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2006

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Articles 1 - 30 of 57

Full-Text Articles in Optics

Slow Light With Large Fractional Delays By Spectral Hole-Burning In Rubidium Vapor, Ryan M. Camacho, Michael V. Pack, John C. Howell Sep 2006

Slow Light With Large Fractional Delays By Spectral Hole-Burning In Rubidium Vapor, Ryan M. Camacho, Michael V. Pack, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We report on the experimental realization of large fractional pulse delays in a hot, Doppler-broadened rubidium vapor. A pump laser burns a deep spectral hole in the inhomogeneously broadened vapor. The delay is shown to be widely tunable by both power broadening the resonance and frequency modulating the pump laser. The simplicity of the scheme opens up the possibility for practical optical delays and buffers.


Fast Scene Based Nonuniformity Correction With Minimal Temporal Latency, Christopher A. Rice Sep 2006

Fast Scene Based Nonuniformity Correction With Minimal Temporal Latency, Christopher A. Rice

Theses and Dissertations

The focus of this research was to derive a new algorithm for correction of gain nonuniformities in LIDAR focal plane arrays using as few frames as possible. Because of the current low production rate of LIDAR focal plane arrays there is a natural tendency for extreme nonuniformities to exist on a pixel by pixel basis as the manufacturing technique has not yet been perfected. Generally, nonuniformity correction techniques require a large number of frames and/or have obscure requirements on the translational shifts in the input image frames. This thesis presents a solution for finding multiplicative nonuniformities that exist in a …


Investigation Of Negative Refractive Index In Reciprocal Chiral Materials, Monish Ranjan Chatterjee, Partha P. Banerjee, Pradeep R. Anugula Aug 2006

Investigation Of Negative Refractive Index In Reciprocal Chiral Materials, Monish Ranjan Chatterjee, Partha P. Banerjee, Pradeep R. Anugula

Electrical and Computer Engineering Faculty Publications

It is well known that there exist both natural materials (such as milk or sugar solution) possessing chiral (or handed) properties, as well as an increasing list of man-made materials (such as sodium bromate) that exhibit chirality. One of the principal properties of chirality is that light of any arbitrary polarization, when propagating through a chiral material, splits up into two circular polarizations propagating in different directions. In the past decade or longer, researchers have investigated electromagnetic transverse (plane) wave propagation across a non-chiral/chiral interface, and determined the electromagnetic Fresnel coefficients for such propagation. Traditionally, such coefficients are derived under …


Transients Of The Electromagnetically-Induced-Transparency-Enhanced Refractive Kerr Nonlinearity: Theory, M. V. Pack, R. M. Camacho, John C. Howell Jul 2006

Transients Of The Electromagnetically-Induced-Transparency-Enhanced Refractive Kerr Nonlinearity: Theory, M. V. Pack, R. M. Camacho, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We present a theory describing the transients and rise times of the refractive Kerr nonlinearity which is enhanced using electromagnetically induced transparency (EIT). We restrict our analysis to the case of a pulsed signal field with continuous-wave EIT fields, and all fields are well below saturation. These restrictions enable the reduction of an EIT Kerr, four-level, density-matrix equation to a two-level Bloch-vector equation which has a simple and physically intuitive algebraic solution. The physically intuitive picture of a two-level Bloch vector provides insights that are easily generalized to more complex and experimentally realistic models. We consider generalization to the cases …


Investigation Of Ultracold Rubidium Atoms In A Pulsed Far Off Resonance Trap, Minarni Minarni Jul 2006

Investigation Of Ultracold Rubidium Atoms In A Pulsed Far Off Resonance Trap, Minarni Minarni

Physics Theses & Dissertations

This dissertation reports on the design, construction, and investigation of a pulsed optical dipole force trap which uses laser light to confine ultracold rubidium (Rb) atoms. Because the laser frequency is detuned far from the atomic resonance frequency, the optical dipole force trap is also called a "far-off-resonance trap" (FORT). The use of pulsed laser light to create an optical trap may find application in expanding the number of atomic species which can be confined. The experiments reported here are principally aimed, however, at understanding the physics of pulsed FORT dynamics in anticipation of using the free electron laser (FEL) …


Low-Distortion Slow Light Using Two Absorption Resonances, Ryan M. Camacho, Michael V. Pack, John C. Howell Jun 2006

Low-Distortion Slow Light Using Two Absorption Resonances, Ryan M. Camacho, Michael V. Pack, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We consider group delay and broadening using two strongly absorbing and widely spaced resonances. We derive relations which show that very large pulse bandwidths coupled with large group delays and small broadening can be achieved. Unlike single resonance systems, the dispersive broadening dominates the absorptive broadening which leads to a dramatic increase in the possible group delay. We show that the double resonance systems are excellent candidates for realizing all-optical delay lines. We report on an experiment which achieved up to 50 pulse delays with 40% broadening.


Role Of Beat Noise In Limiting The Sensitivity Of Optical Coherence Tomography, Richard C. Haskell, David Liao, Adam E. Pivonka, Tera L. Bell, Brendan R. Haberle, Barbara M. Hoeling, Daniel C. Petersen Jun 2006

Role Of Beat Noise In Limiting The Sensitivity Of Optical Coherence Tomography, Richard C. Haskell, David Liao, Adam E. Pivonka, Tera L. Bell, Brendan R. Haberle, Barbara M. Hoeling, Daniel C. Petersen

All HMC Faculty Publications and Research

The sensitivity and dynamic range of optical coherence tomography (OCT) are calculated for instruments utilizing two common interferometer configurations and detection schemes. Previous researchers recognized that the performance of dual-balanced OCT instruments is severely limited by beat noise, which is generated by incoherent light backscattered from the sample. However, beat noise has been ignored in previous calculations of Michelson OCT performance. Our measurements of instrument noise confirm the presence of beat noise even in a simple Michelson interferometer configuration with a single photodetector. Including this noise, we calculate the dynamic range as a function of OCT light source power, and …


An Analysis Of Nonlinear Elastic Deformations For A Homogeneous Beam At Varying Tip Loads And Pitch Angles, Robert J. Mcgraw Jun 2006

An Analysis Of Nonlinear Elastic Deformations For A Homogeneous Beam At Varying Tip Loads And Pitch Angles, Robert J. Mcgraw

Theses and Dissertations

The Princeton beam experiments of 1975 were performed in hopes of producing viable data for beam nonlinear elastic deformation models in hopes of improving helicopter main beam designs. The recorded data, specifically for homogeneous beams of 7075 aluminum, have been referenced as a baseline for the past thirty years to validate numerous computer models and theories in an effort to build beams capable of withstanding aeroelastic, static, and dynamic loading. The purpose of this study is to improve upon the data recorded in 1975 using newer technologies including a laser distance meter, digital inclinometer, and three-dimensional traverse to test X-axis, …


Characterizing A Co-Flow Nozzle For Use In A Filtered Rayleigh Scattering System, David S. Miceli Jun 2006

Characterizing A Co-Flow Nozzle For Use In A Filtered Rayleigh Scattering System, David S. Miceli

Theses and Dissertations

Research was conducted on the flow field exiting a co-annular flow nozzle for use in filtered Rayleigh scattering flow visualizations. More specifically, the flow visualizations were of the flow field exiting a coflow nozzle and illuminated by a tunable, nominal 4.2 watt narrow line width Argon laser operating at 514.5nm. ND:YAG lasers are typically used in this application, but some of the properties of a tunable Argon laser make it an attractive alternative. Before generating flow visualizations, the coflow nozzle was characterized both experimentally and computationally. Due to a flow asymmetry in the outer annulus flow field, the nozzle was …


Erratum: Exploring The Optimal Sensitivity Of Sum-Variance Nonseparability Critera For Spin-1/2 Systems, Irfan Ali Khan, John C. Howell Apr 2006

Erratum: Exploring The Optimal Sensitivity Of Sum-Variance Nonseparability Critera For Spin-1/2 Systems, Irfan Ali Khan, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

No abstract provided.


Phase Shifts In Frustrated Total Internal Reflection And Optical Tunneling By An Embedded Low-Index Thin Film, R. M.A. Azzam Apr 2006

Phase Shifts In Frustrated Total Internal Reflection And Optical Tunneling By An Embedded Low-Index Thin Film, R. M.A. Azzam

Electrical Engineering Faculty Publications

Simple and explicit expressions for the phase shifts that p- and s-polarized light experience in frustrated total internal reflection (FTIR) and optical tunneling by an embedded low-index thin film are obtained. The differential phase shifts in reflection and transmission Δr,Δt are found to be identical, and the associated ellipsometric parameters ψr,ψt are governed by a simple relation, independent of film thickness. When the Fresnel interface reflection phase shifts for the pand s polarizations or their average are quarter-wave, the corresponding overall reflection phase shifts introduced by the embedded layer are also quarter-wave for all values of film …


Performance-Metric Driven Atmospheric Compensation For Robust Free-Space Laser Communication, Peter N. Crabtree Apr 2006

Performance-Metric Driven Atmospheric Compensation For Robust Free-Space Laser Communication, Peter N. Crabtree

Theses and Dissertations

The effect of turbulence on laser propagation is a significant challenge to current electro-optical systems. While atmospheric compensation techniques in space object imaging and high-energy laser weapons have been thoroughly investigated, optimizing these techniques for Laser Communication (LaserCom) has not been examined to the same degree. Average Strehl ratio is the typical design metric for current atmospheric compensation systems. However, fade probability is the relevant metric for LaserCom. This difference motivated the investigation into metric-driven atmospheric compensation. Metric-based tracking techniques for fade mitigation is the first major focus of this research. In a moderate range air-to-air scenario, focal plane spot …


Comparison Of Climatological Optical Turbulence Profiles To Standard, Statistical And Numerical Models Using Heleeos, Liesebet E. Gravley Mar 2006

Comparison Of Climatological Optical Turbulence Profiles To Standard, Statistical And Numerical Models Using Heleeos, Liesebet E. Gravley

Theses and Dissertations

Optical turbulence within earth’s atmosphere plays a significant role in electromagnetic radiation propagation from a high energy laser. The index of refraction structure constant, Cn2, characterizes turbulent spatial fluctuations due to temperature gradients. These changes in the index of refraction affect the intensity of the laser wave front on its intended target. It is important to characterize this parameter throughout the atmosphere, the boundary layer and above, for its applications regarding the Airborne Laser (ABL) and the Advanced Tactical Laser (ATL). There are several ways to obtain values of optical turbulence, including standard and statistical models, physically-based numerical models, and …


Experimental Demonstration Of High Two-Photon Time-Energy Entanglement, Irfan Ali Khan, John C. Howell Mar 2006

Experimental Demonstration Of High Two-Photon Time-Energy Entanglement, Irfan Ali Khan, John C. Howell

Mathematics, Physics, and Computer Science Faculty Articles and Research

We report on the experimental demonstration of high energy-time entanglement in two-photon states created in the process of spontaneous parametric down-conversion. We show that the classical variance product, which we violate by three orders of magnitude, actually represents a lower bound estimate of the number of information eigenmodes K. Explicit measurements estimate K to be greater than 100, with theoretical estimates predicting a value of as high as 1×106. These results provide incentive for the practical feasibility of large bandwidth quantum information processing, particularly in cryptography over large distances.


Polar Phase Screens: A Comparison With Other Methods Of Random Phase Screen Generation, Rebecca J. Eckert Mar 2006

Polar Phase Screens: A Comparison With Other Methods Of Random Phase Screen Generation, Rebecca J. Eckert

Theses and Dissertations

This research provides the first organized comparison of random phase screen generation methods, including logarithmic polar Fourier series, using structure functions. Random phase screens are essential elements of simulating light propagation through turbulent media. In order to be effective, they must accurately reflect theory and be practical to implement. This research explains and evaluates three methods of generating random phase screens: using a Fourier series upon a polar frequency grid with logarithmic spacing; using the fast Fourier transform, with its Cartesian frequency grid; and using Zernike polynomials. It provides a comparison of the Polar Fourier Series technique with the two …


Control Demonstration Of A Thin Deformable In-Plane Actuated Mirror, Gina A. Peterson Mar 2006

Control Demonstration Of A Thin Deformable In-Plane Actuated Mirror, Gina A. Peterson

Theses and Dissertations

Current imaging satellites are limited in resolution and coverage area by the aperture size of their primary optical mirror. To get a large optical mirror into space, current launch weight and size restrictions must be overcome. Membrane-like optical mirrors can overcome these restrictions with their very lightweight and flexible properties. However, thin, deformable membrane mirrors are very susceptible to the space environment and require active control for surface stabilization and shaping. The primary goal of this research is to demonstrate that an in-plane actuated membrane-like deformable optical mirror can be controlled to optical wavelength tolerances in a closed-loop system. Fabrication …


Characteristics Of Two-Dimensional Triangular And Three-Dimensional Face-Centered-Cubic Photonic Crystals, Jeffery D. Clark Mar 2006

Characteristics Of Two-Dimensional Triangular And Three-Dimensional Face-Centered-Cubic Photonic Crystals, Jeffery D. Clark

Theses and Dissertations

The fabrication of photonic crystals (PhC) with photonic band gaps (PBG) in the visible range is a difficult task due to the small structural feature sizes of the PhC. The particular type of PhC examined is a two-dimensional (2-D) triangular structure with a PBG designed for visible wavelengths with applications in visible integrated photonic systems. This work examines the processes involved and viability of fabricating 2-D triangular PhC's by a variety of techniques: focused ion beam, electron lithography and holographic photo-polymerization/lithography. The design of the PhC was based on a program created to display gap maps for triangular structures. The …


Active Optical Tracking With Spatial Light Modulators, Steven R. Mawhorter Mar 2006

Active Optical Tracking With Spatial Light Modulators, Steven R. Mawhorter

Theses and Dissertations

Two spatial light modulators are utilized for beam splitting, steering and tracking. Both linear and holographic phase screens are used in a demonstration of technology to allow real time tracking to communicate in a one-to-several type scenario. One SLM is used to apply a linear phase modulation to steer multiple beams onto a detector. The spots that are produced represent the targets as they move around the field of view of the central communication node. A Gerchberg-Saxton algorithm will subsequently use the detected spots as the desired pointing locations. Using this as input, the Gerchberg-Saxton algorithm yields a phase only …


Multi-Dimensional Wave Front Sensing Algorithms For Embedded Tracking And Adaptive Optics Applications, Christopher C. Wood Mar 2006

Multi-Dimensional Wave Front Sensing Algorithms For Embedded Tracking And Adaptive Optics Applications, Christopher C. Wood

Theses and Dissertations

Current tracking and adaptive optics techniques cannot compensate for fast-moving extended objects, which is important for ground-based telescopes providing space situational awareness. To fill this need, a vector-projection maximum-likelihood wave-front sensing algorithm development and testing follows for this application. A derivation and simplification of the Cramer-Rao Lower Bound for wavefront sensing using a laser guide star bounds the performance of these systems and guides implementation of a vastly optimized maximum-likelihood search algorithm. A complete analysis of the bias, mean square error, and variance of the algorithm demonstrates exceptional performance of the new sensor. A proof of concept implementation shows feasibility …


Lqg/Ltr Tilt And Tip Control For The Starfire Optical Range 3.5-Meter Telescope's Adaptive Optics System, Neil D. Paris Mar 2006

Lqg/Ltr Tilt And Tip Control For The Starfire Optical Range 3.5-Meter Telescope's Adaptive Optics System, Neil D. Paris

Theses and Dissertations

The Air Force Research Laboratory has sponsored research on the tracking control loop portion of the adaptive optics system in the Starfire Optical Range 3.5-meter telescope at Kirtland Air Force Base. The control loop includes two steering mirrors (Coarse Steering Mirror and Fine Steering Mirror) used to remove wavefront tilt and tip phase distortion from light entering the telescope. The objective of this research is to design a single Linear Quadratic Gaussian controller to control both steering mirrors in order to eliminate wavefront tilt and tip distortions induced by the earth's atmosphere, and to evaluate the stability robustness and performance …


Fast Ground State Manipulation Of Neutral Atoms In Microscopic Optical Traps, D. D. Yavuz, P. B. Kulatunga, E. Urban, Todd A. Johnson, N. Proite, T. Henage, T. G. Walker, M. Saffman Feb 2006

Fast Ground State Manipulation Of Neutral Atoms In Microscopic Optical Traps, D. D. Yavuz, P. B. Kulatunga, E. Urban, Todd A. Johnson, N. Proite, T. Henage, T. G. Walker, M. Saffman

Physics Faculty Publications

We demonstrate Rabi flopping at MHz rates between ground hyperfine states of neutral 87Rb atoms that are trapped in two micron sized optical traps. Using tightly focused laser beams we demonstrate high fidelity, site specific Rabi rotations with cross talk on neighboring sites separated by 8  μm at the level of 10−3. Ramsey spectroscopy is used to measure a dephasing time of 870  μs, which is ≈5000  times longer than the time for a π/2 pulse.


Characterization Of An Acrylaminde Based Photopolymer For Fabrication Of Liquid Crystal Devices, Pavani Kotakonda Jan 2006

Characterization Of An Acrylaminde Based Photopolymer For Fabrication Of Liquid Crystal Devices, Pavani Kotakonda

Conference Papers

Photopolymers are increasingly interesting as new materials for the fabrication of electro optical liquid crystal devices. Photoinduced surface relief gratings in dry, self developing acrylamide based photopolymers can be used to align liquid crystals (LCs) as an alternative to the rubbing technique. These optically recorded surface relief patterns can be used to fabricate electro-optical switchable LC Bragg gratings. An investigation of the dependence of photoinduced surface relief gratings on recording intensity and thickness of the photopolymer layer is reported. The surface relief gratings were filled with E7 LCs and a switchable LC diffraction grating was fabricated.


Replay At Optical Communications Wavelengths Of Holographic Gratings Recorded In The Visible, Vincent Toal, Maurice Whelan, Alberto Volcan, Izabela Naydenova, Suzanne Martin Jan 2006

Replay At Optical Communications Wavelengths Of Holographic Gratings Recorded In The Visible, Vincent Toal, Maurice Whelan, Alberto Volcan, Izabela Naydenova, Suzanne Martin

Conference Papers

In this paper we report on holographic diffraction gratings recorded at visible light wavelength, which can be probed at telecommunication wavelengths. The recording material is an easily prepared, self-processing photopolymer, all of whose components are water soluble. Transmission gratings of various types, namely unslanted, slanted, totally internally reflecting and Bragg gratings were all fabricated. Diffraction efficiencies at telecommunications wavelengths compare favourably with those obtained in visible light.


Comparison Of Three Electronic Speckle Pattern Shearing Interferometers Using Photopolymer Holographic Optical Elements., Emilia Mihaylova, Izabela Naydenova, Vincent Toal, Suzanne Martin Jan 2006

Comparison Of Three Electronic Speckle Pattern Shearing Interferometers Using Photopolymer Holographic Optical Elements., Emilia Mihaylova, Izabela Naydenova, Vincent Toal, Suzanne Martin

Conference Papers

Three electronic speckle pattern shearing interferometers (ESPSI) using photopolymer holographic gratings to produce the sheared image are presented. In the first ESPSI system two holographic gratings are used. The gratings are placed between the object and an imaging lens in front of the CCD camera. In the second ESPSI system one grating is used in combination with a sheet of ground glass. The sheared images on the ground glass are further imaged onto a CCD camera. In the third ESPSI system only one grating is used - it is placed in front of the object. The image and the sheared …


Characterization Of An Acrylamide Based Photopolymer For Fabrication Of Liquid Crystal Devices, Pavani Kotakonda, Izabela Naydenova, Suzanne Martin, Vincent Toal Jan 2006

Characterization Of An Acrylamide Based Photopolymer For Fabrication Of Liquid Crystal Devices, Pavani Kotakonda, Izabela Naydenova, Suzanne Martin, Vincent Toal

Conference Papers

Photopolymers are increasingly interesting as new materials for the fabrication of electro optical liquid crystal devices. Photoinduced surface relief gratings in dry, self developing acrylamide based photopolymers can be used to align liquid crystals (LCs) as an alternative to the rubbing technique. These optically recorded surface relief patterns can be used to fabricate electro-optical switchable LC Bragg gratings. An investigation of the dependence of photoinduced surface relief gratings on recording intensity and thickness of the photopolymer layer is reported. The surface relief gratings were filled with E7 LCs and a switchable LC diffraction grating was fabricated.


Holographic Recording In Nanoparticle-Doped Photopolymer, Izabela Naydenova, Hosam Sherif, Svetlana Mintova, Suzanne Martin, Vincent Toal Jan 2006

Holographic Recording In Nanoparticle-Doped Photopolymer, Izabela Naydenova, Hosam Sherif, Svetlana Mintova, Suzanne Martin, Vincent Toal

Conference Papers

A nanoparticle-doped acrylic photopolymer is characterised as a material for holographic recording. The influence of nanoparticles on the photopolymer dynamic range, dynamics of recording, temporal stability and mechanical stability in terms of shrinkage has been studied. The dynamics of recording and the temporal stability are investigated by real time monitoring of the build up of diffraction gratings of spatial frequencies of 200 to 2000 l/mm. The shrinkage has been characterised by recording slanted transmission gratings and observation of the change in the Bragg angle.


Polarimetry Of Random Fields, Jeremy Ellis Jan 2006

Polarimetry Of Random Fields, Jeremy Ellis

Electronic Theses and Dissertations

On temporal, spatial and spectral scales which are small enough, all fields are fully polarized. In the optical regime, however, instantaneous fields can rarely be examined, and, instead, only average quantities are accessible. The study of polarimetry is concerned with both the description of electromagnetic fields and the characterization of media a field has interacted with. The polarimetric information is conventionally presented in terms of second order field correlations which are averaged over the ensemble of field realizations. Motivated by the deficiencies of classical polarimetry in dealing with specific practical situations, this dissertation expands the traditional polarimetric approaches to include …


Molecular Structure-Nonlinear Optical Property Relationships For A Series Of Polymethine And Squaraine Molecules, Jie Fu Jan 2006

Molecular Structure-Nonlinear Optical Property Relationships For A Series Of Polymethine And Squaraine Molecules, Jie Fu

Electronic Theses and Dissertations

This dissertation reports on the investigation of the relationships between molecular structure and two-photon absorption (2PA) properties for a series of polymethine and squaraine molecules. Current and emerging applications exploiting the quadratic dependence upon laser intensity, such as two-photon fluorescence imaging, three-dimensional microfabrication, optical data storage and optical limiting, have motivated researchers to find novel materials exhibiting strong 2PA. Organic materials are promising candidates because their linear and nonlinear optical properties can be optimized for applications by changing their structures through molecular engineering. Polymethine and squaraine dyes are particularly interesting because they are fluorescent and showing large 2PA. We used …


Pocket Deformable Mirror For Adaptive Optics Applications, Leonid A. Beresnev, Mikhail Vorontsov, Peter Wangsness Jan 2006

Pocket Deformable Mirror For Adaptive Optics Applications, Leonid A. Beresnev, Mikhail Vorontsov, Peter Wangsness

Electrical and Computer Engineering Faculty Publications

Adaptive/active optical elements are designed to improve optical system performance in the presence of phase aberrations. For atmospheric optics and astronomical applications, an ideal deformable mirror should have sufficient frequency bandwidth for compensation of fast changing wave front aberrations induced by either atmospheric turbulences or by turbulent air flows surrounding a flying object (air optical effects). In many applications, such as atmospheric target tracking, remote sensing from flying aircraft, boundary layer imaging, laser communication and laser beam projection over near horizontal propagation paths the phase aberration frequency bandwidth can exceed several kHz. These fast-changing aberrations are currently compensated using relatively …


Adaptive Beam Director For A Tiled Fiber Array, Mikhail Vorontsov, Jim F. Riker, Ernst Polnau, Svetlana Lachinova, Venkata S. Rao Gudimetla Jan 2006

Adaptive Beam Director For A Tiled Fiber Array, Mikhail Vorontsov, Jim F. Riker, Ernst Polnau, Svetlana Lachinova, Venkata S. Rao Gudimetla

Electrical and Computer Engineering Faculty Publications

We present the concept development of a novel atmospheric compensation system based on adaptive tiled fiber array architecture operating with target-in-the-loop scenarios for directed beam applications. The adaptive tiled fiber array system is integrated with adaptive beam director (ABD). Wavefront control and sensing functions are performed directly on the beam director telescope primary mirror. The beam control of the adaptive tiled fiber array aims to compensate atmospheric turbulence-induced dynamic phase aberrations and results in a corresponding brightness increase on the illuminated extended object. The system is specifically designed for tiled fiber system architectures operating in strong intensity scintillation and speckle-modulation …