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PURPOSE To investigate the effect of varying the fluid reservoir (FR) thickness of scleral lenses (SL) on corrected distance visual acuity (CDVA), contrast sensitivity (CS) and higher-order aberrations (HOAs) in keratoconic eyes. METHODS Forty eyes with keratoconus were fitted with a diagnostic Boston Sight SL having three different FR thicknesses. CDVA, CS and HOAs were measured before and after 30 min of lens wear. An i-Trace aberrometer and anterior segment optical coherence tomography (AS-OCT) were used to measure HOAs and FR thickness, respectively. RESULTS Statistically significant improvements in CDVA and CS were seen with different FR thickness lenses (p

Purpose : This study was conducted to improve the performance of a low-end f-theta lens for application to laser scanning unit. Methods : A f-theta lens system was newly designed using ZemaxTM program. Results of this study were compared and evaluated in three items, such as spot diagram, ray fan, and Seidel aberrations. Results : The newly designed f-theta lens system reduced the spot size and distortion of the incident laser beam, and particularly its spherical aberration was drastically reduced up to 77%. Conclusion : The f-theta lens system designed in this study has greatly improved overall image quality and performance, and is expected to be applied to laser printer equipment.

Fluorescence microscopy with optical sectioning capabilities is extensively utilized in biological research to obtain three-dimensional structural images of volumetric samples. Tunable lenses have been applied in microscopy for axial scanning to acquire multiplane images. However, images acquired by conventional tunable lenses suffer from spherical aberration and distortions. Here, we design, fabricate, and implement a dielectric Moiré metalens for fluorescence imaging. The Moiré metalens consists of two complementary phase metasurfaces, with variable focal length, ranging from ∼10 to ∼125 mm at 532 nm by tuning mutual angles. In addition, a telecentric configuration using the Moiré metalens is designed for high-contrast multiplane fluorescence imaging. The performance of our system is evaluated by optically sectioned images obtained from HiLo illumination of fluorescently labeled beads, as well as ex vivo mice intestine tissue samples. The compact design of the varifocal metalens may find important applications in fluorescence microscopy and endoscopy for clinical purposes.

PURPOSE Spherical orthokeratology and soft multifocal contact lenses are commonly used for myopia control and correction, but have been shown to increase spherical aberration, coma and total higher order root mean square (HORMS) aberrations. There are limited myopia control contact lens options for patients with moderate to high astigmatism. The purpose of this study was to quantify changes in higher order aberrations (HOA) in myopic astigmatic eyes fitted with toric orthokeratology (TOK) and soft toric multifocal (STM) contact lenses. METHODS Ocular wavefront aberrations were measured in both eyes of 30 adult subjects and are reported through the 6th radial order over a 5 mm, dilated pupil. All eyes met refractive criteria of myopia (-5.00 D to plano) and cylinder (-3.50 to -1.25 D). Three measurements were taken at baseline and after 10 ± 2 days of lens wear (TOK, STM). Sixteen subjects achieved logMAR high contrast visual acuity of 0.30 or better in both eyes and were included in this analysis. Repeated measures analysis of variance and post-hoc paired t-tests were used, as appropriate, with Benjamini-Hochberg correction. RESULTS Higher order root mean square, spherical aberration (C12), and coma RMS (C7, C8) increased with TOK (0.641 [0.222], 0.409 [0.157], 0.426 [0.187] µm, respectively) and STM (0.481 [0.107], 0.223 [0.139], 0.320 [0.130] µm, respectively) from baseline (all p

Lens is a basic optical element that is widely used in daily life, such as in cameras, glasses, and microscopes. Conventional lenses are designed based on the classical refractive optics, which results in inevitable imaging aberrations, such as chromatic aberration, spherical aberration and coma. To solve these problems, conventional imaging systems impose multiple curved lenses with different thicknesses and materials to eliminate these aberrations. As a unique photonic technology, metasurfaces can accurately manipulate the wavefront of light to produce fascinating and peculiar optical phenomena, which has stimulated researchers’ extensive interests in the field of planar optics. Starting from the introduction of phase modulation methods, this review summarizes the design principles and characteristics of metalenses. Although the imaging quality of existing metalenses is not necessarily better than that of conventional lenses, the multi-dimensional and multi-degree-of-freedom control of metasurfaces provides metalenses with novel functions that are extremely challenging or impossible to achieve with conventional lenses. [Image: see text]

Based on the theory of matrix optics, the first-order properties of the zoom system of the three-element variable focal power devices were analyzed, and the control equation of the focal power based on the system magnification was obtained. Combined with the initial parameters of the three-element system and taking the minimum spherical aberration as the objective, the initial structure of the system was designed, the control function of the shape parameters of the lens was obtained, and the focal power and image quality were evaluated and calculated. Finally, the design example was compared and verified. The results show that the solution of the optimal value of the minimum spherical aberration is reliable. The starting point and method of the design provide a theoretical research reference for the further design of zoom system by using variable focal power devices.

A novel optical-transmission rear mounted augmented reality head-up display, which can be used to improve the safety of a driving vehicle, is introduced and investigated in this paper. The proposed system uses an off-axis free-form mirror that serves as asymmetric aberration corrector. The off-axis aberration of the system is analyzed and the mirror is designed to correct both linear astigmatism and spherical aberration. This makes it possible to optimize the whole optical system. We also analyze the relationship between human eyes and the virtual image to obtain a registration matrix. The experimental results show that the size of the virtual image is 11 inches, the imaging distance is 2.8 meters, and the area of the eye box is 140 * 60 mm2. The novel system makes it possible to fuse the virtual image with the real-life scene to improve driver safety.

The existence of the spherical aberration of the thermal lens in the crystal has a certain regulatory effect on the distribution of laser modes. In this paper, using the impact of this aberration on the superposition area of TEM01 and TEM10 modes, we carry out an experimental study of a 1064 nm hollow beam and its nonlinear frequency conversion providing a 532 nm hollow beam. Using a plano-concave cavity structure, under 21.92 W pump power at 808 nm, a 1064 nm hollow beam with an output power of 4.01 W is generated. Based on this result, a 532 nm hollow beam with an output power of 1.08 W is obtained by intracavity frequency doubling with type I phase matching in an LBO crystal. The conversion efficiency is 26.9%.

In most textbooks, lens aberrations are usually described in the briefest possible manner, without any attempt for their proper derivation. At the same time, monographs which do go into more detail are often inaccessible to most students and non-specialists interested in deeper understanding of this topic. This article tries to fill this gap and provide an introduction to what happens when basic formulas of Geometrical Optics are extended by third-order terms in Taylor’s expansion of sin (α). The presentation is accessible to most undergraduate students as it requires only some knowledge of basic calculus and planar geometry. The resulting five aberrations are then described in detail, including a novel derivation of the exact shape of coma. A simple Mathematica program is included to facilitate numerical exploration of the magnitude of the resulting aberrations for various optical systems.

A new, to the best of our knowledge, method for designing a thick-lens achromatic doublet based on the concept of a caustic surface to correct both third- and fifth-order spherical aberration is presented. We consider two different wavelengths brought into coincidence at the back focal length instead of the effective focal length as it is usually done, to calculate the radii of curvature assuming predefined values for axial thicknesses and their indices of refraction for both lenses. Alternatively, we apply Taylor’s series around the optical axis, and to vanish the approximate caustic surface, we obtain the values for the conic constants, which reduce at third- and fifth-order spherical aberration. Two designs for cemented doublets are provided assuming that the lenses are cemented. Finally, we propose a method to qualitatively test doublet lenses by using null screens, considering to place the detection plane at arbitrary positions.

Significance Fitting specialty contact lenses (hybrid and miniscleral) can be a useful option in keratoconus patients to decrease higher-order aberrations (HOAs) and increase the quality of vision. Purpose The aim of the present study was to compare corneal HOAs between miniscleral and hybrid lenses in keratoconus patients. Methods The target population of this study was 37 patients with bilateral keratoconus aged 20 to 35 years who were referred to a specialized contact lens clinic by a corneal specialist. Pre-fitting examinations included objective and subjective refraction, measurement of uncorrected and best spectacle-corrected visual acuity, and measurement of corneal HOAs. Lens fitting was performed in the next step. Finally, post-fitting measurements including contact lens-corrected visual acuity and corneal HOAs were performed. Results The root mean square of the total HOAs significantly decreased after fitting both miniscleral and hybrid lens designs. There was a significant change in the third-order vertical coma and spherical aberration after fitting the miniscleral lens. In the hybrid lens group, a significant change was found only in vertical coma after fitting. There was no significant difference in the post-fitting HOA change between the two groups. Conclusions The results of this study showed the effectiveness of both miniscleral and hybrid lenses in decreasing HOAs in keratoconus patients. No significant difference was observed between these two lenses in this regard.

This paper presents the simulated performance assessment of an artificial iris embedded on a scleral contact lens using real data from an aniridia patient. The artificial iris is based on guest–host liquid crystal cells (GH-LCD) in order to actively modify the transmittance of the lens and effective pupil size. Experimental validation of the GH-LCD spectrum and iris contrast (determined to be 1:2.1) enabled the development of optical models that include the effect of a small pupil on image quality and visual quality on an optical system with aniridia characteristics. Visual simulations at different light conditions (high/low photopic and mesopic) demonstrated the theoretical capacity of the customized artificial iris smart contact lens to expand the depth-of-focus and decrease the optical aberrations (in particular, the spherical aberration). The visual modelling suggests a maximum depth-of-focus value for a 2-mm pupil diameter for both eyes as follows: 3D (1,000 cd/m2), 2D (10 cd/m2) and 0.75D (1 cd/m2). This work demonstrates the beneficial optical effects of an active artificial iris, based on visual simulations in response to different light levels, and enables further experimental investigation on patients to validate the dynamic light attenuation and visual performance of smart contact lenses with GH-LCD.

To compare the results of using small incision lenticule extraction (SMILE) and wavefront-guided femtosecond-assisted laser in situ keratomileusis (WFG FS-LASIK) to correct high myopia and myopic astigmatism. The 94 eyes of 47 patients with high myopia or myopic astigmatism, if not both, who had undergone SMILE were compared with the 94 eyes of 47 patients with high myopia or myopic astigmatism, also if not both, who had undergone WFG FS-LASIK. Only eyes with high myopic or myopic astigmatism errors greater than − 6.0 diopter (D) spherical refraction and 0–3 D cylindrical refraction were included. Values of uncorrected distance visual acuity, corrected distance visual acuity, efficacy index, safety index, predictability, and high-order aberration between the patient groups were compared. The SMILE and WFG FS-LASIK groups did not significantly differ according to sex or age. Values of preoperative and postoperative spherical refraction, cylindrical refraction, spherical equivalent, uncorrected distance visual acuity, and corrected distance visual acuity between the groups also did not significantly differ nor did values of predictability, the efficacy index, or the safety index. SMILE induced more coma and trefoil (p

Spherical aberration (SA) occurs when light rays entering at different points of a spherical lens are not focused to the same point of the optical axis. SA that occurs inside the lens elements of a fluorescence microscope is well understood and corrected for. However, SA is also induced when light passes through an interface of refractive index (RI)-mismatched substances (i.e., a discrepancy between the RI of the immersion medium and the RI of the sample). SA due to RI mismatches has many deleterious effects on imaging. Perhaps most important for 3D imaging is that the distance the image plane moves in a sample is not equivalent to the distance traveled by an objective (or stage) during z-stack acquisition. This non-uniform translation along the z axis gives rise to artifactually elongated images (if the objective is immersed in a medium with a higher RI than that of the sample) or compressed images (if the objective is immersed in a medium with a lower RI than that of the sample) and alters the optimal axial sampling rate. In this tutorial, we describe why this distortion occurs, how it impacts quantitative measurements and axial resolution, and what can be done to avoid SA and thereby prevent distorted images. In addition, this tutorial aims to better inform researchers of how to correct RI mismatch–induced axial distortions and provides a practical ImageJ/Fiji-based tool to reduce the prevalence of volumetric measurement errors and lost axial resolution. This tutorial describes the main causes of sample-induced spherical aberration artifacts in 3D microscopy. In addition, the authors provide a practical ImageJ/Fiji-based solution to correct these aberrations during or after image acquisition.

Achromatization of a three-component diffraction system consisting of one thick and two thin hologram optical elements is considered in the work. Analytical expressions are obtained for correcting the chromatic aberration of the position of a thick focusing hologram optical element by two scattering thin hologram optical elements in a given spectrum range. It is shown that achromatization is achieved for such a three-component system using two thin hologram elements located symmetrically on both sides of the thick element and having a value of the working diffraction order greater than the ratio of the focal length to the distance from the thin element to the image plane (at a given wavelength). The proposed three-component holographic system can be used to convert both an imaginary image into a real image and a real into an imaginary image in predetermined spectral regions of the visible, ultraviolet or infrared ranges of the spectrum.

Objectives To compare the asphericity and higher-order aberration (HOA) outcomes of single-step transepithelial photorefractive keratectomy (tPRK) and conventional alcohol-assisted PRK (aaPRK) in patients with myopia and myopic astigmatism. Materials and methods Of the 108 eyes of 54 patients enrolled in the study, tPRK was performed on 54 (50%) eyes and aaPRK was performed on 54 (50%) eyes. The following parameters were compared: corrected distance visual acuity (CDVA), spherical equivalent (SE), flat and steep keratometry, intraocular pressure, central corneal thickness, asphericity, and HOAs including horizontal and vertical coma, horizontal and vertical trefoil, spherical aberration, second-order vertical coma, and aberration coefficient. Results The demographic and baseline characteristics were similar between the two groups (p>0.05, for all). The aberration coefficient value was significantly lower in patients treated with aaPRK compared to patients treated with tPRK at postoperative 3 months, 6 months, and 1 year (p=0.022, p=0.019, and p=0.017, respectively). Differences in the other variables were statistically insignificant (p>0.05 for all). Conclusion Both tPRK and aaPRK procedures obtain similar postoperative CDVA, SE, asphericity, and HOA outcomes, except the aberration coefficient value.

Purpose To compare the visual outcomes and corneal aberrations between wavefront-optimized (WFO) and corneal wavefront-guided (WFG) photorefractive keratectomy (PRK) in low to moderate myopia. Methods Twenty-seven eyes treated with WFO and 29 eyes treated with WFG PRK using a Schwind Amaris 750S Excimer laser were included after 6 months of postoperative follow-up. Uncorrected distance visual acuity, corrected distance visual acuity, refractive errors, corneal higher-order aberrations (HOA) and corneal thickness obtained using a Scheimpflug system, and central ablation depth and volume were evaluated during the preoperative period and again at the postoperative 6-month visits. Results Postoperatively, uncorrected distance visual acuity, corrected distance visual acuity, manifest spherical equivalent, and refractive astigmatism were improved in both groups, and there was no statistically significant difference between the two groups. There was no significant difference in safety, efficacy, or predictability of the refractive outcome. Postoperative total corneal HOA root mean square (RMS), coma RMS, and spherical aberration were significantly increased in both groups. Among these, only spherical aberration showed a significant difference between the two groups, with greater increase in the WFO group at 6 months postoperatively. The changes in corneal HOA RMS and spherical aberration were smaller in the WFG group, and this benefit was marked in eyes with high HOA RMS (≥0.4 μm) and spherical aberration (≥0.2 μm). Even though ablation volume in the WFG group was much larger than that of the WFO group, there was no significant difference in postoperative central and peripheral corneal thickness between the two groups. Conclusions Both WFO and WFG PRK using a Schwind Amaris 750S laser for low to moderate myopia were safe and effective at improving visual and refractive outcomes. However, WFG PRK induced fewer spherical aberrations than WFO PRK and may be more advantageous for eyes with high HOA root mean square or spherical aberration.

PURPOSE: To compare ray-tracing aberrometry, Hartmann-Shack wavefront analysis, automated refraction, and manifest refraction in patients with echelette diffractive intraocular lenses (IOLs) and patients with monofocal IOLs with negative spherical aberration. METHODS: Pseudophakic patients implanted with an echelette diffractive IOL (Tecnis ZXR00; Johnson & Johnson Vision) and a control group consisting of patients implanted with a negative spherical aberration monofocal IOL (Tecnis ZCBOO, Johnson & Johnson Vision) were included in this study. Ray-tracing aberrometry (iTrace; Tracey Technologies Corp.), Hartmann-Shack wavefront analysis (LADARWave; Alcon Laboratories, Inc.), automated refraction (Topcon KR-8800; Topcon Medical Systems, Inc.), and manifest refraction spherical equivalent were performed 1 to 3 months postoperatively. RESULTS: Thirty-two eyes implanted with a ZXR00 IOL and 30 eyes implanted with a ZCBOO IOL were enrolled in this study. The ZXR00 IOL group yielded more myopic results with automated refactions (−0.62 ± 0.41 diopters [D]), Hartmann-Shack wavefront analysis (−0.85 ± 0.40 D), and ray-tracing aberrometry (−0.45 ± 0.64 D), compared to manifest refraction (−0.12 ± 0.44 D) ( P < .001). Hartmann-Shack wavefront analysis showed a statistically significant myopic shift (−0.39 ± 0.47 D) in the ZCBOO group compared to ray-tracing aberrometry, automated refraction, and manifest refraction spherical equivalent (−0.14 ± 0.56, −0.14 ± 0.50, and −0.06 ± 0.44 D, respectively; P < .001). CONCLUSIONS: Manifest refraction techniques unique to echelette technology should be used to avoid over-minus end points. Autorefractors and aberrometers commonly use near-infrared light; thus, myopic results are expected with echelette achromatic technology. [ J Refract Surg . 2020;36(5):334–339.]

Ordered nanoporous materials including zeolites, zeotypes, and metal-organic frameworks (MOFs) are widely used in the fields of heterogeneous catalysis, ion exchange and gas storage/separation. In addition, due to their particular structural features new applications are continuously being explored as a consequence of their well-defined porous network, thermal stability, acidity and guest-species confinement. All physicochemical properties are directly structure related and therefore characterization at atomic level is highly desired. In the current work, we have aimed to review the recent progress of electron microscopy science applied to the characterization of different nanoporous materials since the first work that made use of spherical aberration (C-s) corrected electron microscopy in 2010. All difficulties encountered for the application of this technique will be presented, together with the excellent degree of information that can be extracted and the scientific responses that only C-s-corrected electron microscopy can provide in the area of nanoporous materials, zeolites, zeotypes and MOFs.

This chapter elucidates the general introduction of light, perception of colour, mechanism of image formation in the eye, basic principles of light microscope and components of light microscope along with guidelines of handling of the microscope. The spherical lens of the microscope may have several optical faults or aberrations. Image distortion occurs due to these various optical aberrations. The common aberrations include chromatic aberration, spherical aberration, astigmatism and curvature of field. This chapter highlights the causes of these aberrations and their solutions. In addition various other microscopes have also been discussed in this chapter.

A method to integrate metasurfaces in lens design is proposed. Thanks to a model based on effective medium theory used in conjunction with lens design software, the optical properties of custom metasurfaces within a complex system can be calculated. Compared to simple phase surfaces embedded in common lens design software, the phase shift profile given by our model is dependent on the wavelength and field of view. We thus demonstrate that those phase surfaces cannot accurately reproduce the behaviour of metasurfaces in every system. As a proof- of-concept, a hybrid refractive and metalens design was also made. The metasurface located within two refractive lenses corrects mainly the spherical aberration and allows the system to be almost diffraction-limited for the whole field of view.

Purpose: To assess the outcomes of implanting a new polymethylmethacrylate (PMMA) ring (Neoring; AJL Ophthalmic) in pre-descemet deep anterior lamellar keratoplasty (PD-DALK) procedure for moderate-advanced keratoconus.Methods: This prospective study included 10 eyes of 10 patients with moderate-advanced keratoconus who underwent PD-DALK with Neoring implantation. Neoring was implanted in a pre-descemetic pocket. The post-operative examination included refraction, corrected distance visual acuity (CDVA), corneal tomography, and endothelial cell density (ECD). The root mean squares (RMSs) for coma-like aberrations and spherical aberration were evaluated for a pupil size of 4.5 mm. The junctional graft (Tg) and host (Th) thicknesses were measured. The post-operative follow-up was 24 months.Results: Post-operative CDVA was 0.82 ± 0.14 (decimal scale), 100% of the eyes achieved a CDVA of 0.7 (decimal scale). The refractive cylinder was −2.86 ± 1.65 2-years after surgery. No eyes had a post-operative refractive cylinder ≥5.00 D and in five eyes (50%), it was ≤2.50 D. At the last visit, the mean keratometry was 45.64 ± 1.96 D, the RMS for coma-like aberrations was 0.30 ± 0.15 μm and spherical aberration was 0.22 ± 0.09. The mean ECD remains without changes over the follow-up (P = 0.07). At the last visit, Tg and Th were 679.9 ± 39.0 and 634.8 ± 41.2 μm, respectively. The thickness of the complex (host-Neoring) was 740.6 ± 35.6 μm. In all cases, this thickness was thicker than Tg.Conclusion: The results of this study suggest that PD-DALK along Neoring implantation is a viable, effective, and safe option to optimize the post-operative results for moderate-severe keratoconus.

It is known that, besides being stigmatic, spherical refracting surfaces are aplanatic at their Young points since they satisfy the Abbe sine condition rigorously. The Abbe sine condition is commonly applied to different optical systems using numerical methods or optimization processes, obtaining a design of approximately aplanatic systems. Here, we found several families of Cartesian surfaces, whose sets of each of these families constitute exactly aplanatic systems free of spherical aberration and coma. So, studying the different types of systems, it is found that rigorous aplanatism occurs for objects and images on curved surfaces.

Purpose Using raytracing simulation to study the effect of corneal imaging metrics for different aperture sizes as a function of object distances with different schematic model eyes. Methods This raytracing simulation determined the best focus (with the least root‐mean‐square (rms) ray scatter) and the best wavefront focus (with least rms wavefront error) for four schematic model eyes (Liou‐Brennan (LBME), Atchison (ATCHME), Gullstrand (GULLME) and Navarro (NAVME)) with 4 aperture sizes (2–5 mm) and 30 object distances in a logscale from 10 cm to 10 m plus infinity. For each configuration, 10,000 rays were traced through the cornea, and the aperture stop was located at the lens front apex plane as described in the model eyes. The wavefront was decomposed into Zernike components to extract the spherical aberration term. Results The focal distance with respect to the corneal front apex increases from around 31 mm for objects at infinity to around 40 mm for objects at 10 cm. The best (wavefront) focus was systematically closer to the cornea compared with the paraxial focus, and the overestimation of focal length with the paraxial focus was larger for large aperture sizes and small object distances. The rms ray scatter and wavefront error were both systematically larger with large aperture and small object sizes. At best focus the rms wavefront error was systematically larger, and the rms ray scatter was systematically smaller compared to the best wavefront focus. Spherical aberration varied more with GULLME than with LBME or NAVME, and increased strongly at smaller object distances. Conclusions The imaging properties of the cornea, especially spherical aberration, increase strongly as the object distance decreases. This effect should be considered, especially when considering aberration correcting lenses for near vision such as multifocal or enhanced depth of focus lenses.

This paper describes a computational 3-D imaging system based on diffraction grating imaging with laser sources of multiple wavelengths. It was proven that a diffraction grating imaging system works well as a 3-D imaging system in our previous studies. The diffraction grating imaging system has advantages such as no spherical aberration and a low-cost system, compared with the well-known 3-D imaging systems based on a lens array or a camera array. However, a diffraction grating imaging system still suffers from noises, artifacts, and blurring due to the diffraction nature and illumination of single wavelength lasers. In this paper, we propose a diffraction grating imaging system with multiple wavelengths to overcome these problems. The proposed imaging system can produce multiple volumes through multiple laser illuminators with different wavelengths. Integration of these volumes can reduce noises, artifacts, and blurring in grating imaging since the original signals of 3-D objects inside these volumes are integrated by our computational reconstruction method. To apply the multiple wavelength system to a diffraction grating imaging system efficiently, we analyze the effects on the system parameters such as spatial periods and parallax angles for different wavelengths. A computational 3-D imaging system based on the analysis is proposed to enhance the image quality in diffraction grating imaging. Optical experiments with three-wavelength lasers are conducted to evaluate the proposed system. The results indicate that our diffraction grating imaging system is superior to the existing method.

Photophoresis can trap opaque microscopic particles in a focused laser beam surrounded by a gas such as air. The particle is heated by the laser, and in turn, interactions with the ambient gas provide a stabilizing force that holds the particle in a specific region of the beam. The particles can stay trapped while the beam ismoved side to side up to 2 m/s, enabling three-dimensional images to be traced out in a display application. Structure in the laser beam is associated with the trapping phenomenon, but the fundamental mechanism for stability of the trap remains mysterious. Particles prefer regions of the beam with diffraction features such as those that arise from spherical aberration. Nevertheless, the ability of near-unidirectional light, albeit light that undergoes focusing and exhibits structure, to provide a restoring force to trapped particles in the direction opposite to beam propagation needs to be explained. Through repeated trials of capturing particles in a well characterized beam, we map out the preferred locations for particle capture and correlate them with diffraction features of the beam. The specific beam locations that host trapped particles, when compared with neighboring regions that do not, can offer insight into the stability mechanism. We analyze the Poynting vector in the vicinity of trapped particles. The flow of light energy can provide important clues into the trapping mechanism.

We derive an explicit partial-wave (Mie) series for the image of a dielectric microsphere collected by a typical infinity-corrected microscope. We model the propagation of the illumination and scattered vector fields through the optical components of the microscope by using the angular-spectrum theorem with the help of Wigner rotation matrix elements, allowing us to identify the contribution from spin-orbit helicity reversal. We consider a high numerical aperture objective well beyond the validity range of the paraxial approximation. The spherical aberration introduced by refraction at the planar interface between the sample and the glass slide is fully taken into account. By comparing our theoretical model with images of colloidal particles placed at different positions with respect to the objective focal plane, we characterize their radii and refractive index. We employ polystyrene microspheres with a known refractive index in order to fit the transverse attenuation length describing the transmission loss of the scattered field. As an application, we measure the radius and refractive index of individual silica beads. We compare the result for the radius with an independent measurement using high-resolution scanning electron microscopy. To validate the result for the refractive index, we develop a second method, independent of the theoretical model, based on the image contrast in glycerin-water solutions. In all cases we find very good agreement between our method and the validation procedures. In addition, the nonparaxial theory provides a reliable description of the images found for all focal-plane positions and for both polystyrene and silica microspheres. Our approach allows a common optical microscope to be used to measure the refractive index and radius of spherical particles covering the entire size range from the Rayleigh regime to the ray optics one.

Since radio telescope is the main tool for human being to search the universe secret, the astronomer reached unanimity at the 24th URSI Conference in Kyota, Japan, 1993, and proposed to construct the next generation of the large radio telescope (LT) (Nan & Peng, 2000). From then on, the astronomer of China began the project of Five-hundred meter Aperture Spherical radio Telescope (FAST) (Qiu, 1998; Li, 1998). It is well known that Arecibo is the breakthrough of radio telescope. Its main mirror, 305m in diameter, is fixed on the karst base, and an elaborately designed feed system illuminates a part of the mirror which forms an effective aperture of the telescope with about 200m. The feed system is movable at a height of about 100 m for tracking the object to be observed. The enormous receiving area of the telescope will enable it to make many important astronomical discoveries inaccessible to lesser instruments, despite its small sky coverage (20° zenith scan angle), due to geometrical configuration, and narrow frequency bandwidth, originated from spherical aberration. An upgrade project has recently been carried out for the Arecibo telescope, in which a heavy and complex hence expensive Gregorian dualreflector feed system is introduced for correcting the spherical aberration and a broad bandwidth is affected (Duan, 1999). For the sake of satisfying the requirements of low cost and broad bandwidth, the project group of FAST decided to substitute the fixed spherical reflector with active reflector units. As shown in Fig. 1(a), the reflector consists of almost 2000 elementary reflector units. Fig. 1(b) shows some active reflector units and supporting mechanisms. The reflector unit is small part of spherical surface of regular hexagon and is driven by a supporting mechanism. The part of spherical reflector illuminated by the feed is continuously adjusted to fit a paraboloid of revolution in real-time, synchronous with the motion of the feed while tracking the object to be observed. As it is now free from spherical aberration, a simple, light, hence cheap feed system may be adopted to achieve broad bandwidth and full polarization. In order to fit a paraboloid of revolution, it is necessary that every reflector units should be driven by a supporting mechanism with two rotational degrees of freedom and one translational degree of freedom (Luo et al., 2000). That means almost 6000 control nodes on the whole active reflector should be managed and controled at the same time. It is supposed to be very difficult, so a sharing strategy is derived to decrease the number of nodes, which

Investigating the earliest stages of crystallization requires the transmission electron microscope (TEM) and is particularly challenging for materials which can be affected by the electron beam. Typically, when imaging at magnifications high enough to observe local crystallinity, the electron beam's current density must be high to produce adequate image contrast. Yet, minimizing the electron dose is necessary to reduce the changes caused by the beam. With the advent of a sensitive, high-speed, direct-detection camera for a TEM that is corrected for spherical aberration, it is possible to probe the early stages of crystallization at the atomic scale. High-quality images with low contrast can now be analyzed using new computing methods. In the present paper, this approach is illustrated for crystallization in a Ge2Sb2Te5 (GST-225) phase-change material which can undergo particularly rapid phase transformations and is sensitive to the electron beam. A thin (20 nm) film of GST-225 has been directly imaged in the TEM and the low-dose images processed using Python scripting to extract details of the nanoscale nuclei. Quantitative analysis of the processed images in a video sequence also allows the growth of such nuclei to be followed.

The influence of the numerical aperture of a light beam that probes a layered object on the magnitude of the quantity measured with a confocal interference microscope upon determining the object thickness has been studied theoretically and experimentally for the case in which the signal is significantly affected by the spherical aberration arising in the probing beam as it passes through the object. The dependence of the quantity to be measured on the numerical aperture is obtained taking into account the influence of the spherical aberration on the signal. The criterion of the “nonaberrational” propagation of the beam probing the object is determined and the condition under which the influence of the spherical aberration on the signal of the confocal microscope can be neglected is found. An approximate analytical expression is obtained, which makes it possible to determine the “nonaberrational” width of the angular spectrum of the light beam probing the object, taking into account an empirical correction factor. The applicability limits of the analytical dependence of the quantity to be measured on the numerical aperture, which has been previously obtained for the case of a negligibly weak influence of the spherical aberration on the signal from the confocal microscope, have been determined.

We demonstrate an application of the differential algebraic method in optimization of a hexapole corrector of spherical aberration for the transmission regime of the standard scanning electron microscope. We introduce the method by visualization of the effect of all correcting elements to illustrate the principle of the corrector. Special interest is given to parasitic aberrations and their correction using additional deflectors before and inside the corrector. They can alter the off-axial position and tilt of the beam in the hexapoles. The critical values of the parasitic aberration coefficients are calculated using a wave-optical method, which determines the stability of the deflection system, the lens doublet, and the hexapoles. The derived properties of the parasitic aberrations are used in an alignment procedure of the system with the corrector.

In this paper, we propose and experimentally demonstrate a tunable liquid lens integrated with an aspherical surface for spherical aberration and distortion compensation. Through optimizing the aspherical surface’s morphology, the spherical aberration and distortion can be significantly reduced. The root mean square spot size at focus is distinctly reduced from 55. 7 μ m to 2. 095 μ m after performing optimum optimization. The tunable liquid lens is integrated with the aspheric surface with 6 mm clear aperture and 19.2 mm minimum focal length and demonstrate the improvement in optical performance over the conventional lens without an aspheric surface over a focal length range. Its applications in microscope system and tunable-focus eyeglasses are foreseeable.

Laser scanning microscopes can be miniaturized for in vivo imaging by substituting optical microelectromechanical system (MEMS) devices in place of larger components. The emergence of multifunctional active optical devices can support further miniaturization beyond direct component replacement because those active devices enable diffraction-limited performance using simpler optical system designs. In this paper, we propose a catadioptric microscope objective lens that features an integrated MEMS device for performing biaxial scanning, axial focus adjustment, and control of spherical aberration. The MEMS-in-the-lens architecture incorporates a reflective MEMS scanner between a low-numerical-aperture back lens group and an aplanatic hyperhemisphere front refractive element to support high-numerical-aperture imaging. We implemented this new optical system using a recently developed hybrid polymer/silicon MEMS three-dimensional scan mirror that features an annular aperture that allows it to be coaxially aligned within the objective lens without the need for a beam splitter. The optical performance of the active catadioptric system is simulated and imaging of hard targets and human cheek cells is demonstrated with a confocal microscope that is based on the new objective lens design., Microscopy: a new angle on miniaturization Microscopes that generate images by laser scanning could be miniaturized using microelectromechanical systems (MEMS) to replace the larger components currently required, allowing more-effective imaging of small structures in laboratory animals and humans. Researchers in the USA led by David Dickensheets at Montana State University, developed the new concept using simulation studies and experiments to examine human cheek cells. The process uses a recently developed MEMS mirror to both scan and focus the laser beam. The mirror is part of a catadioptric lens, meaning one that builds its images using both the reflection and the refraction of light. This allows light to be gathered across a wide range of angles—technically described as a high numerical aperture—to generate the images. The system’s advantages are likely to allow improved diagnosis of medical conditions, including cancer.

We report an automated target positioning method with an accuracy of 2 μ m for a compact laser proton accelerator. This method is based on micrometer-scale dots on the images of transparent targets. In order to interpret the variation of these dots quantitatively, we developed a defocusing method making transparent targets visible as phase objects and applied it in target positioning. Automated positioning of transparent targets can be realized by means of minimizing the standard deviations σ of the pixel values of the images. Fast positioning based on the relationship between the radius of spherical aberration ring and defocusing distance is also discussed. Laser proton acceleration experiments have been carried out to demonstrate the performance of this positioning method.

A high-beam-quality and high-energy long-pulse laser has been developed with VRM(variable reflectivity mirror)coupling and spherical aberration compensation. The thermal lens and the thermal birefringence are compensated for by the 10 mm DL rod side-pumped laser module. The output mirror employs VRM coupling with R=35% in the center, which presents a energy of 1.04 J at a pulse width of 195 μs and a repetition rate of 400 Hz with a beam quality of M2≈8.4. The spherical aberration compensation improves the beam quality M2 factor to 2.15; the power stability (RMS) is 0.4% at 5 min, and the optical-optical efficiency is 19.7%.

A light-field camera captures both the intensity and the direction of incoming light1–5. This enables a user to refocus pictures and afterwards reconstruct information on the depth of field. Research on light-field imaging can be divided into two components: acquisition and rendering. Microlens arrays have been used for acquisition, but obtaining broadband achromatic images with no spherical aberration remains challenging. Here, we describe a metalens array made of gallium nitride (GaN) nanoantennas6 that can be used to capture light-field information and demonstrate a full-colour light-field camera devoid of chromatic aberration. The metalens array contains an array of 60 × 60 metalenses with diameters of 21.65 μm. The camera has a diffraction-limited resolution of 1.95 μm under white light illumination. The depth of every object in the scene can be reconstructed slice by slice from a series of rendered images with different depths of focus. Full-colour, achromatic light-field cameras could find applications in a variety of fields such as robotic vision, self-driving vehicles and virtual and augmented reality. A metalens array of GaN nanoantennas is used to make a full-colour achromatic light-field camera.

Liquid cell electron microscopy possesses a combination of spatial and temporal resolution that provides a unique view of static structures and dynamic processes in liquids. Optimizing the resolution in liquids requires consideration of both the microscope performance and the properties of the sample. In this Review, we survey the competing factors that determine spatial and temporal resolution for transmission electron microscopy and scanning transmission electron microscopy of liquids. We discuss the effects of sample thickness, stability and dose sensitivity on spatial and temporal resolution. We show that for some liquid samples, spatial resolution can be improved by spherical and chromatic aberration correction. However, other benefits offered by aberration correction may be even more useful for liquid samples. We consider the greater image interpretability offered by spherical aberration correction and the improved dose efficiency for thicker samples offered by chromatic aberration correction. Finally, we discuss the importance of detector and sample parameters for higher resolution in future experiments. Liquid cell electron microscopy provides a unique combination of spatial and temporal resolution, which is useful for imaging static and dynamic processes in liquids. In this Review, we discuss the resolution expected when imaging liquid specimens in transmission electron microscopy and scanning transmission electron microscopy and consider the benefits of spherical and chromatic aberration for resolution, image interpretability and dose efficiency.

We present the design of a dielectric lens to correct the spherical aberration in spherical reflector antennas for use at centimeter through submillimeter wavelengths. A set of near-field measurements at a frequency of 100 GHz of a 30 cm diameter spherical antenna with 30 cm radius of curvature confirm improvement in illumination efficiency from 20.2% for the feed at the paraxial focus of the spherical primary to 42.4% with the feed position optimized as described by [M. Alonso-DelPino, P. Goldsmith, C. Elmaleh, T. Reck, and G. Chattopadhyay, “Efficiency optimization of spherical reflectors by feed position adjustments,” IEEE Antennas and Wireless Propagation Letters, vol. 16, pp. 2865–2868, 2017] to 53.1% with the present TPX corrective lens. Further improvement should be possible by antireflection treatment of the lens surfaces, and by using both lens surfaces to optimize the amplitude in addition to the phase distribution of the antenna illumination. This technique offers advantages for antenna systems used for communication and for a variety of remote sensing applications.

A method for studying internal phase inhomogeneities in transparent optical materials by point-to-point three-dimensional laser heterodyne microprobing is proposed. The light microprobe in this case is a traveling micrograting formed in the zone of overlapping of two focused coherent light beams: reference and signal. The size of the microprobe in the x, y, z directions and the degree of influence of spherical aberration with a change in the microprobing depth are estimated. The capabilities of the method are illustrated by examples of detection and subsequent imaging of phase inhomogeneities in the volume of laser ceramics and its random layers.

Free Space Optics (FSO) has the potential to offer fast broad-bandwidth communication, but experiences signal loss due to atmospheric attenuation. Our study assesses the performance of different lens configurations to mitigate the fog scattering loss in a low-cost visible-band FSO communication system. We built a fog-testing chamber and novel transmitter board to evaluate our FSO link at four different visible-band wavelengths and three different lens configurations. We also analyze the receiver signal strength to determine the fog-induced attenuation and compare each lens performance in the system. To design and evaluate the optimum lens system, several novel transmitterreceiver lens configurations are analyzed and compared: plano-convex to plano-convex (P-P), bi-convex to planoconvex (B-P), and bi-convex to bi-convex (B-B). We observe that the visible-band wavelength can minimizes the amount of fog-induced signal loss. The lens configuration in conjunction with the most optimal visible-band wavelength is then analyzed with various fog levels. We determine the most efficient double-lens configuration in the FSO system with fog-induced noise. On average, the biconvex-planoconvex system performed 63.85% better than the planoconvex-planoconvex system and 50.42% better than the biconvex-biconvex system. These results can be attributed to the spherical aberration from the transmitter lens and will be discussed in the paper.

We demonstrate that a pair of wedge prisms with opposite angular dispersion can be designed to have zero spherical aberration, zero coma, and zero astigmatism and be simultaneously achromatic in convergent rays, and the system can easily reach the diffraction limit and be utilized in precise three-dimensional imaging, special optical testing, etc., for widening the imaging range. Aberration equations of a pair of thin wedge prisms in paraxial optics are first derived, from which a special solution is obtained by making a few presuppositions. Then three initial structures are built to verify our inference. The near-zero Zernike standard coefficients and tiny rms radii of the image spots given by OpticStudio prove that the derived equations hold. After that the refractive indices of two prisms are both tested, where the testing results show that prisms with high-refractive indices are more capable of compensating monochromatic aberrations. With the aid of Monte-Carlo analysis method, tolerance analysis is carried on with the worst cases of the three optimized systems. The results show that a pair of wedge prisms with the opposite angular dispersion can effectively work within the diffraction limit even if the optical manufacturing and assembly errors are large. In the end, the system design limitations are given, and we suggest that the working F-number of the eyepiece should preferably be larger than 8.0.

Purpose To analyse corneal power based on a large optical coherence tomography dataset using raytracing, and to evaluate corneal power with respect to the corneal front apex plane for different definitions of best focus. Methods A large OCT dataset (10,218 eyes of 8,430 patients) from the Casia 2 (Tomey, Japan) was post-processed in MATLAB (MathWorks, USA). Using radius of curvature, corneal front and back surface asphericity, central corneal thickness, and pupil size (aperture) a bundle of rays was traced through the cornea. Various best focus definitions were tested: a) minimum wavefront error, b) root mean squared ray scatter, c) mean absolute ray scatter, and d) total spot diameter. All 4 target optimisation criteria were tested with each best focus plane. With the best-fit keratometer index the difference of corneal power and keratometric power was evaluated using a multivariate linear model. Results The mean corneal powers for a/b/c/d were 43.02±1.61/42.92±1.58/42.91±1.58/42.94±1.59 dpt respectively. The root mean squared deviations of corneal power from keratometric power (nK = 1.3317/1.3309/1.3308/1.3311 for a/b/c/d) were 0.308/0.185/0.171/0.209 dpt. With the multivariate linear model the respective RMS error was reduced to 0.110/0.052/0.043/0.065 dpt (R² = 0.872/0.921/0.935/0.904). Conclusions Raytracing improves on linear Gaussian optics by considering the asphericity of both refracting surfaces and using Snell’s law of refraction in preference to paraxial simplifications. However, there is no unique definition of best focus, and therefore the calculated corneal power varies depending on the definition of best focus. The multivariate linear model enabled more precise estimation of corneal power compared to the simple keratometer equation.

The effect of spherical aberration on the radius of image beam waist in the design of laser optical system is discussed in detail, and the relationship between the spherical aberration and the image beam waist radius in the laser optical system is deduced. Radius variation of image beam waist due to spherical aberration which varies with the position of object beam waist and the optical system focus is analyzed by the form of curve. The analysis results indicate that the effect of spherical aberration on the radius of image beam waist should be considered according to the position of object beam waist in the design of a laser optical system. Finally, a design example of the optical system used for atmospheric laser communication system is given to illustrate the effect of spherical aberration on the image beam waist.

This paper designs an imaging optical system with a large relative aperture and large field of view based on the improved Mangin mirror. And it proposes a design method by analyzing the aberrations of Mangin mirror. The system uses the structure of a combination of catadioptric optical system and modified Mangin mirror. The system works in 450–850 nm band with 4° × 4° field of view, 1.8 F number, and 380 mm effective focal length. The imaging detector is a CMOS with detector with 2 μm × 2 μm pixels. The modulation transfer function value is greater than 0.50 at the Nyquist frequency 250 lp/mm and close to the diffraction limit. The secondary mirror of the system is designed, which is based on the theory of achromatic lens and Mangin mirror. The focal power of the achromatic Mangin mirror is solved by PW method which is based on the spherical aberration and off sine aberration obtained from the preliminary optimization analysis of the system initial structure. The focal power and radius of three surfaces of the achromatic Mangin mirror can be calculated by the achromatic conditions and residual chromatic aberration of the system. The system has good imaging quality with small monochromatic aberrations and chromatic aberrations.

Electron beams can be reflected by an electrode that is at a more negative potential than the cathode from which the beam is emitted. We want to design a mirror with a flat mirror electrode where the electrons are reflected at a plane very close to the electrode. The wave front of an electron can then be shaped when the mirror contains a surface topography or modulated potential. However, electron beams reflected by flat electron mirrors are usually characterized by high coefficients of chromatic and spherical aberration. When the mirror is combined with an electrostatic lens to form a tetrode mirror system, the situation deteriorates even further. This places a restrictive limit on the maximum aperture angle of the beam, and consequently also limits the attainable resolution at the image plane. We have numerically studied the dependence of these aberrations as a function of design parameters of the tetrode mirror consisting of a ground, lens, cap, and mirror electrode, and limited ourselves to only using flat electrodes with round apertures, at fixed electrode spacing. It turns out that the third order spherical aberration can be made negative. The negative third order aberration is then used to partially compensate the positive fifth order aberration. This way, a system configuration is obtained that, at 2 keV beam energy, provides a diffraction limited resolution of 7.6 nm at an image plane 25 mm from the mirror at beam semi-angles of 2.3 mrad, enabling an illumination radius of 40 μ m at the mirror. The presented tetrode mirror design could spark innovative use of patterned electron mirrors as phase plates for electron microscopy in general, and for use as coherent beam splitters in Quantum Electron Microscopy in particular. An appendix presents a method to calculate the spot size of a focused beam in the presence of both third and fifth order spherical aberration coefficients, which is also applicable to Scanning (Transmission) Electron Microscopes with aberration correctors.

The use of electron mirrors in aberration correction and surface-sensitive microscopy techniques such as low-energy electron microscopy has been established. However, in this work, by implementing an easy to construct, fully electrostatic electron mirror system under a sample in a conventional scanning electron microscope (SEM), we present a new imaging scheme which allows us to form scanned images of the top and bottom surfaces of the sample simultaneously. We believe that this imaging scheme could be of great value to the field of in-situ SEM which has been limited to observation of dynamic changes such as crack propagation and other surface phenomena on one side of samples at a time. We analyze the image properties when using a flat versus a concave electron mirror system and discuss two different regimes of operation. In addition to in-situ SEM, we foresee that our imaging scheme could open up avenues towards spherical aberration correction by the use of electron mirrors in SEMs without the need for complex beam separators.

Nanocomposites allow for controlling the magnitude and dispersion of the effective refractive index within broad regions. Exploiting this tunability offers a high potential for improving the performance or reducing the size of optical systems. This is because the different monochromatic and chromatic aberrations in optical systems depend critically on the materials’ properties. In the previous chapter, I have shown that a key part of this potential is that nanocomposites allow for the design of highly efficient DOEs. However, the full potential of dispersion-engineered nanocomposites goes beyond this application. In fact, I have already demonstrated that the high refractive index of nanocomposites is highly useful for reducing spherical aberration. In this chapter, I now focus on using nanocomposites, or novel dispersion-engineered materials in general, for correcting chromatic aberrations, that is, the design of achromatic optical systems. My goal for this chapter is to advanced concepts on how such materials can be used. I emphasize that evaluating the full potential of dispersion-engineered materials is only possible through systematic optical design studies for different systems. As one promising application for novel dispersion-engineered materials, I investigate the potential of such materials for enabling a new generation of smartphone cameras in the final section of this chapter.

The paper presents a methodology of calculation of the inner structure of two- and three-component hybrid liquid-membrane lenses with variable focal length that have corrected spherical aberration and coma. Specifically, the formulas for calculation of initial-design inner parameters (radii of curvatures of individual surfaces, axial thickness, and refractive indices of a material of the lens) of a thin-lens system are derived for a hybrid two-component system (doublet) made by one glass and one liquid-membrane lens, and a hybrid three-component lens (triplet) made by one glass lens and two liquid-membrane lenses, which both have variable focal length and corrected spherical aberration and coma for an object at infinity. As optimization during the optical design process requires the starting point be very close to the optimal solution, the presented approach can be successfully used for its calculation, as it is based on fundamental proven formulas of optical aberrations.