Lens Geometry Research Articles

A bilateral dispensing evaluation of two different toric lens geometries

A bilateral dispensing evaluation of two different toric lens geometries

Peripheral corneal characterization for large diameter corneal contact lenses fitting in a patient with keratoconus

Purpose: To describe a case in which large diameter corneal contact lenses (CL) were fit to a patient with asymmetric stage IV (RE) and stage I (LE) keratoconus (Amsler-Krumeich scale) to improve visual quality and comfort. Contact lens geometry was spherical-progressive, with four concentric radii obtained by a novel corneal characterization method based on Scheimpflug images (Oculus Pentacam HR®)

Friction Weldability of a High Nb Containing TiAl Alloy.

The friction weldability of Ti-45Al-8.5Nb-0.2W-0.2B-0.02Y alloy has been investigated by optimizing process parameters and analyzing the microstructures and tensile properties of the joints. The as-cast alloy with a nearly lamellar (NL) microstructure and the as-forged alloys with a duplex (DP) microstructure have been successfully welded. All the joints have a severe deformation zone (SDZ) and a transition zone (TZ) between the parent metal (PM) and SDZ. SDZ, showing a biconcave lens geometry, has a maximum thickness of hundreds of micrometers at the periphery. TZ is hundreds of micrometers thick. All SDZs have a fine-grained DP microstructure with a grain size of a few micrometers. For the joint of the as-cast alloy, the TZ consists of deformed lamellar colonies as the major constituent and partially recrystallized grains as the minor constituent. For the joint of the as-forged alloy, the TZ is similar to both the PM and SDZ, showing a DP microstructure. The grain size, volume fraction of γ grains, and the remnant lamellar colonies all increase with the distance from the SDZ. All joints presented perfect metallurgical bonding. The strengths of the joints are higher than those of the corresponding PMs. This indicates that the studied alloy has good friction weldability.

Ultrasound Axicon: Systematic Approach to Optimize Focusing Resolution through Human Skull Bone.

The use of axicon lenses is useful in many high-resolution-focused ultrasound applications, such as mapping, detection, and have recently been extended to ultrasonic brain therapies. However, in order to achieve high spatial resolution with an axicon lens, it is necessary to adjust the separation, called stand-off (δ), between a conventional transducer and the lens attached to it. Comprehensive ultrasound simulations, using the open-source k-Wave toolbox, were performed for an axicon lens attached to a piezo-disc type transducer with a radius of 14 mm, and a frequency of about 0.5 MHz, that is within the range of optimal frequencies for transcranial transmission. The materials properties were measured, and the lens geometry was modelled. Hydrophone measurements were performed through a human skull phantom. We obtained an initial easygoing design model for the lens angle and optimal stand-off using relatively simple formulas. The skull is not an obstacle for focusing of ultrasound with optimized axicon lenses that achieve an identical resolution to spherical transducers, but with the advantage that the focusing distance is shortened. An adequate stand-off improves the lateral resolution of the acoustic beam by approximately 50%. The approach proposed provides an effective way of designing polydimethylsiloxane (PDMS)-based axicon lenses equipped transducers.

Computational study of electrostatic focusing of aerosol nanoparticles using an einzel lens

This study computationally explores the possibility of focusing charged aerosol nanoparticles using electrostatics, similar to focusing of electrons and ions. A non-dimensional electrostatic focusing parameter χe, defined as the ratio of electrostatic potential energy to the kinetic energy of an aerosol nanoparticle, significantly determines focusing performance. The focusing device considered here is a 3-electrode electrostatic (“einzel”) lens. The average focal length of the lens is seen to have an inverse power relationship with χe. For low values of χe ∼3 in this study, the particles are seen to cross the lens axis once, while at higher χe multiple axis cross-over points appear. Similar to electron and ion optics, nanoparticle focusing is also limited by spherical aberration and beam divergence due to finite spread of particles in the inlet cross section of the lens and spatial non-uniformity of the focusing electric field. Other factors that influence focusing performance such as the electrostatic lens geometry, and the distribution of velocity and kinetic energy of the particles at the inlet of the lensing region are recognized, but not considered here for simplicity. In vacuum, good focusing performance (i.e.) a narrow beam of nanoparticles with minimum spherical aberration and small divergence angle is theoretically possible if χe<1 and if spread of particles in the inlet is confined to 20% of radius of the cylindrical lens. The effect of gas pressure is also probed to understand the degradation of focusing performance due to particle-gas interactions. It is seen that, for particles of specified size and density, a certain maximum pressure exists beyond which the device can no longer be efficiently used to focus nanoparticles. Likewise, below a certain pressure, the focusing performance is nearly independent of gas pressure, thereby enabling the selection of an operating pressure for such devices.

Development of an in vivo magnetic resonance imaging and computer modelling platform to investigate the physiological optics of the crystalline lens.

We have developed and validated in vivo magnetic resonance imaging (MRI) protocols to extract parameters (T2 and geometry) of the human lens that, combined with biometric measures of the eye and optical modelling, enable us to investigate the relative contributions made by the gradient of refractive index (GRIN) and the shape of the lens to the refractive properties of each subject tested. Seven young and healthy participants (mean age: 25.6 ± 3.6 years) underwent an ophthalmic examination, and two sessions of MRI scans using a 3 T clinical magnet. Our MRI protocols for studying lens physiological optics and geometrical measurements were repeatable and reliable, using both 1D (95% confidence interval (CI) for mean differences for exponents = [-2.1, 2.6]) and 2D analysis (anterior T2 CI for differences [-6.4, 8.1] ms; posterior T2 CI for differences [-6.4, 8.3] ms). The lens thickness measured from MRI showed good correlation with that measured with clinical 'gold standard' LenStar (mean differences = [-0.18, 0.2] mm). The predicted refractive errors from ZEMAX had reasonable agreements with participants' clinic records (mean differences = [-1.7, 1.2] D). Quantitative measurements of lens geometry and GRIN with our MRI technique showed high inter-day repeatability. Our clinical MRI technique also provides reliable measures of lens geometry that are comparable to optical biometry. Finally, our ZEMAX optical models produced accurate refractive error and lens power estimations.

High beam-current density of a 10-keV nano-focus X-ray source

Abstract The electron beam-current density at a target greatly affects imaging intensity and contrast when using a low-energy nano-focus X-ray source. This paper proposes a new electron gun comprising a 10-keV nano-focus X-ray source with a single-pole magnetic lens to improve its effective brightness and beam-current density. After analyzing the effect of the electric field on the extended Schottky emission, we first optimized the anode with high effective brightness and a fine virtual spot with enough intensity for nano-focus X-ray imaging. High effective beam-current density was then obtained by optimizing the position, geometry and electrical supplies of the single-pole magnetic lens. The effective brightness of this electron gun is 1.70 × 108 A•cm−2•sr−1, and the nano-focus X-ray source has a spot size of 41 nm when its tube current is 2 μ A. This electron gun achieves higher beam current density (1.6 × 105A•cm−2), and its collimated landing beam efficiently transports the beam current in the X-ray source.

Microstructure and properties of friction welding joint of Ti–45Al-8.5Nb-0. 2W-0. 2B-0. 02Y alloy

High Nb containing TiAl alloys have prospect to be used for turbo wheel and exhaust valve for vehicle engine. Friction welding is a suitable process for fabricating these components. For investigating the weldability of these alloys, cylindrical samples of Ti–45Al-8.5Nb-0.2W-0.2B-0.02Y (in at%) alloy with a diameter of 10 mm were welded by continuous drive friction welding process, and the microstructures and the mechanical properties of the joints were analyzed in this paper. The results showed that the weldability of the present alloy was very good. At parameters of rotational speed of 2400 r/min, friction pressure of 320 MPa, burn-off distance of 3 mm and upset pressure of 360 MPa, completely metallurgical bonding interfaces were obtained. The joint had a severely plastic deformation zone (SPDZ) with a biconcave lens geometry. The thicknesses of the center and periphery of SPDZ were about 40 μm and 800 μm, respectively. There existed a transition zone (TZ) between parent metal (PM) and SPDZ. SPDZ exhibited the deformation flow lines and had a randomly-oriented recrystallized duplex (DP) microstructure with the average grain size of 2.5 μm, in contrast, PM presented a nearly lamellar (NL) microstructure with a colony size of 150 μm. TZ showed a mixture microstructure combining deformed lamellar colonies and partially recrystallized grains. At room temperature, 750 °C and 800 °C, welding joints had better tensile properties than PM.

Geometry-controllable micro-optics with laser catapulting

Individual or arrayed microlenses offer remarkable opportunities in optics and photonics. However, their usage is currently limited by the lack of manufacturing technologies capable of tailoring the lens geometry to target devices. Here, we demonstrate how laser catapulting (LCP), a recent laser-based additive manufacturing technique, enables the preparation of microlenses with controlled geometry and curvature. LCP exploits single laser pulses to catapult polymeric microdisks into user-selectable positions on a substrate, which are converted into microlenses following a thermal reflow treatment. By shaping the irradiance distribution of the incident laser beam, we obtained arrays of circular, triangular, and cylindrical microlenses with a radius between 50-250 µm and 100% fill-factor. The good quantitative agreement between beam shape and microlens geometry, combined with the in-situ fabrication capabilities and high-throughput of LCP, can help the consolidation of laser additive methods for micro-optics in scientific and industrial applications.

A camera model for cameras with hypercentric lenses and some example applications

We propose a camera model for cameras with hypercentric lenses. Because of their geometry, hypercentric lenses allow to image the top and the sides of an object simultaneously. This makes them useful for certain inspections tasks, for which otherwise multiple images would have to be acquired and stitched together. After describing the projection geometry of hypercentric lenses, we derive a camera model for hypercentric lenses that is intuitive for the user. Furthermore, we describe how to determine the parameter values of the model by calibrating the camera with a planar calibration object. We also apply our camera model to two example applications: in the first application, we show how two cameras with hypercentric lenses can be used for dense 3D reconstruction. For an efficient reconstruction, the images are rectified such that corresponding points occur in the same image row. Standard rectification methods would result in perspective distortions in the images that would prevent stereo matching algorithms from robustly establishing correspondences. Therefore, we propose a new rectification method for objects that are approximately cylindrical in shape, which enables a robust and efficient reconstruction. In the second application, we show how to unwrap cylindrical objects to simplify further inspection tasks. For the unwrapping, the pose of the cylinder must be known. We show how to determine the pose of the cylinder based on a single camera image and based on two images of a stereo camera setup.

SIMBIO-SYS/STC stereo camera calibration: Geometrical distortion.

The STereo imaging Channel (STC) is the first push-frame stereo camera on board an European Space Agency (ESA) satellite, i.e., the ESA-Japan Aerospace eXploration Agency mission BepiColombo. It was launched in October 2018, and it will reach its target, Mercury, in 2025. The STC main aim is to provide the global three-dimensional reconstruction of the Mercury surface. STC, the stereo channel of spectrometer and imagers for Mercury Planetary Orbiter BepiColombo-Integrated Observatory System, is based on an original optical design that incorporates the advantages of a compact unique detector instrument and the convenience of a double direction acquisition system. In fact, STC operates in a push-frame imaging mode and its two optical sub-channels will converge the incoming light on a single focal plane assembly allowing to minimize mass and volume. The focal plane of the instrument is housing six different filters: two panchromatic filters in the range 600-800 nm and four broadband filters with central wavelengths in the range 420-920 nm. In this paper, the geometrical calibration of the instrument, including the optical setups used, will be described. The methods used to derive the focal lengths, the boresights, and the reference systems of the different filter models are presented, and the related distortion results are discussed. The STC off-axis configuration forced to develop a distortion map model based on the RFM (rational function model). In contrast to other existing models, which allow linear estimates, the RFM is not referred to specific lens geometry, but it is sufficiently general to model a variety of distortion types, as it will be demonstrated in this particular case.

Design of low‐concentration static III‐V/Si partial CPV module with 27.3% annual efficiency for car‐roof application

AbstractA low‐concentration static III‐V/Si partial concentrator photovoltaic (CPV) module for area‐limited car roofs was designed and experimentally demonstrated. The concentrator lens geometry was optimized for an incidence‐angle dependency of annual global irradiance on a car‐roof (horizontal‐flat) surface by considering arbitrary car orientations. The designed lens with a geometrical concentration ratio of 3.5× for III‐V triple‐junction (3‐junction) cells can collect 46.6% and 36.4% of the annual irradiation onto a III‐V 3‐juction and Si cells, respectively, which are located under the III‐V cell. The module design was validated by indoor and outdoor tests using a prototype submodule. The results show that the present module can potentially achieve up to 27.3% annual module efficiency, as projected from the actual daily submodule efficiency of 20.8% assuming state‐of‐the‐art record cell efficiency. Furthermore, the outdoor test on a real curved car roof demonstrated that the effect of the curved surface on the power generation performance is comparable with that of a conventional PV module.

Optimizing the Fresnel-Lens Solar-Concentrator Design for Tracking Error Mitigation in Thermal Applications, Using a Statistical Algorithm

The driving motive of this work is to enhance the tolerability of a flat Fresnel-lens concentrator to tracking errors, without the use of secondary optics or sophisticated, and normally costly, meticulous tracking equipment. This is achieved by optimizing the prismatic geometry of the Fresnel lens through a statistical approach that incorporates laws of light refraction and trigonometry. The proposed design produces high focal heat flux that is more suitable for thermal applications. A comparative simulation analysis was conducted for two case studies from literature, each with a different design method for the Fresnel lens. On basis of equivalent geometric concentration ratio and f-number, the flat-spot lenses, designed by this study, returned higher values of the concentration acceptance product ( $$CAP$$ ). In case #1 of a 212× cylindrical lens with an f-number of unity, an equivalent flat lens by this work almost doubled the $$CAP$$ from 0.165 to 0.34. For the design case #2 of a 559× aspheric Fresnel lens made by simple geometrical optics, a 60.7% enhanced $$CAP$$ was achieved by this work’s lens, from 0.206 to 0.331, at an f-number of 0.83.

Ultrafast Relaxation of Photocarriers in Cadmium Sulfide

Experiments are performed on registering induced changes in the refractive index of a cadmium sulfide single crystal with femtosecond time resolution in the transient lens and transient gratings geometries. The lifetime of photoexcited charge carriers (photocarriers) is estimated at 230 ps. An additional component, characterized by a decay time of units of picoseconds, is found in the efficiency decay of the transient grating of free carrier concentration. It is shown that this time is determined by the thermalization rate of photocarriers.

Improvement of the Optical Performance of the Geometrical Parameters of Snorkel Magnetic Lens

Two models of asymmetrical magnetic objective lens geometries have been designed and studied. These two models are called Pinhole and Snorkel lenses. The comparison between these models was realized by the aid of simulation EOD program (Electron Optical Design), using the finite element method to analyze the magnetic flux density and optical properties at constant excitation (NI=2000A-t). The optimal model (Snorkel Lens) gives the best characteristics that were compatible with the research purposes in details, such as the changing of air gap and the axial polepiece bore diameter on the optical performance of the snorkel magnetic lens. This type of lens was used in low energies scanning electron microscope (SEM), which achieved the lowest values of the aberrations coefficient at long working distance.

Characterisation of seismic site effects influenced by near-surface structures using 3D waveform modelling

Seismic waves propagating from source to surface can be significantly affected by vertical and lateral heterogeneities of the near-surface geology. These modified waves can lead to local amplification or attenuation effects of the wave amplitude at the surface. In the assessment of seismic events and the evaluation of possible impacts on infrastructures, the analysis of such site effects is an important issue. In this study, the amplification behaviour of typical near-surface structures in Northern Germany is investigated depending on various parameters to assemble a catalogue of typical structures in the area, which can be used to quickly assess the impact of induced seismic events at the surface. The effect of incoming seismic waves on simple model structures as layer, channel and lens geometries is analysed using 3D waveform simulations with dominant signal frequencies between 1 and 10 Hz based on the spectral element method. The dimensions of the modelled structures range from tens of metres to a few hundred metres. The parameter study shows the dependency of the resulting amplitude at the surface on the impedance contrast, geometrical features and the dominant signal frequency, which are quantified as amplification (attenuation) factors. Simple layer structures reveal low amplification values ranging from 1 to 3.5 and smooth amplification curves, which become more complex for channel and lens type structures while the maximum amplification increases by a factor of two. Focusing and interference effects could be observed depending on the structure type itself as well on the edge shape of the structure. Furthermore, the results of the simple model simulations are used in combination with additional borehole, geological and geophysical data to generate a first large-scale model of the area of the natural gas fields in Northern Germany. Waveform simulations of the large-scale model illustrate the influence of near-surface structures on wave propagation and allow to calculate the amplification behaviour at the surface. These (regional) model simulations can be essential for the reliable assessment of site effects and minimising uncertainties in the interpolation of the ground velocity distribution.

Relative time delay in a spinning black hole as a diagnostic for no-hair theorem

The spinning regular black hole (spin a) metric proposed by Johannsen shares the Kerr horizon but contains independent dimensionless parameters marking deviation from the Kerr metric. Non-zero value of any of the parameters would indicate violation of the no-hair theorem. We shall find the influence of these parameters on the relative time delay (not Shapiro time delay) treated here as a diagnostic for no-hair theorem using aligned, finite, thin-lens approximation in realistic spinning astrophysical configurations. Precise measurement of this delay would then help us determine, from observational perspective, whether or not any of the parameters is really non-zero. We shall also point out that the aligned spinning lens is completely equivalent to a “static” lens with a fictitious lens geometry, which would enable us to re-express the relative time delay components in terms of the spin a. Numerical values are tabulated for three astrophysical lens systems. The advantage of the present treatment is that it can accommodate a variety of spinning lens systems that are likely to be detected in the near future.

Isogeometric shape optimization for nonlinear ultrasound focusing

The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. We formulate the shape optimization problem by introducing a tracking-type cost functional to match a desired pressure distribution in the focal region. Westervelt's equation, a nonlinear acoustic wave equation, is used to model the pressure field. We apply the optimize first, then discretize approach, where we first rigorously compute the shape derivative of our cost functional. A gradient-based optimization algorithm is then developed within the concept of isogeometric analysis, where the geometry is exactly represented by splines at every gradient step and the same basis is used to approximate the equations. Numerical experiments in a $ 2 $D setting illustrate our findings.

Investigation of `glitches' in the energy spectrum induced by single-crystal diamond compound X-ray refractive lenses.

Single-crystal diamond stands out among all the candidate materials that could be exploited to fabricate compound refractive lenses (CRLs) owing to its extremely stable properties. Among all related experimental features, beam divergence, χ-angles relative to the incoming beam in Eulerian geometry and different positions of the X-ray beam relative to the lens geometry may influence the transmission energy spectrum of CRLs. In addition, the orientation of the single-crystal diamond sample may also affect the glitches significantly. To verify these initial assumptions, two experiments, an energy scan and an ω-scan, were set up by employing a polished diamond plate consisting of five biconcave lenses. The results show that beam divergence does not affect the spectrum, nor do χ-angles when ω is set to zero. Nevertheless, different incident positions have an appreciable effect on the transmission spectrum, in particular the `strengths' of the glitches. This is attributed to absorption. The ω-scan setup is capable of determining the so-called orientation matrix, which may be used to predict both `energy positions' and `strengths' of the glitches.

Design and Fabrication of a Custom-Dielectric Fresnel Multi-Zone Plate Lens Antenna Using Additive Manufacturing Techniques

Dielectric flat plate lens antennas fabricated using 3D printing offer several attractive designs features including volumetric efficient geometries, beam-steering capabilities, and relative ease of fabrication. This paper seeks to synthesize and optimize a lens design for microwave applications utilizing additive manufacturing techniques to implement custom-tailored dielectric materials that overcome the inadequacies of commercially available dielectric resources. Starting with a multi-dielectric Fresnel zone plate lens geometry previously reported in this paper, techniques are implemented to achieve customized dielectric properties. A study of 3D printing materials is conducted to identify commercially available supplies that offer appropriate dielectric properties. Measurement techniques are reviewed to verify the accuracy of the material characteristics (both dielectric constant and loss tangent). Finally, three inhomogeneous concentric-ring lens designs are manufactured using the proposed methods and evaluated to assess the overall performance of the antenna gain patterns and beam-steering capabilities. The result is a low-profile antenna configuration, offering simple, and low-cost fabrication, which can be integrated into compact microwave wireless system applications.