We examine the Seidel aberrations of thin spherical lenses composed of media with refractive index not restricted to be positive. We find that consideration of this expanded parameter space allows reduction or elimination of more aberrations than is possible with only positive index media. In particular we find that spherical lenses possessing real aplanatic focal points are possible only with negative index. We perform ray tracing, using custom code that relies only on Maxwell's equations and conservation of energy, that confirms the results of the aberration calculations.
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.
This paper demonstrates a method of interpreting the mechanism of aberration of optical systems based on non-Fourier transform optical transfer function (OTF). According to the parameters of object plane cosine fringe, we obtain the position on the pupil plane of the two beams of the interference pair emitted by the cosine fringes. By combining the aberrations of the lens, the phase of the cosine fringe of each interference pair in the image plane can be obtained. Then the intensity of the cosine fringe formed by all the interference pattern is superimposed to obtain the brightness distributio…
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…
Optical complex materials offer unprecedented opportunity to engineer fundamental band dispersion which enables novel optoelectronic functionality and devices. Exploration of photonic Dirac cone at the center of momentum space has inspired an exceptional characteristic of zero-index, which is similar to zero effective mass in fermionic Dirac systems. Such all-dielectric zero-index photonic crystals provide an in-plane mechanism such that the energy of the propagating waves can be well confined along the chip direction. A straightforward example is to achieve the anomalous focusing effect witho…
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…
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 …
Diffraction-limited focusing deep into biological tissue is challenging due to spherical aberrations that lead to a broadening of the focal spot particularly in axial direction. While the diffraction-limit can be restored employing aberration correction with a deformable mirror or spatial light modulator, a bulky optical setup results due to the required beam-folding. We propose a bi actor adaptive lens, that enables axial scanning and at the same time correction of specimen induced spherical aberrations while offering a compact setup. Using the bi-actor lens in a confocal microscope, we show …
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…
Traditional optical imaging systems can provide high-quality imaging with complicated and expensive optical design by eliminating aberrations. With the help of optical memory effect (ME), not independently improving single imaging parameter, but simultaneously improving several imaging parameters by adding scattering media to the imaging systems was demonstrated firstly. As an example, in a simple single-lens imaging system, except the depth-of-field (DOF) was improved greatly, spherical aberration, coma aberration and chromatic aberration were eliminated simultaneously by placing a scattering…
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 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 …
Holographic microscopy combined with forward modeling and inference allows colloidal particles to be characterized and tracked in three dimensions with high precision. However, current models ignore the effects of optical aberrations on hologram formation. We investigate the effects of spherical aberration on the structure of single-particle holograms and on the accuracy of particle characterization. We find that in a typical experimental setup, spherical aberration can result in systematic shifts of about 2% in the inferred refractive index and radius. We show that fitting with a model that a…
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.
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…
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…
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…
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…
By using the optical design software Zemax, on the basis of geometric optics and primary aberration theory, the optimal design method of collimating mirror is discussed and proposed, which eliminates the influence of conical concave acoustic lens on beam transmission. The lens system imaging before and after the optimization of the calibration lens is simulated by numerical simulation: from the simulation results, after the calibration mirror is optimized, the spherical aberration of the system is greatly reduced,. The root mean square radius of the spot under the 0 degree field of view change…
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…
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）
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 …
In recent years, dielectric rod based metasurface lenses have been particularly investigated for their potential applications in replacing the traditional bulky lens with high efficiency. However, the isolated granular structure may lead to robustness and chromatic aberration concerns. In this work, a low refractive-index embedding medium was applied to solve the structural stability problem that also enables the device to be transferable to desired position or surface. Based on this, a compound metasurface lens composed of randomly interleaved frequency-selective zone sectors is proposed to b…
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.…
Nearly twenty years ago, following a sixty year struggle, scientists succeeded in correcting the bane of electron lenses, spherical aberration, using electromagnetic aberration correction. However, such correctors necessitate re-engineering of the electron column, additional space, a power supply, water cooling, and other requirements. Here, we show how modern nanofabrication techniques can be used to surpass the resolution of an uncorrected scanning transmission electron microscope more simply by sculpting a foil of material into a refractive corrector that negates spherical aberration. This …
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…
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…
We report experimental and theoretical results on the production of macroscopic fluidic lenses with high dioptric power, tunable focal distance and aperture shape, for applications in adaptive eyewear for the sub-normal vision segment. The lense is 17 mm wide and is made of an elastic PDMS polymer, which can adaptively restore accommodation distance within several centimeters according to the fluidic volume mechanically pumped in. Moreover, the lens can provide for magnification in the range of +25 Diopter to +100 Diopter with optical aberrations on the order of the wave-length, and overall le…
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…
We present the design, simulation, and planned fabrication process of a flat high resistivity silicon gradient index (GRIN) lens for millimeter and submillimeter wavelengths with very low absorption losses. The gradient index is created by subwavelength holes whose size increases with the radius of the lens. The effective refractive index created by the subwavelength holes is constant over a very wide bandwidth, allowing the fabrication of achromatic lenses up to submillimeter wavelengths. The designed GRIN lens was successfully simulated and shows an expected efficiency better than that of a …
In this Letter we present a Fresnel lens fabricated on the end of an optical fiber. The lens is fabricated using nanoimprint lithography of a functional high refractive index material, which is suitable for mass production. The main advantage of the presented Fresnel lens compared to a conventional fiber lens is its high refractive index (n=1.69), which enables efficient light focusing even inside other media such as water or adhesive. Measurement of the lens performance in an immersion liquid (n=1.51) shows a near diffraction limited focal spot of 810 nm in diameter at the 1/e2 intensity leve…
Low-index contrast waveguides such as silica waveguides are indispensable part of passive integrated optical components. Reducing the bending radius of silica waveguides with low bend loss is vital in miniaturizing silica planar lightwave circuits. The Eaton lens is a gradient index lens that can bend parallel light rays by 90°, 180°, or 360°. We present a low-loss and compact 90° waveguide bend with a radius of 9 $μ$m designed by truncating the Eaton lens. The performance of the designed bend, implemented by graded photonic crystal, was evaluated by full-wave two-dimensional finite element me…
