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.

A Novel Method for Radio Propagation Simulation Based on Automatic 3D Environment Reconstruction

In this paper, a novel method to simulate radio propagation is presented. The method consists of two steps: automatic 3D scenario reconstruction and propagation modeling. For 3D reconstruction, a machine learning algorithm is adopted and improved to automatically recognize objects in pictures taken from target regions, and 3D models are generated based on the recognized objects. The propagation model employs a ray tracing algorithm to compute signal strength for each point on the constructed 3D map. Our proposition reduces, or even eliminates, infrastructure cost and human efforts during the construction of realistic 3D scenes used in radio propagation modeling. In addition, the results obtained from our propagation model proves to be both accurate and efficient

Distributed target tracking based on belief propagation consensus

Distributed target tracking in wireless sensor networks (WSN) is an important problem, in which agreement on the target state can be achieved using conventional consensus methods, which take long to converge. We propose distributed particle filtering based on belief propagation (DPF-BP) consensus, a fast method for target tracking. According to our simulations, DPF-BP provides better performance than DPF based on standard belief consensus (DPF-SBC) in terms of disagreement in the network. However, in terms of root-mean square error, it can outperform DPF-SBC only for a specific number of consensus iterations.

A novel method for radio propagation simulation based on automatic 3D environment reconstruction

In this paper, a novel method to simulate radio propagation is presented. The method consists of two steps: automatic 3D scenario reconstruction and propagation modeling. For 3D reconstruction, a machine learning algorithm is adopted and improved to automatically recognize objects in pictures taken from target region, and 3D models are generated based on the recognized objects. The propagation model employs a ray tracing algorithm to compute signal strength for each point on the constructed 3D map. By comparing with other methods, the work presented in this paper makes contributions on reducing human efforts and cost in constructing 3D scene; moreover, the developed propagation model proves its potential in both accuracy and efficiency.

Effect of substrate-target distance and sputtering pressure in the synthesis of AlN thin films

In this work, we analyze the influence of the processing pressure and the substrate–target distance on the synthesis by reactive sputtering of c-axis oriented polycrystalline aluminum nitride thin films deposited on Si(100) wafers. The crystalline quality of AlN has been characterized by high-resolution X-ray diffraction (HR-XRD). The films exhibited a very high degree of c-axis orientation especially when a low process pressure was used. After growth, residual stress measurements obtained indirectly from radius of curvature measurements of the wafer prior and after deposition are also provided. Two different techniques are used to determine the curvature—an optically levered laser beam and a method based on X-ray diffraction. There is a transition from compressive to tensile stress at a processing pressure around 2 mTorr. The transition occurs at different pressures for thin films of different thickness. The degree of c-axis orientation was not affected by the target–substrate distance as it was varied in between 30 and 70 mm.

A new label fusion method using graph cuts: application to hippocampus segmentation

The aim of this paper is to develop a probabilistic modeling framework for the segmentation of structures of interest from a collection of atlases. Given a subset of registered atlases into the target image for a particular Region of Interest (ROI), a statistical model of appearance and shape is computed for fusing the labels. Segmentations are obtained by minimizing an energy function associated with the proposed model, using a graph-cut technique. We test different label fusion methods on publicly available MR images of human brains.

Optimal laser intensity profiles for a uniform target illumination in direct-drive inertial confinement fusion

A numerical method providing the optimal laser intensity profiles for a direct-drive inertial confinement fusion scheme has been developed. The method provides an alternative approach to phase-space optimization studies, which can prove computationally expensive. The method applies to a generic irradiation configuration characterized by an arbitrary number NB of laser beams provided that they irradiate the whole target surface, and thus goes beyond previous analyses limited to symmetric configurations. The calculated laser intensity profiles optimize the illumination of a spherical target. This paper focuses on description of the method, which uses two steps: first, the target irradiation is calculated for initial trial laser intensities, and then in a second step the optimal laser intensities are obtained by correcting the trial intensities using the calculated illumination. A limited number of example applications to direct drive on the Laser MegaJoule (LMJ) are described.

Multiple feature points representation in target localization of wireless visual sensor networks

This paper discusses the target localization problem in wireless visual sensor networks. Additive noises and measurement errors will affect the accuracy of target localization when the visual nodes are equipped with low-resolution cameras. In the goal of improving the accuracy of target localization without prior knowledge of the target, each node extracts multiple feature points from images to represent the target at the sensor node level. A statistical method is presented to match the most correlated feature point pair for merging the position information of different sensor nodes at the base station. Besides, in the case that more than one target exists in the field of interest, a scheme for locating multiple targets is provided. Simulation results show that, our proposed method has desirable performance in improving the accuracy of locating single target or multiple targets. Results also show that the proposed method has a better trade-off between camera node usage and localization accuracy.

ANALISANDO A RELAÇÃO DOS VOLUMES DE EXPORTAÇÃO E DE IMPORTAÇÃO, PIB, TAXAS DE CÂMBIO E INFLAÇÃO NO PERÍODO DE 2004 A 2014.

Esta dissertação visa deslumbrar uma análise macroeconômica do Brasil, especialmente no que se refere à relação dos índices mensais dos volumes das exportações e das importações com os volumes mensais do PIB, da Taxa SELIC e as Taxas de Câmbio, conforme dados coletados no período de janeiro de 2004 a dezembro de 2014, através de pesquisa literária referente aos históricos sobre cada conceito envolvido no âmbito da macroeconomia das varáveis estudadas. Foi realizado um estudo de caso embasado em dados de sites governamentais, no período delimitado, empregando-se o método de regressão linear, com base na Teoria da correlação de Pearson, demonstrando os resultados obtidos no período do estudo para as varáveis estudadas. Desta maneira, conseguiu-se estudar e analisar como as variáveis dependentes (resposta): volume das exportações e volume das importações estão relacionadas com as varáveis independentes (explicativas): PIB, Taxa Selic e taxa de Câmbio. Os resultados apurados no presente estudo permitem identificar que existe correlação moderada e negativa, quando analisadas a Taxa Selic e a Taxa de Câmbio com os volumes das exportações e das importações, enquanto o PIB apresenta correlação forte e positiva na análise com os volumes das exportações e das importações

Identification and characterization of the ARP1 gene, a target for the human acute leukemia ALL1 gene

ALL1, the human homologue of Drosophila trithorax, is directly involved in human acute leukemias associated with abnormalities at 11q23. Using the differential display method, we isolated a gene that is down-regulated in All1 double-knockout mouse embryonic stem (ES) cells. The gene, designated ARP1 (also termed RIEG, Ptx2, or Otlx2), is a member of a family of homeotic genes containing a short motif shared with several homeobox genes. Using a bacterially synthesized All1 polypeptide encompassing the AT-hook motifs, we identified a 0.5-kb ARP1 DNA fragment that preferentially bound to the polypeptide. Within this DNA, a region of ≈100 bp was protected by the polypeptide from digestion with ExoIII and DNase I. Whole-mount in situ hybridization to early mouse embryos of 9.5–10.5 days indicated a complex pattern of Arp1 expression spatially overlapping with the expression of All1. Although the ARP1 gene is expressed strongly in bone marrow cells, no transcripts were detected in six leukemia cell lines with 11q23 translocations. These results suggest that ARP1 is up-regulated by the All1 protein, possibly through direct interaction with an upstream DNA sequence of the former. The results are also consistent with the suggestion that ALL1 chimeric proteins resulting from 11q23 abnormalities act in a dominant negative fashion.

A method for the generation of conditional gene repair mutations in mice

Conditional gene repair mutations in the mouse can assist in cell lineage analyses and provide a valuable complement to conditional gene inactivation strategies. We present a method for the generation of conditional gene repair mutations that employs a loxP-flanked (floxed) selectable marker and transcriptional/translational stop cassette (neostop) located within the first intron of a target gene. In the absence of Cre recombinase, expression of the targeted allele is suppressed generating a null allele, while in the presence of Cre, excision of neostop restores expression to wild-type levels. To test this strategy, we have generated a conditional gene repair allele of the mouse Huntington’s disease gene homolog (Hdh). Insertion of neostop within the Hdh intron 1 generated a null allele and mice homozygous for this allele resembled nullizygous Hdh mutants and died after embryonic day 8.5. In the presence of a cre transgene expressed ubiquitously early in development, excision of neostop restored Hdh expression and rescued the early embryonic lethality. A simple modification of this strategy that permits the generation of conventional gene knockout, conditional gene knockout and conditional gene repair alleles using one targeting construct is discussed.

Complementation of an Escherichia coli adhE mutant by the Entamoeba histolytica EhADH2 gene provides a method for the identification of new antiamebic drugs.

The pathogenic protozoan parasite Entamoeba histolytica, the cause of amebic dysentery and amebic liver abscess, is an obligate anaerobe, and derives energy from the fermentation of glucose to ethanol with pyruvate and acetyl coenzyme A as intermediates. We have isolated EhADH2, a key enzyme in this pathway, that is a NAD+- and Fe2+-dependent bifunctional enzyme with acetaldehyde dehydrogenase and alcohol dehydrogenase activities. EhADH2 is the only known eukaryotic member of a newly defined family of prokaryotic multifunctional enzymes, which includes the Escherichia coli AdhE enzyme, an enzyme required for anaerobic growth of E. coli. Because of the critical role of EhADH2 in the amebic fermentation pathway and the lack of known eukaryotic homologues of the EhADH2 enzyme, EhADH2 represents a potential target for antiamebic chemotherapy. However, screening of compounds for antiamebic activity is hampered by the cost of large scale growth of Ent. histolytica, and difficulties in quantitating drug efficacy in vitro. To approach this problem, we expressed the EhADH2 gene in a mutant strain of E. coli carrying a deletion of the adhE gene. Expression of EhADH2 restored the ability of the mutant E. coli strain to grow under anaerobic conditions. By screening compounds for the ability to inhibit the anaerobic growth of the E. coli/EhADH2 strain, we have developed a rapid assay for identifying compounds with anti-EhADH2 activity. Using bacteria to bypass the need for parasite culture in the initial screening process for anti-parasitic agents could greatly simplify and reduce the cost of identifying new therapeutic agents effective against parasitic diseases.

Suppression subtractive hybridization: a method for generating differentially regulated or tissue-specific cDNA probes and libraries.

A new and highly effective method, termed suppression subtractive hybridization (SSH), has been developed for the generation of subtracted cDNA libraries. It is based primarily on a recently described technique called suppression PCR and combines normalization and subtraction in a single procedure. The normalization step equalizes the abundance of cDNAs within the target population and the subtraction step excludes the common sequences between the target and driver populations. In a model system, the SSH technique enriched for rare sequences over 1,000-fold in one round of subtractive hybridization. We demonstrate its usefulness by generating a testis-specific cDNA library and by using the subtracted cDNA mixture as a hybridization probe to identify homologous sequences in a human Y chromosome cosmid library. The human DNA inserts in the isolated cosmids were further confirmed to be expressed in a testis-specific manner. These results suggest that the SSH technique is applicable to many molecular genetic and positional cloning studies for the identification of disease, developmental, tissue-specific, or other differentially expressed genes.

Sequence scanning: A method for rapid sequence acquisition from large-fragment DNA clones.

A strategy of "sequence scanning" is proposed for rapid acquisition of sequence from clones such as bacteriophage P1 clones, cosmids, or yeast artificial chromosomes. The approach makes use of a special vector, called LambdaScan, that reliably yields subclones with inserts in the size range 8-12 kb. A number of subclones, typically 96 or 192, are chosen at random, and the ends of the inserts are sequenced using vector-specific primers. Then long-range spectrum PCR is used to order and orient the clones. This combination of shotgun and directed sequencing results in a high-resolution physical map suitable for the identification of coding regions or for comparison of sequence organization among genomes. Computer simulations indicate that, for a target clone of 100 kb, the scanning of 192 subclones with sequencing reads as short as 350 bp results in an approximate ratio of 1:2:1 of regions of double-stranded sequence, single-stranded sequence, and gaps. Longer sequencing reads tip the ratio strongly toward increased double-stranded sequence.

Direct detection and isolation of restriction landmark genomic scanning (RLGS) spot DNA markers tightly linked to a specific trait by using the RLGS spot-bombing method.

We have developed a technique for isolating DNA markers tightly linked to a target region that is based on RLGS, named RLGS spot-bombing (RLGS-SB). RLGS-SB allows us to scan the genome of higher organisms quickly and efficiently to identify loci that are linked to either a target region or gene of interest. The method was initially tested by analyzing a C57BL/6-GusS mouse congenic strain. We identified 33 variant markers out of 10,565 total loci in a 4.2-centimorgan (cM) interval surrounding the Gus locus in 4 days of laboratory work. The validity of RLGS-SB to find DNA markers linked to a target locus was also tested on pooled DNA from segregating backcross progeny by analyzing the spot intensity of already mapped RLGS loci. Finally, we used RLGS-SB to identify DNA markers closely linked to the mouse reeler (rl) locus on chromosome 5 by phenotypic pooling. A total of 31 RLGS loci were identified and mapped to the target region after screening 8856 loci. These 31 loci were mapped within 11.7 cM surrounding rl. The average density of RLGS loci located in the rl region was 0.38 cM. Three loci were closely linked to rl showing a recombination frequency of 0/340, which is < 1 cM from rl. Thus, RLGS-SB provides an efficient and rapid method for the detection and isolation of polymorphic DNA markers linked to a trait or gene of interest.