We find that the function that describes the surface of spherical aberration free lenses can be used for both positive and negative refractive index media. With the inclusion of negative index, this function assumes the form of all the conic sections and expands the theory of aplanatic optical surfaces. There are two different symmetry centers with respect to the index that create an asymmetric relationship between positive and negative index lens profiles. In the thin lens limit the familiar formulas for image position and magnification hold for any index.
Free electrons moving in an optical standing wave field feel the ponderomotive potential, acting as a refractive-index medium in electron optics. Emerging technologies involving this potential have been proposed and realized in electron microscopy, such as electron phase-contrast imaging using a laser standing wave in an optical enhancement cavity. However, the interaction between electrons with a cylindrically distributed optical field has not been investigated although its suitability for electron-optical imaging systems. In this study, we theoretically show that the divergence and convergen…
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 …
The properties of electron round lenses produced by the ponderomotive potential are investigated in geometrical optics. The potential proportional to the intensity distribution of a focused first-order Bessel or Laguerre-Gaussian beam is exploited to produce an electron round lens and a third-order spherical aberration corrector. Several formulas for the focal length and spherical aberration coefficients in the thin-lens approximation are derived to set the lens properties and associated light beam parameters. When the mode field of the optical beam is small, the electron trajectory calculatio…
An analytical closed-form formula for the design of freeform lenses free of spherical aberration is presented. Given the equation of the freeform input surface, the formula gives the equation of the second surface in order to correct the spherical aberration. The derivation is based on the formal application of the variational Fermat principle under the standard geometrical optics approximation.
Compound refractive lenses (CRL) offer outstanding potential for probe formation in X-ray micro- and nano-analysis as well as for imaging applications, but effective aberration-free focusing of X-rays is a key consideration when high spatial resolution and intensities are required. Available refractive optics have non-negligible aberrations which degrade their final performance. We describe a framework based on physical-optics for simulating the effect of imperfect CRL upon an X-ray beam, taking into account measured phase errors obtained from at-wavelength metrology. We model, with increasing…
The key to optimizing spatial resolution in a state-of-the-art scanning transmission electron microscope is the ability to precisely measure and correct for electron optical aberrations of the probe-forming lenses. Several diagnostic methods for aberration measurement and correction with maximum precision and accuracy have been proposed, albeit often at the cost of relatively long acquisition times. Here, we illustrate how artificial intelligence can be used to provide near-real-time diagnosis of aberrations from individual Ronchigrams. The demonstrated speed of aberration measurement is impor…
In their article -Appl. Opt. 58, 1010_1015 (2019)- González-Acuña et al claimed:"an analytical closed-form formula for the design of freeform lenses free of spherical aberration and astigmatism." However, as we show here, their formula can only be applied when the object and image are both real and the image is inversed, additionally, the refractive index in the object and image media is the same. Here, we present the complete solution of this particular formula.
We propose a novel coaxial spherical-lens shaping system to achieve a flat-top focus profile by exploiting the spherical aberration of the lens. The well-known aspherical-lens shaping system is compared to ours, and a comparison of etching on silicon is conducted between a Gaussian beam and the one shaped by the proposed system. Analytical and experimental results show that the proposed system is able to achieve flat-top beam shaping using only spherical lenses. Compared with the existing systems, our proposed one is capable of shaping Gaussian beams with different wavelengths and waist radii.…
The interaction between free electrons and optical near fields is attracting increasing attention as a way to manipulate the electron wave function in space, time, and energy. Relying on currently attainable experimental capabilities, we design optical near-field plates to imprint a lateral phase on the electron wave function that can largely correct spherical aberration without the involvement of electric or magnetic lenses in the electron optics, and further generate on-demand lateral focal spot profiles. Our work introduces a disruptive and powerful approach toward aberration correction bas…
We experimentally demonstrate imaging in the longwave-infrared (LWIR) spectral band (8um to 12um) using a single polymer flat lens based upon multi-level diffractive optics. The device thickness is only 10μm, and chromatic aberrations are corrected over the entire LWIR band with one surface. Due to the drastic reduction in device thickness, we are able to utilize polymers with absorption in the LWIR, allowing for inexpensive manufacturing via imprint lithography. The weight of our lens is less than 100 times those of comparable refractive lenses. We fabricated and characterized two different f…
Conventional optical components have been proposed to realize high-quality line focusing with uniform intensity distribution such as cylindrical lenses, segmented wedge-arrays, or a combination of prisms and spherical mirrors. However, numerous factors such as the manufacturing tolerances of conventional lenses or the need for precise alignment of the lenses cause wavefront aberrations that impact the performance of optical systems. These aforementioned limitations of conventional optical components affect the uniformity of the intensity distribution. Here, we numerically and experimentally de…
In this work we present the numerical evaluation of a new design of fractal intraocular lens studied through a ray-tracing program. To determine the monochromatic and polychromatic performance of these lenses in different theoretical model eyes the Modulation Transfer Function (MTF) and the area above the MTF (AMTF) have been used. These merit functions show the same behavior for different values of asphericity (Q), independently from the theoretical model eye, even though there are differences due to the Spherical Aberration (SA) considered in each model.
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…
In light optics, beams with orbital angular momentum (OAM) can be produced by employing a properly-tuned two-cylinder-lens arrangement, also called $π$/2 mode converter. It is not possible to convey this concept directly to the beam in an electron microscope due to the non-existence of cylinder lenses in commercial transmission electron microscope (TEM). A viable work-around are readily-available electron optical elements in the form of quadrupole lenses. In a proof-of-principle experiment in 2012, it has been shown that a single quadrupole in combination with a Hilbert phase plate produces a …
Optimization of airgap in a monocentric lens assembly and metasurface based anti-reflecting coating in the long-wave IR regime
Indian Institute of Technology Roorkee（印度理工学院罗尔基）；National Institute of Technology Warangal（瓦朗加尔国家技术学院）；Instruments Research and Development Establishment（仪器研发局）
Remote focusing (RF) is a technique that greatly extends the aberration-free axial scan range of an optical microscope. To maximise the diffraction limited depth range in an RF system, the magnification of the relay lenses should be such that the pupil planes of the objectives are accurately mapped on to each other. In this paper we study the tolerance of the RF system to magnification mismatch and quantify the amount of residual spherical aberration present at different focusing depths. We observe that small deviations from ideal magnification results in increased amounts of residual spherica…
Towards Blind Lens Aberration Correction via Large LensLib Pre-training and Discrete Degradation Priors
National Research Center for Optical Instrumentation, Zhejiang University（浙江省光学仪器研究中心，浙江大学）；INSAIT, Sofia University "St. Kliment Ohridski"（INSAIT，索菲亚大学"圣克莱门特·欧弗里迪斯基"）；School of Artificial Intelligence and Robotics, Hunan University（人工智能与机器人学院，湖南大学）；National Engineering Research Center of Robot Visual Perception and Control Technology, Hunan University（机器人视觉感知与控制技术国家工程研究中心，湖南大学）
The chiton Acanthopleura granulata uses aragonitic lenses embedded in its shell to focus light onto photoreceptors. Because aragonite is biaxially birefringent, the microstructure of the lens greatly impacts the optical performance. In addition, the chiton lives in the intertidal, so lenses experience two environments with different refractive indices: air and water. Using EBSD, we find that the lens is polycrystalline and contains curved grain boundaries. A combination of large, twinned grains and nanotwins ensure that the aragonitic <001> axis is consistent across the lens. However, the orie…
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…
OmniLens: Towards Universal Lens Aberration Correction via LensLib-to-Specific Domain Adaptation
State Key Laboratory of Extreme Photonics and Instrumentation, College of Optical Science and Engineering（极端光子学与仪器国家重点实验室，光学科学与工程学院）；School of Artificial Intelligence and Robotics（人工智能与机器人学院）；National Engineering Research Center of Robot Visual Perception and Control Technology（机器人视觉感知与控制技术国家工程研究中心）；Sofia University St. ``Kliment Ohridski''（索菲亚大学圣·克里门特·奥赫里迪斯基大学）
Optical aberrations have been studied for centuries, placing fundamental limits on the achievable resolution in focusing and imaging. In the context of structured light, the spatial pattern is distorted in amplitude and phase, often arising from optical imperfections, element misalignment, or even from dynamic processes due to propagation through perturbing media such as living tissue, free-space, underwater and optical fibre. Here we show that the polarisation inhomogeneity that defines vectorial structured light is immune to all such perturbations, provided they are unitary. By way of exampl…
Most camera lens systems are designed in isolation, separately from downstream computer vision methods. Recently, joint optimization approaches that design lenses alongside other components of the image acquisition and processing pipeline -- notably, downstream neural networks -- have achieved improved imaging quality or better performance on vision tasks. However, these existing methods optimize only a subset of lens parameters and cannot optimize glass materials given their categorical nature. In this work, we develop a differentiable spherical lens simulation model that accurately captures …
Zhejiang University（浙江大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；ETH Zürich（苏黎世联邦理工学院）
Panoramic Annular Lens (PAL) composed of few lenses has great potential in panoramic surrounding sensing tasks for mobile and wearable devices because of its tiny size and large Field of View (FoV). However, the image quality of tiny-volume PAL confines to optical limit due to the lack of lenses for aberration correction. In this paper, we propose an Annular Computational Imaging (ACI) framework to break the optical limit of light-weight PAL design. To facilitate learning-based image restoration, we introduce a wave-based simulation pipeline for panoramic imaging and tackle the synthetic-to-re…
