Field Aberrations Research Articles

Experimental study for a field diversity phase retrieval wavefront sensing approach

Field diversity wavefront sensing is one of the image-based wavefront methods, where the intensity measurements with phase diversities are directly obtained from different field positions of one image, without the need for any additional instruments (e.g., beam splitter) or operations (e.g., focus adjusting). While the phase diversities between different positions are unknown to us, this method is realized based on an in-depth understanding of the net aberration fields induced by misalignments and figure errors. However, this novel, to the best of our knowledge, image-based wavefront sensing method has not been experimentally studied, which restricts the application and promotion of this method. In this work, the analytic gradient of the field diversity wavefront sensing is derived, and the accuracy and effectiveness of this method in the active alignment of real three-mirror anastigmatic (TMA) optical systems are systematically demonstrated. The results show that this method can be applicable to wavefront sensing of large space telescopes.

Research on the influence law of geomagnetic field on magnetic signals and compensation modeling

To study the influence law and mechanism of the geomagnetic field on magnetic signals in the process of magnetic memory testing, the linear scanning detection results of defective specimens with three different initial magnetization strengths (0 A/m, −70 A/m, 105 A/m) along the horizontal and vertical directions in the geomagnetic field ambient are analyzed and discussed. The result shows that the magnetic signals in the defect-free region only change in amplitude with the change of detection angle, and have no effect on the overall shape of the magnetic signal curve; the characteristic parameters Sm and Km of the peaks of the magnetic signals in the defective region show a corresponding relationship with the measurement angle in the horizontal detection. The initial magnetization strength of the specimen itself affects the change rule of the defective characteristic peaks. The mechanism analysis reveals that the extracted magnetic signals are affected by the combination of the geomagnetic field, the induced magnetic field of the specimen itself, and the leakage magnetic field. Finally, aiming at the problem that the geomagnetic field will change the topography of the defect peaks along different detection orientations, a geomagnetic compensation model is proposed for the barrel-shaped equipment when performing circumferential scanning detection, which can reduce the interference of the geomagnetic field aberration on the detection results, to prevent the misjudgment and omission of the specimen’s defect location.

Revolutioning Lens-Based Systems Design: Showcasing the power of OptiMat

OptiMat, by Sagittal Optics, is a tool developed to generate spherical designs for color-corrected lens-based systems. OptiMat analytically achieves optimum optical materials selection, key to correcting chromatic aberration. However, this tool extends beyond material selection; it is also used to establish initial systems in the design process, which optical designers can further refine. By selecting from a catalog of materials and specifying the number of lenses in the system, optical designers receive ideal assemblies correcting chromaticity, spherical and field aberrations, together with a set of parameters to further improve the provided systems. Additionally, engineers can filter combinations based on different metrics, such as chromatic and monochromatic aberrations. By handling material selection and lens shaping at the project's outset, OptiMat significantly streamlines optical system design times.

Sigma vector calculations in nodal aberration theory and experimental validation using a Cassegrain telescope

Nodal Aberration Theory (NAT) was developed to explain the field dependency of aberration field centers in the image plane of nominally rotationally symmetric optical systems that have lost their symmetry through misalignments. A new insight into the theory led to calculating the sigma vectors, which locate the aberration field centers, using the angle between a real-ray trace of the optical axis ray (OAR) and the normal of the local surface where “local” refers to the object and image optical spaces of that surface. Here, we detail the sigma vector calculations for general optical systems and provide an experimental investigation of a misaligned system with a high-precision customized Cassegrain telescope. In the simulations, a Newtonian telescope, a Cassegrain telescope, and a three-mirror anastigmat telescope were misaligned intentionally in ray-tracing software. The sigma vectors were calculated analytically for the third-order aberrations of astigmatism and coma. Experimentally, the same perturbations were implemented for the Cassegrain telescope system, and the aberrations were quantified through interferometric measurements on a grid of field points in the image plane that verified the analytical derivation and simulations.

Nonlinear Resonance in Dual-Frequency Paul Trap on Account of Hexapole Field Aberrations

Nonlinear Resonance in Dual-Frequency Paul Trap on Account of Hexapole Field Aberrations

Active Alignment of Large-Aperture Space Telescopes for Optimal Ellipticity Performance

Ellipticity performance of space telescopes is important for exploration of dark matter. However, traditional on-orbit active optical alignment of space telescopes often takes “minimum wavefront error across the field of view” as the correction goal, and the ellipticity performance after correcting the wave aberration is not optimal. This paper proposes an active optical alignment strategy to achieve optimal ellipticity performance. Based on the framework of nodal aberration theory (NAT), the aberration field distribution corresponding to the optimal full field-of-view ellipticity is determined using global optimization. The degrees of freedom (DOFs) of the secondary mirror and the folded flat mirror are taken as the compensation DOFs to achieve the optimal ellipticity performance. Some valuable insights into aberration field characteristics corresponding to optimal ellipticity performance are presented. This work lays a basis for the correction of ellipticity for complicated optical systems.

TEMGYM Advanced – NanoMi lens characterisation

A complete analysis including finite element method (FEM) calculation, focal length properties, and thirdorder geometric aberrations of the open-source electrostatic lens from the NanoMi project is presented. The analysis is carried out by the software TEMGYM Advanced, a free package developed to carry out ray-tracing and lens characterisation in Python. Previously TEMGYM Advanced has shown how to analyse the aberrations of analytical lens fields; this paper expands upon this work to demonstrate how to apply a suitable fitting method to discrete lens fields obtained via FEM methods so that the aberrations of real lens designs can be calculated. Each software platform used in this paper is freely available in the community and creates a free and viable alternative to commercial lens design packages.

Analysis and correction of misalignment-induced aberrations in two-mirror telescopes with stop on the secondary mirror.

We study the problem of misalignment aberration analysis and correction of the two-mirror telescopes with stop on the secondary mirror. The variation law of the system's aberration field is analyzed with nodal aberration theory when the primary mirror with an astigmatic figure error is misaligned. The analytic expression among the system wave aberration, misalignments, and astigmatism figure error is given, and the correction model of system misalignment aberration is established. The simulation experiment shows that the relative error of the prediction of system misalignment coma and astigmatism based on this model is less than 4.1%.

Calculation of aberration fields for freeform imaging systems using field-dependent footprints on local tangent planes.

Aberration theory is a fundamental understanding of the optical aberrations and remains the best way to guide optical system design. The nodal aberration theory, which can be used to describe the aberration fields of freeform imaging systems, is limited by the small field of view (FOV) of the imaging system. In this paper, we propose a method to predict the induced aberration of Fringe Zernike terms with field-dependent footprints. The footprint of each field point is calculated in its corresponding local tangent plane of the optical surface; therefore, a more accurate prediction of the induced aberrations of Fringe Zernike terms can be achieved. Both the FOV and highly tilted architecture of freeform imaging systems are considered when calculating the footprints. Two examples are presented to verify the effectiveness of the proposed method, which we believe can provide good guidance for the design of freeform imaging systems with a relatively large FOV.

Wave Aberration Correction for an Unobscured Off-Axis Three-Mirror Astronomical Telescope Using an Aberration Field Compensation Mechanism

Studying how to use the coupling characteristics of net aberration fields induced by different perturbation parameters to realize the wave aberration compensation correction of perturbed telescopes is of great significance for the development of active optics. Based on nodal aberration theory, this paper studies the wave aberration compensation correction method of an unobscured off-axis three-mirror telescope. Specifically, first of all, it theoretically analyzes the coupling effects and compensation relationships of net aberration fields induced by different perturbation parameters of the telescope. Furthermore, it establishes wave aberration correction models with the secondary mirror as the compensator and the third mirror as the compensator for the telescope, respectively. In the end, it verifies the two compensation correction models by simulations. The results show that the tolerance of the secondary mirror compensation correction mode (SMCM) to the perturbation parameter threshold is significantly better than that of the third mirror compensation correction model (TMCM). When the introduced perturbation parameter threshold is small, the correction accuracy of the two models for the wave aberrations is equivalent, and both reach the order of 10−3λ (RMS, λ = 632.8 nm). When the perturbation parameter threshold is increased, the correction accuracy of SMCM can still be maintained at the order of 10−3λ but the correction accuracy of TMCM would decrease by an order of magnitude.

Non-paraxial diffraction analysis for developing DMD-based optical systems.

We propose a non-paraxial diffraction model of the digital micromirror device (DMD) by combining the conventional Fraunhofer diffraction and a simple method of coordinative mapping. It is equivalent to adding aberrations of diffracted wave fields to the aberration-free Fraunhofer diffraction instead of complex integral calculations, allowing the simulated diffraction patterns to be consistent with the actual experimental counterparts. Moreover, it is verified by the experiments and literature that the diffraction angles, orders, and efficiency can all be well predicted for arbitrary incident angles and wavelengths. Especially for diffracted zenith angles within 50°, the predicted values reveal ∼1% error, and in a broader range, the predicted errors of diffracted azimuth angles are less than 4%. To the best of our knowledge, it is the first model capable of describing the non-paraxial diffraction behavior of the DMD. The proposed model with universality and effectiveness will help users to optimally construct DMD-based optical systems by guiding optical layouts, selection of light sources, and utilization and suppression of diffraction effects.

Improved performance of a hybrid optical/digital imaging system with fast piecewise Wiener deconvolution.

We quantitatively investigate how spatially varying deblurring algorithms can improve the imaging performance of hybrid optical/digital systems affected by field aberrations. To this end, we validate a theoretical model of the maximal gain that linear and spatially varying deblurring can bring to any given lens, and derive a practical algorithm to implement this type of deblurring with low computational complexity. The results demonstrate the usefulness to properly coordinate and balance the roles of the imaging optical system and raw image post-processing: optimal final imaging quality can be obtained by a lens that has been optically designed to reduce field aberrations at the price of lower average raw optical quality, associated with a fast and "slightly" spatially varying piecewise Wiener deconvolution algorithm.

Four-dimensional emittance measurements of ultrafast electron diffraction optics corrected up to sextupole order

Ultrafast electron diffraction (UED) is a technique in which short-pulse electron beams can probe the femtosecond-scale evolution of atomic structure in matter driven far from equilibrium. As an accelerator physics challenge, UED imposes stringent constraints on the brightness of the probe electron beam. The low normalized emittance employed in UED, often at the 10-nm scale and below, is particularly sensitive to both applied field aberrations and space-charge effects. The role of aberrations is increasingly important in small probe systems that often feature multiple orders of magnitude variations in beam size during transport. In this work, we report the correction of normal quadrupole, skew quadrupole, and sextupole aberrations via dedicated corrector elements in an ultrafast electron microdiffraction beamline. To do this, we generate precise four-dimensional phase space maps of rf-compressed electron beams and find excellent agreement with aberration-free space-charge simulations. Finally, we discuss the role a probe-forming aperture can play in improving the brightness of bunches with appreciable space-charge effects.

Two-component compensators of field aberrations of optical systems

Subject of study. Two-component optical schemes of compensators of field aberrations of optical systems calculated based on the third-order aberration theory and modular method of optical system design [Izv. Vyssh. Uchebn. Zaved., Priborostr.57, 57 (2014)] are proposed. These compensators enable correction of two aberrations: Petzval field curvature and astigmatism or longitudinal chromatic aberration and lateral color or transverse chromatic aberration. Method. A modular method for the design of optical systems based on the third-order aberration theory was used in the calculation. This method consists of synthesis of the systems using optical elements (modules) with known correcting properties [Izv. Vyssh. Uchebn. Zaved., Priborostr.57, 57 (2014)]. Aplanatic menisci with different linear magnifications and a hyperchromatic lens were used as optical modules. The aplanatic menisci were used to calculate the compensator of Petzval field curvature and astigmatism, whereas the hyperchromatic lens was used to calculate the compensator of longitudinal and transverse chromatic aberrations. Main results. The use of two-component compensators of field aberrations enables significant enhancements in the aberrational properties of the objectives, improves the image quality of optical systems, and increases their optical parameters, particularly the angular field of doublet objectives (fivefold) using the correcting properties of optical modules (menisci and hyperchromatic lens). Practical significance. The introduction of a compensator composed of two aplanatic menisci positioned at a significant distance from each other into the optical system makes it possible to correct such aberrations as field curvature and astigmatism regardless of the number of lenses in the objective and increase the angular field. The introduction of a compensator of chromatic aberrations into an optical scheme of a high-aperture microscope objective with 100×1.25 oil immersion corrects the longitudinal and transverse chromatic aberrations. This makes it possible to cease the use of compensating eyepieces with a complex optical scheme and replace them with standard eyepieces as well as to use a microscope where the optical radiation is detected by a charge-coupled device array or complementary metal oxide semiconductor detector instead of the human eye.

Alignment algorithm of nonsymmetric off-axis reflective astronomical telescopes based on the modified third-order nodal aberration theory.

For pupil-offset off-axis reflective astronomical telescopes with designed tilts and decenters, owing to the absence of symmetry, axial and lateral misalignments exhibit strong coupling. The astigmatic and coma aberration fields of the misaligned optical systems are not only effected by lateral misalignments but also closely related to axial misalignments. However, the traditional misalignment algorithm based on nodal aberration theory (NAT) usually ignore the effect of axial misalignments on the aberration fields of optical systems when constructing calculation models. As a result, the presence of axial misalignments in pupil-offset off-axis telescopes with designed tilts and decenters will invalidate the traditional NAT-based lateral misalignment algorithm, which makes it difficult to be applied to actual computer-aided alignment experiments. In order to solve this issue, on the framework of modified NAT, third-order astigmatic, third-order coma, and third-order spherical net aberration fields of pupil-offset off-axis systems with designed tilts and decenters induced by axial and lateral misalignments are separated from the total aberration fields, and their inherent relations are analytically expressed. On this basis, in order to construct a solution model that can simultaneously and quantitatively calculate the axial and lateral misalignments, a method is proposed to fit the partial derivative coefficient matrix of misalignments according to field dependence of the net aberrations induced by misalignments. The simulation and actual alignment experiments were performed on a real wide-field off-axis three-mirror telescope using the constructed solution model, which proved the feasibility of the proposed method. Simulation experiments show that for different misalignment conditions generated randomly, both axial and lateral misalignments have achieved convergent solution results. In the actual alignment experiment, the average RMS wavefront errors of the nine field of views is corrected from 1.9 λ to 0.12 λ (λ = 632.8nm) through 3-5 iterations.

Misalignment algorithm of a wide-field survey telescope based on third-order quadratic nodal aberration theory

Off-axis three-mirror anastigmatic (TMA) telescopes with designed decenters and tilts, have many misalignment degrees of freedom and strong coupling between each misalignment degree of freedom. Therefore, it is difficult to establish misalignment equations only using A222 and A131 in nodal aberration theory (NAT). In addition, for off-axis TMA optical systems with designed decenters and tilts, the robustness of the existing fifth-order NAT misalignment calculation algorithm based on high-order Zernike coefficients and boresight errors decreases, so it is difficult to realize its engineering application. To solve the issue of insufficient practicality of the existing misalignment algorithm based on fifth-order NAT, a third-order NAT calculation algorithm based on quadratic aberration field decenter vectors is derived and established. Two concepts of inherent aberration field decenter vector and misalignment aberration field decenter vector are proposed. Taking an off-axis TMA optical system with 6-m focal length as the research object, simulations, and alignment verification experiments were carried out. Compared with the existing fifth-order NAT misalignment algorithm, the results show that when measurement noise is not considered, the two methods can both obtain convergent calculation results, and the average RMS wavefront errors (WFE) of the optical system are both corrected to be below 0.0574 waves. When different levels of measurement noise are introduced, the robustness of the fifth-order NAT misalignment algorithm decreases, and there are even cases where the optical system completely fails to be corrected. However, the algorithm based on quadratic aberration field decenter vectors shows better robustness. Under different levels of measurement noise, this algorithm could correct the average RMS WFE of the optical system to around 0.0574 waves.

An advanced plasmonic photocatalyst containing silver(0) single atoms for selective borylation of aryl iodides

A conventional plasmonic Ag-AgCl photocatalyst consists of Ag nanoparticles (AgNPs) and AgCl. Here, we converted a small amount of Ag+ on the surfaces of AgCl particles into single-atom Ag(0) (SAAg). SAAg was characterized with high-angle annular dark field aberration corrected (HAADF AC)-STEM and quantified with electron spin resonance (ESR). The obtained AgEG/Mg(OH)2 material was efficient and afforded excellent selectivity control between hydrodehalogenation and deiodination-borylation under visible light irradiation. SAAg acted as the 1e−-reducing site of the photocatalyst and its loading is linearly correlated with the initial reaction rate. While the quantity of SAAg was only 6.0 × 10–8 mol g−1, the TOF of SAAg reached 1.4 × 104 h−1. The oxidation state of SAAg retained 0 in both the resting and the working states. This study suggests SAAg may be an effective cocatalyst in general for reductive dehalogenation of organic halides.

Arrayed wide-field astronomical camera system for spectroscopic surveys on Extremely Large Telescopes: system architecture, proof-of-concept, and enabling technologies

The next generation Extremely Large Telescopes (ELTs) are promising a profound transformation of humanity’s understanding of the universe by opening our eyes to a myriad of previously unseen astronomical objects across cosmic space time. Some of the key observational contributions to this transformation will, once again, be made through large-scale ultradeep spectroscopic surveys. Such surveys will call for a wide-field system to expand field of view and correct atmospheric dispersion beyond what an uncorrected ELT is canonically capable of. Although the traditional monolithic form of field correctors served our needs very well on 2- to 8-m class telescopes, we recognize challenges around scaling this traditional design to the ELT level, and hence, as detailed here, present a fundamentally different architecture, called the arrayed wide-field astronomical corrector system or AWACS, for the ELTs of two-mirror construction. The AWACS accomplishes field expansion via an array of small units populated over a telescope’s focal surface, compensating for field aberrations and atmospheric dispersion locally but simultaneously. The AWACS units share one common electro-opto-mechanical design, permitting cost-effective high-volume part manufacturing. We detail the architectural features and proof-of-concept on-sky demonstration of the AWACS. In addition, we highlight our recent development results of randomly nano-textured antireflective (AR) surface structures in terms of an immediately viable, super-broadband, high-performance AR solution for not only the AWACS optics, but also broader ranges of electro-optical devices, particularly those subjected to harsh environments such as high-power laser, cryogenic, and space systems. With continuous advances in other relevant fields, the AWACS is uniquely positioned to enable, either by itself or by complementing traditional correctors, wide-field multi-object spectroscopic surveys in the ELT era and beyond.

Aberration compensation strategy for the radius of curvature error of the primary mirror in off-axis three-mirror anastigmatic telescopes.

This paper discusses compensation strategies for the aberration fields caused by the error in the radius of curvature (ROC) of the primary mirror (PM) in pupil-offset off-axis three-mirror anastigmatic (TMA) astronomical telescopes. Based on the nodal aberration theory framework, the specific astigmatic and coma aberrations of the off-axis three-mirror system in the presence of the ROC error of the PM are derived. It is demonstrated that some field-dependent aberration components can be induced by ROC error in the off-axis TMA telescopes, apart from the dominating field-constant aberration terms. To reduce the influence of the ROC error on the aberration fields, we propose two aberration compensation strategies: adjusting the position of the PM and introducing axial misalignment of the secondary mirror (SM). Through theoretical analysis and simulations, we conclude that the compensation strategy of changing the axial position of the PM can make the aberration distribution close to the nominal state; the compensation strategy of axially adjusting the SM can make the aberration distribution meet the observation requirements, which is more suitable for space applications. We also discuss compensating the effect of the ROC error using lateral misalignments.

Modeling light interference figures and isogyres of uniaxial and biaxial birefringent optical elements

Using polarization fields, light interference figures and isogyres of some uniaxial and biaxial birefringent optical elements are modeled. The effects of diattenuation, and linear and circular birefringence are included, and the Airy spiral is displayed for various cases. The two branches of the Airy spiral are shown to separate and surround separately the melatopes in the case of biaxial elements with linear and circular birefringence. A connection and discussion with the aberration field of astigmatism, in particular binodal, is presented.