Utilizing Gaussian-Schell model beams to mitigate atmospheric turbulence in free space optical communications / by Kyle R. Drexler.

Turbulence affects traditional free space optical communication by causing speckle to appear in the received beam profile. This occurs due to changes in the refractive index of the atmosphere that are caused by fluctuations in temperature and pressure, resulting in an inhomogeneous medium. The Gaussian-Schell model of partial coherence has been suggested as a means of mitigating these atmospheric inhomogeneities on the transmission side. This dissertation analyzed the Gaussian-Schell model of partial coherence by verifying the Gaussian-Schell model in the far-field, investigated the number of independent phase control screens necessary to approach the ideal Gaussian-Schell model, and showed experimentally that the Gaussian-Schell model of partial coherence is achievable in the far-field using a liquid crystal spatial light modulator. A method for optimizing the statistical properties of the Gaussian-Schell model was developed to maximize the coherence of the field while ensuring that it does not exhibit the same statistics as a fully coherent source. Finally a technique to estimate the minimum spatial resolution necessary in a spatial light modulator was developed to effectively propagate the Gaussian-Schell model through a range of atmospheric turbulence strengths. This work showed that regardless of turbulence strength or receiver aperture, transmitting the Gaussian-Schell model of partial coherence instead of a fully coherent source will yield a reduction in the intensity fluctuations of the received field. By measuring the variance of the intensity fluctuations and the received mean, it is shown through the scintillation index that using the Gaussian-Schell model of partial coherence is a simple and straight forward method to mitigate atmospheric turbulence instead of traditional adaptive optics in free space optical communications.

Fading pdf of free-space optical communication system with pointing error

A free-space optical (FSO) laser communication system with perfect fast-tracking experiences random power fading due to atmospheric turbulence. For a FSO communication system without fast-tracking or with imperfect fast-tracking, the fading probability density function (pdf) is also affected by the pointing error. In this thesis, the overall fading pdfs of FSO communication system with pointing errors are calculated using an analytical method based on the fast-tracked on-axis and off-axis fading pdfs and the fast-tracked beam profile of a turbulence channel. The overall fading pdf is firstly studied for the FSO communication system with collimated laser beam. Large-scale numerical wave-optics simulations are performed to verify the analytically calculated fading pdf with collimated beam under various turbulence channels and pointing errors. The calculated overall fading pdfs are almost identical to the directly simulated fading pdfs. The calculated overall fading pdfs are also compared with the gamma-gamma (GG) and the log-normal (LN) fading pdf models. They fit better than both the GG and LN fading pdf models under different receiver aperture sizes in all the studied cases. Further, the analytical method is expanded to the FSO communication system with beam diverging angle case. It is shown that the gamma pdf model is still valid for the fast-tracked on-axis and off-axis fading pdfs with point-like receiver aperture when the laser beam is propagated with beam diverging angle. Large-scale numerical wave-optics simulations prove that the analytically calculated fading pdfs perfectly fit the overall fading pdfs for both focused and diverged beam cases. The influence of the fast-tracked on-axis and off-axis fading pdfs, the fast-tracked beam profile, and the pointing error on the overall fading pdf is also discussed. At last, the analytical method is compared with the previous heuristic fading pdf models proposed since 1970s. Although some of previously proposed fading pdf models provide close fit to the experiment and simulation data, these close fits only exist under particular conditions. Only analytical method shows accurate fit to the directly simulated fading pdfs under different turbulence strength, propagation distances, receiver aperture sizes and pointing errors.

Robustness of speckle imaging techniques applied to horizontal imaging scenarios

Atmospheric turbulence near the ground severely limits the quality of imagery acquired over long horizontal paths. In defense, surveillance, and border security applications, there is interest in deploying man-portable, embedded systems incorporating image reconstruction methods to compensate turbulence effects. While many image reconstruction methods have been proposed, their suitability for use in man-portable embedded systems is uncertain. To be effective, these systems must operate over significant variations in turbulence conditions while subject to other variations due to operation by novice users. Systems that meet these requirements and are otherwise designed to be immune to the factors that cause variation in performance are considered robust. In addition robustness in design, the portable nature of these systems implies a preference for systems with a minimum level of computational complexity. Speckle imaging methods have recently been proposed as being well suited for use in man-portable horizontal imagers. In this work, the robustness of speckle imaging methods is established by identifying a subset of design parameters that provide immunity to the expected variations in operating conditions while minimizing the computation time necessary for image recovery. Design parameters are selected by parametric evaluation of system performance as factors external to the system are varied. The precise control necessary for such an evaluation is made possible using image sets of turbulence degraded imagery developed using a novel technique for simulating anisoplanatic image formation over long horizontal paths. System performance is statistically evaluated over multiple reconstruction using the Mean Squared Error (MSE) to evaluate reconstruction quality. In addition to more general design parameters, the relative performance the bispectrum and the Knox-Thompson phase recovery methods is also compared. As an outcome of this work it can be concluded that speckle-imaging techniques are robust to the variation in turbulence conditions and user controlled parameters expected when operating during the day over long horizontal paths. Speckle imaging systems that incorporate 15 or more image frames and 4 estimates of the object phase per reconstruction provide up to 45% reduction in MSE and 68% reduction in the deviation. In addition, Knox-Thompson phase recover method is shown to produce images in half the time required by the bispectrum. The quality of images reconstructed using Knox-Thompson and bispectrum methods are also found to be nearly identical. Finally, it is shown that certain blind image quality metrics can be used in place of the MSE to evaluate quality in field scenarios. Using blind metrics rather depending on user estimates allows for reconstruction quality that differs from the minimum MSE by as little as 1%, significantly reducing the deviation in performance due to user action.

Statistics of the received power for free space optical channels

Free space optical (FSO) communication links can experience extreme signal degradation due to atmospheric turbulence induced spatial and temporal irradiance fuctuations (scintillation) in the laser wavefront. In addition, turbulence can cause the laser beam centroid to wander resulting in power fading, and sometimes complete loss of the signal. Spreading of the laser beam and jitter are also artifacts of atmospheric turbulence. To accurately predict the signal fading that occurs in a laser communication system and to get a true picture of how this affects crucial performance parameters like bit error rate (BER) it is important to analyze the probability density function (PDF) of the integrated irradiance fuctuations at the receiver. In addition, it is desirable to find a theoretical distribution that accurately models these ?uctuations under all propagation conditions. The PDF of integrated irradiance fuctuations is calculated from numerical wave-optic simulations of a laser after propagating through atmospheric turbulence to investigate the evolution of the distribution as the aperture diameter is increased. The simulation data distribution is compared to theoretical gamma-gamma and lognormal PDF models under a variety of scintillation regimes from weak to very strong. Our results show that the gamma-gamma PDF provides a good fit to the simulated data distribution for all aperture sizes studied from weak through moderate scintillation. In strong scintillation, the gamma-gamma PDF is a better fit to the distribution for point-like apertures and the lognormal PDF is a better fit for apertures the size of the atmospheric spatial coherence radius ρ0 or larger. In addition, the PDF of received power from a Gaussian laser beam, which has been adaptively compensated at the transmitter before propagation to the receiver of a FSO link in the moderate scintillation regime is investigated. The complexity of the adaptive optics (AO) system is increased in order to investigate the changes in the distribution of the received power and how this affects the BER. For the 10 km link, due to the non-reciprocal nature of the propagation path the optimal beam to transmit is unknown. These results show that a low-order level of complexity in the AO provides a better estimate for the optimal beam to transmit than a higher order for non-reciprocal paths. For the 20 km link distance it was found that, although minimal, all AO complexity levels provided an equivalent improvement in BER and that no AO complexity provided the correction needed for the optimal beam to transmit. Finally, the temporal power spectral density of received power from a FSO communication link is investigated. Simulated and experimental results for the coherence time calculated from the temporal correlation function are presented. Results for both simulation and experimental data show that the coherence time increases as the receiving aperture diameter increases. For finite apertures the coherence time increases as the communication link distance is increased. We conjecture that this is due to the increasing speckle size within the pupil plane of the receiving aperture for an increasing link distance.

Application of MFBD Algorithms to Image Reconstruction Under Anisoplanatic Conditions

All optical systems that operate in or through the atmosphere suffer from turbulence induced image blur. Both military and civilian surveillance, gun-sighting, and target identification systems are interested in terrestrial imaging over very long horizontal paths, but atmospheric turbulence can blur the resulting images beyond usefulness. My dissertation explores the performance of a multi-frame-blind-deconvolution technique applied under anisoplanatic conditions for both Gaussian and Poisson noise model assumptions. The technique is evaluated for use in reconstructing images of scenes corrupted by turbulence in long horizontal-path imaging scenarios and compared to other speckle imaging techniques. Performance is evaluated via the reconstruction of a common object from three sets of simulated turbulence degraded imagery representing low, moderate and severe turbulence conditions. Each set consisted of 1000 simulated, turbulence degraded images. The MSE performance of the estimator is evaluated as a function of the number of images, and the number of Zernike polynomial terms used to characterize the point spread function. I will compare the mean-square-error (MSE) performance of speckle imaging methods and a maximum-likelihood, multi-frame blind deconvolution (MFBD) method applied to long-path horizontal imaging scenarios. Both methods are used to reconstruct a scene from simulated imagery featuring anisoplanatic turbulence induced aberrations. This comparison is performed over three sets of 1000 simulated images each for low, moderate and severe turbulence-induced image degradation. The comparison shows that speckle-imaging techniques reduce the MSE 46 percent, 42 percent and 47 percent on average for low, moderate, and severe cases, respectively using 15 input frames under daytime conditions and moderate frame rates. Similarly, the MFBD method provides, 40 percent, 29 percent, and 36 percent improvements in MSE on average under the same conditions. The comparison is repeated under low light conditions (less than 100 photons per pixel) where improvements of 39 percent, 29 percent and 27 percent are available using speckle imaging methods and 25 input frames and 38 percent, 34 percent and 33 percent respectively for the MFBD method and 150 input frames. The MFBD estimator is applied to three sets of field data and the results presented. Finally, a combined Bispectrum-MFBD Hybrid estimator is proposed and investigated. This technique consistently provides a lower MSE and smaller variance in the estimate under all three simulated turbulence conditions.

Dynamics of settling charged particles in turbulence : theory and experiments

It has been proposed that inertial clustering may lead to an increased collision rate of water droplets in clouds. Atmospheric clouds and electrosprays contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. In this thesis, we present the investigation of charged inertial particles embedded in turbulence. We have developed a theoretical description for the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb ’terminalar speed to turbulence dissipation velocity scale), and the settling parameter (the ratio of the gravitational terminal speed to turbulence dissipation velocity scale). For the monodispersion particles, The peak in the radial distribution function is well predicted by the balance between the particle terminal velocity under Coulomb repulsion and a time-averaged ’drift’ velocity obtained from the nonuniform sampling of fluid strain and rotation due to finite particle inertia. The theory is compared to measured radial distribution functions for water particles in homogeneous, isotropic air turbulence. The radial distribution functions are obtained from particle positions measured in three dimensions using digital holography. The measurements support the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of ’gravity’ is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity. The relation between the radial distribution functions and inward mean radial relative velocity is established for charged particles.