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.

Review of free-space optical communications with diverging beam

The report reviews the technology of Free-space Optical Communication (FSO) and simulation methods for testing the performance of diverged beam in the technology. In addition to the introduction, the theory of turbulence and its effect over laser is also reviewed. In the simulation revision chapter, on-off keying (OOK) and diverged beam is assumed in the transmitter, and in the receiver, avalanche photodiode (APD) is utilized to convert the photon stream into electron stream. Phase screens are adopted to simulate the effect of turbulence over the phase of the optical beam. Apart from this, the method of data processing is introduced and retrospected. In the summary chapter, there is a general explanation of different beam divergence and their performance.

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.

Four-window technique for measuring optical-phase-space-time-frequency tomography

A new approach, the four-window technique, was developed to measure optical phase-space-time-frequency tomography (OPSTFT). The four-window technique is based on balanced heterodyne detection with two local oscillator (LO) fields. This technique can provide independent control of position, momentum, time and frequency resolution. The OPSTFT is a Wigner distribution function of two independent Fourier transform pairs, phase-space and time-frequency. The OPSTFT can be applied for early disease detection.

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.

Orbits design for Leo space based solar power satellite system

Space Based Solar Power satellites use solar arrays to generate clean, green, and renewable electricity in space and transmit it to earth via microwave, radiowave or laser beams to corresponding receivers (ground stations). These traditionally are large structures orbiting around earth at the geo-synchronous altitude. This thesis introduces a new architecture for a Space Based Solar Power satellite constellation. The proposed concept reduces the high cost involved in the construction of the space satellite and in the multiple launches to the geo-synchronous altitude. The proposed concept is a constellation of Low Earth Orbit satellites that are smaller in size than the conventional system. For this application a Repeated Sun-Synchronous Track Circular Orbit is considered (RSSTO). In these orbits, the spacecraft re-visits the same locations on earth periodically every given desired number of days with the line of nodes of the spacecraft’s orbit fixed relative to the Sun. A wide range of solutions are studied, and, in this thesis, a two-orbit constellation design is chosen and simulated. The number of satellites is chosen based on the electric power demands in a given set of global cities. The orbits of the satellites are designed such that their ground tracks visit a maximum number of ground stations during the revisit period. In the simulation, the locations of the ground stations are chosen close to big cities, in USA and worldwide, so that the space power constellation beams down power directly to locations of high electric power demands. The j2 perturbations are included in the mathematical model used in orbit design. The Coverage time of each spacecraft over a ground site and the gap time between two consecutive spacecrafts visiting a ground site are simulated in order to evaluate the coverage continuity of the proposed solar power constellation. It has been observed from simulations that there always periods in which s spacecraft does not communicate with any ground station. For this reason, it is suggested that each satellite in the constellation be equipped with power storage components so that it can store power for later transmission. This thesis presents a method for designing the solar power constellation orbits such that the number of ground stations visited during the given revisit period is maximized. This leads to maximizing the power transmission to ground stations.

Computational study of internal and external condensing flows and experimental synthesis to investigate their attainability and stability in ground-based and space-based environments

This doctoral thesis presents the computational work and synthesis with experiments for internal (tube and channel geometries) as well as external (flow of a pure vapor over a horizontal plate) condensing flows. The computational work obtains accurate numerical simulations of the full two dimensional governing equations for steady and unsteady condensing flows in gravity/0g environments. This doctoral work investigates flow features, flow regimes, attainability issues, stability issues, and responses to boundary fluctuations for condensing flows in different flow situations. This research finds new features of unsteady solutions of condensing flows; reveals interesting differences in gravity and shear driven situations; and discovers novel boundary condition sensitivities of shear driven internal condensing flows. Synthesis of computational and experimental results presented here for gravity driven in-tube flows lays framework for the future two-phase component analysis in any thermal system. It is shown for both gravity and shear driven internal condensing flows that steady governing equations have unique solutions for given inlet pressure, given inlet vapor mass flow rate, and fixed cooling method for condensing surface. But unsteady equations of shear driven internal condensing flows can yield different “quasi-steady” solutions based on different specifications of exit pressure (equivalently exit mass flow rate) concurrent to the inlet pressure specification. This thesis presents a novel categorization of internal condensing flows based on their sensitivity to concurrently applied boundary (inlet and exit) conditions. The computational investigations of an external shear driven flow of vapor condensing over a horizontal plate show limits of applicability of the analytical solution. Simulations for this external condensing flow discuss its stability issues and throw light on flow regime transitions because of ever-present bottom wall vibrations. It is identified that laminar to turbulent transition for these flows can get affected by ever present bottom wall vibrations. Detailed investigations of dynamic stability analysis of this shear driven external condensing flow result in the introduction of a new variable, which characterizes the ratio of strength of the underlying stabilizing attractor to that of destabilizing vibrations. Besides development of CFD tools and computational algorithms, direct application of research done for this thesis is in effective prediction and design of two-phase components in thermal systems used in different applications. Some of the important internal condensing flow results about sensitivities to boundary fluctuations are also expected to be applicable to flow boiling phenomenon. Novel flow sensitivities discovered through this research, if employed effectively after system level analysis, will result in the development of better control strategies in ground and space based two-phase thermal systems.

Space trajectories optimization using variable-chromosome-length genetic algorithms

The problem of optimal design of a multi-gravity-assist space trajectories, with free number of deep space maneuvers (MGADSM) poses multi-modal cost functions. In the general form of the problem, the number of design variables is solution dependent. To handle global optimization problems where the number of design variables varies from one solution to another, two novel genetic-based techniques are introduced: hidden genes genetic algorithm (HGGA) and dynamic-size multiple population genetic algorithm (DSMPGA). In HGGA, a fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective (hidden) genes. Hidden genes are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. In DSMPGA, sub-populations of fixed size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members based on their relative fitness. The resulting sub-populations have different sizes from their initial sizes. The process repeats, leading to increasing the size of sub-populations of more fit solutions. Both techniques are applied to several MGADSM problems. They have the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. The results show that solutions obtained using the developed tools match known solutions for complex case studies. The HGGA is also used to obtain the asteroids sequence and the mission structure in the global trajectory optimization competition (GTOC) problem. As an application of GA optimization to Earth orbits, the problem of visiting a set of ground sites within a constrained time frame is solved. The J2 perturbation and zonal coverage are considered to design repeated Sun-synchronous orbits. Finally, a new set of orbits, the repeated shadow track orbits (RSTO), is introduced. The orbit parameters are optimized such that the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days.

RAPID SPACE TRAJECTORY GENERATION USING A FOURIER SERIES SHAPE-BASED APPROACH

With the insatiable curiosity of human beings to explore the universe and our solar system, it is essential to benefit from larger propulsion capabilities to execute efficient transfers and carry more scientific equipment. In the field of space trajectory optimization the fundamental advances in using low-thrust propulsion and exploiting the multi-body dynamics has played pivotal role in designing efficient space mission trajectories. The former provides larger cumulative momentum change in comparison with the conventional chemical propulsion whereas the latter results in almost ballistic trajectories with negligible amount of propellant. However, the problem of space trajectory design translates into an optimal control problem which is, in general, time-consuming and very difficult to solve. Therefore, the goal of the thesis is to address the above problem by developing a methodology to simplify and facilitate the process of finding initial low-thrust trajectories in both two-body and multi-body environments. This initial solution will not only provide mission designers with a better understanding of the problem and solution but also serves as a good initial guess for high-fidelity optimal control solvers and increases their convergence rate. Almost all of the high-fidelity solvers enjoy the existence of an initial guess that already satisfies the equations of motion and some of the most important constraints. Despite the nonlinear nature of the problem, it is sought to find a robust technique for a wide range of typical low-thrust transfers with reduced computational intensity. Another important aspect of our developed methodology is the representation of low-thrust trajectories by Fourier series with which the number of design variables reduces significantly. Emphasis is given on simplifying the equations of motion to the possible extent and avoid approximating the controls. These facts contribute to speeding up the solution finding procedure. Several example applications of two and three-dimensional two-body low-thrust transfers are considered. In addition, in the multi-body dynamic, and in particular the restricted-three-body dynamic, several Earth-to-Moon low-thrust transfers are investigated.

Translation Studies on an Annular Field Reversed Configuration Device for Space Propulsion

This research investigated annular field reversed configuration (AFRC)devices for high power electric propulsion by demonstrating the acceleration of these plasmoids using an experimental prototype and measuring the plasmoid's velocity, impulse, and energy efficiency. The AFRC plasmoid translation experiment was design and constructed with the aid of a dynamic circuit model. Two versions of the experiment were built, using underdamped RLC circuits at 10 kHz and 20 kHz. Input energies were varied from 100 J/pulse to 1000 J/pulse for the 10 kHz bank and 100 J/pulse for the 20 kHz bank. The plasmoids were formed in static gas fill of argon, from 1 mTorr to 50 mTorr. The translation of the plasmoid was accomplished by incorporating a small taper into the outer coil, with a half angle of 2°. Magnetic field diagnostics, plasma probes, and single-frame imaging were used to measure the plasmoid's velocity and to diagnose plasmoid behavior. Full details of the device design, construction, and diagnostics are provided in this dissertation. The results from the experiment demonstrated that a repeatable AFRC plasmoid was produced between the coils, yet failed to translate for all tested conditions. The data revealed the plasmoid was limited in lifetime to only a few (4-10) μs, too short for translation at low energy. A global stability study showed that the plasma suffered a radial collapse onto the inner wall early in its lifecycle. The radial collapse was traced to a magnetic pressure imbalance. A correction made to the circuit was successful in restoring an equilibrium pressure balance and prolonging radial stability by an additional 2.5 μs. The equilibrium state was sufficient to confirm that the plasmoid current in an AFRC reaches a steady-state prior to the peak of the coil currents. This implies that the plasmoid will always be driven to the inner wall, unless it translates from the coils prior to peak coil currents. However, ejection of the plasmoid before the peak coil currents results in severe efficiency losses. These results demonstrate the difficulty in designing an AFRC experiment for translation as balancing the different requirements for stability, balance, and efficient translation can have competing consequences.

Preserving and interpreting the mining company office : landscape, space and technological change in the management of the copper industry

The purpose of this research is to examine the role of the mining company office in the management of the copper industry in Michigan’s Keweenaw Peninsula between 1901 and 1946. Two of the largest and most influential companies were examined – the Calumet & Hecla Mining Company and the Quincy Mining Company. Both companies operated for more than forty years under general managers who were arguably the most influential people in the management of each company. James MacNaughton, general manager at Calumet and Hecla, worked from 1901 through 1941; Charles Lawton, general manager at Quincy Mining Company, worked from 1905 through 1946. In this case, both of these managers were college-educated engineers and adopted scientific management techniques to operate their respective companies. This research focused on two main goals. The first goal of this project was to address the managerial changes in Michigan’s copper mining offices of the early twentieth century. This included the work of MacNaughton and Lawton, along with analysis of the office structures themselves and what changes occurred through time. The second goal of the project was to create a prototype virtual exhibit for use at the Quincy Mining Company office. A virtual exhibit will allow visitors the opportunity to visit the office virtually, experiencing the office as an office worker would have in the early twentieth century. To meet both goals, this project used various research materials, including archival sources, oral histories, and material culture to recreate the history of mining company management in the Copper Country.

DEVELOPMENT OF ION EXCHANGE MODELS FOR WATER TREATMENT AND APPLICATION TO THE INTERNATIONAL SPACE STATION WATER PROCESSOR

The International Space Station (ISS) requires a substantial amount of potable water for use by the crew. The economic and logistic limitations of transporting the vast amount of water required onboard the ISS necessitate onboard recovery and reuse of the aqueous waste streams. Various treatment technologies are employed within the ISS water processor to render the waste water potable, including filtration, ion exchange, adsorption, and catalytic wet oxidation. The ion exchange resins and adsorption media are combined in multifiltration beds for removal of ionic and organic compounds. A mathematical model (MFBMODEL™) designed to predict the performance of a multifiltration (MF) bed was developed. MFBMODEL consists of ion exchange models for describing the behavior of the different resin types in a MF bed (e.g., mixed bed, strong acid cation, strong base anion, and weak base anion exchange resins) and an adsorption model capable of predicting the performance of the adsorbents in a MF bed. Multicomponent ion exchange ii equilibrium models that incorporate the water formation reaction, electroneutrality condition, and degree of ionization of weak acids and bases for mixed bed, strong acid cation, strong base anion, and weak base anion exchange resins were developed and verified. The equilibrium models developed use a tanks-inseries approach that allows for consideration of variable influent concentrations. The adsorption modeling approach was developed in related studies and application within the MFBMODEL framework was demonstrated in the Appendix to this study. MFBMODEL consists of a graphical user interface programmed in Visual Basic and Fortran computational routines. This dissertation shows MF bed modeling results in which the model is verified for a surrogate of the ISS waste shower and handwash stream. In addition, a multicomponent ion exchange model that incorporates mass transfer effects was developed, which is capable of describing the performance of strong acid cation (SAC) and strong base anion (SBA) exchange resins, but not including reaction effects. This dissertation presents results showing the mass transfer model's capability to predict the performance of binary and multicomponent column data for SAC and SBA exchange resins. The ion exchange equilibrium and mass transfer models developed in this study are also applicable to terrestrial water treatment systems. They could be applied for removal of cations and anions from groundwater (e.g., hardness, nitrate, perchlorate) and from industrial process waters (e.g. boiler water, ultrapure water in the semiconductor industry).