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Paraxial diffraction modeling based on the Fourier transform has seen widespread implementation for simulating the response of a diffraction-limited optical system. For systems where the paraxial assumption is not sufficient, a class of algorithms has been developed that employs hybrid propagation physics to compute the propagation of an elementary beamlet along geometric ray paths. These "beamlet decomposition" algorithms include the well-known Gaussian beamlet decomposition (GBD) algorithm, of which several variants have been created. To increase the computational efficiency of the GBD algorithm, we derive an alternative expression of the technique that utilizes the analytical propagation of beamlets to tilted planes. We then use this accelerated algorithm to conduct a parameter-space search to find the optimal combination of free parameters in GBD to construct the analytical Airy function. The experiment is conducted on a consumer-grade CPU, and a high-performance GPU, where the new algorithm is 34 times faster than the previously published algorithm on CPUs, and 67,513 times faster on GPUs.

Serum lipid levels have been associated with an increased risk of suicidal behaviors. This retrospective cohort study aimed to investigate the association between serum lipid levels and death by suicide among suicide attempters according to sex. Suicide attempters visiting emergency departments between 2007 and 2011 were followed up until the date of all-cause death or December 31, 2012. Sex-stratified Cox proportional hazards regression and competing risk models were constructed to obtain the hazard ratios (HR) of serum lipid measures and suicide. For each significant lipid variable in the final models, Kaplan-Meier survival analysis and cumulative incidence function (CIF) were employed to compare the time to suicide between the high- and low-lipid groups based on the best cutoff point from the receiver operating characteristic curve. In 408 female attempters (65.8 %), the HR in the Cox regression model and subdistribution HR in the competing risk model for increased total cholesterol (TC) were 0.968 and 0.970, respectively. In the Kaplan-Meier survival analysis and CIF, increased death by suicide was demonstrated in the low-TC group (< 165 mg/dL). Lower serum TC levels among female suicide attempters may predict suicide. More careful monitoring is warranted in women with lower TC levels who recently attempted suicide., Competing Interests: Declaration of competing interest None., (Copyright © 2024. Published by Elsevier B.V.)

Deterministic computer-controlled optical finishing is an essential approach for achieving high-quality optical surfaces. Its determinism and convergence rely heavily on precise and smooth motion control to guide the machine tool over an optical surface to correct residual errors. One widely supported and smooth motion control model is position-velocity-time (PVT), which employs piecewise cubic polynomials to describe positions. Our prior research introduced a PVT-based velocity scheduling method, demonstrating sub-nanometer level convergence in ion beam figuring (IBF) processes. However, three challenges remained. Firstly, this method relies on quadratic programming, resulting in computational intensiveness for dense tool paths. Secondly, the dynamics constraints and velocity and acceleration continuities are not comprehensively considered, limiting the full potential of PVT-based control. Thirdly, no compensation mechanism existed when dynamics constraints are exceeded. In this study, in response to these challenges, we proposed the Enhanced PVT (E-PVT) method, reducing the time complexity from O(n 3 ) to O(n) while fully addressing dynamics constraints and continuities. A novel compensation method utilizing particle swarm optimization was proposed to address situations where dynamics constraints might be exceeded while maintaining the overall processing efficiency. Validation through simulation and experimentation confirmed the improved performance of E-PVT.

In interferometry measurement, the retrace error often limits its high-precision metrology applications. Retrace error calibration with tilted flats can give a relation between the retrace error and the introduced tilt angles, but there is still an ambiguity between the introduced tilt angles and the tilt terms in the created retrace error. We propose a novel, to the best of our knowledge, two-step calibration method to resolve this tilt ambiguity. It involves additional measurements of spherical mirror(s) with known curvature(s). The experiment shows that the curvature deviation due to the tilt ambiguity can be significantly reduced after applying the proposed method.

Metasurfaces, optics made from subwavelength-scale nanostructures, have been limited to millimeter-sizes by the scaling challenge of producing vast numbers of precisely engineered elements over a large area. In this study, we demonstrate an all-glass 100 mm diameter metasurface lens (metalens) comprising 18.7 billion nanostructures that operates in the visible spectrum with a fast f -number ( f /1.5, NA = 0.32) using deep-ultraviolet (DUV) projection lithography. Our work overcomes the exposure area constraints of lithography tools and demonstrates that large metasurfaces are commercially feasible. Additionally, we investigate the impact of various fabrication errors on the imaging quality of the metalens, several of which are specific to such large area metasurfaces. We demonstrate direct astronomical imaging of the Sun, the Moon, and emission nebulae at visible wavelengths and validate the robustness of such metasurfaces under extreme environmental thermal swings for space applications.

The manufacturing and characterization of freeform optical surfaces are influenced by their high sensitivity to misalignments. In this work, the computational sampling moiré technique combined with phase extraction is developed for the precise alignment of freeform optics during fabrication and in metrology applications. This novel, to the best of our knowledge, technique achieves near-interferometry-level precision in a simple and compact configuration. This robust technology can be applied to industrial manufacturing platforms (such as diamond turning machines, lithography, and other micro-nano-machining techniques) as well as their metrology equipment. In a demonstration of computational data processing and precision alignment using this method, iterative manufacturing of freeform optical surfaces with a final-form accuracy of about 180 nm was accomplished.

We introduce a method of geometric screen modification to remove ghost reflections commonly observed in deflectometry optical testing. The proposed method modifies the optical layout and illumination source area to bypass the generation of reflected rays from the undesired surface. The layout flexibility of deflectometry allows us to design specific system layouts that avoid the generation of interrupting secondary rays. The proposed method is supported by optical raytrace simulations, and experimental results are demonstrated with convex and concave lens case studies. Finally, the limitations of the digital masking method are discussed.

Grazing-incidence reflective optics are commonly used in synchrotron radiation and free-electron laser facilities to transport and focus the emitted X-ray beams. To preserve the imaging capability at the diffraction limit, the fabrication of these optics requires precise control of both the residual height and slope errors. However, all the surface figuring methods are height based, lacking the explicit control of surface slopes. Although our preliminary work demonstrated a one-dimensional (1D) slope-based figuring model, its 2D extension is not straightforward. In this study, a novel 2D slope-based figuring method is proposed, which employs an alternating objective optimization on the slopes in the x- and y-directions directly. An analytical simulation revealed that the slope-based method achieved smaller residual slope errors than the height-based method, while the height-based method achieved smaller residual height errors than the slope-based method. Therefore, a hybrid height and slope figuring method was proposed to further enable explicit control of both the height and slopes according to the final mirror specifications. An experiment to finish an elliptical-cylindrical mirror using the hybrid method with ion beam figuring was then performed. Both the residual height and slope errors converged below the specified threshold values, which verified the feasibility and effectiveness of the proposed ideas., (open access.)

OASIS (Orbiting Astronomical Satellite for Investigating Stellar Systems) is a space-based observatory with a 14 m diameter inflatable primary antenna that will perform high spectral resolution observations at terahertz frequencies. The large inflatable aperture, non-traditional surface configuration, and the double layered membrane structure afford unique challenges to the modeling and testing of the primary antenna. A 1-meter prototype of the primary antenna (A1) was built to validate our technical approach. A laser radar coordinate measuring system was adopted to measure the shape of A1. In addition, deflectometry was performed to monitor the stability of A1 during the radar measurement. Test cases pertaining to specific operational conditions expected for the 14 m OASIS primary were explored. The measured data were then compared to the Fichter model and Finite-element Analyzer for Inflatable Membranes (FAIM).

We introduce an on-axis deflectometry test configuration for axicon metrology. Axicons are challenging to measure due to their characteristically steep, convex geometry. However, if an axicon is coaxially aligned with a camera and a surrounding cylindrical illumination source, high-resolution surface measurements can be obtained via the principle of deflectometry. Emitted from the temporally modulated source, light deflects at the conical surface and into the entrance pupil of a camera, illuminating the full axicon aperture except the ø 0.5-mm rounded tip. Deflectometry measurements of a 100° and 140° axicon show holistic cone angle agreement within 0.035° against touch probe data and up to 7.93 root μ m mean square difference from a best-fit cone. We discuss the non-planar illumination architecture, sensitivity, and experimental results of arbitrary apex angle axicons.

Deterministic optics fabrication using sub-aperture tools has been vital for manufacturing precision optical surfaces. The fabrication process requires the tool influence function and the tool path to calculate the dwell time that guides the tool to bring surface quality within tight design tolerances. Widely used spiral and raster paths may leave excess waviness from the tool path, and the unavoidable constant removal layer is added to obtain positive dwell time. This waviness can be removed by either using smaller tools sequentially or randomizing the tool path. However, the existing tool-path solutions can hardly adapt to different surface aperture shapes and localized surface errors. Process efficiency and accuracy are also not well considered in tool-path planning. We propose an innovative zonal Random Adaptive Path (RAP) to solve these problems in this study. Firstly, RAP can be flexibly adapted to different surface aperture shapes by introducing part boundary. Secondly, an average threshold strategy is used in the RAP planning to improve efficiency, enabling the surface errors to be selectively corrected. Finally, the threshold is performed in several passes within one processing cycle, each with its RAP, until the desired residual is achieved. The performance of the proposed RAP is studied by comparing it with the conventional tool paths. The results demonstrated that RAP takes the least processing time and achieves the best surface quality, which verifies the effectiveness of RAP in deterministic optics fabrication.

The surface quality of optical lenses is highly required in imaging functions. Normally, ultra-precision turning is employed to fabricate the optical lenses. However, ultra-precision turning cannot meet the surface quality demands due to the tool marks. In this study, a new damping-clothed (DC) tool and chemical enhanced non-Newtonian ultrafine (CNNU) slurry for non-contact polishing are proposed to achieve sub-nanometer roughness on aspherical optical molds. A material removal model based on the hydrodynamic pressure and velocity simulation was established to calculate the dwell time in curved surface machining. The formation mechanism of sub-nanometer roughness is clarified. The proposed method and slurry were verified by the experiments in processing NiP alloy aspheric optical mold. After the process, surface roughness Sa achieved 0.54 nm and the form accuracy is less than PV 600 nm.

With the rapid development of precision technologies, the demand of high-precision optical surfaces has drastically increased. These optical surfaces are mainly fabricated with computer controlled optical surfacing (CCOS). In a CCOS process, a target surface removal profile is achieved by scheduling the dwell time for a set of machine tools. The optimized dwell time should be positive and smooth to ensure convergence to the target while considering CNC dynamics. The total run time of each machine tool is also expected to be balanced to improve the overall processing efficiency. In the past few decades, dwell time optimization for a single machine tool has been extensively developed. While the methods are applicable to multi-tool scenarios, they fail to consider the overall contributions of multiple tools simultaneously. In this paper, we conduct a systematic study on the strategies for multi-tool dwell time optimization and propose an innovative method for simultaneously scheduling dwell time for multiple tools for the first time. First, the influential factors to the positiveness and smoothness of dwell time solutions for a single machine tool are analyzed. The compensation strategies that minimize the residual while considering the CNC dynamics limit are then proposed. Afterwards, these strategies are extended to the proposed multi-tool optimization that further balances the run time of machine tools. Finally, the superiority of each strategy is carefully studied via simulation and experiment. The experiment is performed by bonnet polishing a 60 mm × 60 mm mirror with three tools of different diameters (i.e., 12 mm, 8 mm, and 5 mm). The figure error of the mirror is reduced from 45.42 nm to 11.18 nm root mean square in 13.28 min. Moreover, the measured polishing result well coincides with the estimation, which proves the effectiveness of the proposed method.

Computer Controlled Optical Surfacing (CCOS) is widely applied for fabricating large aspheric optical surfaces. For large optics fabrication, various sizes of polishing tools are used sequentially. This raises the importance of efficient and globally optimized dwell time map of each tool. In this study, we propose a GEnetic Algorithm-powered Non-Sequential (GEANS) optimization technique to improve the feasibility of the conventional non-sequential optimization technique. GEANS consists of two interdependent parts: i) compose an influence matrix by imposing constraints on adjacent dwell points and ii) induce the desired dwell time map through the genetic algorithm. CCOS simulation results show that GEANS generates a preferable dwell time map that provides high figuring efficiency and structural similarity with the shape of target removal map, while improving computational efficiency more than 1000 times over the conventional non-sequential optimization method. The practicability of GEANS is demonstrated through error analyses. Random tool positioning error and tool influence function errors are imposed on dwell time maps. Compared to the conventional non-sequential optimization method, the power spectral density values of residual surface error from GEANS remain stable. GEANS also shows superior applicability when the maximum acceleration of a tool is applied.

A radial shearing dynamic wavefront sensor is theorized and experimentally verified. The proposed sensor is based on a geometric phase lens pair that generates two radially sheared wavefronts. A polarization pixelated camera instantaneously obtains polarization-multiplexed phase maps from a single acquired image using a spatial phase-shifting technique. Experimental tests applied several wavefront shapes with a deformable mirror. The results were compared with a Shack-Hartmann wavefront sensor to evaluate the performance.

One of deflectometry's cardinal strengths is its ability to measure highly dynamically sloped optics without needing physical null references. Accurate surface measurements using deflectometry, however, require precise calibration processes. In this Letter, we introduce an alignment technique using a computational fiducial to align a deflectometry system without additional hardware equipment (i.e., algorithmic innovation). Using the ray tracing program, we build relationships between the plane of the screen and detector and algorithmically generate a fiducial pattern for the deflectometry configuration. Since the fiducial pattern is based on ideal system geometry, misalignment of the unit under test with its target position causes a discrepancy between the actual image on the camera detector and the ideal fiducial image. We leverage G and C vector polynomials to quantify misalignment and estimate the alignment status through a reverse optimization method. Simulation and experimental results demonstrate that the proposed algorithm can align the 195 m m ×80 m m of a rectangular aperture freeform optic within 10 µm of peak-to-valley accuracy. The computational fiducial-based alignment algorithm is simple to apply and can be an essential procedure for conventional methods of deflectometry system alignment.

Computer-Controlled Optical Surfacing (CCOS) has been greatly developed and widely used for precision optical fabrication in the past three decades. It relies on robust dwell time solutions to determine how long the polishing tools must dwell at certain points over the surfaces to achieve the expected forms. However, as dwell time calculations are modeled as ill-posed deconvolution, it is always non-trivial to reach a reliable solution that 1) is non-negative, since CCOS systems are not capable of adding materials, 2) minimizes the residual in the clear aperture 3) minimizes the total dwell time to guarantee the stability and efficiency of CCOS processes, 4) can be flexibly adapted to different tool paths, 5) the parameter tuning of the algorithm is simple, and 6) the computational cost is reasonable. In this study, we propose a novel Universal Dwell time Optimization (UDO) model that universally satisfies these criteria. First, the matrix-based discretization of the convolutional polishing model is employed so that dwell time can be flexibly calculated for arbitrary dwell points. Second, UDO simplifies the inverse deconvolution as a forward scalar optimization for the first time, which drastically increases the solution stability and the computational efficiency. Finally, the dwell time solution is improved by a robust iterative refinement and a total dwell time reduction scheme. The superiority and general applicability of the proposed algorithm are verified on the simulations of different CCOS processes. A real application of UDO in improving a synchrotron X-ray mirror using Ion Beam Figuring (IBF) is then demonstrated. The simulation indicates that the estimated residual in the 92.3 mm × 15.7 mm CA can be reduced from 6.32 nm Root Mean Square (RMS) to 0.20 nm RMS in 3.37 min. After one IBF process, the measured residual in the CA converges to 0.19 nm RMS, which coincides with the simulation.

A polarized imaging interpreter to simultaneously measure rotational angles of multiple objects is proposed and experimentally verified. Based on the multiplexed optical configuration using a polarization pixelated camera, the proposed sensor has the unique feature to precisely monitor the standard and the non-standard clocking motions in static or dynamic applications at once.

Neuropathic pain is a chronic pain state characterized by nerve damage, inflammation, and nociceptive neuron hyperactivity. As the underlying pathophysiology is complex, a more effective therapy for neuropathic pain would be one that targets multiple elements. Here, we generated recombinant adeno-associated viruses (AAVs) encoding three therapeutic genes, namely, glutamate decarboxylase 65 , glial cell-derived neurotrophic factor , and interleukin-10 , with various combinations. The efficacy for pain relief was evaluated in a rat spared nerve injury model of neuropathic pain. The maximal analgesic effect was achieved when the AAVs expressing all three genes were administered to rats with neuropathic pain. The combination of two virus constructs expressing the three genes was named KLS-2031 and evaluated as a potential novel therapeutic for neuropathic pain. Single transforaminal epidural injections of KLS-2031 into the intervertebral foramen to target the appropriate dorsal root ganglion produced notable long-term analgesic effects in female and male rats. Furthermore, KLS-2031 mitigated the neuroinflammation, neuronal cell death, and dorsal root ganglion hyperexcitability induced by the spared nerve injury. These results suggest that KLS-2031 represents a promising therapeutic option for refractory neuropathic pain., (© 2020 The Authors.)

Background: The epidemiology of pharmaceutically treated depression (PTD) and treatment resistant depression (TRD) is largely unknown in South Korea. The aim of this study was to develop a greater understanding of the characteristics of PTD and TRD in nearly the entire adult population in South Korea using the Health Insurance Review and Assessment Service (HIRA)., Method: Diagnostic codes and prescription data for South Korean adults were extracted from the HIRA. Subjects were included in the PTD cohort if they received at least one prescription for antidepressants and were diagnosed with depression. TRD was defined as PTD having two or more regimen failures of antidepressants or antipsychotics., Results: In 2012, there were 41,256,396 adults in South Korea with 834,694 meeting the criteria for PTD (2.0%). Among subjects with PTD, 57% stopped treatment in less than 28 days of antidepressant supply. Tricyclic and tetracyclic antidepressants were the most frequently used antidepressants as a first-line regimen for PTD (44.3% of PTD) followed by selective serotonin reuptake inhibitors (32.1% of PTD). Results also indicated that 34,812 subjects developed TRD (4.2% of PTD). Median PTD and TRD durations were 28 and 623 days respectively. Proportions of psychiatric and non-psychiatric comorbidities were higher in TRD cases than in PTD cases that were not treatment resistant., Conclusions: Despite a small proportion of patients with TRD, the prolonged duration of illness and higher comorbidity implies the need for better treatment., Competing Interests: G.C and M.K are employees of Janssen Korea. They were involved in the study design. Other authors declare no conflict of interests.

Identifying predictors of planned suicide attempts (PSA) is critical because these are associated with grave consequences. Using data of suicide attempters visiting emergency departments, we investigated whether the Columbia-Suicide Severity Rating Scale (C-SSRS) subscales, by retrospectively evaluating ideation before an attempt, could predict the occurrence of PSA versus unplanned suicide attempts using logistic regression analyses. The severity subscale was used as a continuous (model A) and a categorical (model B) variable. In model A, higher scores on each subscale were associated with increased risk of PSA. In model B, the highest score on the severity subscale and a higher intensity subscale score predicted PSA. The severity and intensity subscales had areas under receiver operating curves of 0.712 and 0.688 with optimum cutoff points of 4/5 and 15/16, respectively. In addition, being aged 30 to 49 and 50 to 69 years, being male, interpersonal stress, and depressive and adjustment disorders increased PSA risk. The C-SSRS subscales, along with sociodemographic and clinical risk factors, can predict PSA.

The first objective of this paper is to prove the existence and uniqueness of global solutions for a Kirchhoff-type wave equation with nonlinear dissipation of the form Ku'' + M(|A (1/2) u|(2))Au + g(u') = 0 under suitable assumptions on K, A, M(·), and g(·). Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation g. Lastly, numerical simulations in order to verify the analytical results are given.