Parabolic Lenses Research Articles

Accommodating version of a schematic eye for emmetropia and myopia.

To develop an accommodating, wide-angle, schematic eye for emmetropia and myopia in which spectacle refraction and accommodation level are input parameters. The schematic eye is based on an earlier unaccommodated refraction-dependent eye for myopia developed by Atchison in 2006. This has a parabolic gradient index lens and parameters derived from biometric and optical measurements on young adults. Several parameters are linearly dependent upon spectacle refraction (anterior radius of curvature of the cornea, axial length and vertex radii of curvature and conic asphericities of a biconic retina). The new accommodated schematic eye incorporates accommodation-dependent changes in several lens-related parameters. These changes are based on literature values for anterior chamber depth, lens thickness, vitreous chamber depth, lens surface radii of curvature and lens front surface asphericity. A parabolic variation of refractive index with relative distance from the lens centre is retained, with the same edge and centre refractive indices as the earlier model, but the distribution has been manipulated to maintain focus near the retina for the emmetropic case at 0 and 4 D accommodation. The asphericity of the lens back surface is changed so that spherical aberration and peripheral refraction approximately match typical literature trends. The model is used to compare spherical aberration and peripheral refraction in eyes with up to 4 D of myopia and 4 D of accommodation. The levels of spherical aberration in the unaccommodated schematic eyes are similar to literature values for young adults, but the changes in spherical aberration with accommodation are approximately two-thirds of that found in an experimental study. As intended, peripheral refractions in the accommodated schematic eyes are similar to those of their unaccommodated counterparts. The wide-angle model extends the range of schematic eyes to include both refraction and accommodation as variable input parameters. It may be useful in predicting aspects of retinal image quality.

Recent advancements in solar collector-evaporator for direct expansion solar heat pump

The direct expansion solar heat pump (DX-SHP) is a competent and sustainable option for domestic heating and drying applications. The solar collector-evaporator is a vital component of DX-SHP, which operates on solar energy and low-temperature ambient energy. The heat collection capacity, coefficient of performance, and evaporation temperature are used to quantify its performance. In this context, a systematic literature review on recent advancements in the collector-evaporator of DX-SHP is presented. This paper highlights and discusses the various configurations of solar collector-evaporators, theoretical and experimental investigations, and the selection method of eco-friendly refrigerants. The impact of different performance factors, such as ambient conditions, structural parameters, and types of refrigerants, on solar collector-evaporators is also reviewed. The optimal range for solar radiation, wind speed, and temperature is found to be 350 W/m2-700 W/m2, 0.5 m/s -2.5m/s, and 5°C to 35°C. The DX-SHP system produces hot water from 15°C to 60°C, with an average COP of 1.5 to 4.5. The finned solar collector-evaporator with R290 refrigerant performs optimally in various climatic conditions. Integrating solar collector-evaporators with innovative technologies such as microchannel, heat pipe, thermoelectric generators, photovoltaic thermal collectors with compound parabolic and Fresnel lenses can improve the system's performance. In this review, researchers can find scope for performance enhancement of the collector-evaporator used in DX-SHP.

Numerical design and characterization of a novel parallel beam combined lens based on X-ray capillary optics

A novel parallel beam combined lens (PBCL) was designed based on a parabolic monocapillary x-ray lens (PMXRL). The proposed PBCL converted a divergent X-ray beam into a near-solid parallel one, which retains the low divergence characteristics of PMXRL and significantly improves the intensity gain by about one order of magnitude. Compared with the traditional polycapillary parallel x-ray lens (PPXRL), the divergence performance of this lens is improved by an order of magnitude, and the light intensity gain is improved by 3-4 times. In addition, we developed a MATLAB-based visualization tool to simulate X-ray transmission within the PBCL through ray tracing. This tool facilitated the assessment of the PBCL's transmission efficiency and its comparison with conventional PMXRL and the PPXRL. The transport process of the PBCL is systematically investigated under the comprehensive consideration of multiple parameters. This study provided a new idea and theoretical basis for the further development of X-ray modulation technology.

Teardrop and Parabolic Lens Yield Curves for Viscous‐Plastic Sea Ice Models: New Constitutive Equations and Failure Angles

AbstractMost viscous‐plastic sea ice models use the elliptical yield curve. This yield curve has a fundamental flaw: it excludes acute angles between deformation features at high resolution. Conceptually, the teardrop (TD) and parabolic lens (PL) yield curves offer an attractive alternative. These yield curves feature a non‐symmetrical shape, a Coulombic behavior for the low‐medium compressive stress, and a continuous transition to the ridging‐dominant mode, but their published formulation leads to negative or zero bulk and shear viscosities and, consequently, poor numerical convergence with stress states at times outside the yield curve. These issues are a consequence of the original assumption that the constitutive equations of the commonly used elliptical yield curve are also applicable to non‐symmetrical yield curves and yield curves with tensile strength. We derive a corrected formulation for the constitutive relations of the TD and PL yield curves. Results from simple uni‐axial loading experiments show that with the new formulation the numerical convergence of the solver improves and much smaller nonlinear residuals after a smaller number of total solver iterations can be reached, resulting in significant improvements in numerical efficiency and representation of the stress and deformation fields. The TD and PL yield curves lead to smaller angles of failure that better agree with observations. They are promising candidates to replace the elliptical yield curve in high‐resolution pan‐Arctic sea ice simulations.

Finite voxel size compensation for microprinting of parabolic X-ray lenses by two-photon lithography

3D-microprinting by two-photon lithography can be applied to fabricate X-ray lenses. However, when the lens’ curvature radius approaches voxel size, the lens’ refractive surface essentially differs from the defined model. This shape distortion leads to defocusing of X-ray irradiation and astigmatism. In current work we suggest the compensation of the parabolic lens model taking into account finite voxel size.

Continuous Vat Photopolymerization for Optical Lens Fabrication

Optical lenses require feature resolution and surface roughness that are beyond most (3D) printing methods. A new continuous projection-based vat photopolymerization process is reported that can directly shape polymer materials into optical lenses with microscale dimensional accuracy (< 14.7µm) and nanoscale surface roughness (< 20nm) without post-processing. The main idea is to utilize frustum layer stacking, instead of the conventional 2.5D layer stacking, to eliminate staircase aliasing. A continuous change of mask images is achieved using a zooming-focused projection system to generate the desired frustum layer stacking with controlled slant angles. The dynamic control of image size, objective and imaging distances, and light intensity involved in the zooming-focused continuous vat photopolymerization are systematically investigated. The experimental results reveal the effectiveness of the proposed process. The 3D-printed optical lenses with various designs, including parabolic lenses, fisheye lenses, and a laser beam expander, are fabricated with a surface roughness of 3.4nm without post-processing. The dimensional accuracy and optical performance of the 3D-printed compound parabolic concentrators and fisheye lenses within a few millimeters are investiagted. These results highlight the rapid and precise nature of this novel manufacturing process, demonstrating a promising avenue for future optical component and device fabrication.

Finite Voxel Size Compensation for Microprinting of Parabolic X-ray Lenses by Two-Photon Lithography

Finite Voxel Size Compensation for Microprinting of Parabolic X-ray Lenses by Two-Photon Lithography

Vortex-Bessel beam generation by 3D direct printing of an integrated multi-optical element on a fiber tip.

Shaping light beams as they propagate out of the tips of optical fibers is a desired ability, as the light could be tailored for various applications in a miniaturized, integrated, and cost-effective manner. However, fabricating sophisticated refractive elements directly onto fibers is challenging. By using 3D-direct laser writing (3D-DLW), high-quality optical devices could be fabricated directly on top of the fiber's facet by the two-photon absorption process. Here, we demonstrate how a high-order Bessel beam carrying orbital angular momentum (OAM) could be generated by using this lithography process. The beam is shaped using an integrated micro-optical system that consists of a twisted axicon and parabolic lens in an adapted fiber configuration. This work provides the analysis and measurements of the generated beam, along with simulated predictions. The far-field pattern, at a distance of 2 mm from the fiber, was examined, and we have found that the size of the central ring remained nearly unchanged, as expected for this type of beam. The beam's OAM value was measured using either an interference pattern or a mode convertor. Furthermore, the near-field and far-field Bessel beam profiles were investigated simultaneously at various laser power values, reaching intensities of up to 3.8 MW/cm2. This work may pave the way for future integrated beam manipulation on fibers, enabling the use of higher laser outputs.

Covers

Next article FreeCoversPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreCover: Frederick Eversley, Untitled (Parabolic Lens), 1971. Three-color, three-layer cast polyester, 36 ½ diam. × 9 ⅞ in. Museum of Modern Art, Acquired through the generosity of Michael S. Ovitz and Gary and Karen Winnick, and Committee on Painting and Sculpture Funds. Digital Image © The Museum of Modern Art / Licensed by SCALA / Art Resource, N.Y. © Fred Eversley, Courtesy of the artist and David Kordansky GalleryBack cover: Edward Greene Malbone, Robert Macomb (left) and Mrs. Robert Macomb (Mary Cornell Pell) (right), ca. 1806. Watercolor on ivory, each 3 ¾ × 3 in. Metropolitan Museum of Art, New York, Bequest of Irving S. Olds, 1963 Next article DetailsFiguresReferencesCited by American Art Volume 36, Number 3Fall 2022 Sponsored by the Smithsonian American Art Museum Article DOIhttps://doi.org/10.1086/723297 © 2022 by Smithsonian Institution. All rights reserved.PDF download Crossref reports no articles citing this article.

Diatom optical element: a quantized version of the generalized spiral lens

Here we introduce a diatom optical element—a special case of the generalized spiral lens widely used for generation of light fields with orbital angular momentum. The profile of such an element is visually similar to the structure of a diatom. In contrast to currently existing special cases (axicon, parabolic lens, or autofocusing optical element) of a generalized spiral lens, diatom optical elements shape light fields with an intensity distribution that is neither a spiral nor a ring. In addition, the light fields shaped with these elements show the autofocusing properties and invariance of their symmetry order during propagation. Experimentally obtained results are in good agreement with those from modeling.

High-quality quasi-parallel X-ray beam obtained by a parabolic monocapillary X-ray lens with a square beam stop

Parabolic monocapillary X-ray lens (PMXRL) is an ideal optical device for constraining the point divergent X-ray beams to quasi-parallel beams, but the overlap of direct X-rays and reflected X-rays through PMXRL deteriorates the outgoing beam divergence. Aiming to solve this problem, this study designs and tests a square-shaped lead occluder (SSLO) embedded in PMXRL to block the direct X-rays passing through the PMXRL. Python simulations are employed to determine the geometric parameters of the SSLO as well as the optimal position of the SSLO in the PMXRL according to our proposed model. The PMXRL with a conic parameter p of 0.000939 mm and a length L of 60.8 mm is manufactured and the SSLO with a size of 0.472 mm×0.472 mm×3.4 mm is embedded into it. An optical path system based on this PMXRL is built to measure the divergence of the outgoing X-ray beam. The experimental results show that the quasi-parallel X-ray beam reaches a divergence of 0.36 mrad in the range from 15-45 mm at the PMXRL outlet. This divergence is 10 times lower than the theoretical divergence without SSLO. Our work provides an alternative method for obtaining highly parallel X-ray beam and is beneficial to generate or facilitate new applications of monocapillary optics in X-ray technology.

Adiabatically focusing X-rays to the nanometer scale by one dimensional long kinoform lenses: comparison between an ideal Cartesian oval refocusing lens and a parabolic lens.

The nano-focusing performance of adiabatically designed Cartesian oval refocusing lenses is compared with other well known compound refractive lenses with parabolic profiles (both simple concave and kinoform types). Using beam propagation method (BPM) simulation, it is shown that our design based on oval lenses does significantly improve the focusing properties compared to other parabolic lens based designs, e.g. adiabatically focusing lenses (AFLs), which doesn't take into account of the refocusing effect. This points to the importance of optimizing complex lens design in improving nano-focusing lens performance.

Structure Optimization of Optical Compensator Design of Parabolic Lens

Structure Optimization of Optical Compensator Design of Parabolic Lens

Generation and numerical simulation of the focused OAM beams

The generation of the focused orbital angular momentum (OAM) beams using concentric uniform circular array (CUCA) is proposed in this paper. Since the ring shaped beams of the traditional electromagnetic (EM) vortex wave diverge along the propagation axis, only part of the beam is utilized for target detection, leading to a low efficiency. In this paper, two schemes are proposed to generate the focused OAM beams using concentric uniform circular antenna array (CUCA). Different from the traditional beam convergence method by reducing the divergence angle using parabolic reflector or lens, the proposed method employs a group of OAM beams with same divergence angle so that the superposed beam is focused at a certain azimuth angle. The feed amplitudes and phases of the elements of CUCA are firstly designed and validated using array factor multiplication. Then full wave simulations are conducted based on multilevel fast multipole algorithm (MLFMA) to calculate the radiation patterns and near field distributions of CUCA consist of micro strip patch antenna to further validate the proposed schemes. Simulation results indicate that the focused OAM beam can be achieved and the phase of the radiated field keeps the vortex property.

Generalization of ray tracing in symmetric gradient-index media by Fermat's ray invariants.

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.

Ultradeep microaxicons in lithium niobate by focused Xe ion beam milling

Refractive axicons are conically shaped optical devices that are capable of generating nondiffracting Bessel-like beams over extended depths-of-focus (DOFs). In addition to the substantially longer DOF compared to those produced by parabolic focusing lenses, the axicons can generate beams with better resolution for the same form-factor of the optical element, e.g., its diameter and sag height. These properties make the axicons useful in numerous applications in imaging, particle trapping, and many others. Miniaturized refractive axicons or microaxicons are challenging to realize in hard substrates due to the lack of sufficiently precise and rapid fabrication technologies. Here, we report on the rapid fabrication of ultradeep microaxicons in lithium niobate using high-current focused Xe ion beam milling. Microaxicons with 230-μm diameter with ultradeep sag heights between 21 and 48 μm were milled using 200 nA of beam current. Furthermore, the microaxicons were milled in single-crystal lithium niobate—a material with a high refractive index of &amp;gt;2.2 but which inertness makes it a challenging material in microfabrication. The performance of the lenses was characterized by mapping the transmitted intensity at different positions. The measured spot sizes of the produced beams are in excellent agreement with the theoretical expectations and range from 750 down to 250 nm (∼λ/2) beam spot size for the shallowest and the deepest microaxicons in this study, respectively. The corresponding DOFs are from 500 down to ∼50 μm for the ultradeep microaxicon. The results verify the applicability of high-current milling with a focused Xe ion beam for the fabrication of high-performance optical elements.

Caustics of Non-Paraxial Perfect Optical Vortices Generated by Toroidal Vortex Lenses

In this paper, we consider the comparative formation of perfect optical vortices in the non-paraxial mode using various optical elements: non-paraxial and parabolic toroidal vortex lenses, as well as a vortex axicon in combination with a parabolic lens. The theoretical analysis of the action of these optical elements, as well as the calculation of caustic surfaces, is carried out using a hybrid geometrical-optical and wave approach. Numerical analysis performed on the basis of the expansion in conical waves qualitatively confirms the results obtained and makes it possible to reveal more details associated with diffraction effects. Equations of 3D-caustic surfaces are obtained and the conditions of the ring radius dependence on the order of the vortex phase singularity are analyzed. In the non-paraxial mode, when small light rings (several tens of wavelengths) are formed, a linear dependence of the ring radius on the vortex order is shown. The revealed features should be taken into account when using the considered optical elements forming the POV in various applications.

Small object recognition with trainable lens

Lenses are used to form images of objects. They follow a parabolic profile, as dictated by the physics of imaging optics. The clarity of images is essential for object recognition. However, challenging image conditions limit the capability of forming clear images. This happens when objects are very small or far away. Such images make it difficult to apply neural networks for object recognition. Here, we overcome this challenge by replacing the parabolic lens with a trainable lens, which lets us extend the learning process from the digital into the physical world. The lens profile is parameterized by over 10 000 trainable parameters. When used for recognizing small objects with low resolution, the profile adapts to maximize the accuracy of the recognition. The resulting profile could be significantly different from a typical parabolic lens. We show that the object recognition accuracy is improved by more than 25% when the objects are 16 times smaller than their original size. Besides, incorporating the trainable lens before digital computing adds minimal computational time. Our method has potential application in biology, such as cell detection, in the semiconductor industry, such as detecting defects, and in salvage.

Toward the Use of Re-configurable Intelligent Surfaces in VLC Systems: Beam Steering

The emergence of visible light communication (VLC) technology as a solution to solve radio frequency impediments, such as spectrum shortage, is continuously appealing. In addition to its large and unlicensed bandwidth, VLC provides a high level of security in a closed room with zero radio frequency interference. However, loss of the VLC signal is experienced when the receiver rotates or moves. This challenge requires a special solution for integration into portable devices. On the other hand, re-configurable intelligent surface (RIS) is a technology exploited in radio frequency to solve dead zones and loss of signal. RIS elements are characterized by tunable physico-chemical characteristics including physical depth and refractive index. In this article, we exploit these RIS attributes to steer the incident light beam, offer the VLC receiver a large range of rotation angle, and improve its field-of-view. We show that instead of using convex, parabolic, or spherical lenses, adopting a meta-lens with artificial muscles or a thin-film Liquid-Crystal with embedded Titanium dioxide nano-disk, a VLC receiver can detect light rays at a high incidence angle with high precision and considerable improvement in the detected light intensity, even with a miniaturized single photodetector.

A Modularized Interchangeable Multibeam Slot Array Antenna Using Hybrid Substrates for Mass Production

A substrate integrated waveguide multibeam antenna based on a parabolic lens beam-forming network is presented. The proposed antenna is comprised of a port deck (Rogers RT/duroid 5880, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ϵ_r</i> = 2.2, tan <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">δ</i> = 0.0009) and an antenna deck (Rogers RT/duroid 6002, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ϵ_r</i> = 2.94, tan <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">δ</i> = 0.0012). By fabricating the antenna deck with substrates of different permittivity, while the port deck does not have to be changed, the proposed antenna features flexible beam tunability. Experimental results show that the proposed antenna can operate from 27∼28 GHz with the gain up to 14.5 dBi. The maximum radiation efficiency is 85%. Five beams pointing from −59° to 62° are achieved. Compared with counterparts, the proposed antenna features desirable performance but simpler structure. The short turn-around design circle and low cost from the modularized interchangeable design make it preferable for 5G mobile terminals in mass production.