal is to evaluate the performance achievable by the computationally more expensive KF approach, which explicitly accounts for the atmospheric turbulence temporal behavior through a first-order autoregressive evolution model, and the simpler MV algorithm, with and without temporal prediction. For a representative example, the Gemini-South 8 m telescope multiconjugate adaptive optics system performance of the KF and the MV controllers has been compared with respect to their turbulence compensation capability. We show that the KF algorithm, as expected, shows superior performance to that of the MV algorithm, especially for extremely low sampling rates and large control latencies. We also show that for moderate control latencies the MV algorithm with a temporal prediction step added to it approaches the performance of the KF technique.     

Analysis of BPSK modulated asynchronous band-limited DS-CDMA systems with diversity receivers over generalised-K fading channels

The authors studied bit-error rate (BER) performance of asynchronous band-limited direct-sequence code-division multiple-access (DS-CDMA) systems with various diversity-combining receivers over Generalised-K fading channels. The effects of band-limited pulse shapes, multitone jamming, multiple-access interference as well as both flat and frequency-selective fading are considered. The Generalised-K model is adopted in order to include the effects of shadowing and fading of a wireless channel. The authors consider binary phase-shift keying as the modulation technique. The analytical expressions are valid for any arbitrary value of Generalised-K distribution parameters. Two types of band-limited pulses, namely spectrum raised cosine and Beaulieu-Tan-Damen (BTD) pulses, are incorporated in the analysis. Numerical results show that the system with BTD pulse outperforms the one with SRC pulse for various diversity-combining receivers under various channel conditions. Furthermore, by incorporating a minimum mean-square error stage in the multipath diversity receiver, the BER performance can be further improved.     

Beaconless stochastic parallel gradient descent laser beam control: numerical experiments

We apply a target-in-the-loop strategy to the case of adaptive optics beam control in the presence of strong atmospheric turbulence for air-to-ground directed energy laser applications. Using numerical simulations we show that in the absence of a cooperative beacon to probe the atmosphere it is possible to extract information suitable for effective beam control from images of the speckled and strongly turbulence degraded intensity distribution of the laser energy at the target. We use a closed-loop, single-deformable-mirror adaptive optics system driven by a target-in-the-loop stochastic parallel gradient descent optimization algorithm minimizing a mean-radius performance metric defined on the image of the laser beam intensity distribution formed at the receiver. We show that a relatively low order 25-channel zonal adaptive optical beam control system controlled in this way is capable of achieving a high degree of turbulence compensation with respect to energy concentration if the tilt can be corrected separately.     

Incorporating higher-order modal measurements in tilt estimation: natural and laser guide star applications

Tilt compensation performance is generally suboptimal when phase measurements from natural or laser guide stars are used as the conjugate phase in an adaptive optics system. Optimal compensation is obtained when the conjugate-phase coefficients are estimated from beacon measurements, given knowledge of the correlation between the on-axis object phase and the beacon measurements. We apply optimal compensation theory to tilt correction for the case of an off-axis beacon. Because off-axis higher-order modes are correlated with the on-axis tilt components, a performance gain can be realized when the tilt estimator includes higher-order modal measurements. For natural guide star compensation, it is shown that equivalent tilt compensation can be achieved at beacon offsets that are three times larger when higher-order modes through Zernike 15 are used in the tilt estimator. For a laser guide star, although tilt information cannot be measured directly because of beam reciprocity, off-axis higher-order modal measurements can be used to estimate tilt components, leading to a maximum Strehl ratio of approximately 0.3 for the relative aperture diameter D/r(0) = 4 and the relative turbulence outer scale L(0)/D = 10.     

Durham extremely large telescope adaptive optics simulation platform

Adaptive optics systems are essential on all large telescopes for which image quality is important. These are complex systems with many design parameters requiring optimization before good performance can be achieved. The simulation of adaptive optics systems is therefore necessary to categorize the expected performance. We describe an adaptive optics simulation platform, developed at Durham University, which can be used to simulate adaptive optics systems on the largest proposed future extremely large telescopes as well as on current systems. This platform is modular, object oriented, and has the benefit of hardware application acceleration that can be used to improve the simulation performance, essential for ensuring that the run time of a given simulation is acceptable. The simulation platform described here can be highly parallelized using parallelization techniques suited for adaptive optics simulation, while still offering the user complete control while the simulation is running. The results from the simulation of a ground layer adaptive optics system are provided as an example to demonstrate the flexibility of this simulation platform.