Showing papers on "Lens (optics) published in 2016"

Optically reconfigurable metasurfaces and photonic devices based on phase change materials

Abstract: Photonic components with adjustable parameters, such as variable-focal-length lenses or spectral filters, which can change functionality upon optical stimulation, could offer numerous useful applications. Tuning of such components is conventionally achieved by either micro- or nanomechanical actuation of their constituent parts, by stretching or by heating. Here, we report a novel approach for making reconfigurable optical components that are created with light in a non-volatile and reversible fashion. Such components are written, erased and rewritten as two-dimensional binary or greyscale patterns into a nanoscale film of phase-change material by inducing a refractive-index-changing phase transition with tailored trains of femtosecond pulses. We combine germanium–antimony–tellurium-based films with a diffraction-limited resolution optical writing process to demonstrate a variety of devices: visible-range reconfigurable bichromatic and multi-focus Fresnel zone plates, a super-oscillatory lens with subwavelength focus, a greyscale hologram, and a dielectric metamaterial with on-demand reflection and transmission resonances.

Two-photon direct laser writing of ultracompact multi-lens objectives

Abstract: Femtosecond two-photon direct laser writing is used to create 100-µm-scale high-performance multi-lens objectives.

Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations

Abstract: Optical metasurfaces are two-dimensional arrays of nano-scatterers that modify optical wavefronts at subwavelength spatial resolution They are poised to revolutionize optics by enabling complex low-cost systems where multiple metasurfaces are lithographically stacked and integrated with electronics For imaging applications, metasurface stacks can perform sophisticated image corrections and can be directly integrated with image sensors Here we demonstrate this concept with a miniature flat camera integrating a monolithic metasurface lens doublet corrected for monochromatic aberrations, and an image sensor The doublet lens, which acts as a fisheye photographic objective, has a small f-number of 09, an angle-of-view larger than 60° × 60°, and operates at 850 nm wavelength with 70% focusing efficiency The camera exhibits nearly diffraction-limited image quality, which indicates the potential of this technology in the development of optical systems for microscopy, photography, and computer vision

Multispectral Chiral Imaging with a Metalens.

Abstract: The vast majority of biologically active compounds, ranging from amino acids to essential nutrients such as glucose, possess intrinsic handedness. This in turn gives rise to chiral optical properties that provide a basis for detecting and quantifying enantio-specific concentrations of these molecules. However, traditional chiroptical spectroscopy and imaging techniques require cascading of multiple optical components in sophisticated setups. Here, we present a planar lens with an engineered dispersive response, which simultaneously forms two images with opposite helicity of an object within the same field-of-view. In this way, chiroptical properties can be probed across the visible spectrum using only the lens and a camera without the addition of polarizers or dispersive optical devices. We map the circular dichroism of the exoskeleton of a chiral beetle, Chrysina gloriosa, which is known to exhibit high reflectivity of left-circularly polarized light, with high spatial resolution limited by the numerical...

Multiwavelength metasurfaces through spatial multiplexing.

Abstract: Metasurfaces are two-dimensional arrangements of optical scatterers rationally arranged to control optical wavefronts. Despite the significant advances made in wavefront engineering through metasurfaces, most of these devices are designed for and operate at a single wavelength. Here we show that spatial multiplexing schemes can be applied to increase the number of operation wavelengths. We use a high contrast dielectric transmittarray platform with amorphous silicon nano-posts to demonstrate polarization insensitive metasurface lenses with a numerical aperture of 0.46, that focus light at 915 and 1550 nm to the same focal distance. We investigate two different methods, one based on large scale segmentation and one on meta-atom interleaving, and compare their performances. An important feature of this method is its simple generalization to adding more wavelengths or new functionalities to a device. Therefore, it provides a relatively straightforward method for achieving multi-functional and multiwavelength metasurface devices.

Holographic display for see-through augmented reality using mirror-lens holographic optical element.

Abstract: A holographic display system for realizing a three-dimensional optical see-through augmented reality (AR) is proposed. A multi-functional holographic optical element (HOE), which simultaneously performs the optical functions of a mirror and a lens, is adopted in the system. In the proposed method, a mirror that is used to guide the light source into a reflection type spatial light modulator (SLM) and a lens that functions as Fourier transforming optics are recorded on a single holographic recording material by utilizing an angular multiplexing technique of volume hologram. The HOE is transparent and performs the optical functions just for Bragg matched condition. Therefore, the real-world scenes that are usually distorted by a Fourier lens or an SLM in the conventional holographic display can be observed without visual disturbance by using the proposed mirror-lens HOE (MLHOE). Furthermore, to achieve an optimized optical recording condition of the MLHOE, the optical characteristics of the holographic material are measured. The proposed holographic AR display system is verified experimentally.

Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing.

Abstract: We exploit the inherent dispersion in diffractive optics to demonstrate planar chromatic-aberration-corrected lenses. Specifically, we designed, fabricated and characterized cylindrical diffractive lenses that efficiently focus the entire visible band (450 nm to 700 nm) onto a single line. These devices are essentially pixelated, multi-level microstructures. Experiments confirm an average optical efficiency of 25% for a three-wavelength apochromatic lens whose chromatic focus shift is only 1.3 μm and 25 μm in the lateral and axial directions, respectively. Super-achromatic performance over the continuous visible band is also demonstrated with averaged lateral and axial focus shifts of only 1.65 μm and 73.6 μm, respectively. These lenses are easy to fabricate using single-step grayscale lithography and can be inexpensively replicated. Furthermore, these devices are thin (<3 μm), error tolerant, has low aspect ratio (<1:1) and offer polarization-insensitive focusing, all significant advantages compared to alternatives that rely on metasurfaces. Lastly, our design methodology offers high design flexibility in numerical aperture and focal length, and is readily extended to 2D.

Lens regeneration using endogenous stem cells with gain of visual function

Abstract: The repair and regeneration of tissues using endogenous stem cells represents an ultimate goal in regenerative medicine. To our knowledge, human lens regeneration has not yet been demonstrated. Currently, the only treatment for cataracts, the leading cause of blindness worldwide, is to extract the cataractous lens and implant an artificial intraocular lens. However, this procedure poses notable risks of complications. Here we isolate lens epithelial stem/progenitor cells (LECs) in mammals and show that Pax6 and Bmi1 are required for LEC renewal. We design a surgical method of cataract removal that preserves endogenous LECs and achieves functional lens regeneration in rabbits and macaques, as well as in human infants with cataracts. Our method differs conceptually from current practice, as it preserves endogenous LECs and their natural environment maximally, and regenerates lenses with visual function. Our approach demonstrates a novel treatment strategy for cataracts and provides a new paradigm for tissue regeneration using endogenous stem cells.

Atomically thin optical lenses and gratings

Abstract: Two-dimensional (2D) materials have emerged as promising candidates for miniaturized optoelectronic devices due to their strong inelastic interactions with light. On the other hand, a miniaturized optical system also requires strong elastic light–matter interactions to control the flow of light. Here we report that a single-layer molybdenum disulfide (MoS2) has a giant optical path length (OPL), around one order of magnitude larger than that from a single-layer of graphene. Using such giant OPL to engineer the phase front of optical beams we have demonstrated, to the best of our knowledge, the world’s thinnest optical lens consisting of a few layers of MoS2 less than 6.3 nm thick. By taking advantage of the giant elastic scattering efficiency in ultra-thin high-index 2D materials, we also demonstrated high-efficiency gratings based on a single- or few-layers of MoS2. The capability of manipulating the flow of light in 2D materials opens an exciting avenue towards unprecedented miniaturization of optical components and the integration of advanced optical functionalities. More importantly, the unique and large tunability of the refractive index by electric field in layered MoS2 will enable various applications in electrically tunable atomically thin optical components, such as micro-lenses with electrically tunable focal lengths, electrical tunable phase shifters with ultra-high accuracy, which cannot be realized by conventional bulk solids. Optical components that are just a few atomic layers thick have been made from the two-dimensional material molybdenum disulfide (MoS2). Researchers from the Australian National University and the University of Wisconsin in the USA fabricated a miniature concave optical lens that was just 6.3 nm thick by etching a several-layer-thick flake of MoS2 into a bowl shape. The lens had a focal length of –240 μm. In addition, the team fabricated highly efficient gratings by milling periodic patterns into MoS2 flakes up to six layers thick. Such ultrathin optical devices can be realized due to the very strong interaction between light and MoS2. In particular, the optical path length and elastic scattering efficiency of MoS2 are much larger than those of other materials.

3-D Printed Millimeter-Wave and Terahertz Lenses with Fixed and Frequency Scanned Beam

Abstract: High-gain and beam-scanning antennas are extremely important in the applications of millimeter-wave (MMW) and terahertz (THz) technologies. Dielectric lens is a suitable candidate for this purpose, because it has no metal and quite small feeding loss. In this paper, discrete dielectric lenses are studied in which periodic antireflection (AR) structures are added to reduce impedance mismatch at the air–dielectric interfaces, leading to higher directivity. Meanwhile, a multifrequency phase matching method is proposed to realize a beam-scanning lens in both MMW and THz regions. The design concept of the beam-scanning lens is applicable to other frequency ranges as well, which opens new opportunities for future lens design. Moreover, three-dimensional (3-D) printing technology is employed to simplify the manufacturing process and reduce the cost. Experiments are done in both MMW and THz regions, and the results verify the concept of lens design. The 3-D printed MMW and THz lenses with fixed and scanning beams demonstrated in this work could be an important step toward MMW and THz communications, radar, and imaging systems for practical applications.

2-D Beam-Steerable Integrated Lens Antenna System for 5G $E$ -Band Access and Backhaul

Abstract: The new services available through smart devices require very high cellular network capacity. The capacity requirement is expected to increase exponentially with the forthcoming 5G networks. The only available spectrum for truly wideband communication (>1 GHz) is at millimeter wavelengths. The high free space loss can be overcome by using the directive and beam-steerable antennas. This paper describes a design and the measurement results for a lens antenna system for $E$ -band having 2-D beam-steering capability. Continuous beam-switching range of about $\pm 4 {^{\circ }} \times \pm 17^{\circ }$ is demonstrated with the lens having the maximum measured directivity of 36.7 dB. Link budget calculation for backhaul application using the presented lens antenna system is presented and compared with the measurement results of the implemented demo system.

Gradient-index phononic crystal lens-based enhancement of elastic wave energy harvesting

Abstract: We explore the enhancement of structure-borne elastic wave energy harvesting, both numerically and experimentally, by exploiting a Gradient-Index Phononic Crystal Lens (GRIN-PCL) structure. The proposed GRIN-PCL is formed by an array of blind holes with different diameters on an aluminum plate, where the blind hole distribution is tailored to obtain a hyperbolic secant gradient profile of refractive index guided by finite-element simulations of the lowest asymmetric mode Lamb wave band diagrams. Under plane wave excitation from a line source, experimentally measured wave field validates the numerical simulation of wave focusing within the GRIN-PCL domain. A piezoelectric energy harvester disk located at the first focus of the GRIN-PCL yields an order of magnitude larger power output as compared to the baseline case of energy harvesting without the GRIN-PCL on the uniform plate counterpart.

Dual lens digital zoom

Abstract: A camera with a pair of lens/sensor combinations, the two lenses having different focal lengths, so that the image from one of the combinations has a field of view approximately two to three times greater than the image from the other combination. As a user of the camera requests a given amount of zoom, the zoomed image provided will come from the lens/sensor combination having the field of view that is next larger than the requested field of view. Thus, if the requested field of view is less than the smaller field of view combination, the zoomed image will be created from the image captured by that combination, using cropping and interpolation if necessary. Similarly, if the requested field of view is greater than the smaller field of view combination, the zoomed image will be created from the image captured by the other combination, using cropping and interpolation if necessary.

Quantitative measurement of the orbital angular momentum of light with a single, stationary lens.

Abstract: We show that the average orbital angular momentum (OAM) of twisted light can be measured simply and robustly with a single stationary cylindrical lens and a camera. Theoretical motivation is provided, along with self-consistent optical modeling and experimental results. In contrast to qualitative interference techniques for measuring OAM, we quantitatively measure non-integer average OAM in mode superpositions.

A High-Gain Broadband Gradient Refractive Index Metasurface Lens Antenna

Abstract: The design, simulation, and measurement results of a high-gain broadband gradient refractive index (GRIN) planar lens fed by an antipodal exponential taper slot antenna (ATSA) are presented. As a constituent part of this lens, a novel nonresonant metamaterial unit cell, composed of bilayer triple rectangular rings, is proposed and its equivalent circuit model is developed and described. It is shown that, by utilizing this element, stronger capacitive couplings between adjacent metallic layers are realized resulting in a large refractive index variation of about 2.5, and hence, a thin lens with a thickness of $0.38\lambda_{0}$ , where $\lambda_{0}$ is the wavelength at 9.5 GHz. In addition, since the unit cell is designed to resonate at higher frequencies, its refractive index response is smoothly increased over a broad frequency range and this considerably enhances the operating bandwidth of the lens. The achieved measured results demonstrate a broad matching and $-3\;{\rm dB}$ gain bandwidths of 52% (7–12 GHz) and 65% (7–13.2 GHz), respectively. Furthermore, this lens offers a high aperture efficiency of 50% (21.2 dB gain) at the center frequency, and its sidelobe and cross-polarization levels are less than $-20\;{\rm dB}$ and $-26\;{\rm dB}$ across the entire matched band, respectively.

Surgical visualization systems and displays

Abstract: A medical apparatus is described for providing visualization of a surgical site. The medical apparatus includes an electronic display disposed within a display housing. The medical apparatus includes a display optical system disposed within the display housing, the display optical system comprising a plurality of lens elements disposed along an optical path. The display optical system is configured to receive images from the electronic display.

Electro-active opthalmic lens having an optical power blending region

Abstract: A spectacle lens is disclosed. The disclosed lens provides a vision correcting area for the correction of a wearer's refractive error. The viewing correction area provides correction for non-conventional refractive error to provide at least a part of the wearer's vision correction. The lens has a prescription based on a wave front analysis of the wearer's eye and the lens can further be modified to fit within an eyeglass frame.

A Flat-Lensed Spiral Phase Plate Based on Phase-Shifting Surface for Generation of Millimeter-Wave OAM Beam

Abstract: A multilayer phase-shifting-surface-based flat plate is designed to offer a combination of lens and spiral phase plate (SPP) for orbital angular momentum (OAM) beam generation and convergence at 60 GHz. The proposed design consists of a series of phase-shift unit cells to control the emergent phase and form a flat lens for the purpose of beam focusing. The results of simulation and experiment verify that the OAM beam with small divergence angle can be achieved.

Parity-Time Symmetric Nonlocal Metasurfaces: All-Angle Negative Refraction and Volumetric Imaging

Abstract: Lenses are critical to a variety of fields of science, but optical aberrations such as astigmatism are common problems. A ``perfect'' lens made of two metasurfaces is theoretically developed.

Multibeam SIW Slotted Waveguide Antenna System Fed by a Compact Dual-Layer Rotman Lens

Abstract: A multibeam antenna system fed by a compact Rotman lens is presented in multilayer substrate integrated waveguide (SIW) technology. The lens is implemented in two layers using a new transition based on several star-shaped coupling slots and an SIW integrated reflector. Compared to standard rectangular coupling slots, this transition is broadband and maximizes power transfer between the two layers of the lens regardless the position of the beam port along the focal arc of the Rotman lens. The radiating part is an array of 15 slotted waveguides. These waveguides are centrally fed to enhance their bandwidth and reduce the “long line effect.” To validate the proposed concepts, an antenna system has been prototyped at 24.15 GHz. The designed transition leads to a physical size reduction of about 50% for the Rotman lens, and more than 33% for the antenna footprint compared to standard single-layer implementations. The experimental results demonstrate a scanning range of $\pm {33}^\circ $ and a 4% bandwidth for $\text{VSWR} ; the isolation between input ports is better than $- {10}\;\text{dB}$ .

Clinically Relevant Optical Properties of Bifocal, Trifocal, and Extended Depth of Focus Intraocular Lenses

Abstract: PURPOSE To experimentally compare the optical performance of three types of hydrophobic intraocular lenses (IOLs): extended depth of focus, bifocal, and trifocal. METHODS The tested IOLs were: TECNIS ZMB00 (bifocal; Abbott Medical Optics, Abbott Park, IL), TECNIS Symfony ZXR00 (extended depth of focus; Abbott Medical Optics), and FineVision GFree hydrophobic (trifocal; PhysIOL, Liege, Belgium). Their surface topography was analyzed by optical microscopy. Modulation transfer function (MTF) and spherical aberrations were determined on optical bench for variable pupil apertures and with two cornea models (0 µm and +0.28 µm). United States Air Force target imaging was analyzed for different focal points (near, intermediate, and far). Point spread function (PSF) and halos were quantified and compared. RESULTS The three lenses presented step-like optic topography. For a pupil size of 3 mm or greater, clearly distinctive MTF peaks were observed for all lenses: two peaks for the extended depth of focus and bifocal lenses with +1.75 and +4.00 diopters (D) addition, respectively, and three peaks for the trifocal lens with +1.75 and +3.50 addition for intermediate and near vision, respectively. The extended depth of focus and bifocal lens had slightly higher MTF at best focus with the +0.28 µm cornea model than with the 0 µm model, whereas the trifocal lens was likely to be more independent of the corneal spherical aberrations. CONCLUSIONS It appears that the three lenses rely on light diffraction for their optical performance, presenting halos with comparable intensities. For small pupil apertures (< 3 mm), the MTF peaks for the far and intermediate focal distances of the trifocal and extended depth of focus lenses overlap, but the trifocal lens presented an additional MTF peak for the near focal points.

3D-printed planar graded index lenses

Abstract: The authors introduce two flat graded-index (GRIN) lens designs in this study. First of these is a thick lens, which was designed and fabricated by using the three-dimensional (3D)-printing technique. Second, a thin dial-a-dielectric (DaD) lens, which uses state-of-the-art artificially engineered dielectric materials for design and for which they present only the simulated results, with plans to fabricate it in the future. Both designs overcome the difficulties faced in finding desired commercial off-the-shelf materials, either for 3D-printing or for fabricating conventional GRIN lenses. The lenses comprise of several concentric dielectric rings with bespoke relative permittivities for transforming spherical waves into plane waves and vice versa. The 3D-printed thick flat lens is low-cost and light-weight, but provides broadband and high gain performance. Measurement results show that the realised gain of the thick lens is 9–11 dB over the frequency band of 12–18 GHz. The designed DaD lens has the desirable characteristics of low loss, low reflection and broadband properties.

Metasurface Device with Helicity-Dependent Functionality

Abstract: Driven by miniaturization and system integration, ultrathin, multifunction optical elements are urgently needed. Traditional polarization-selective optical elements are mainly based on birefringence, which is realized by using the well-designed structure of each phase pixel. However, further reduction of the pixel size and improvement of the phase levels are hindered by the complicated fabrication process. An approach is proposed to realize a metasurface device that possesses two distinct functionalities. The designed metasurface device, consisting of gold nanorods with spatially varying orientation, has been experimentally demonstrated to function as either a lens or a hologram, depending on the helicity of the incident light. As the phase of the scattered light is controlled by the orientation of the nanorods, arbitrary phase levels and dispersionless phase profile can be realized through a much simpler fabrication process than the conventional device. This approach provides an unconventional alternative to realize multifunction optical element, dramatically increasing the functionality density of the optical systems.

Space Warps II. New gravitational lens candidates from the CFHTLS discovered through citizen science

Abstract: We report the discovery of 29 promising (and 59 total) new lens candidates from the CFHT Legacy Survey (CFHTLS) based on about 11 million classifications performed by citizen scientists as part of the first Space Warps lens search. The goal of the blind lens search was to identify lens candidates missed by robots (the RingFinder on galaxy scales and ArcFinder on group/cluster scales) which had been previously used to mine the CFHTLS for lenses. We compare some properties of the samples detected by these algorithms to the Space Warps sample and find them to be broadly similar. The image separation distribution calculated from the Space Warps sample shows that previous constraints on the average density profile of lens galaxies are robust. SpaceWarps recovers about 65% of known lenses, while the new candidates show a richer variety compared to those found by the two robots. This detection rate could be increased to 80% by only using classifications performed by expert volunteers (albeit at the cost of a lower purity), indicating that the training and performance calibration of the citizen scientists is very important for the success of Space Warps. In this work we present the SIMCT pipeline, used for generating in situ a sample of realistic simulated lensed images. This training sample, along with the false positives identified during the search, has a legacy value for testing future lens finding algorithms. We make the pipeline and the training set publicly available.

Achromatic flat optical components via compensation between structure and material dispersions

Abstract: Chromatism causes great quality degradation of the imaging system, especially for diffraction imaging. The most commonly method to overcome chromatism is refractive/diffractive hybrid optical system which, however, sacrifices the light weight and integration property of diffraction elements. A method through compensation between the structure dispersion and material dispersion is proposed to overcome the chromatism in flat integrated optical components. This method is demonstrated by making use of silver nano-slits waveguides to supply structure dispersion of surface plasmon polaritons (SPP) in metal-insulator-metal (MIM) waveguide to compensate the material dispersion of metal. A broadband deflector and lens are designed to prove the achromatic property of this method. The method demonstrated here may serve as a solution of broadband light manipulation in flat integrated optical systems.

Vacuum-coating system for coating lenses

Abstract: The invention relates to a vacuum-coating system for coating lenses, comprising a vacuum chamber, an electrode holder (14) having one or more electrodes (16), and a lens holder receptacle (18) having one or more lens holders (17) for accommodating one lens (19) each. To each lens (19), a separate electrode (16) is assigned. A surface of the electrode (16) located opposite the lens (19) is a curved surface. In an outer region (8), the curvature of the surface of the electrode (n) (16) can be greater than in an inner region (9). The distance between the electrode (16) and the associated lens (19) can be adjustable.

Space Warps – I. Crowdsourcing the discovery of gravitational lenses

Abstract: We describe SpaceWarps, a novel gravitational lens discovery service that yields samples of high purity and completeness through crowd-sourced visual inspection. Carefully produced colour composite images are displayed to volunteers via a webbased classification interface, which records their estimates of the positions of candidate lensed features. Images of simulated lenses, as well as real images which lack lenses, are inserted into the image stream at random intervals; this training set is used to give the volunteers instantaneous feedback on their performance, as well as to calibrate a model of the system that provides dynamical updates to the probability that a classified image contains a lens. Low probability systems are retired from the site periodically, concentrating the sample towards a set of lens candidates. Having divided 160 square degrees of Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) imaging into some 430,000 overlapping 82 by 82 arcsecond tiles and displaying them on the site, we were joined by around 37,000 volunteers who contributed 11 million image classifications over the course of 8 months. This Stage 1 search reduced the sample to 3381 images containing candidates; these were then refined in Stage 2 to yield a sample that we expect to be over 90% complete and 30% pure, based on our analysis of the volunteers performance on training images. We comment on the scalability of the SpaceWarps system to the wide field survey era, based on our projection that searches of 105 images could be performed by a crowd of 105 volunteers in 6 days.

Optical imaging lens

Abstract: Present embodiments provide for an optical imaging lens. The optical imaging lens comprises a first lens element, a second lens element, a third lens element, a fourth lens element, a fifth lens element and a sixth lens element positioned in an order from an object side to an image side. Through controlling the convex or concave shape of the surfaces of the lens elements and designing parameters satisfying at least one inequality, the optical imaging lens shows better optical characteristics and enlarge field angle the total length of the optical imaging lens is shortened.

Three-dimensional Luneburg lens at optical frequencies

Abstract: A Luneburg lens is a fascinating gradient refractive index (GRIN) lens that can focus parallel light on a perfect point without aberration in geometrical optics. Constructing a three-dimensional (3D) Luneburg lens at optical frequencies is a challenging task due to the difficulty of fabricating the desired GRIN materials. Here, we present the practical implementation of a 3D Luneburg lens at optical frequencies. Such a 3D Luneburg lens is designed with GRIN 3D simple cubic metamaterial structures, and fabricated with dielectric metamaterials by femtosecond laser direct writing in the commercial negative-photoresist IP-L. Simulated and experimental results exhibit an interesting 3D ideal focus for the infrared light. The protocol for developing the 3D Luneburg lens with ideal focus would prompt the potential applications in integrated light-coupled devices and lab-on-chip integrated biological sensors based on infrared light.

Designing large, high-efficiency, high-numerical-aperture, transmissive meta-lenses for visible light

Abstract: A metasurface lens (meta-lens) bends light using nanostructures on a flat surface. Macroscopic meta-lenses (mm- to cm-scale diameter) have been quite difficult to simulate and optimize, due to the large area, the lack of periodicity, and the billions of adjustable parameters. We describe a method for designing a large-area meta-lens that allows not only prediction of the efficiency and far-field, but also optimization of the shape and position of each individual nanostructure, with a computational cost that is almost independent of the lens size. As examples, we design three large NA = 0.94 meta-lenses: One with 79% predicted efficiency for yellow light, one with dichroic properties, and one broadband lens. All have a minimum feature size of 100nm.