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.

Berry-Esseen bounds for nonlinear statistics, and asymptotic relative efficiency between correlation statistics

Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.

Parametric combustion modeling for ethanol-gasoline fuelled spark ignition engines

Ethanol-gasoline fuel blends are increasingly being used in spark ignition (SI) engines due to continued growth in renewable fuels as part of a growing renewable portfolio standard (RPS). This leads to the need for a simple and accurate ethanol-gasoline blends combustion model that is applicable to one-dimensional engine simulation. A parametric combustion model has been developed, integrated into an engine simulation tool, and validated using SI engine experimental data. The parametric combustion model was built inside a user compound in GT-Power. In this model, selected burn durations were computed using correlations as functions of physically based non-dimensional groups that have been developed using the experimental engine database over a wide range of ethanol-gasoline blends, engine geometries, and operating conditions. A coefficient of variance (COV) of gross indicated mean effective pressure (IMEP) correlation was also added to the parametric combustion model. This correlation enables the cycle combustion variation modeling as a function of engine geometry and operating conditions. The computed burn durations were then used to fit single and double Wiebe functions. The single-Wiebe parametric combustion compound used the least squares method to compute the single-Wiebe parameters, while the double-Wiebe parametric combustion compound used an analytical solution to compute the double-Wiebe parameters. These compounds were then integrated into the engine model in GT-Power through the multi-Wiebe combustion template in which the values of Wiebe parameters (single-Wiebe or double-Wiebe) were sensed via RLT-dependence. The parametric combustion models were validated by overlaying the simulated pressure trace from GT-Power on to experimentally measured pressure traces. A thermodynamic engine model was also developed to study the effect of fuel blends, engine geometries and operating conditions on both the burn durations and COV of gross IMEP simulation results.

Parametric estimation of pulse arrival time: a robust approach to pulse wave velocity

Pulse wave velocity (PWV) is a surrogate of arterial stiffness and represents a non-invasive marker of cardiovascular risk. The non-invasive measurement of PWV requires tracking the arrival time of pressure pulses recorded in vivo, commonly referred to as pulse arrival time (PAT). In the state of the art, PAT is estimated by identifying a characteristic point of the pressure pulse waveform. This paper demonstrates that for ambulatory scenarios, where signal-to-noise ratios are below 10 dB, the performance in terms of repeatability of PAT measurements through characteristic points identification degrades drastically. Hence, we introduce a novel family of PAT estimators based on the parametric modeling of the anacrotic phase of a pressure pulse. In particular, we propose a parametric PAT estimator (TANH) that depicts high correlation with the Complior(R) characteristic point D1 (CC = 0.99), increases noise robustness and reduces by a five-fold factor the number of heartbeats required to obtain reliable PAT measurements.

Age modeling of young non-varved lake sediments: methods and limits. Examples from two lakes in Central Chile

High-resolution and highly precise age models for recent lake sediments (last 100–150 years) are essential for quantitative paleoclimate research. These are particularly important for sedimentological and geochemical proxies, where transfer functions cannot be established and calibration must be based upon the relation of sedimentary records to instrumental data. High-precision dating for the calibration period is most critical as it determines directly the quality of the calibration statistics. Here, as an example, we compare radionuclide age models obtained on two high-elevation glacial lakes in the Central Chilean Andes (Laguna Negra: 33°38′S/70°08′W, 2,680 m a.s.l. and Laguna El Ocho: 34°02′S/70°19′W, 3,250 m a.s.l.). We show the different numerical models that produce accurate age-depth chronologies based on 210Pb profiles, and we explain how to obtain reduced age-error bars at the bottom part of the profiles, i.e., typically around the end of the 19th century. In order to constrain the age models, we propose a method with five steps: (i) sampling at irregularly-spaced intervals for 226Ra, 210Pb and 137Cs depending on the stratigraphy and microfacies, (ii) a systematic comparison of numerical models for the calculation of 210Pb-based age models: constant flux constant sedimentation (CFCS), constant initial concentration (CIC), constant rate of supply (CRS) and sediment isotope tomography (SIT), (iii) numerical constraining of the CRS and SIT models with the 137Cs chronomarker of AD 1964 and, (iv) step-wise cross-validation with independent diagnostic environmental stratigraphic markers of known age (e.g., volcanic ash layer, historical flood and earthquakes). In both examples, we also use airborne pollutants such as spheroidal carbonaceous particles (reflecting the history of fossil fuel emissions), excess atmospheric Cu deposition (reflecting the production history of a large local Cu mine), and turbidites related to historical earthquakes. Our results show that the SIT model constrained with the 137Cs AD 1964 peak performs best over the entire chronological profile (last 100–150 years) and yields the smallest standard deviations for the sediment ages. Such precision is critical for the calibration statistics, and ultimately, for the quality of the quantitative paleoclimate reconstruction. The systematic comparison of CRS and SIT models also helps to validate the robustness of the chronologies in different sections of the profile. Although surprisingly poorly known and under-explored in paleolimnological research, the SIT model has a great potential in paleoclimatological reconstructions based on lake sediments

Evaluation of texture features in hepatic tissue characterization from non-enhanced CT images

Aim of this paper is to evaluate the diagnostic contribution of various types of texture features in discrimination of hepatic tissue in abdominal non-enhanced Computed Tomography (CT) images. Regions of Interest (ROIs) corresponding to the classes: normal liver, cyst, hemangioma, and hepatocellular carcinoma were drawn by an experienced radiologist. For each ROI, five distinct sets of texture features are extracted using First Order Statistics (FOS), Spatial Gray Level Dependence Matrix (SGLDM), Gray Level Difference Method (GLDM), Laws' Texture Energy Measures (TEM), and Fractal Dimension Measurements (FDM). In order to evaluate the ability of the texture features to discriminate the various types of hepatic tissue, each set of texture features, or its reduced version after genetic algorithm based feature selection, was fed to a feed-forward Neural Network (NN) classifier. For each NN, the area under Receiver Operating Characteristic (ROC) curves (Az) was calculated for all one-vs-all discriminations of hepatic tissue. Additionally, the total Az for the multi-class discrimination task was estimated. The results show that features derived from FOS perform better than other texture features (total Az: 0.802+/-0.083) in the discrimination of hepatic tissue.

Non-ignorable loss to follow-up: correcting mortality estimates based on additional outcome ascertainment

Loss to follow-up (LTFU) is a common problem in many epidemiological studies. In antiretroviral treatment (ART) programs for patients with human immunodeficiency virus (HIV), mortality estimates can be biased if the LTFU mechanism is non-ignorable, that is, mortality differs between lost and retained patients. In this setting, routine procedures for handling missing data may lead to biased estimates. To appropriately deal with non-ignorable LTFU, explicit modeling of the missing data mechanism is needed. This can be based on additional outcome ascertainment for a sample of patients LTFU, for example, through linkage to national registries or through survey-based methods. In this paper, we demonstrate how this additional information can be used to construct estimators based on inverse probability weights (IPW) or multiple imputation. We use simulations to contrast the performance of the proposed estimators with methods widely used in HIV cohort research for dealing with missing data. The practical implications of our approach are illustrated using South African ART data, which are partially linkable to South African national vital registration data. Our results demonstrate that while IPWs and proper imputation procedures can be easily constructed from additional outcome ascertainment to obtain valid overall estimates, neglecting non-ignorable LTFU can result in substantial bias. We believe the proposed estimators are readily applicable to a growing number of studies where LTFU is appreciable, but additional outcome data are available through linkage or surveys of patients LTFU. Copyright © 2013 John Wiley & Sons, Ltd.

Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

A Parametric Test of Perfect Ranking in Balanced Ranked Set Sampling

Many techniques based on data which are drawn by Ranked Set Sampling (RSS) scheme assume that the ranking of observations is perfect. Therefore it is essential to develop some methods for testing this assumption. In this article, we propose a parametric location-scale free test for assessing the assumption of perfect ranking. The results of a simulation study in two special cases of normal and exponential distributions indicate that the proposed test performs well in comparison with its leading competitors.

Cardiac biomarkers and clinical scores for risk stratification in elderly patients with non-high-risk pulmonary embolism.

OBJECTIVE To determine the prognostic accuracy of cardiac biomarkers alone and in combination with clinical scores in elderly patients with non-high-risk pulmonary embolism (PE). DESIGN Ancillary analysis of a Swiss multicentre prospective cohort study. SUBJECTS A total of 230 patients aged ≥65 years with non-high-risk PE. MAIN OUTCOME MEASURES The study end-point was a composite of PE-related complications, defined as PE-related death, recurrent venous thromboembolism or major bleeding during a follow-up of 30 days. The prognostic accuracy of the Pulmonary Embolism Severity Index (PESI), the Geneva Prognostic Score (GPS), the precursor of brain natriuretic peptide (NT-proBNP) and high-sensitivity cardiac troponin T (hs-cTnT) was determined using sensitivity, specificity, predictive values, receiver operating characteristic (ROC) curve analysis, logistic regression and reclassification statistics. RESULTS The overall complication rate during follow-up was 8.7%. hs-cTnT achieved the highest prognostic accuracy [area under the ROC curve: 0.75, 95% confidence interval (CI): 0.63-0.86, P < 0.001). At the predefined cut-off values, the negative predictive values of the biomarkers were above 95%. For levels above the cut-off, the risk of complications increased fivefold for hs-cTnT [odds ratio (OR): 5.22, 95% CI: 1.49-18.25] and 14-fold for NT-proBNP (OR: 14.21, 95% CI: 1.73-116.93) after adjustment for both clinical scores and renal function. Reclassification statistics indicated that adding hs-cTnT to the GPS or the PESI significantly improved the prognostic accuracy of both clinical scores. CONCLUSION In elderly patients with nonmassive PE, NT-proBNP or hs-cTnT could be an adequate alternative to clinical scores for identifying low-risk individuals suitable for outpatient management.

Years of potential life lost among Hispanics and non-Hispanics in Bexar County

While numerous studies have found similar mortality rates for Hispanics compared to non-Hispanic whites, surprisingly little is known about years of potential life lost (YPLL) differentials in mortality. The primary purpose of this paper is to quantify the effect that YPLL has on Hispanics in order to determine if YPLL differs between Hispanics and non-Hispanic whites. Using YPLL may bring attention to dissimilarities that are often obscured through traditional measures. Bexar County 2000-2004 data from the Texas Department of State Health Services, Vital Statistics Unit was analyzed for the descriptive analysis and 2003 Bexar County Multiple Cause Death data was analyzed for the regression analysis. The multiple regression models were used to examine Hispanic and non-Hispanic white differences in years of potential life lost (YPLL) before age 75 from all-causes of death. For this analysis, YPLL was regressed on ethnicity, education level and marital status for men and women. The descriptive analysis found YPLL from all-causes was greater among non-Hispanic whites than Hispanics. However, the regression analysis found Hispanics lost more year of potential from all-causes of death compared to non-Hispanic whites. This indicates that the effect of ethnicity on YPLL differs for different methods of analysis. Future research efforts should keep in mind the method of analysis when using YPLL. Understanding differences in mortality among Hispanics and non-Hispanic whites is important for targeting future health policies and research to aid in eliminating Hispanic health disparities. ^

Slope estimation in a parametric measurement error model: A simulation study

In regression analysis, covariate measurement error occurs in many applications. The error-prone covariates are often referred to as latent variables. In this proposed study, we extended the study of Chan et al. (2008) on recovering latent slope in a simple regression model to that in a multiple regression model. We presented an approach that applied the Monte Carlo method in the Bayesian framework to the parametric regression model with the measurement error in an explanatory variable. The proposed estimator applied the conditional expectation of latent slope given the observed outcome and surrogate variables in the multiple regression models. A simulation study was presented showing that the method produces estimator that is efficient in the multiple regression model, especially when the measurement error variance of surrogate variable is large.^

Genome instability quantified in constitutive tissues as well as putatively stable tumor tissue in hereditary non -polyposis colon cancer patients by small pool PCR

Microsatellite instability (MSI) is a hallmark of the mutator phenotype associated with Hereditary Non-Polyposis Colon Cancer (HNPCC). The MSI-High (MSI-H) HNPCC population has been well characterized, but the microsatellite low and stable (MSI-L/MSS) HNPCC population is much less understood. We hypothesize there are significant levels of MSI in HNPCC DNA classified as MSI-L/MSS, but no single variant allele makes up a sufficient population in the tumor DNA to be detected by standard analysis. Finding variants would suggest there is a mutator phenotype for the MSI-L/MSS HNPCC population that is distinct from the MSI-H HNPCC populations. This study quantified and compared MSI in HNPCC patients previously shown to be MSI-H, MSI-L/MSS and an MSI-H older, sporadic colorectal cancer patient. Small-pool Polymerase Chain Reactions (SP-PCRs) were conducted where the DNAs from each sample and controls are diluted into multiple pools, each containing approximately single genome equivalents. At least 100 alleles/sample were studied at six microsatellite loci. Mutant fragments were identified, quantified, and compared using Poisson statistics. Most of the variants were small deletions or insertions, with more mutants being deletions, as has been previously described in yeast and transgenic mice. SP-PCR, where most of the pools contained only 3 or less fragments, enabled identification of variants too infrequent to be detected by large pool PCR. Mutant fragments in positive control MSI-H tumor samples ranged from 0.26 to 0.68 in at least 4 of the 6 loci tested and were consistent with their MSI-H status. In the so called MSS tumors and constitutive tissues (normal colon tissue, and PBLs) of all the HNPCC patients, low, but significant levels of MSI were seen in at least two of the loci studied. This phenomenon was not seen in the sporadic MSI constitutive tissues nor the normal controls and suggests haploinsufficiency, gain-of-function, or a dominant/negative basis of the instability in HNPCC patients carrying germline mutations for tumor suppressor genes. A different frequency and spectrum of mutant fragments suggests a different genetic basis (other than a major mutation in MLH1 or MSH2) for disease in MSI-L and MSS HNPCC patients. ^

Evaluation of Non-Survey International IO Construction Methods with the Asian-Pacific Input-Output Table

This paper presents four non-survey methods to construct a full-information international input-output table from national IO tables and international import and export statistics, and this paper tests these four methods against the semi-survey international IO table for nine East-Asian countries and the USA, which is constructed by the Institute of Developing Economies in Japan. The tests show that the impact on the domestic flows of using self-sufficiency ratios is small, except for Singapore and Malaysia, two countries with large volumes of smuggling and transit trade. As regards the accuracy of the international flows, all methods show considerable errors, of 10%-40% for commodities and of 10%-70% for services. When more information is added, i.e. going from Method 1 to 4, the accuracy increases, except for Method 2 that generally produces larger errors than Method 1. In all, it seems doubtful whether replacing the semi-survey Asian-Pacific IO table with one of the four non-survey tables is justified, except when the semi-survey table itself is also considered to be just another estimate.

Advances in the Simultaneous Multiple Surface optical design method for imaging and non-imaging applications

Classical imaging optics has been developed over centuries in many areas, such as its paraxial imaging theory and practical design methods like multi-parametric optimization techniques. Although these imaging optical design methods can provide elegant solutions to many traditional optical problems, there are more and more new design problems, like solar concentrator, illumination system, ultra-compact camera, etc., that require maximum energy transfer efficiency, or ultra-compact optical structure. These problems do not have simple solutions from classical imaging design methods, because not only paraxial rays, but also non-paraxial rays should be well considered in the design process. Non-imaging optics is a newly developed optical discipline, which does not aim to form images, but to maximize energy transfer efficiency. One important concept developed from non-imaging optics is the “edge-ray principle”, which states that the energy flow contained in a bundle of rays will be transferred to the target, if all its edge rays are transferred to the target. Based on that concept, many CPC solar concentrators have been developed with efficiency close to the thermodynamic limit. When more than one bundle of edge-rays needs to be considered in the design, one way to obtain solutions is to use SMS method. SMS stands for Simultaneous Multiple Surface, which means several optical surfaces are constructed simultaneously. The SMS method was developed as a design method in Non-imaging optics during the 90s. The method can be considered as an extension to the Cartesian Oval calculation. In the traditional Cartesian Oval calculation, one optical surface is built to transform an input wave-front to an out-put wave-front. The SMS method however, is dedicated to solve more than 1 wave-fronts transformation problem. In the beginning, only 2 input wave-fronts and 2 output wave-fronts transformation problem was considered in the SMS design process for rotational optical systems or free-form optical systems. Usually “SMS 2D” method stands for the SMS procedure developed for rotational optical system, and “SMS 3D” method for the procedure for free-form optical system. Although the SMS method was originally employed in non-imaging optical system designs, it has been found during this thesis that with the improved capability to design more surfaces and control more input and output wave-fronts, the SMS method can also be applied to imaging system designs and possesses great advantage over traditional design methods. In this thesis, one of the main goals to achieve is to further develop the existing SMS-2D method to design with more surfaces and improve the stability of the SMS-2D and SMS-3D algorithms, so that further optimization process can be combined with SMS algorithms. The benefits of SMS plus optimization strategy over traditional optimization strategy will be explained in details for both rotational and free-form imaging optical system designs. Another main goal is to develop novel design concepts and methods suitable for challenging non-imaging applications, e.g. solar concentrator and solar tracker. This thesis comprises 9 chapters and can be grouped into two parts: the first part (chapter 2-5) contains research works in the imaging field, and the second part (chapter 6-8) contains works in the non-imaging field. In the first chapter, an introduction to basic imaging and non-imaging design concepts and theories is given. Chapter 2 presents a basic SMS-2D imaging design procedure using meridian rays. In this chapter, we will set the imaging design problem from the SMS point of view, and try to solve the problem numerically. The stability of this SMS-2D design procedure will also be discussed. The design concepts and procedures developed in this chapter lay the path for further improvement. Chapter 3 presents two improved SMS 3 surfaces’ design procedures using meridian rays (SMS-3M) and skew rays (SMS-1M2S) respectively. The major improvement has been made to the central segments selections, so that the whole SMS procedures become more stable compared to procedures described in Chapter 2. Since these two algorithms represent two types of phase space sampling, their image forming capabilities are compared in a simple objective design. Chapter 4 deals with an ultra-compact SWIR camera design with the SMS-3M method. The difficulties in this wide band camera design is how to maintain high image quality meanwhile reduce the overall system length. This interesting camera design provides a playground for the classical design method and SMS design methods. We will show designs and optical performance from both classical design method and the SMS design method. Tolerance study is also given as the end of the chapter. Chapter 5 develops a two-stage SMS-3D based optimization strategy for a 2 freeform mirrors imaging system. In the first optimization phase, the SMS-3D method is integrated into the optimization process to construct the two mirrors in an accurate way, drastically reducing the unknown parameters to only few system configuration parameters. In the second optimization phase, previous optimized mirrors are parameterized into Qbfs type polynomials and set up in code V. Code V optimization results demonstrates the effectiveness of this design strategy in this 2-mirror system design. Chapter 6 shows an etendue-squeezing condenser optics, which were prepared for the 2010 IODC illumination contest. This interesting design employs many non-imaging techniques such as the SMS method, etendue-squeezing tessellation, and groove surface design. This device has theoretical efficiency limit as high as 91.9%. Chapter 7 presents a freeform mirror-type solar concentrator with uniform irradiance on the solar cell. Traditional parabolic mirror concentrator has many drawbacks like hot-pot irradiance on the center of the cell, insufficient use of active cell area due to its rotational irradiance pattern and small acceptance angle. In order to conquer these limitations, a novel irradiance homogenization concept is developed, which lead to a free-form mirror design. Simulation results show that the free-form mirror reflector has rectangular irradiance pattern, uniform irradiance distribution and large acceptance angle, which confirm the viability of the design concept. Chapter 8 presents a novel beam-steering array optics design strategy. The goal of the design is to track large angle parallel rays by only moving optical arrays laterally, and convert it to small angle parallel output rays. The design concept is developed as an extended SMS method. Potential applications of this beam-steering device are: skylights to provide steerable natural illumination, building integrated CPV systems, and steerable LED illumination. Conclusion and future lines of work are given in Chapter 9. Resumen La óptica de formación de imagen clásica se ha ido desarrollando durante siglos, dando lugar tanto a la teoría de óptica paraxial y los métodos de diseño prácticos como a técnicas de optimización multiparamétricas. Aunque estos métodos de diseño óptico para formación de imagen puede aportar soluciones elegantes a muchos problemas convencionales, siguen apareciendo nuevos problemas de diseño óptico, concentradores solares, sistemas de iluminación, cámaras ultracompactas, etc. que requieren máxima transferencia de energía o dimensiones ultracompactas. Este tipo de problemas no se pueden resolver fácilmente con métodos clásicos de diseño porque durante el proceso de diseño no solamente se deben considerar los rayos paraxiales sino también los rayos no paraxiales. La óptica anidólica o no formadora de imagen es una disciplina que ha evolucionado en gran medida recientemente. Su objetivo no es formar imagen, es maximazar la eficiencia de transferencia de energía. Un concepto importante de la óptica anidólica son los “rayos marginales”, que se pueden utilizar para el diseño de sistemas ya que si todos los rayos marginales llegan a nuestra área del receptor, todos los rayos interiores también llegarán al receptor. Haciendo uso de este principio, se han diseñado muchos concentradores solares que funcionan cerca del límite teórico que marca la termodinámica. Cuando consideramos más de un haz de rayos marginales en nuestro diseño, una posible solución es usar el método SMS (Simultaneous Multiple Surface), el cuál diseña simultáneamente varias superficies ópticas. El SMS nació como un método de diseño para óptica anidólica durante los años 90. El método puede ser considerado como una extensión del cálculo del óvalo cartesiano. En el método del óvalo cartesiano convencional, se calcula una superficie para transformar un frente de onda entrante a otro frente de onda saliente. El método SMS permite transformar varios frentes de onda de entrada en frentes de onda de salida. Inicialmente, sólo era posible transformar dos frentes de onda con dos superficies con simetría de rotación y sin simetría de rotación, pero esta limitación ha sido superada recientemente. Nos referimos a “SMS 2D” como el método orientado a construir superficies con simetría de rotación y llamamos “SMS 3D” al método para construir superficies sin simetría de rotación o free-form. Aunque el método originalmente fue aplicado en el diseño de sistemas anidólicos, se ha observado que gracias a su capacidad para diseñar más superficies y controlar más frentes de onda de entrada y de salida, el SMS también es posible aplicarlo a sistemas de formación de imagen proporcionando una gran ventaja sobre los métodos de diseño tradicionales. Uno de los principales objetivos de la presente tesis es extender el método SMS-2D para permitir el diseño de sistemas con mayor número de superficies y mejorar la estabilidad de los algoritmos del SMS-2D y SMS-3D, haciendo posible combinar la optimización con los algoritmos. Los beneficios de combinar SMS y optimización comparado con el proceso de optimización tradicional se explican en detalle para sistemas con simetría de rotación y sin simetría de rotación. Otro objetivo importante de la tesis es el desarrollo de nuevos conceptos de diseño y nuevos métodos en el área de la concentración solar fotovoltaica. La tesis está estructurada en 9 capítulos que están agrupados en dos partes: la primera de ellas (capítulos 2-5) se centra en la óptica formadora de imagen mientras que en la segunda parte (capítulos 6-8) se presenta el trabajo del área de la óptica anidólica. El primer capítulo consta de una breve introducción de los conceptos básicos de la óptica anidólica y la óptica en formación de imagen. El capítulo 2 describe un proceso de diseño SMS-2D sencillo basado en los rayos meridianos. En este capítulo se presenta el problema de diseñar un sistema formador de imagen desde el punto de vista del SMS y se intenta obtener una solución de manera numérica. La estabilidad de este proceso se analiza con detalle. Los conceptos de diseño y los algoritmos desarrollados en este capítulo sientan la base sobre la cual se realizarán mejoras. El capítulo 3 presenta dos procedimientos para el diseño de un sistema con 3 superficies SMS, el primero basado en rayos meridianos (SMS-3M) y el segundo basado en rayos oblicuos (SMS-1M2S). La mejora más destacable recae en la selección de los segmentos centrales, que hacen más estable todo el proceso de diseño comparado con el presentado en el capítulo 2. Estos dos algoritmos representan dos tipos de muestreo del espacio de fases, su capacidad para formar imagen se compara diseñando un objetivo simple con cada uno de ellos. En el capítulo 4 se presenta un diseño ultra-compacto de una cámara SWIR diseñada usando el método SMS-3M. La dificultad del diseño de esta cámara de espectro ancho radica en mantener una alta calidad de imagen y al mismo tiempo reducir drásticamente sus dimensiones. Esta cámara es muy interesante para comparar el método de diseño clásico y el método de SMS. En este capítulo se presentan ambos diseños y se analizan sus características ópticas. En el capítulo 5 se describe la estrategia de optimización basada en el método SMS-3D. El método SMS-3D calcula las superficies ópticas de manera precisa, dejando sólo unos pocos parámetros libres para decidir la configuración del sistema. Modificando el valor de estos parámetros se genera cada vez mediante SMS-3D un sistema completo diferente. La optimización se lleva a cabo variando los mencionados parámetros y analizando el sistema generado. Los resultados muestran que esta estrategia de diseño es muy eficaz y eficiente para un sistema formado por dos espejos. En el capítulo 6 se describe un sistema de compresión de la Etendue, que fue presentado en el concurso de iluminación del IODC en 2010. Este interesante diseño hace uso de técnicas propias de la óptica anidólica, como el método SMS, el teselado de las lentes y el diseño mediante grooves. Este dispositivo tiene un límite teórica en la eficiencia del 91.9%. El capítulo 7 presenta un concentrador solar basado en un espejo free-form con irradiancia uniforme sobre la célula. Los concentradores parabólicos tienen numerosas desventajas como los puntos calientes en la zona central de la célula, uso no eficiente del área de la célula al ser ésta cuadrada y además tienen ángulos de aceptancia de reducido. Para poder superar estas limitaciones se propone un novedoso concepto de homogeneización de la irrandancia que se materializa en un diseño con espejo free-form. El análisis mediante simulación demuestra que la irradiancia es homogénea en una región rectangular y con mayor ángulo de aceptancia, lo que confirma la viabilidad del concepto de diseño. En el capítulo 8 se presenta un novedoso concepto para el diseño de sistemas afocales dinámicos. El objetivo del diseño es realizar un sistema cuyo haz de rayos de entrada pueda llegar con ángulos entre ±45º mientras que el haz de rayos a la salida sea siempre perpendicular al sistema, variando únicamente la posición de los elementos ópticos lateralmente. Las aplicaciones potenciales de este dispositivo son varias: tragaluces que proporcionan iluminación natural, sistemas de concentración fotovoltaica integrados en los edificios o iluminación direccionable con LEDs. Finalmente, el último capítulo contiene las conclusiones y las líneas de investigación futura.