Cooperative Effects of Electron Donors and Acceptors for the Stabilization of Elusive Metal Cluster Frameworks: Synthesis and Solid-State Structures of Pt-19(CO)(24)(mu(4)-AuPPh3)(3)](-) and Pt-19(CO)(24){mu(4)-Au-2(PPh3)(2)}(2)]

The anionic cluster Pt-19(CO)(22)](4-) (1), of pentagonal symmetry, reacts with CO and AuPPh3+ fragments. Upon increasing the Au:Pt-19, molar ratio, different species are sequentially formed, but only the last two members of the series could be characterized by X-ray diffraction, namely, Pt-19(CO)(24)(mu(4)-AuPPh3)(3)](-) (2) and Pt-19(CO)(24){mu(4)-Au-2(PPh3)(2)}(2)] (3).The metallic framework of the starting cluster is completely modified after the addition of CO and AuL+, and both products display the same platinum core of trigonal symmetry, with closely packed metal atoms. The three AuL+ units cap three different square faces in 2, whereas four AuL+ fragments are grouped in two independent bimetallic units in the neutral cluster 3. Electrochemical and spectroelectrochemical studies on 2 showed that its redox ability is comparable with that of the homometallic 1.

Focal white matter changes in spasmodic dysphonia: a combined diffusion tensor imaging and neuropathological study.

Spasmodic dysphonia is a neurological disorder characterized by involuntary spasms in the laryngeal muscles during speech production. Although the clinical symptoms are well characterized, the pathophysiology of this voice disorder is unknown. We describe here, for the first time to our knowledge, disorder-specific brain abnormalities in these patients as determined by a combined approach of diffusion tensor imaging (DTI) and postmortem histopathology. We used DTI to identify brain changes and to target those brain regions for neuropathological examination. DTI showed right-sided decrease of fractional anisotropy in the genu of the internal capsule and bilateral increase of overall water diffusivity in the white matter along the corticobulbar/corticospinal tract in 20 spasmodic dysphonia patients compared to 20 healthy subjects. In addition, water diffusivity was bilaterally increased in the lentiform nucleus, ventral thalamus and cerebellar white and grey matter in the patients. These brain changes were substantiated with focal histopathological abnormalities presented as a loss of axonal density and myelin content in the right genu of the internal capsule and clusters of mineral depositions, containing calcium, phosphorus and iron, in the parenchyma and vessel walls of the posterior limb of the internal capsule, putamen, globus pallidus and cerebellum in the postmortem brain tissue from one patient compared to three controls. The specificity of these brain abnormalities is confirmed by their localization, limited only to the corticobulbar/corticospinal tract and its main input/output structures. We also found positive correlation between the diffusivity changes and clinical symptoms of spasmodic dysphonia (r = 0.509, P = 0.037). These brain abnormalities may alter the central control of voluntary voice production and, therefore, may underlie the pathophysiology of this disorder.

Implementing the plasma-lasing potential for tabletop nano-imaging

Implementing the plasma-lasing potential for tabletop nano-imaging on across a hot plasma medium drives short-wavelength lasing, promising for "turnkey" nano-imaging setups. A systematic study of the illumination characteristics, combined with design-adapted objectives, is presented. It is shown how the ultimate nano-scale feature is dictated by either the diffraction-limited or the wavefront-limited resolution, which imposed a combined study of both the source and the optics. For nano-imaging, the spatial homogeneity of the illumination (spot noise) was shown as critical. Plasma-lasing from a triple grazing-incidence pumping scheme compensated for the missing spot homogeneity in classical schemes. We demonstrate that a collimating mirror pre-conditions both the pointing stability and the divergence below half a mrad.

Anti-PSMA antibody-coupled gold nanorods detection by optical and electron microscopies

While cancer is one of the greatest challenges to public health care, prostate cancer was chosen as cancer model to develop a more accurate imaging assessment than those currently available. Indeed, an efficient imaging technique which considerably improves the sensitivity and specificity of the diagnostic and predicting the cancer behavior would be extremely valuable. The concept of optoacoustic imaging using home-made functionalized gold nanoparticles coupled to an antibody targeting PSMA (prostate specific membrane antigen) was evaluated on different cancer cell lines to demonstrate the specificity of the designed platform. Two commonly used microscopy techniques (indirect fluorescence and scanning electron microscopy) showed their straightforwardness and versatility for the nanoparticle binding investigations regardless the composition of the investigated nanoobjects. Moreover most of the research laboratories and centers are equipped with fluorescence microscopes, so indirect fluorescence using Quantum dots can be used for any active targeting nanocarriers (polymers, ceramics, metals, etc.). The second technique based on backscattered electron is not only limited to gold nanoparticles but also suits for any study of metallic nanoparticles as the electronic density difference between the nanoparticles and binding surface stays high enough. Optoacoustic imaging was finally performed on a 3D cellular model to assess and prove the concept of the developed platform.

Direct observation of liquid crystals using cryo-TEM: Specimen preparation and low-dose imaging

Liquid crystals (LCs) represent a challenging group of materials for direct transmission electron microscopy (TEM) studies due to the complications in specimen preparation and the severe radiation damage. In this paper, we summarize a series of specimen preparation methods, including thin film and cryo-sectioning approaches, as a comprehensive toolset enabling high-resolution direct cryo-TEM observation of a broad range of LCs. We also present comparative analysis using cryo-TEM and replica freeze-fracture TEM on both thermotropic and lyotropic LCs. In addition to the revisits of previous practices, some new concepts are introduced, e.g., suspended thermotropic LC thin films, combined high-pressure freezing and cryo-sectioning of lyotropic LCs, and the complementary applications of direct TEM and indirect replica TEM techniques. The significance of subnanometer resolution cryo-TEM observation is demonstrated in a few important issues in LC studies, including providing direct evidences for the existence of nanoscale smectic domains in nematic bent-core thermotropic LCs, comprehensive understanding of the twist-bend nematic phase, and probing the packing of columnar aggregates in lyotropic chromonic LCs. Direct TEM observation opens ways to a variety of TEM techniques, suggesting that TEM (replica, cryo, and in situ techniques), in general, may be a promising part of the solution to the lack of effective structural probe at the molecular scale in LC studies. Microsc. Res. Tech. 77:754-772, 2014. © 2014 Wiley Periodicals, Inc.

Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.

Electron cryomicroscopy of E. coli reveals filament bundles involved in plasmid DNA segregation.

Bipolar elongation of filaments of the bacterial actin homolog ParM drives movement of newly replicated plasmid DNA to opposite poles of a bacterial cell. We used a combination of vitreous sectioning and electron cryotomography to study this DNA partitioning system directly in native, frozen cells. The diffraction patterns from overexpressed ParM bundles in electron cryotomographic reconstructions were used to unambiguously identify ParM filaments in Escherichia coli cells. Using a low-copy number plasmid encoding components required for partitioning, we observed small bundles of three to five intracellular ParM filaments that were situated close to the edge of the nucleoid. We propose that this may indicate the capture of plasmid DNA within the periphery of this loosely defined, chromosome-containing region.

Materials properties from electron density distributions: Molecular magnetism and linear optical properties

The general goal of this thesis is correlating observable properties of organic and metal-organic materials with their ground-state electron density distribution. In a long-term view, we expect to develop empirical or semi-empirical approaches to predict materials properties from the electron density of their building blocks, thus allowing to rationally engineering molecular materials from their constituent subunits, such as their functional groups. In particular, we have focused on linear optical properties of naturally occurring amino acids and their organic and metal-organic derivatives, and on magnetic properties of metal-organic frameworks. For analysing the optical properties and the magnetic behaviour of the molecular or sub-molecular building blocks in materials, we mostly used the more traditional QTAIM partitioning scheme of the molecular or crystalline electron densities, however, we have also investigated a new approach, namely, X-ray Constrained Extremely Localized Molecular Orbitals (XC-ELMO), that can be used in future to extracted the electron densities of crystal subunits. With the purpose of rationally engineering linear optical materials, we have calculated atomic and functional group polarizabilities of amino acid molecules, their hydrogen-bonded aggregates and their metal-organic frameworks. This has enabled the identification of the most efficient functional groups, able to build-up larger electric susceptibilities in crystals, as well as the quantification of the role played by intermolecular interactions and coordinative bonds on modifying the polarizability of the isolated building blocks. Furthermore, we analysed the dependence of the polarizabilities on the one-electron basis set and the many-electron Hamiltonian. This is useful for selecting the most efficient level of theory to estimate susceptibilities of molecular-based materials. With the purpose of rationally design molecular magnetic materials, we have investigated the electron density distributions and the magnetism of two copper(II) pyrazine nitrate metal-organic polymers. High-resolution X-ray diffraction and DFT calculations were used to characterize the magnetic exchange pathways and to establish relationships between the electron densities and the exchange-coupling constants. Moreover, molecular orbital and spin-density analyses were employed to understand the role of different magnetic exchange mechanisms in determining the bulk magnetic behaviour of these materials. As anticipated, we have finally investigated a modified version of the X-ray constrained wavefunction technique, XC-ELMOs, that is not only a useful tool for determination and analysis of experimental electron densities, but also enables one to derive transferable molecular orbitals strictly localized on atoms, bonds or functional groups. In future, we expect to use XC-ELMOs to predict materials properties of large systems, currently challenging to calculate from first-principles, such as macromolecules or polymers. Here, we point out advantages, needs and pitfalls of the technique. This work fulfils, at least partially, the prerequisites to understand materials properties of organic and metal-organic materials from the perspective of the electron density distribution of their building blocks. Empirical or semi-empirical evaluation of optical or magnetic properties from a preconceived assembling of building blocks could be extremely important for rationally design new materials, a field where accurate but expensive first-principles calculations are generally not used. This research could impact the community in the fields of crystal engineering, supramolecular chemistry and, of course, electron density analysis.

Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets

The accurate electron density distribution and magnetic properties of two metal-organic polymeric magnets, the quasi-one-dimensional (1D) Cu(pyz)(NO3)2 and the quasi-two-dimensional (2D) [Cu(pyz)2(NO3)]NO3·H2O, have been investigated by high-resolution single-crystal X-ray diffraction and density functional theory calculations on the whole periodic systems and on selected fragments. Topological analyses, based on quantum theory of atoms in molecules, enabled the characterization of possible magnetic exchange pathways and the establishment of relationships between the electron (charge and spin) densities and the exchange-coupling constants. In both compounds, the experimentally observed antiferromagnetic coupling can be quantitatively explained by the Cu-Cu superexchange pathway mediated by the pyrazine bridging ligands, via a σ-type interaction. From topological analyses of experimental charge-density data, we show for the first time that the pyrazine tilt angle does not play a role in determining the strength of the magnetic interaction. Taken in combination with molecular orbital analysis and spin density calculations, we find a synergistic relationship between spin delocalization and spin polarization mechanisms and that both determine the bulk magnetic behavior of these Cu(II)-pyz coordination polymers.

Modeling Techniques for the High-Resolution Interpretation of Cryo-Electron Microscopy Reconstructions

Essential biological processes are governed by organized, dynamic interactions between multiple biomolecular systems. Complexes are thus formed to enable the biological function and get dissembled as the process is completed. Examples of such processes include the translation of the messenger RNA into protein by the ribosome, the folding of proteins by chaperonins or the entry of viruses in host cells. Understanding these fundamental processes by characterizing the molecular mechanisms that enable then, would allow the (better) design of therapies and drugs. Such molecular mechanisms may be revealed trough the structural elucidation of the biomolecular assemblies at the core of these processes. Various experimental techniques may be applied to investigate the molecular architecture of biomolecular assemblies. High-resolution techniques, such as X-ray crystallography, may solve the atomic structure of the system, but are typically constrained to biomolecules of reduced flexibility and dimensions. In particular, X-ray crystallography requires the sample to form a three dimensional (3D) crystal lattice which is technically di‑cult, if not impossible, to obtain, especially for large, dynamic systems. Often these techniques solve the structure of the different constituent components within the assembly, but encounter difficulties when investigating the entire system. On the other hand, imaging techniques, such as cryo-electron microscopy (cryo-EM), are able to depict large systems in near-native environment, without requiring the formation of crystals. The structures solved by cryo-EM cover a wide range of resolutions, from very low level of detail where only the overall shape of the system is visible, to high-resolution that approach, but not yet reach, atomic level of detail. In this dissertation, several modeling methods are introduced to either integrate cryo-EM datasets with structural data from X-ray crystallography, or to directly interpret the cryo-EM reconstruction. Such computational techniques were developed with the goal of creating an atomic model for the cryo-EM data. The low-resolution reconstructions lack the level of detail to permit a direct atomic interpretation, i.e. one cannot reliably locate the atoms or amino-acid residues within the structure obtained by cryo-EM. Thereby one needs to consider additional information, for example, structural data from other sources such as X-ray crystallography, in order to enable such a high-resolution interpretation. Modeling techniques are thus developed to integrate the structural data from the different biophysical sources, examples including the work described in the manuscript I and II of this dissertation. At intermediate and high-resolution, cryo-EM reconstructions depict consistent 3D folds such as tubular features which in general correspond to alpha-helices. Such features can be annotated and later on used to build the atomic model of the system, see manuscript III as alternative. Three manuscripts are presented as part of the PhD dissertation, each introducing a computational technique that facilitates the interpretation of cryo-EM reconstructions. The first manuscript is an application paper that describes a heuristics to generate the atomic model for the protein envelope of the Rift Valley fever virus. The second manuscript introduces the evolutionary tabu search strategies to enable the integration of multiple component atomic structures with the cryo-EM map of their assembly. Finally, the third manuscript develops further the latter technique and apply it to annotate consistent 3D patterns in intermediate-resolution cryo-EM reconstructions. The first manuscript, titled An assembly model for Rift Valley fever virus, was submitted for publication in the Journal of Molecular Biology. The cryo-EM structure of the Rift Valley fever virus was previously solved at 27Å-resolution by Dr. Freiberg and collaborators. Such reconstruction shows the overall shape of the virus envelope, yet the reduced level of detail prevents the direct atomic interpretation. High-resolution structures are not yet available for the entire virus nor for the two different component glycoproteins that form its envelope. However, homology models may be generated for these glycoproteins based on similar structures that are available at atomic resolutions. The manuscript presents the steps required to identify an atomic model of the entire virus envelope, based on the low-resolution cryo-EM map of the envelope and the homology models of the two glycoproteins. Starting with the results of the exhaustive search to place the two glycoproteins, the model is built iterative by running multiple multi-body refinements to hierarchically generate models for the different regions of the envelope. The generated atomic model is supported by prior knowledge regarding virus biology and contains valuable information about the molecular architecture of the system. It provides the basis for further investigations seeking to reveal different processes in which the virus is involved such as assembly or fusion. The second manuscript was recently published in the of Journal of Structural Biology (doi:10.1016/j.jsb.2009.12.028) under the title Evolutionary tabu search strategies for the simultaneous registration of multiple atomic structures in cryo-EM reconstructions. This manuscript introduces the evolutionary tabu search strategies applied to enable a multi-body registration. This technique is a hybrid approach that combines a genetic algorithm with a tabu search strategy to promote the proper exploration of the high-dimensional search space. Similar to the Rift Valley fever virus, it is common that the structure of a large multi-component assembly is available at low-resolution from cryo-EM, while high-resolution structures are solved for the different components but lack for the entire system. Evolutionary tabu search strategies enable the building of an atomic model for the entire system by considering simultaneously the different components. Such registration indirectly introduces spatial constrains as all components need to be placed within the assembly, enabling the proper docked in the low-resolution map of the entire assembly. Along with the method description, the manuscript covers the validation, presenting the benefit of the technique in both synthetic and experimental test cases. Such approach successfully docked multiple components up to resolutions of 40Å. The third manuscript is entitled Evolutionary Bidirectional Expansion for the Annotation of Alpha Helices in Electron Cryo-Microscopy Reconstructions and was submitted for publication in the Journal of Structural Biology. The modeling approach described in this manuscript applies the evolutionary tabu search strategies in combination with the bidirectional expansion to annotate secondary structure elements in intermediate resolution cryo-EM reconstructions. In particular, secondary structure elements such as alpha helices show consistent patterns in cryo-EM data, and are visible as rod-like patterns of high density. The evolutionary tabu search strategy is applied to identify the placement of the different alpha helices, while the bidirectional expansion characterizes their length and curvature. The manuscript presents the validation of the approach at resolutions ranging between 6 and 14Å, a level of detail where alpha helices are visible. Up to resolution of 12 Å, the method measures sensitivities between 70-100% as estimated in experimental test cases, i.e. 70-100% of the alpha-helices were correctly predicted in an automatic manner in the experimental data. The three manuscripts presented in this PhD dissertation cover different computation methods for the integration and interpretation of cryo-EM reconstructions. The methods were developed in the molecular modeling software Sculptor (http://sculptor.biomachina.org) and are available for the scientific community interested in the multi-resolution modeling of cryo-EM data. The work spans a wide range of resolution covering multi-body refinement and registration at low-resolution along with annotation of consistent patterns at high-resolution. Such methods are essential for the modeling of cryo-EM data, and may be applied in other fields where similar spatial problems are encountered, such as medical imaging.

Electron spin resonance (ESR) and 14C dating in sediments of Bonaire, Leeward Antilles

The coastal deposits of Bonaire, Leeward Antilles, are among the most studied archives for extreme-wave events (EWEs) in the Caribbean. Here we present more than 400 electron spin resonance (ESR) and radiocarbon data on coarse-clast deposits from Bonaire's eastern and western coasts. The chronological data are compared to the occurrence and age of fine-grained extreme-wave deposits detected in lagoons and floodplains. Both approaches are aimed at the identification of EWEs, the differentiation between extraordinary storms and tsunamis, improving reconstructions of the coastal evolution, and establishing a geochronological framework for the events. Although the combination of different methods and archives contributes to a better understanding of the interplay of coastal and archive-related processes, insufficient separation, superimposition or burying of coarse-clast deposits and restricted dating accuracy limit the use of both fine-grained and coarse-clast geoarchives to unravel decadal- to centennial-scale events. At several locations, distinct landforms are attributed to different coastal flooding events interpreted to be of tsunamigenic origin. Coastal landforms on the western coast have significantly been influenced by (sub)-recent hurricanes, indicating that formation of the coarse-clast deposits on the eastern coast is likely to be related to past events of higher energy.

Spatial compartmentalization of free radical formation and mitochondrial heterogeneity in bivalve gills revealed by live-imaging techniques, supplementary material

Live-imaging techniques (LIT) utilize target-specific fluorescent dyes to visualize biochemical processes using confocal and multiphoton scanning microscopy, which are increasingly employed as non-invasive approach to physiological in-vivo and ex-vivo studies. Here we report application of LIT to bivalve gills for ex-vivo analysis of gill physiology and mapping of reactive oxygen (ROS) and nitrogen (RNS) species formation in the living tissue. Our results indicate that H2O2, HOO. and ONOO- radicals (assessed through C-H2DFFDA staining) are mainly formed within the blood sinus of the filaments and are likely to be produced by hemocytes as defense against invading pathogens. The oxidative damage in these areas is controlled by enhanced CAT (catalase) activities recorded within the filaments. The outermost areas of the ciliated epithelial cells composing the filaments, concentrated the highest mitochondrial densities (MTK Deep Red 633 staining) and the most acidic pH values (as observed with ageladine-a). These mitochondria have low (depolarized) membrane potentials (D psi m) (JC-1 staining), suggesting that the high amounts of ATP required for ciliary beating may be in part produced by non-mitochondrial mechanisms, such as the enzymatic activity of an ATP-regenerating kinase. Nitric oxide (NO, DAF-2DA staining) produced in the region of the peripheral mitochondria may have an effect on mitochondrial electron transport and possibly cause the low membrane potential. High DAF-2DA staining was moreover observed in the muscle cells composing the wall of the blood vessels where NO may be involved in regulating blood vessel diameter. On the ventral bend of the gills, subepithelial mucus glands (SMG) contain large mucous vacuoles showing higher fluorescence intensities for O2.- (DHE staining) than the rest of the tissue. Given the antimicrobial properties of superoxide, release of O2.- into the mucus may help to avoid the development of microbial biofilms on the gill surface. However, cells of the ventral bends are paying a price for this antimicrobial protection, since they show significantly higher oxidative damage, according to the antioxidant enzyme activities and the carbonyl levels, than the rest of the gill tissue. This study provides the first evidence that one single epithelial cell may contain mitochondria with significantly different membrane potentials. Furthermore, we provide new insight into ROS and RNS formation in ex-vivo gill tissues which opens new perspectives for unraveling the different ecophysiological roles of ROS and RNS in multifunctional organs such as gills.

Mineralogy of Hawaiian Arch sediments

The mineralogy of both bulk- and clay-sized (<2 µm) fractions of sediments from Holes 842A and 842B of Ocean Drilling Program Leg 136 was determined by X-ray diffraction. The sediments consist of a combination of terrigenous (quartz, plagioclase, smectite, illite, kaolinite, and chlorite), volcaniclastic (augite, plagioclase, and volcanic glass), and diagenetic minerals (smectite, phillipsite, clinoptilolite, and opal-CT). Although biogenic silica (radiolarians and diatoms) is common in near-seafloor (<10 mbsf) sediments, biogenic calcite is rare. Variations with depth in abundances of the terrigenous minerals reflect temporal changes in the flux of eolian material to the site. Volcanogenic material derived from the Hawaiian Islands is present in lithologic Unit 1 (0-19.9 meters below seafloor) both as discrete layers and as finely disseminated silt- and clay-sized material. Volcanic glass is present only in the upper 10 m of the sediment column. In Unit 2 (19.9-35.7 mbsf), increased smectite and zeolite abundances with depth as well as indurated, zeolite-rich layers are thought to be the alteration products of volcanogenic material. The source of this older (late Oligocene to middle Miocene) volcanogenic detritus may be continental volcanism. Microfabrics imaged using back-scattered electron imaging reflect the effects of compaction and diagenesis on sediment porosity and matrix structure. As porosity decreases during burial, the matrix changes from an open, floc-like fabric, to an interlocking network of clay mineral domains, and finally to a dense intergrowth of clay minerals and zeolites. Despite the substantial changes in sediment microfabric and mineralogy, correlations between physical and acoustic properties and mineralogy are weak or absent. The sediment has maintained high porosity (>70%), and water content appears to dominate the sediment's physical character and acoustic response.

Analysis of Super Imaging Properties of Spherical Geodesic Waveguide Using COMSOL Multyphisics

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit using materials of negative dielectric and magnetic constants. Recently, two devices with positive refraction, the Maxwell Fish Eye lens (MFE) (Leonhardt et al 2000) and the Spherical Geodesic Waveguide (SGW)(Minano et all 2011) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Moreover, recent analysis of the SGW with defined object and image surfaces, which are both conical sections of the sphere, has shown that the system transmits images bellow diffraction limit. The key assumption is the use of a perfectly absorbing receptor called perfect drain. This receptor is capable to absorb all the radiation without reflection or scattering. Here, it is presented the COMSOL analysis of the SGW using a perfect drain that absorbs perfectly two modes. The design procedure for PD capable to absorb k modes is proposed, as well.

Perfect imaging analysis of the spherical geodesic waveguide

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to ?/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.