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Brain-machine interfaces (BMIs) are useful tools for controlling assistive devices. One current approach in this field is continuous trajectory reconstruction (CTR), which decodes variables from electroencephalographic (EEG) signals. In this study, the CTR approach was applied to estimate kinetic variables from lower limb joints during pre-gait movements. The methodology consisted of a multi-layer perceptron capable of detecting patterns that represent the relation between EEG and torque signals acquired during motion tasks. The study also searched for an optimal subset of EEG channels based on the resulting patterns. A group of volunteers was recruited to execute pre-gait movements with both lower limbs to test the methodology. Results show that decodings of extracted patterns were successful in terms of the selected performance metrics; that is, the coefficient of determination, correlation coefficient, and signal-to-noise ratio. These metrics suggest that decodings for the right lower limb are better than for the left one, and that the most frequent electrodes in the optimal subsets for each task and joint show a tendency to lateralize. The results obtained suggest that this machine learning scheme could be used for future studies of the CTR of kinetic variables.

Ray tracing in gradient-index (GRIN) media has been traditionally performed either by using the analytical or numerical solutions to the Eikonal equation or by creating a layered medium where Snell’s law is calculated in each layer. In this paper, an exact general method to perform ray tracing in GRIN media is presented based on the invariants of the system as stated by Fermat’s principle when the media presents symmetries. Its advantage, compared with other methods reported in the literature, relies on its easy implementation. Besides the GRIN distribution and the initial conditions of the incident ray, once the invariants of the system are stated the resulting math is simple to solve and interpret. To benchmark the algorithm, ray tracing in typical cases of GRIN media is calculated, finding minimal discrepancies between the analytical solutions and our simulations. The used media are axial refractive index and parabolic index fiber and lenses with spherical gradient-index symmetry, such as: Luneburg’s, Gutman’s, generalized Maxwell’s Fish-eye, Eaton’s, and concentrator lenses. Our method can be further applied to distributions with symmetries associated with other common curvilinear orthogonal coordinate systems, in particular to those associated to the separability of the Helmholtz equation that would allow us to investigate wave optics in these GRIN media with the associated geometries.

To the best of our knowledge, at the present time there is no answer to the fundamental question stated in the title that provides a complete and satisfactory physical description of the structured nature of Hermite-Gauss beams. The purpose of this manuscript is to provide proper answers supported by a rigorous mathematical-physics framework that is physically consistent with the observed propagation of these beams under different circumstances. In the process we identify that the paraxial approximation introduces spurious effects in the solutions that are unphysical. By removing them and using the property of self-healing, that is characteristic to structured beams, we demonstrate that Hermite-Gaussian beams are constituted by the superposition of four traveling waves.

A system based on the use of two artificial neural networks (ANNs) to determine the location of the scleral spur of the human eye in ocular images generated by an ultrasound biomicroscopy is presented in this paper. The two ANNs establish a relationship between the distance of four manually placed landmarks in an ocular image with the coordinates of the scleral spur. The latter coordinates are generated by the expert knowledge of a subject matter specialist. Trained ANNs that generate good results for scleral spur location are incorporated into a software system. Statistical indicators and results yield an efficiency performance above 95%.

In the seminal paper on elegant Gaussian beams, Siegman introduced them as a complex-argument variant of standard Gaussian beams and proved that they cannot be eigenmodes of spherical resonators. In this work, we demonstrate that this intrinsic asymmetry can be overcome by judiciously superposing a finite number of elegant Laguerre–Gauss beams, all of them having the same amount of orbital angular momentum. In other words, we found a new family of elegant modes that are eigenmodes of confocal resonators and will call them Siegman’s elegant resonator modes.

In recent work, we showed how the optical response of the human eye’s crystalline lens can be modeled using a single function. We believe that this development will inform designs for applications such as intraocular implant lenses, and that it also has wider potential applications in areas including biomedical optics, ophthalmology and engineering.

The lens is a complex optical component of the human eye because of its physiological structure: the surface is aspherical and the structural entities create a gradient refractive index (GRIN). Most existent models of the lens deal with its external shape independently of the refractive index and, subsequently, through optimization processes, adjust the imaging properties. In this paper, we propose a physiologically realistic GRIN model of the lens based on a single function for the whole lens that accurately describes different accommodative states simultaneously providing the corresponding refractive index distribution and the external shape of the lens by changing a single parameter that we associate with the function of the ciliary body. This simple, but highly accurate model, is incorporated into a schematic eye constructed with reported experimental biometric data and accommodation is simulated over a range of 0 to 6 diopters to select the optimum levels of image quality. Changes with accommodation in equatorial and total axial lens thicknesses, as well as aberrations, are found to lie within reported biometric data ranges.

When a circular aperture is uniformly illuminated, it is possible to observe in the far field an image of a bright circle surrounded by faint rings known as the Airy pattern or Airy disk. This pattern is described by the first-order Bessel function of the first type divided by its argument expressed in circular coordinates. We introduce the higher-order Bessel functions with a vortex azimuthal factor to propose a family of functions to generalize the function defining the Airy pattern. These functions, which we call vortex Jinc functions, happen to form an orthogonal set. We use this property to investigate their usefulness in fitting various surfaces in a circular domain, with applications in precision optical manufacturing, wavefront optics, and visual optics, among others. We compare them with other well-known sets of orthogonal functions, and our findings show that they are suitable for these tasks and can pose an advantage when dealing with surfaces that concentrate a considerable amount of their information near the center of a circular domain, making them suitable applications in visual optics or analysis of aberrations of optical systems, for instance, to analyze the point spread function.

In this Letter, a Gabor superlens with variable focus is presented. This configuration uses tunable liquid lenses in the third microlens array of the Gabor superlens. By applying voltage, the radius of curvature of the micro-tunable doublet arrays changes, and the Gabor conditions are fulfilled at different focal planes. As a consequence, the magnification of the image at the focal planes changes, and a zoom effect is observed. The marginal depth plane for this system goes from 0.86 to 0.89 mm. The optical simulation, calculations, and results of the simulated optical system performance are presented.

By means of numerical simulations we provide proof of concept for a low cost cone locating system whose function is based on vortex beams. The system described here does not lose precision compared to commercial standards. We investigate the advantages of imaging individual cones using vortex phase masks of different topological charge. We provide numerical simulations of two different setups that are combined to take advantage of optical vortices for two purposes: (a) resolve pairs of cones within the photoreceptor mosaic, and (b) to pinpoint positions of unresolved cones, we study the stability of this configuration against basic wavefront aberrations. The combination of setups can perform detection and positioning tasks with no correction for aberrations required. We show a simulation of how the system would produce a map of retinal cones.

We present a new design of a plasmonic Luneburg lens made from a gradient-index metasurface that was constructed with an array of nanometer-sized holes in a dielectric thin film. The fabricated structure consists of a planar lens with a diameter of 8.7 μm composed of a rectangular array of holes with a periodicity of 300 nm. The experimental characterization includes leakage-radiation microscopy imaging in the direction and frequency space. The former allows for characterization of the point spread function and phase distribution, whereas the latter grants access to qualitative measurements of the effective mode indices inside the plasmonic lens. The experimental results presented here are in good agreement with the expected average performance predicted by the numerical calculations. Nevertheless, the robustness of the characterization techniques presented here is also exploited to determine deviations from the design parameters.

Ray tracing in spherical Luneburg lenses has always been represented in 2D. All propagation planes in a 3D spherical Luneburg lens generate the same ray tracing, due to its radial symmetry. A geometry without radial symmetry generates a different ray tracing. For this reason, a new ray tracing method in 3D through spherical and elliptical Luneburg lenses using 2D methods is proposed. The physics of the propagation is shown here, which allows us to make a ray tracing associated with a vortex beam. A 3D ray tracing in a composite modified Luneburg lens that represents the human eye lens is also presented.

Multi-aperture optics based on insects and arthropods eyes, is an interesting topic related to the development of miniaturized non-conventional optical designs. This novel concept has been used in image formation devices that offer many benefits in miniaturization and in improving certain optical characteristics, like a widef field of view. Energy concentration presents a good application for this technology. We show here, the description of the propagation of multiple laser beams through an ultra-thin objective lens that consists of a series of microlens arrays, and the fact that they have a common focal point, give us the option to achieve a high power concentration that results in the addition of the multiple lasers intensity. Lens configuration, equations, propagation, and optical performance are described.

A new lens model based on the gradient-index Luneburg lens and composed of two oblate half spheroids of different curvatures is presented. The spherically symmetric Luneburg lens is modified to create continuous isoindicial contours and to incorporate curvatures that are similar to those found in a human lens. The imaging capabilities of the model and the changes in the gradient index profile are tested for five object distances, for a fixed geometry and for a fixed image distance. The central refractive index decreases with decreasing object distance. This indicates that in order to focus at the same image distance as is required in the eye, a decrease in refractive power is needed for rays from closer objects that meet the lens surface at steeper angles compared to rays from more distant objects. This ensures a highly focused image with no spherical aberration.