Optical Aberrations Research Articles

Efficient Optimization of a Regional Water Elevation Model With an Automatically Generated Adjoint

AbstractCalibration of unknown model parameters is a common task in many ocean model applications. We present an adjoint‐based optimization of an unstructured mesh shallow water model for the Baltic Sea. Spatially varying bottom friction parameter is tuned to minimize the misfit with respect to tide gauge sea surface height (SSH) observations. A key benefit of adjoint‐based optimization is that computational cost does not depend on the number of unknown variables. Adjoint models are, however, typically very laborious to implement. In this work, we leverage a domain specific language framework in which the discrete adjoint model can be obtained automatically. The adjoint model is both exactly compatible with the discrete forward model and computationally efficient. A gradient‐based quasi‐Newton method is used to minimize the misfit. Optimizing spatially‐variable parameters is typically an under‐determined problem and can lead to over‐fitting. We employ Hessian‐based regularization to penalize the spatial curvature of the friction field to overcome this problem. The SSH dynamics in the Baltic Sea are simulated for a 3‐month period. Optimization of the bottom friction parameter results in significant improvement of the model performance. The results are especially encouraging in the complex Danish Straits region, highlighting the benefit of unstructured meshes. Domain specific language frameworks enable automated model analysis and provide easy access to adjoint modeling. Our application shows that this capability can be enabled with few efforts, and the optimization procedure is robust and computationally efficient.

Non-paraxial region adaptive aberration compensation using the phase transfer function.

The optical transfer function is crucial for imaging system design and characterization. However, practical optical systems often deviate from linear spatial invariance due to aberrations and field-of-view considerations, posing challenges for optical transfer function characterization and aberration compensation in non-paraxial region imaging. Partitioning the field-of-view into isoplanatic regions and measuring the optical transfer function for each region is a potential solution, but practical implementation is hindered by the lack of field-of-view information. This Letter introduces a compensation method for the phase modulation function based on spatial frequency domain division, specifically tailored for scenarios where high imaging quality is not essential. The proposed method addresses the challenge by filling the phase transfer function in an annular form corresponding to aberrations in different isoplanatic regions, offers a valuable solution for adaptive aberration compensation in non-paraxial region imaging, and presents a practical illustration of its effectiveness.

AlN-based piezoelectric MEMS deformable mirror.

An AlN-based piezoelectric micro-electromechanical system (MEMS) continuous membrane deformable mirror (DM) prototype is presented for the first time. Its effective aperture diameter is 5 mm and it is equipped with 25 independently controlled actuators. Owing to the advantages associated with the AlN piezoelectric thin-film technology, attractive characteristics including CMOS compatible fabrication, bidirectional linear and negligible hysteresis actuation, and excellent linear superposition control capability have been successfully demonstrated. Moreover, good optical aberration correction performance is also validated via the surface contour fitting experiment to the Zernike polynomials up to the first 14 orders despite the non-optimized device structure design, representing great application perspective.

Automatic and Quantitative Measurement of Spectrometer Aberrations.

The performance of electron energy loss spectrometers can often be limited by their electron optical aberrations. Due to recent developments in high energy resolution and momentum-resolved electron energy loss spectroscopy (EELS), there is renewed interest in optimizing the performance of such spectrometers. For example, the "ω - q" mode of momentum-resolved EELS, which uses a small convergence angle and requires aligning diffraction spots with the slot aperture, presents a challenge in the realignments of the spectrometer required by the adjustment of the projection lenses. Automated and robust alignment can greatly benefit such a process. The first step toward this goal is automatic and quantitative measurement of spectrometer aberrations. We demonstrate the measurement of geometric aberrations and distortions in EELS within a monochromated scanning transmission electron microscope (STEM). To better understand the results, we present a wave mechanical simulation of the experiment. Using the measured aberration and distortion coefficients as inputs to the simulation, we find a good match between the simulation and experiment, verifying formulae used in the simulation. From verified simulations with known aberration coefficients, we can assess the accuracy of measurements. Understanding the errors and inaccuracies in the procedure can guide further progress in aberration measurement and correction for new spectrometer developments.

Multidisciplinary integrated optimal design process for optomechanical structures.

This paper presents an integrated design process for optomechanical structures based on multidisciplinary optimization. The proposed integrated optimal design process comprises a finite element analysis by ANSYS Workbench, the MATLAB optomechanical transfer program, an optical analysis by ZEMAX, and the multidisciplinary optimization solver by Isight. In ANSYS Workbench, the deformation of optical surfaces, structures, and responses according to the design requirements is calculated in one project. Then, Zernike polynomial coefficients are calculated from surface deformation data of optical surfaces through a MATLAB optomechanical transfer program. In ZEMAX, the Zernike polynomial coefficients are imported into optical surface models of an optical system; then, optical performance parameters, such as the wavefront error, optical aberration, MTF, and OPD, are calculated. In the Isight environment, automatic iterative computations are performed between these three programs and, as a result, the design dimensions of optomechanical structures are determined, satisfying the design requirements and improving the performance of an optical system. By using this integrated optimal design process, the optimal design and analysis for a complete optomechanical structure, as well as individual structure parts, can be performed successfully. In this paper, the optimal design problem for three parts of a Cassegrain telescope, which consists of a primary mirror with an outer diameter of 156mm and a secondary mirror with an outer diameter of 46mm, was taken as an example. By using optimal parts, the image wavefront error of the Cassegrain telescope was decreased from 29.9 to 16.1nm.

Analysis of Imaging Characteristics of Wide-field Lobster Eye Lens

The lobster-eye lens is a reflected type focusing optics. It can be used for backscattering imaging that is a single-sided access technology for homeland security, detection of improvised explosive devices, non-destructive testing, and medical imaging. The aim of this study was to investigate the imaging characteristic of meridional lobster-eye lens with a planar imaging surface. The larger the field of view, the greater the spherical aberration, and the larger the field curvature of the edge field of view. Both spherical aberration and field curvature increase the size of the focal spot, and the images become blurry. Rays with a large angle of grazing incidence have large spherical aberration and curvature. The reflectivity of these rays drops sharply as the energy of photons increases. Therefore, spherical aberration and field curvature have a greater effect on photons with low energy. These conclusions can help improve the design of a lobster-eye lens for wide-field imaging applications.

Recent progress on femtosecond laser micro-/nano-fabrication of functional photonic structures in dielectric crystals: A brief review and perspective

Femtosecond (Fs) laser micro-/nano-fabrication technology allows direct definition of on-demand nanostructures with three-dimensional (3D) geometric features and tailored photonic functionalities in a facile manner. In addition, such a strategy is widely applicable to various material families, including dielectrics, semiconductors, and metals. Based on diverse dielectric crystals, fs-laser direct writing of optical waveguides with flexible geometries and functional waveguide-based photonic devices have been well-developed. Beyond waveguide architectures, the combination of 3D nanofabrication of fs lasers and the multi-functionalities of dielectric crystals has also lighted up the future development of novel photonic structures with features even beyond the optical diffraction limit. In this article, promising research topics on domain engineering for nonlinear optics, color centers and waveguides for integrated quantum photonics, and surface processing for integrated photonics enabled by fs laser micro-/nano-fabrication in dielectric crystals are briefly overviewed. We highlight recent progress on these research topics and stress the importance of optical aberration correction during laser fabrication, followed by a discussion of challenges and foreseeing the future development of fs laser defined nanostructures in dielectric crystals toward multi-functional photonics.

Localized Refractive Changes Induced by Symmetric and Progressive Asymmetric Intracorneal Ring Segments Assessed with a 3D Finite-Element Model.

To build a representative 3D finite element model (FEM) for intracorneal ring segment (ICRS) implantation and to investigate localized optical changes induced by different ICRS geometries, a hyperelastic shell FEM was developed to compare the effect of symmetric and progressive asymmetric ICRS designs in a generic healthy and asymmetric keratoconic (KC) cornea. The resulting deformed geometry was assessed in terms of average curvature via a biconic fit, sagittal curvature (K), and optical aberrations via Zernike polynomials. The sagittal curvature map showed a locally restricted flattening interior to the ring (Kmax -11 to -25 dpt) and, in the KC cornea, an additional local steepening on the opposite half of the cornea (Kmax up to +1.9 dpt). Considering the optical aberrations present in the model of the KC cornea, the progressive ICRS corrected vertical coma (-3.42 vs. -3.13 µm); horizontal coma (-0.67 vs. 0.36 µm); and defocus (2.90 vs. 2.75 µm), oblique trefoil (-0.54 vs. -0.08 µm), and oblique secondary astigmatism (0.48 vs. -0.09 µm) aberrations stronger than the symmetric ICRS. Customized ICRS designs inspired by the underlying KC phenotype have the potential to achieve more tailored refractive corrections, particularly in asymmetric keratoconus patterns.

Micropolar Elasticity in Physically-Based Animation

We explore micropolar materials for the simulation of volumetric deformable solids. In graphics, micropolar models have only been used in the form of one-dimensional Cosserat rods, where a rotating frame is attached to each material point on the one-dimensional centerline. By carrying this idea over to volumetric solids, every material point is associated with a microrotation, an independent degree of freedom that can be coupled to the displacement through a material's strain energy density. The additional degrees of freedom give us more control over bending and torsion modes of a material. We propose a new orthotropic micropolar curvature energy that allows us to make materials stiff to bending in specific directions. For the simulation of dynamic micropolar deformables we propose a novel incremental potential formulation with a consistent FEM discretization that is well suited for the use in physically-based animation. This allows us to easily couple micropolar deformables with dynamic collisions through a contact model inspired from the Incremental Potential Contact (IPC) approach. For the spatial discretization with FEM we discuss the challenges related to the rotational degrees of freedom and propose a scheme based on the interpolation of angular velocities followed by quaternion time integration at the quadrature points. In our evaluation we validate the consistency and accuracy of our discretization approach and demonstrate several compelling use cases for micropolar materials. This includes explicit control over bending and torsion stiffness, deformation through prescription of a volumetric curvature field and robust interaction of micropolar deformables with dynamic collisions.

Statistical analysis of discrete dislocation dynamics simulations: initial structures, cross-slip and microstructure evolution

Over the past decades, discrete dislocation dynamics simulations have been shown to reliably predict the evolution of dislocation microstructures for micrometer-sized metallic samples. Such simulations provide insight into the governing deformation mechanisms and the interplay between different physical phenomena such as dislocation reactions or cross-slip. This work is focused on a detailed analysis of the influence of the cross-slip on the evolution of dislocation systems. A tailored data mining strategy using the ‘discrete-to-continuous (D2C) framework’ allows to quantify differences and to quantitatively compare dislocation structures. We analyze the quantitative effects of the cross-slip on the microstructure in the course of a tensile test and a subsequent relaxation to present the role of cross-slip in the microstructure evolution. The precision of the extracted quantitative information using D2C strongly depends on the resolution of the domain averaging. We also analyze how the resolution of the averaging influences the distribution of total dislocation density and curvature fields of the specimen. Our analyzes are important approaches for interpreting the resulting structures calculated by dislocation dynamics simulations.

Comparison of visual performance and image quality between a myopia-control contact lens and a single-vision contact lens

ObjectiveThis study aimed to evaluate the visual performance and image quality of concentric dual-focus-designed contact lenses (CLs) compared with single-vision CLs in myopic Chinese people. MethodsTwenty myopic volunteers aged between 18 and 26 years were recruited at a university eye hospital to wear both defocus-incorporated soft contact (DISC) lenses and single-vision CLs for 1 week in random order. High- and low-contrast visual acuity (VA), contrast sensitivity (CS), ocular higher-order aberrations (HOA), Strehl ratio and the Quality of Vision (QoV) questionnaire were assessed with each type of CL at weekly follow-up. ResultsDistance VA was not affected by DISC lenses compared to single-vision CLs in either high (p = 0.414) or low contrast (p = 0.431). However, there was a significant reduction in low-contrast near VA with DISC lenses compared with single-vision CLs (p = 0.011). The differences of CS between DISC lenses and single-vision CLs were significantly associated with lighting conditions and spatial frequencies (F = 128.81, P < 0.001). Compared with single-vision CLs, wavefront aberrations of DISC lenses were significantly increased in total HOA, trefoil, and spherical aberrations for either 3.0 mm or 6.0 mm pupil size. The Strehl ratio wearing DISC lenses reduced significantly compared to the single-vision CLs (p < 0.001) at a pupil diameter of 6.0 mm. QoV scores were higher overall (p = 0.026) and frequency (p = 0.019) with DISC lenses than with single-vision CLs, indicating poorer visual performance. ConclusionDISC lenses provide satisfactory distance VA. However, the higher scores of the QoV questionnaire with DISC lenses may be related to decreased CS at medium or high spatial frequencies and increased higher-order aberrations.

Efficacy of estimations of Hartmann-Shack sensors in small pupil sizes.

The purpose of this study was to evaluate the in vivo efficacy of the estimations of wavefront analyzers using Hartmann-Shack technology to measure optical aberrations when the pupil size is smaller than the evaluated pupil area. Patients implanted with the monofocal ZCB00 intraocular lens (Johnson and Johnson) were examined with the KR-1W Wavefront Analyzer (Topcon) without pharmacological mydriasis and with it afterward. Optical aberrations were analyzed considering a 4-mm pupil and a 6-mm pupil for both examinations. Sixty-six eyes of 33 patients with a mean axial length of 23.35 ± 0.91 mm were assessed. The mean pupil diameter at the baseline examination was 5.05 ± 0.88 mm and under pharmacological mydriasis, it was 6.29 ± 0.84 mm. Outcomes were similar with and without dilation in the 4-mm comparison. However, there was a great disparity in the 6-mm comparison. Most of the values obtained under mydriasis were statistically lower than at baseline (P < 0.05). The iris interferes with measurements of wavefront aberrations, and therefore, real pupil size should always be checked before evaluating optical aberrations with Hartman-Shack sensors. When pupil size is smaller than the analyzed diameter, ocular, and internal, and sometimes, corneal aberrations are estimated far more positive than real values.

Measurement of linear shear through optical vortices in digital shearing speckle pattern interferometry.

Digital shearing speckle pattern interferometry (DSSPI) is a powerful interferometric technique used to visualize the slope contours undergoing static and dynamic deformations. Precise determination of the shear amount is crucial for quantitative analysis in DSSPI. However, accurately measuring the shear amount is often challenging due to factors such as optical device dimensions, deflections, aberrations, and misalignments. In this paper, we propose a novel method utilizing optical vortices deflection in pseudo-phase for shear measurement. This method eliminates the need for attaching calibration objects and replacing the light source, making it applicable to inaccessible or fragile samples. Experimental results demonstrate the effectiveness and accuracy of the proposed method in determining shear amounts in DSSPI. The method can be easily automated and integrated into existing setups, offering broader application prospects.

DAQE: Enhancing the Quality of Compressed Images by Exploiting the Inherent Characteristic of Defocus

Image defocus is inherent in the physics of image formation caused by the optical aberration of lenses, providing plentiful information on image quality. Unfortunately, existing quality enhancement approaches for compressed images neglect the inherent characteristic of defocus, resulting in inferior performance. This paper finds that in compressed images, significantly defocused regions have better compression quality, and two regions with different defocus values possess diverse texture patterns. These observations motivate our defocus-aware quality enhancement (DAQE) approach. Specifically, we propose a novel dynamic region-based deep learning architecture of the DAQE approach, which considers the regionwise defocus difference of compressed images in two aspects. (1) The DAQE approach employs fewer computational resources to enhance the quality of significantly defocused regions and more resources to enhance the quality of other regions; (2) The DAQE approach learns to separately enhance diverse texture patterns for regions with different defocus values, such that texture-specific enhancement can be achieved. Extensive experiments validate the superiority of our DAQE approach over state-of-the-art approaches in terms of quality enhancement and resource savings.

Third-order aberration analysis of a Fresnel lens

This paper presents expressions for the third-order aberrations of a Fresnel surface (Seidel coefficients). The formulas are derived in a form that allows analytical aberration analysis to be performed at the stage of layout and preliminary design of a system composed of both classical and Fresnel surfaces. In addition to the five major monochromatic Seidel aberrations of the classical surfaces and the line coma which was described for the Fresnel-type surfaces, another aberration, called quadratic astigmatism, is described in this paper. Although the obtained expressions are an approximation for the third-order aberration domain, i.e. higher-order aberrations are ignored, they provide sufficient accuracy in practice, which is also shown in the paper. The derived expressions can be applied to the analysis of aberrations in schemes using a Fresnel lens, which makes it possible to identify the areas of rational use of elements of this type.

Alvarez varifocal X-ray lens

Visible light optical elements such as lenses and mirrors have counterparts for X-rays. In the visible regime, a variable focusing power can be achieved by an Alvarez lens which consists of a pair of inline planar refractors with a cubic thickness profile. When the two refractors are laterally displaced in opposite directions, the parabolic component of the wavefront is changed resulting in a longitudinal displacement of the focus. This paper reports an implementation of this concept for X-rays using two planar microfabricated refractive elements. The Alvarez X-ray lens can vary the focal distance of an elliptical X-ray mirror or a planar compound X-ray lens over several millimetres. The study presents the first demonstration of an Alvarez X-ray lens which adaptively corrects defocus and astigmatism aberrations of X-ray optics. In addition, the Alvarez X-ray lens eliminates coma aberration in an elliptical mirror, to the lowest order, when combining the lens with an adjustment of the pitch angle of the mirror.

Evolved design for telecentric optical systems based on particle swarm optimization and semi-supervised learning

Finite-distance systems are used extensively in the field of machine vision, and engineers need to rely on experience and mathematical basis to design such systems. In this paper, an evolved design method for finite-distance optical systems (telecentric systems) based on particle swarm optimization and semi-supervised learning is proposed. The method establishes a function value based on the Seidel aberration equation and innovatively introduces the Head-To-Tail method to generate the high-quality initial dataset in bulk. The feasibility of the method is verified with an example, and the user only needs to determine the magnification, working distance and NA to obtain a telecentric optical system directly. In this way, the time cost of searching for the initial structure and continuous trying is greatly reduced, and the design threshold is lowered. Meanwhile, it has a positive effect on shortening the design cycle of the whole lens and leaving a surplus for processing.

Dynamic correction of optical aberrations for height-independent selective laser induced etching processing strategies.

Optical aberrations are a critical issue for tight focusing and high precision manufacturing with ultrashort pulsed laser radiation in transparent media. Controlling the wave front of ultrashort laser pulses enable the correction of low order phase front distortion and significantly enhances the simplification of laser-based manufacturing of 3D-parts in glass. The influence of system-inherent, dominating aberrations such as spherical and astigmatic aberrations affect the focal area, the beam caustic and therefore the focus intensity distribution. We correct these aberrations by means of a spatial light modulator (SLM) for various processing depths in glass thickness of up to 12 mm. This flexible aberration correction significantly simplifies the process control and scanning strategies for the selective laser induced etching process. The influence on the selectivity is investigated by comparing the three different focus conditions of the intrinsic microscope objective aberration corrected, the aberrated and the SLM aberration corrected beam profile. The previously necessary pulse energy adjustment for different z positions in the glass volume is compensated via SLM aberration correction in the end. Furthermore, the spatial extend of the modified and etched area is investigated. In consequence, a simplified scan strategy and depth-independent processing parameters can be achieved for the selective laser induced etching process.

Propagation-based phase-contrast imaging method for full-field X-ray microscopy using advanced Kirkpatrick-Baez mirrors.

We demonstrate a propagation-based phase-contrast imaging method for full-field X-ray microscopy based on advanced Kirkpatrick-Baez (AKB) mirrors to achieve high-contrast observations of weak phase objects and correct field curvature aberrations. Through a demonstration performed at SPring-8, the phase contrast of weak phase objects such as polystyrene spheres and chemically fixed cells was successfully observed with high sensitivity (∼0.03 rad). Furthermore, the field of view of the AKB mirrors was expanded to the full area of the obtained images (25 × 30 µm) by correcting the field curvature aberration using reconstructed complex wavefields.

Diameter estimates for submanifolds in manifolds with nonnegative curvature

Given a closed connected manifold smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we estimate the intrinsic diameter of the submanifold in terms of its mean curvature field integral. On the other hand, for a compact convex surface with boundary smoothly immersed in a complete noncompact Riemannian manifold with nonnegative sectional curvature, we can estimate its intrinsic diameter in terms of its mean curvature field integral and the length of its boundary. These results are supplements of previous work of Topping, Wu-Zheng and Paeng.