Design of spherical symmetric gradient index lenses

Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.

On the design of spherical gradient index lenses

Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

Design of a flat-top fiber Bragg filter via quasi-random modulation of the refractive index

The statistics of the reflection spectrum of a short-correlated disordered fiber Bragg grating are studied. The averaged spectrum appears to be flat inside the bandgap and has significantly suppressed sidelobes compared to the uniform grating of the same bandwidth. This is due to the Anderson localization of the modes of a disordered grating. This observation prompts a new algorithm for designing passband reflection gratings. Using the stochastic invariant imbedding approach it is possible to obtain the probability distribution function for the random reflection coefficient inside the bandgap and obtain both the variance of the averaged reflectivity as well as the distribution of the time delay of the grating.

Dosimetric comparison of different treatment modalities for stereotactic radiosurgery of arteriovenous malformations and acoustic neuromas.

PURPOSE: We investigated the influence of beam modulation on treatment planning by comparing four available stereotactic radiosurgery (SRS) modalities: Gamma-Knife-Perfexion, Novalis-Tx Dynamic-Conformal-Arc (DCA) and Dynamic-Multileaf-Collimation-Intensity-Modulated-radiotherapy (DMLC-IMRT), and Cyberknife. MATERIAL AND METHODS: Patients with arteriovenous malformation (n = 10) or acoustic neuromas (n = 5) were planned with different treatment modalities. Paddick conformity index (CI), dose heterogeneity (DH), gradient index (GI) and beam-on time were used as dosimetric indices. RESULTS: Gamma-Knife-Perfexion can achieve high degree of conformity (CI = 0.77 ± 0.04) with limited low-doses (GI = 2.59 ± 0.10) surrounding the inhomogeneous dose distribution (D(H) = 0.84 ± 0.05) at the cost of treatment time (68.1 min ± 27.5). Novalis-Tx-DCA improved this inhomogeneity (D(H) = 0.30 ± 0.03) and treatment time (16.8 min ± 2.2) at the cost of conformity (CI = 0.66 ± 0.04) and Novalis-TX-DMLC-IMRT improved the DCA CI (CI = 0.68 ± 0.04) and inhomogeneity (D(H) = 0.18 ± 0.05) at the cost of low-doses (GI = 3.94 ± 0.92) and treatment time (21.7 min ± 3.4) (p<0.01). Cyberknife achieved comparable conformity (CI = 0.77 ± 0.06) at the cost of low-doses (GI = 3.48 ± 0.47) surrounding the homogeneous (D(H) = 0.22 ± 0.02) dose distribution and treatment time (28.4min±8.1) (p<0.01). CONCLUSIONS: Gamma-Knife-Perfexion will comply with all SRS constraints (high conformity while minimizing low-dose spread). Multiple focal entries (Gamma-Knife-Perfexion and Cyberknife) will achieve better conformity than High-Definition-MLC of Novalis-Tx at the cost of treatment time. Non-isocentric beams (Cyberknife) or IMRT-beams (Novalis-Tx-DMLC-IMRT) will spread more low-dose than multiple isocenters (Gamma-Knife-Perfexion) or dynamic arcs (Novalis-Tx-DCA). Inverse planning and modulated fluences (Novalis-Tx-DMLC-IMRT and CyberKnife) will deliver the most homogeneous treatment. Furthermore, Linac-based systems (Novalis and Cyberknife) can perform image verification at the time of treatment delivery.

Dosimetric comparison of different treatment modalities for stereotactic radiosurgery of meningioma.

BACKGROUND: The objective of this study was to compare the three most prominent systems for stereotactic radiosurgery in terms of dosimetric characteristics: the Cyberknife system, the Gamma Knife Perfexion and the Novalis system. METHODS: Ten patients treated for recurrent grade I meningioma after surgery using the Cyberknife system were identified; the Cyberknife contours were exported and comparative treatment plans were generated for the Novalis system and Gamma Knife Perfexion. Dosimetric values were compared with respect to coverage, conformity index (CI), gradient index (GI) and beam-on time (BOT). RESULTS: All three systems showed comparable results in terms of coverage. The Gamma Knife and the Cyberknife system showed significantly higher levels of conformity than the Novalis system (Cyberknife vs Novalis, p = 0.002; Gamma Knife vs Novalis, p = 0.002). The Gamma Knife showed significantly steeper gradients compared with the Novalis and the Cyberknife system (Gamma Knife vs Novalis, p = 0.014; Gamma Knife vs Cyberknife, p = 0.002) and significantly longer beam-on times than the other two systems (BOT = 66 ± 21.3 min, Gamma Knife vs Novalis, p = 0.002; Gamma Knife vs Cyberknife, p = 0.002). CONCLUSIONS: The multiple focal entry systems (Gamma Knife and Cyberknife) achieve higher conformity than the Novalis system. The Gamma Knife delivers the steepest dose gradient of all examined systems. However, the Gamma Knife is known to require long beam-on times, and despite worse dose gradients, LINAC-based systems (Novalis and Cyberknife) offer image verification at the time of treatment delivery.

Effect of oral nitrate supplementation on pulmonary hemodynamics during exercise and time trial performance in normoxia and hypoxia: a randomized controlled trial.

BACKGROUND: Hypoxia-induced pulmonary vasoconstriction increases pulmonary arterial pressure (PAP) and may impede right heart function and exercise performance. This study examined the effects of oral nitrate supplementation on right heart function and performance during exercise in normoxia and hypoxia. We tested the hypothesis that nitrate supplementation would attenuate the increase in PAP at rest and during exercise in hypoxia, thereby improving exercise performance. METHODS: Twelve trained male cyclists [age: 31 ± 7 year (mean ± SD)] performed 15 km time-trial cycling (TT) and steady-state submaximal cycling (50, 100, and 150 W) in normoxia and hypoxia (11% inspired O2) following 3-day oral supplementation with either placebo or sodium nitrate (0.1 mmol/kg/day). We measured TT time-to-completion, muscle tissue oxygenation during TT and systolic right ventricle to right atrium pressure gradient (RV-RA gradient: index of PAP) during steady state cycling. RESULTS: During steady state exercise, hypoxia elevated RV-RA gradient (p > 0.05), while oral nitrate supplementation did not alter RV-RA gradient (p > 0.05). During 15 km TT, hypoxia lowered muscle tissue oxygenation (p < 0.05). Nitrate supplementation further decreased muscle tissue oxygenation during 15 km TT in hypoxia (p < 0.05). Hypoxia impaired time-to-completion during TT (p < 0.05), while no improvements were observed with nitrate supplementation in normoxia or hypoxia (p > 0.05). CONCLUSION: Our findings indicate that oral nitrate supplementation does not attenuate acute hypoxic pulmonary vasoconstriction nor improve performance during time trial cycling in normoxia and hypoxia.

Trigeminal Neuralgia Secondary to Intracranial Lesions: A Prospective Series of 17 Consecutive Cases

Object: The purpose of the study was to assess the role of Gamma Knife surgery (GKS) in secondary trigeminal neuralgia (TN) caused by space-occupying lesions. Methods: From July 2010 till January 2015, 17 patients had GKS for secondary TN caused by intracranial lesions. The primary outcome was tumor control. The secondary outcomes were the alleviation of pain and the eventual secondary effects. Covariates were the age, duration of symptoms, duration till alleviation etc. Results: The mean age in this series was 63.3 years (range 39-79). The mean follow-up period was 1.85 years (range 0.5-3). Nine (52.9%) were meningiomas, five (29.4%) trigeminal schwannomas, two (11.8%) brain metastases and one (5.9%) arteriovenous malformation (AVM). Eight were located on the right side and nine on the left side. The mean duration of TN was 13.5 months (range 0.5-160). Follow-up was available for 16 patients (94.1%). Pain alleviation appeared after a mean time of 4.6 months (1-11) in 15 patients (88.2%). Five (29.4%) patients completely stopped medication in a mean time of 7 months (range 1-13) and three (17.6%) decreased it at half of the initial doses. No patient developed new hypoesthesia or other cranial nerve complication. The marginal doses for meningiomas and trigeminal schwannomas were 12 Gy (12-14), for metastasis 20 (20-20) and for AVM 24 Gy. The mean target volume was 1.84 cc (range 0.12-8.10). The mean prescription isodose volume was 2.65 cc (0.19-11.90). The mean maximal diameter was 19.9 (range 9-36). The mean number of isocenters was 14.2 (4-27). The mean duration was 76.9 minutes (range 25-172). The mean conformity, selectivity, Paddick and gradient index were: 0.99 (range 0.955-1), 0.701 (range 0.525-0.885), 0.694 (range 0.525-0.885) and 2.904 (range 2.654-3.371). At last follow-up, tumor decreased in 10 (58.8%) patients, was stable in 6 (35.3%) and increased in one (5.9%), the latest at 6 months. Conclusions: Gamma Knife surgery is safe and effective in treating intracranial lesions presenting with secondary TN. The initial pain freedom response was close to 90%, while having no secondary effect. Pain alleviation is achieved even in the absence of a volume variation of the lesions.

Aplicação do Índice Relaçáo Declividade-Extensão - RDE Na Bacia do Rio do Peixe (SP) para Detecção de Deformações Neotectô nicas

This paper presents the identification of tectonic deformation through the application of the stream-gradient index (slope x length) method in the Rio do Peixe hydrographic basin, located in western State of Sã o Paulo. The main principle used is that river valleys are the best tools for this type of analysis because of their fast adjustment to even the most gentle crustal deformations. This type of analysis for structural studies is extremely useful in the western region of the State of São Paulo, where deep chemical weathering results in a thick regolith and scarce outcrops. The stream length index is the ratio of the altimetric amplitude of each drainage and the natural logarithm of its length. The value obtained is plotted on maps at the median point of each drainage, allowing the drawings of lines with the same values (isodefs). Three anomalies (A, B and C) were identified along the Rio do Peixe valley representing uplift sectors indicated by the formation and distribution of Upper Quaternary deposits in terraces and modern fluvial plains and alluvial fans. In correlation with known tectonic data for this region it is possible to attribute the A and B anomalies to the Ribeirão Preto and Presidente Prudente crustal sutures, respectively. The smaller C anomaly needs further field investigation, but it could be associated with the Três Lagoas crustal suture. It must be emphasised that these sutures are inherited from the Precambrian Basement which had a strong influence on the Phanerozoic evolution in the whole sedimentary and volcanic stratigraphic pile of the Paraná Basin and on the dominant structural lineaments directions developed therein .The A, Band C anomalies are suggestive of renewed uplift as a result of neotectonic action in modern times.

Perfil longitudinal e a aplicação do índice de gradiente (RDE) no rio dos Patos, bacia hidrográfica do rio Ivaí, PR

This paper presents the results of the longitudinal profile analysis and the application of gradient index (RDE) in the Patos River, a tributary of the Ivaí River basin, PR. The goal is identify and quantify the anomalous zones along river course concerning their genesis - activity neotectonic or/and lithological imposition. The Patos River has a length of 127 km and a relief amplitude of 660 m, The occurrence of an important knickpoint in the middle course the Patos River can be divided into two stretches. Of the 22 sections measured, 10 were considered anomalous, distributed in both upper and lower course. In the upper course, over a basaltic bedrock of the Serra Geral Formation the RDE values are lower than those in the lower course, where river flows over sedimentary rocks of the Terezina Formation. The 2 nd order anomalies are related to lithological changes, relief alignments and channel confluences - as in the case of São João River. The 1st order anomalies are linked to differences in rock resistance associated with structural control, which provides the formation of waterfalls.

Análise morfotectônica do Planalto Ocidental Paulista, ao sul do Rio Tietê: indicadores de deformações neotectônicas na fisiografia da paisagem

Pós-graduação em Geologia Regional - IGCE

Fiberoptic system for recording dendritic calcium signals in layer 5 neocortical pyramidal cells in freely moving rats

Calcium influx into the dendritic tufts of layer 5 neocortical pyramidal neurons modifies a number of important cellular mechanisms. It can trigger local synaptic plasticity and switch the firing properties from regular to burst firing. Due to methodological limitations, our knowledge about Ca2+ spikes in the dendritic tuft stems mostly from in vitro experiments. However, it has been speculated that regenerative Ca2+ events in the distal dendrites correlate with distinct behavioral states. Therefore it would be most desirable to be able to record these Ca2+ events in vivo, preferably in the behaving animal. Here, we present a novel approach for recording Ca2+ signals in the dendrites of populations of layer 5 pyramidal neurons in vivo, which ensures that all recorded fluorescence changes are due to intracellular Ca2+ signals in the apical dendrites. The method has two main features: 1) bolus loading of layer 5 with a membrane-permeant Ca2+ dye resulting in specific loading of pyramidal cell dendrites in the upper layers and 2) a fiberoptic cable attached to a gradient index lens and a prism reflecting light horizontally at 90 degrees to the angle of the apical dendrites. We demonstrate that the in vivo signal-to-noise ratio recorded with this relatively inexpensive and easy-to-implement fiberoptic-based device is comparable to conventional camera-based imaging systems used in vitro. In addition, the device is flexible and lightweight and can be used for recording Ca2+ signals in the distal dendritic tuft of freely behaving animals.

An optical study of human ocular dimensions

Many workers have studied the ocular components which occur in eyes exhibiting differing amounts of central refractive error but few have ever considered the additional information that could be derived from a study of peripheral refraction. Before now, peripheral refraction has either been measured in real eyes or has otherwise been modelled in schematic eyes of varying levels of sophistication. Several differences occur between measured and modelled results which, if accounted for, could give rise to more information regarding the nature of the optical and retinal surfaces and their asymmetries. Measurements of ocular components and peripheral refraction, however, have never been made in the same sample of eyes. In this study, ocular component and peripheral refractive measurements were made in a sample of young near-emmetropic, myopic and hyperopic eyes. The data for each refractive group was averaged. A computer program was written to construct spherical surfaced schematic eyes from this data. More sophisticated eye models were developed making use of linear algebraic ray tracing program. This method allowed rays to be traced through toroidal aspheric surfaces which were translated or rotated with respect to each other. For simplicity, the gradient index optical nature of the crystalline lens was neglected. Various alterations were made in these eye models to reproduce the measured peripheral refractive patterns. Excellent agreement was found between the modelled and measured peripheral refractive values over the central 70o of the visual field. This implied that the additional biometric features incorporated in each eye model were representative of those which were present in the measured eyes. As some of these features are not otherwise obtainable using in vivo techniques, it is proposed that the variation of refraction in the periphery offers a very useful optical method for studying human ocular component dimensions.

Modelling ocular monochromatic aberrations using schematic eyes with homogeneous optical media

Previous research has indicated that schematic eyes incorporating aspheric surfaces but lacking gradient index are unable to model ocular spherical aberration and peripheral astigmatism simultaneously. This limits their use as wide-angle schematic eyes. This thesis challenges this assumption by investigating the flexibility of schematic eyes comprising aspheric optical surfaces and homogeneous optical media. The full variation of ocular component dimensions found in human eyes was established from the literature. Schematic eye parameter variants were limited to these dimensions. The levels of spherical aberration and peripheral astigmatism modelled by these schematic eyes were compared to the range of measured levels. These were also established from the literature. To simplify comparison of modelled and measured data, single value parameters were introduced; the spherical aberration function (SAF), and peripheral astigmatism function (PAF). Some ocular components variations produced a wide range of aberrations without exceeding the limits of human ocular components. The effect of ocular component variations on coma was also investigated, but no comparison could be made as no empirical data exists. It was demonstrated that by combined manipulation of a number of parameters in the schematic eyes it was possible to model all levels of ocular spherical aberration and peripheral astigmatism. However, the unique parameters of a human eye could not be obtained in this way, as a number of models could be used to produce the same spherical aberration and peripheral astigmatism, while giving very different coma levels. It was concluded that these schematic eyes are flexible enough to model the monochromatic aberrations tested, the absence of gradient index being compensated for by altering the asphericity of one or more surfaces.

Epilithic community development on artificial reefs deployed along a cross-shelf environmental gradient off Paraná state, southern Brazil

Concrete modules were deployed on the bottom of the 11, 18 and 30 meters isobaths along a cross-shelf hydrographic gradient off Paraná State, Southern Brazil, with the purpose of studying the colonization of sessile epilithic macroinvertebrates on artificial surfaces. After one year of submersion a total of 63 species of epilithic organisms were identified, dominated by Ostrea puelchana, Chthamalus bisinuatus, Balanus cf spongicola, Astrangia cf rathbuni, Didemnum spp, poryphers and bryozoans. Diversity index and percent cover at reef stations placed at 11, 18 and 30 meters isobaths were respectively 2.28 and 66.7%, 2.79 and 96.6% and 1.66 and 77.4%. Differences of general community structure among the three assemblages were not clearly related to the general environmental conditions at the bottom layers near the reef stations. Turbidity and larval abundance are discussed as important factors affecting colonization processes. Results indicate that depths between 15-20 meters are more suitable for the implementation of large scale artificial reef systems in the inner shelf off Paraná and, possibly, throughout the inner shelves off southern Brazil with similar hydrographic conditions.

Nonempirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation leads to an alternative point of view on popular hybrid functionals, providing a rationale for why they work and how they can be constructed. A similar representation of the exact correlation functional allows to construct fully nonempirical hyper-generalized-gradient approximations (HGGAs), radically departing from established paradigms of functional construction. Numerical tests of these HGGAs for atomic and molecular correlation energies and molecular atomization energies show that even simple HGGAs match or outperform state-of-the-art correlation functionals currently used in solid-state physics and quantum chemistry.