Flat lenses enable thinner, lighter, and simpler imaging systems. However, large-area and high-NA flat lenses have been elusive due to computational and fabrication challenges. Here, we applied inverse design to create a multi-level diffractive lens (MDL) with thickness <1.35μm, diameter of 4.13mm, NA=0.9 at wavelength of 850nm. Since the MDL is created in polymer, it can be cost-effectively replicated via imprint lithography.
Over the recent years, there have been many reports of achromatic metalenses and diffractive lenses. However, very few (if any) practical applications of such achromatic flat lenses have been demonstrated, which raises questions about the potential of these lenses to provide solutions for real world cases which involve broadband illumination. A recent paper placed limits on the performance of achromatic metalenses. However, is this limit also valid for a diffractive lens? Not necessarily so. In this paper we derive the limits on the performance of achromatic diffractive lenses. In particular, …
We demonstrate imaging over the visible band using a single planar diffractive lens. This is enabled via multi-level diffractive optics that is designed to focus over a broad wavelength range, which we refer to as an achromatic diffractive lens (ADL). We designed, fabricated and characterized two ADLs with numerical apertures of 0.05 and 0.18. Diffraction-limited focusing is demonstrated for the NA=0.05 lens with measured focusing efficiency of over 40% across the entire visible spectrum (450nm to 750nm). We characterized the lenses with a monochromatic and a color CMOS sensor, and demonstrate…
Compressive spectral imaging enables to reconstruct the entire three-dimensional (3D) spectral cube from a few multiplexed images. Here, we develop a novel compressive spectral imaging technique using diffractive lenses. Our technique uses a coded aperture to spatially modulate the optical field from the scene and a diffractive lens such as a photon-sieve for dispersion. The coded field is passed through the diffractive lens and then measured at a few planes using a monochrome detector. The 3D spectral cube is then reconstructed from these highly compressed measurements through sparse recovery…
Recently, there has been an explosion of interest in metalenses for imaging. The interest is primarily based on their sub-wavelength thicknesses. Diffractive lenses have been used as thin lenses since the late 19th century. Here, we show that multi-level diffractive lenses (MDLs), when designed properly can exceed the performance of metalenses. Furthermore, MDLs can be designed and fabricated with larger constituent features, making them accessible to low-cost, large area volume manufacturing, which is generally challenging for metalenses. The support substrate will dominate overall thickness …
We propose a method for designing multifocal diffractive lenses generating prescribed sets of foci with fixed positions at several different wavelengths. The method is based on minimizing the difference between the complex amplitudes of the beams generated by the lens microrelief at the design wavelengths, and the functions of complex transmission of multifocal lenses calculated for these wavelengths. As an example, a zone plate generating three fixed foci at three different wavelengths was designed, fabricated and experimentally investigated. The proof-of-concept experimental results confirm …
We demonstrate a novel imaging approach and associated reconstruction algorithm for far-field coherent diffractive imaging, based on the measurement of a pair of laterally sheared diffraction patterns. The differential phase profile retrieved from such a measurement leads to improved reconstruction accuracy, increased robustness against noise, and faster convergence compared to traditional coherent diffractive imaging methods. We measure laterally sheared diffraction patterns using Fourier-transform spectroscopy with two phase-locked pulse pairs from a high harmonic source. Using this approach…
We designed and fabricated a flat multi-level diffractive lens (MDL) that is achromatic in the SWIR band (875nm to 1675nm). The MDL had a focal length of 25mm, aperture diameter of 8.93mm and thickness of only 2.6um. By pairing the MDL with a SWIR image sensor, we also characterized its imaging performance in terms of the point-spread functions, modulation-transfer functions, and still and video imaging.
Passive mode-locking critically relies on a saturable loss mechanism to form ultrashort pulses. However, in Kerr-lens mode-locking (KLM), no actual absorption takes place, but rather losses appear due to diffraction, and actual light must escape the cavity. The Kerr-lens effect works to generate through diffraction an effective instantaneous saturable absorber that delicately depends on the interplay between the spatial and temporal profiles of the pulse. Despite the importance of KLM as a technique for generating ultrafast pulses and the fundamental role of the diffraction losses in its opera…
In this work, we propose a new diffractive trifocal intraocular lens design with focus extension, conceived to provide a high visual performance at intermediate distances. This design is based on a fractal structure known as the "Devil's staircase". To assess its optical performance, numerical simulations have been performed with a ray tracing program using the Liou-Brennan model eye under polychromatic illumination. The simulated through the focus visual acuity was the merit function employed to test its pupil-dependence and its behavior against decentering. A qualitative assessment of the mu…
Recent theoretical work suggested upper bounds on the operating bandwidths of flat lenses. Here, we show how these bounds can be circumvented via a multi-level diffractive lens (MDL) of diameter = 100 mm, focal length = 200 mm, device thickness = 2.4μ m and operating bandwidth from ? = 400 nm to 800 nm. We further combine the MDL with a refractive lens to demonstrate a hybrid telescope. By appealing to coherence theory, we show that the upper bound on relative bandwidth is surprisingly independent of lens diameter or numerical aperture, but is only limited by the bandwidth of the image sensor.…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Lensless cameras are a class of imaging devices that shrink the physical dimensions to the very close vicinity of the image sensor by replacing conventional compound lenses with integrated flat optics and computational algorithms. Here we report a diffractive lensless camera with spatially-coded Voronoi-Fresnel phase to achieve superior image quality. We propose a design principle of maximizing the acquired information in optics to facilitate the computational reconstruction. By introducing an easy-to-optimize Fourier domain metric, Modulation Transfer Function volume (MTFv), which is related …
We design, fabricate, and characterize multifunctional and compact diffractive microlenses with sub-wavelength thickness and the capability to simultaneously focus visible and near-infrared spectral bands at two different focal positions with 24% and 15% measured focusing efficiency, respectively. Our technology utilizes high-index and low-loss sputtered hydrogenated amorphous Si, enabling a sub-wavelength thickness of only 235nm. Moreover, the proposed flat lens concept is polarization insensitive and can be readily designed to operate across any desired wavelength regime. Imaging under broad…
We propose an efficient inverse design approach for multifunctional optical elements based on adaptive deep diffractive neural networks (a-D$^2$NNs). Specifically, we introduce a-D$^2$NNs and design two-layer diffractive devices that can selectively focus incident radiation over two well-separated spectral bands at desired distances. We investigate focusing efficiencies at two wavelengths and achieve targeted spectral lineshapes and spatial point-spread functions (PSFs) with optimal focusing efficiency. In particular, we demonstrate control of the spectral bandwidths at separate focal position…
A lens performs an approximately one-to-one mapping from the object to the image planes. This mapping in the image plane is maintained within a depth of field (or referred to as depth of focus, if the object is at infinity). This necessitates refocusing of the lens when the images are separated by distances larger than the depth of field. Such refocusing mechanisms can increase the cost, complexity and weight of imaging systems. Here, we show that by judicious design of a multi-level diffractive lens (MDL) it is possible to drastically enhance the depth of focus, by over 4 orders of magnitude.…
Multilevel diffractive lenses (MDLs) have emerged as an alternative to both conventional diffractive optical elements (DOEs) and metalenses for applications ranging from imaging to holographic and immersive displays. Recent work has shown that by harnessing structural parametric optimization of DOEs, one can design MDLs to enable multiple functionalities like achromaticity, depth of focus, wide-angle imaging, etc. with great ease in fabrication. Therefore, it becomes critical to understand how fabrication errors still do affect the performance of MDLs and numerically evaluate the trade-off bet…
It is generally thought that correcting chromatic aberrations in imaging requires multiple surfaces. Here, we show that by allowing the phase in the image plane of a flat lens to be a free parameter, it is possible to correct chromatic aberrations over an almost unlimited bandwidth with a single diffractive surface. Specifically, we designed, fabricated and characterized a flat multi-level diffractive lens (MDL) that images at the wavelengths from 450nm to 850nm. We experimentally characterized the focusing efficiency, modulation-transfer function, wavefront aberrations, vignetting, distortion…
We demonstrate an inverse designed achromatic, flat, polarization-insensitive diffractive optic element, i.e., multilevel diffractive lens (MDL), operating across a broadband range of UV light (250 nm - 400 nm) via numerical simulations. The simulated average on-axis focusing efficiency of the MDL is optimized to be as high as ~86%. We also investigate the off-axis focusing characteristics at different incident angles of the incoming UV radiation such that the MDL has a full field of view of 30 degrees. The simulated average off-axis focusing efficiency is ~67%, which is the highest reported t…
Diffractive optical elements with a large diffraction angle require feature sizes down to sub-wavelength dimensions, which require a rigorous electromagnetic computational model for calculation. However, the computational optimization of these diffractive elements is often limited by the large number of design parameters, making parametric optimization practically impossible due to large computation times. The adjoint method allows calculating the gradient of the target function with respect to all design variables with only two electromagnetic simulations, thus enabling gradient optimization.…
Recently, the multilevel diffractive lenses (MDLs) have attracted considerable attention mainly due to their superior wave focusing performance; however, efforts to correct the chromatic aberration are still in progress. Here, we demonstrate the numerical design and experimental demonstration of high-numerical aperture (NA) (${\sim}0.99$), diffraction-limited achromatic multilevel diffractive lens (AMDL) operating in microwave range $10 GHz$ - $14 GHz$. A multi-objective differential evolution (MO-DE) algorithm is incorporated with the three-dimensional finite-difference time-domain (3D FDTD) …
Despite the recent advances in augmented reality (AR), which has shown the potential to significantly impact on our daily lives by offering a new way to manipulate and interact with virtual information, minimizing visual discomfort due to the vergence-accommodation conflict remains a challenge. Emerging AR technologies often exploit focus-tunable optics to address this problem. Although they demonstrated improved depth perception by enabling proper focus cues, a bulky form factor of focus-tunable optics prevents their use in the form of a pair of eyeglasses. Herein, we describe an ultrathin, f…
The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our experimental results, discuss the fundamental limits of this technique and future plans.
Fibonacci or bifocal terahertz (THz) imaging is demonstrated experimentally employing silicon diffractive zone plate (SDZP) in a continuous wave mode. Images simultaneously recorded in two different planes are exhibited at 0.6 THz frequency with the spatial resolution of wavelength. Multi-focus imaging operation of the Fibonacci lens is compared with a performance of the conventional silicon phase zone plate. Spatial profiles and focal depth features are discussed varying the frequency from 0.3 THz to 0.6 THz. Good agreement between experimental results and simulation data is revealed.
End-to-end optimization of diffractive optical elements (DOEs) profile through a digital differentiable model combined with computational imaging have gained an increasing attention in emerging applications due to the compactness of resultant physical setups. Despite recent works have shown the potential of this methodology to design optics, its performance in physical setups is still limited and affected by manufacturing artifacts of DOE, mismatch between simulated and resultant experimental point spread functions, and calibration errors. Additionally, the computational burden of the digital …
We propose the inverse design of ultracompact, broadband focusing spectrometers based on adaptive deep diffractive neural networks (a-D$^2$NNs). Specifically, we introduce and characterize two-layer diffractive devices with engineered angular dispersion that focus and steer broadband incident radiation along predefined focal trajectories with desired bandwidth and $5$ nm spectral resolution. Moreover, we systematically study the focusing efficiency of two-layer devices with side length $L=100~μ\mathrm{m}$ and focal length $f=300~\,μ\mathrm{m}$ across the visible spectrum and we demonstrate acc…
Thick diffractive optical elements offer a promising way to achieve focusing or imaging at a resolution approaching 1 nm for X-ray wavelengths shorter than about 0.1 nm. Efficient focusing requires that these are fabricated with structures that vary in period and orientation so that rays obey Bragg's law over the entire lens aperture and give rise to constructive interference at the focus. Here the analysis method of ray-tracing of thick diffractive optical elements is applied to such lenses to optimise their designs and to investigate their operating and manufacturing tolerances. Expressions …
It is generally assumed that correcting chromatic aberrations in imaging requires optical elements. Here, we show that by allowing the phase in the image plane to be a free parameter, it is possible to correct chromatic variation of focal length over an extremely large bandwidth, from the visible (Vis) to the longwave infrared (LWIR) wavelengths using a single diffractive surface, i.e., a flat lens. Specifically, we designed, fabricated and characterized a flat, multi-level diffractive lens (MDL) with thickness £ 10μm, diameter ~1mm, and focal length = 18mm, which was constant over the operati…
It is generally thought that correcting chromatic aberrations in imaging requires multiple surfaces. Here, we show that by allowing the phase in the image plane of a flat lens to be a free parameter, it is possible to correct chromatic aberrations over a large continuous bandwidth with a single diffractive surface. We experimentally demonstrate imaging using a single flat lens of diameter > 3mm, focal length = 5mm (NA = 0.3, f/1.59) that is achromatic from 0.45um to 1um. This combination of size, NA and operating bandwidth has not been demonstrated in a flat lens before. We experimentally char…
A hybrid imaging system is a simultaneous physical arrangement of a refractive lens and a multilevel phase mask (MPM) as a diffractive optical element (DOE). The favorable properties of the hybrid setup are improved extended-depth-of-field (EDoF) imaging and low chromatic aberrations. We built a fully differentiable image formation model in order to use neural network techniques to optimize imaging. At the first stage, the design framework relies on the model-based approach with numerical simulation and end-to-end joint optimization of both MPM and imaging algorithms. In the second stage, MPM …
We designed, fabricated and characterized a flat multi-level diffractive lens (MDL) comprised of only silicon with diameter = 15.2mm, focal length of 19mm, and operating over the longwave infrared (LWIR) spectrum of 8um to 14um. We experimentally demonstrated field of view of 46deg, depth of focus >7mm and wavelength-averaged Strehl ratio of 0.46. All these metrics were comparable to those of a conventional refractive lens. The active device thickness is only 8um and its weight (including the silicon substrate) is less than 0.2g.
In principle, diffractive optics, particularly Phase Fresnel Lenses (PFLs), offer the ability to construct large, diffraction-limited, and highly efficient X-ray/$γ$-ray telescopes, leading to dramatic improvement in angular resolution and photon flux sensitivity. As the diffraction limit improves with increasing photon energy, gamma-ray astronomy would offer the best angular resolution over the entire electromagnetic spectrum. A major improvement in source sensitivity would be achieved if meter-size PFLs can be constructed, as the entire area of these optics focuses photons. We have fabricate…
The numerical aperture (NA) of a lens determines its ability to focus light and its resolving capability. Having a large NA is a very desirable quality for applications requiring small light-matter interaction volumes or large angular collections. Traditionally, a large NA lens based on light refraction requires precision bulk optics that ends up being expensive and is thus also a specialty item. In contrast, metasurfaces allow the lens designer to circumvent those issues producing high NA lenses in an ultra-flat fashion. However, so far, these have been limited to numerical apertures on the s…
We analyze the dispersion property of low-index thin lenses by using scalar diffraction and finite difference time domain (FDTD) methods. We compare the dispersion results obtained by using these methods with reported experimental results, and the well-known analytical formula for focal length (f) of diffractive lenses as a function of wavelength (λ),f(λ)=(f_0 λ_0)/λ,where f_0 is the designed focal length for wavelength λ_0. We show that when the analytical formula is applied to thin flat lenses with low-refractive index, the results are accurate for small numerical aperture (NA) up to 0.2. Fo…
Wide field-of-view (FOV) optics are widely used in various imaging, display, and sensing applications. While conventional wide FOV optics rely on cascading multiple elements to suppress coma and other aberrations, it has recently been demonstrated that diffraction-limited, near-180 degree FOV operation can be achieved with a single-piece flat fisheye lens designed via iterative numerical optimization [Nano Lett. 20, 7429(2020)]. Here we derive an analytical solution to enable computationally efficient design of flat wide FOV lenses based on metasurfaces or diffractive optical elements (DOEs). …
By placing a diffractive element in front of an image sensor, we are able to multiplex the spectral and angular information of a scene onto the image sensor. Reconstruction of the angular-spectral distribution is attained by first calibrating the angular-spectral response of the system and then, applying optimization-based matrix inversion. In our proof-of-concept demonstration, we imaged the 1D angle and the spectrum with resolutions of 0.15o and 6nm, respectively. The information is reconstructed from a single frame, thereby enabling snapshot functionality for video-rate imaging.
Traditional lens design is a numerical and forward process based on ray tracing and aberration theory. This method has limitations because the initial configuration of the lens has to be specified and the aberrations of the lenses have to considered. This paper is an initial attempt to investigate an analytic and inverse lens design method, called Lagrange, to overcome these barriers. Lagrange method tries to build differential equations in terms of the system parameters and the system input and output (object and image). The generalized Snell's law in three dimensional space and the normal of…
Metasurfaces are nano-structured devices composed of arrays of subwavelength scatterers (or meta-atoms) that manipulate the wavefront, polarization, or intensity of light. Like other diffractive optical devices, metasurfaces suffer from significant chromatic aberrations that limit their bandwidth. Here, we present a method for designing multiwavelength metasurfaces using unit cells with multiple meta-atoms, or meta-molecules. Transmissive lenses with efficiencies as high as 72% and numerical apertures as high as 0.46 simultaneously operating at 915 nm and 1550 nm are demonstrated. With proper …
A plethora of metalenses and diffractive lenses (flat lenses) have been demonstrated over the years. Recently, attempts have been made to stretch their performance envelope, particularly in the direction of wide-band achromatic performance. While achromatic behavior has been demonstrated, an actual improvement in imaging performance relative to conventional (non-chromatically corrected) flat lenses has not. The reasons for this are use of inappropriate performance metrics, lack of comparison to a baseline conventional design, and lack of a performance metric that combines signal-to-noise ratio…
Coherent diffractive imaging (CDI) provides new opportunities for high resolution X-ray imaging with simultaneous amplitude and phase contrast. Extensions to CDI broaden the scope of the technique for use in a wide variety of experimental geometries and physical systems. Here, we experimentally demonstrate a new extension to CDI that encodes additional information through the use of a series of randomly coded masks. The information gained from the few additional diffraction measurements removes the need for typical object-domain constraints; the algorithm uses prior information about the masks…
Multicolor super-resolution imaging remains an intractable challenge for both far-field and near-field based super-resolution techniques. Planar super-oscillatory lens (SOL), a far-field subwavelength-focusing diffractive lens device, holds great potential for achieving sub-diffraction-limit imaging at multiple wavelengths. However, conventional SOL devices suffer from a numerical aperture (NA) related intrinsic tradeoff among the depth of focus (DoF), chromatic dispersion and focus spot size, being an essential characteristics of common diffractive optical elements. Typically, the limited DoF…
In this paper we propose a method to design a freeform lens including the effect of Fresnel reflections on the transmitted intensity. This method is elaborated for a lens with one freeform surface shaping a far-field target from a point source or collimated input beam. It combines the optical mapping with the energy balance incorporating the loss due to Fresnel reflections, which leads to a generalized Monge-Ampère equation. We adapt a least-squares solver from previous research to solve the model numerically. This is then tested with a theoretical example and a test case related to road light…
Extended depth of focus (EDOF) lenses are important for various applications in computational imaging and microscopy. In addition to enabling novel functionalities, EDOF lenses can alleviate the need for stringent alignment requirements for imaging systems. Existing EDOF lenses, however, are often inefficient or produce an asymmetric point spread function (PSF) that blurs images. Inverse design of nanophotonics, including metasurfaces, has generated strong interest in recent years owing to its potential for generating exotic and innovative optical elements, which are generally difficult to mod…
