Focus Error Research Articles

Comparison of Time and Frequency Domain Solvers for Magnetic Resonance Coils at Different Field Strengths Using a Single Computational Platform

Rapid prototyping and safety assessments are essential in the modern development of radio frequency coils for magnetic resonance imaging. The use of 3D electromagnetic simulations can avoid expensive physical coil prototyping while providing quantities to determine local patient safety which is not measurable in vivo. Currently, 3D electromagnetic simulations are mostly solved on variations of two solver types, namely the time domain and the frequency domain solver. In this work, we compared these solvers and tested key simulation parameters using a single computational platform with state-of-the-art computational methods and computational human models. Our analysis included computational cost, B1+-field and power loss density for a range of common radio frequency setups used at different Larmor frequencies (field strengths, respectively) in magnetic resonance imaging systems. We found that a coarse mesh in a time solver has large unpredictable focal errors (>50%) due to partial volume artifacts while the frequency solver showed more linearity in the errors when reducing computational cost which could allow for more efficient simulations with reduced safety concerns. We expect our work to provide further insights into parameter and solver selection and contribute towards standardization in coil simulation in magnetic resonance imaging.

Effect of hexagonal synthetic aperture on the optical system with focal error

We introduce a new approach by using hexagonal synthetic aperture in an optical system and obtaining a high-resolution image. This paper illustrates two cases of an optical system with a hexagonal synthetic aperture where the study was included, First, study the effect of a hexagonal synthetic aperture on a diffraction-bound optical system, Second, study the effect of hexagonal synthetic aperture on an optical system with a focal error of 25λ and 50λ. The results showed a significant improvement in the central intensity, a clear decrease in the secondary peaks, and a decrease in the width of the central intensity curve, which gives a high-resolution image as a result of improving the signal to noise ratio.

Focal Surface Detection of High Numerical Aperture Objective Lens Based on Differential Astigmatic Method

Defocus detection technology is the key technology in the fields of laser direct writing, optical disc storage, and high-precision lithography, which directly affects the accuracy of line drawing. In this paper, using the principle of astigmatic method, combined with differential technology, a nano-level defocus detection method based on differential astigmatism for the high numerical aperture systems is proposed. Firstly, by establishing a mathematical model, the theoretical analysis and simulation of the defocus detection method based on differential astigmatism are carried out. In addition, the system parameters at the maximum sensitivity of the high numerical aperture defocus detection system is also solved. Secondly, the defocus detection experimental system based on astigmatic method was built for experimental demonstration. Finally, using the objective lens with a numerical aperture of 0.8, the focus error signal curve with a good linear relationship is obtained in this paper. The linear range is 6μm; the system sensitivity can reach 5 nm; the system detection accuracy is 30 nm, and the repeat positioning accuracy can reach 30 nm. The defocus detection method based on the high numerical aperture objective lens has the advantages of large detection range, high detection accuracy and compact system structure, which can be widely used in various new high-precision laser processing fields.

Multiobjective Statistical Learning Optimization of RGB Metalens

Modelling of multi-wavelength metasurfaces relies on adjusting the phase of indi-vidual nanoresonators at several wavelengths.The traditional procedure neglects thenear-field coupling between the nanoresonators, which dramatically reduces the over-all diffraction efficiency, bandwidth, numerical aperture and device diameter.Anotheralternative design strategy is to combine a numerical optimization technique with full-wave simulations to mitigate this problem and optimize the entire metasurface at once.Here, we present a global multiobjective optimization technique that utilizes statisticallearning method to optimize RGB spherical metalenses at the visible wavelengths. Theoptimization procedure, coupled to a high-order full-wave solver, accounts for the nearfield coupling between the resonators. High numerical aperture RGB lenses(NA= 0.47and NA= 0.56) of 8μm and 10μm diameters are optimized with numerical average1 focusing efficiencies of 55% and 45%, with an average focusing error smaller than 6%for the RGB colors. The fabricated and experimentally characterized devices present44.16% and 31.5% respective efficiencies. The reported performances represent thehighest focusing efficiencies for highNA >0.5 RGB metalenses obtained so far. Theintegration of multi-wavelength metasurfaces in portable and wearable electronic de-vices requires high performances to offer a variety of applications ranging from classicalimaging to virtual and augmented reality.

Brightfield, fluorescence, and phase-contrast whole slide imaging via dual-LED autofocusing.

Whole slide imaging (WSI) systems convert the conventional biological samples into digital images. Existing commercial WSI systems usually require an expensive high-performance motorized stage to implement the precise mechanical control, and the cost is prohibitive for most individual pathologists. In this work, we report a low-cost WSI system using the off-the-shelf components, including a computer numerical control (CNC) router, a photographic lens, a programmable LED array, a fluorescence filter cube, and a surface-mount LED. To perform real-time single-frame autofocusing, we exploited two elements of a programmable LED array to illuminate the sample from two different incident angles. The captured image would contain two copies of the sample with a certain separation determined by the defocus distance of the sample. Then the defocus distance can be recovered by identifying the translational shift of the two copies. The reported WSI system can reach a resolution of ∼0.7 µm. The time to determine the optimal focusing position for each tile is only 0.02 s, which is about an 83% improvement compared to our previous work. We quantified the focusing performance on 1890 different tissue tiles. The mean focusing error is ∼0.34 µm, which is well below the ± 0.7 µm depth of field range of our WSI system. The reported WSI system can handle both the semitransparent and the transparent sample, enabling us to demonstrate the implementation of brightfield, fluorescence, and phase-contrast WSI. An automatic digital distortion correction strategy is also developed to avoid the stitching errors. The reported prototype has an affordable cost and can make it broadly available and utilizable for individual pathologists as well as can promote the development of digital pathology.

A Youla-parameterized Gap Control for Next Generation of Optical Storage Systems

With the development of ultra-high-density optical storage technology, the density of storage media is getting higher and higher, but the increase of the capacity of the optical disk leads to the reduce of the lens-disk interface gap and the tolerance of the focus error dramatically. In the case of extremely small spacing, various external disturbances are highly likely to cause a collision between the optical lens and the disc. In order to avoid the collision between the optical lens and disk, effectively eliminate the deterministic disturbance and suppress the unknown random disturbance, in this paper a multi-objective optimal output feedback controller design approach is proposed within the Q (Youla)-parameterized regulator scheme. The optimal Q parameter in the controller is obtained by solving the properly formulated linear matrix inequalities (LMIs). The experimental results show that the designed Q-parameterized controller can eliminate the influence of various disturbances and suppress the occurrence of collisions effectively.

Influence Function Measurement Technique Using the Direct and Indirect Piezoelectric Effect for Surface Shape Control in Adaptive Systems

Since the introduction of adaptive systems for corrective measures, static and dynamic disturbances have been reduced through the manipulation of surface shape in a well-controlled manner. One important application where adaptive systems are highly needed is in the future photo-lithography machines, particularly the wafer table where disturbances affect overlay and focus performance. To reduce overlay and focus errors, a dense array of actuators must be integrated into the wafer table to apply both in- and out-of-plane corrective deformations to the wafer surface. To realize a certain wafer shape, influence functions are linearly superimposed. Accurate models of the influence functions result in an accurate prediction of the final wafer shape. To reduce calibration errors, the influence function of every actuator needs to be determined. Here, we propose a technique to rapidly measure the influence function: the influence function measurement (IFM) technique. Using the actuate-sense property of piezoelectric materials, the influence function is determined by activating one piezo-actuator and measuring the charge induced on the neighboring piezo-actuators. The measured charges are compared to the results of finite element simulations and the absolute difference of 0.3 &#x0025; is reported for the inter-actuator charge coupling parameters. This clearly indicates the potential of the proposed technique. <i>Note to Practitioners</i>&#x2014;A critical step during the integrated-circuit lithographic fabrication process is the exposure. A particular practical challenge in this step is to correct for the mismatch between the optical image plane and the wafer surface, caused by wafer deformations. The mismatch negatively impacts the overlay and focus performance. To reduce the mismatch, actuators can be embedded into the wafer table to counteract wafer deformations, where the overall wafer surface shape is a superposition of each actuator&#x2019;s influence function. As part of the calibration for the embedded actuators, their influence functions are measured and stored. However, errors arise when influence functions are not measured for every actuator. Additionally, for different wafers, the influence functions vary hence the calibration should be done per wafer. This calibration process takes time and should not influence throughput. Our paper presents a viable approach that reduces the calibration time of active wafer tables, which is also relevant for other adaptive systems such as deformable mirrors. Since the technique requires the actuators to be mechanically coupled, it is limited to continuous surfaces. The proposed technique is numerically tested and experimentally verified to demonstrate performance.

Study of Microscope Autofocus Based on Weighted Light Intensity

Microscopes auto focusing is critically important for a great spectrum of scientific and industrial applications. Finding the best focus position for variety of surfaces under measurement proved to be challenging. In order to provide a rapid and accurate method for microscope focusing positioning, a laser focus deviate system was employed for microscope focusing position. The relationship between focusing sensitivity and the surface under measurement was investigated. First, the laser focus deviate technique is introduced in light of characteristic parameters such as the diameter of the focused spot, the laser wavelength and the distance from the optimal focus. Then, the focusing displacement versus spot position curve fitting is performed for a smooth isotropic surface to directly locate the best focusing position. Following, it is analyzed that when applied to anisotropic and rough surfaces, the centroid of the image spot after reflection/scattering from the surface will deviate from its original light intensity distribution, thus deviate from the calculated optimal focus position and cause focusing errors. Finally, a criterion of weighted light intensity value Q is introduced to achieve fast focusing of anisotropic surfaces in combination with the laser focusing deviate technique. The experimental results show that for a 20× microscope objective system, the focusing accuracy of this focusing positioning method is 1.7 μm on smooth surfaces; and is at the micro meter level for rough surfaces. It basically meets the requirements for rapid, stable and reliable microscope auto focusing needs.

Inclination shift signal: thickness or index measurement in transparent media by transmission of generally astigmatic Gaussian beams

The focus error signal is a widespread optical technique that harnesses the shape of a simply astigmatic Gaussian beam to produce an output signal with a well-defined linear range used for many different applications. However, general astigmatic Gaussian beams have not been extensively used for measuring purposes even though they have been known for decades. These beams have interesting properties which were used in this work as a mean to measure a change in the optical path and recover sample information. In this text, the formulae presented by E. Kochkina to represent generally astigmatic Gaussian beams are summarized, the principles of the proposed technique are set forth and two experimental results are presented as a validation of the proposal. A brief introduction to a different approach that enables the setup to perform simultaneous measurements of the thickness and refractive index is also given.

Guided filter based image enhancement for focal error compensation in low cost automated histopathology microscopic system.

Low-cost automated histopathology microscopy systems usually suffer from optical imperfections, producing images that are slightly Out of Focus (OoF). In this work, a guided filter (GF) based image preprocessing is proposed for compensating focal errors and its efficacy is demonstrated on images of healthy and malaria infected red blood cells (h-RBCs and i-RBCs), and PAP smears. Since contrast enhancement has been widely used as an image preprocessing step for the analysis of histopathology images, a systematic comparison is made with six such prominently used methods, namely Contrast Limited Adaptive Histogram Equalization (CLAHE), RIQMC-based optimal histogram matching (ROHIM), modified L0, Morphological Varying(MV)-Bitonic filter, unsharp mask filter and joint bilateral filter. The images enhanced using GF approach lead to better segmentation accuracy (upto 50% improvement over native images) and visual quality compared to other approaches, without any change in the color tones. Thus, the proposed GF approach is a viable solution for rectifying the OoF microscopy images without the loss of the valuable diagnostic information presented by the color tone.

Засіб статичного аналізу .NET програм за допомогою переписувальних правил

A software tool that finds problems of resource consumption in case of work with files using rewriting rules was implemented. To reach the goal, the TermWare system, which could be embedded into those systems running on JVM, was used. In order to work with C#-programs, the special plugin for TermWare, which helps to generate appropriate terms from source code, was developed. The plugin uses the Roslyn compiler, which allows users to find syntax errors in programs and focus on the primary task of generating terms from source code. Also, a practical application based on TermWare system – a static analyzer that finds problems with open-close files, was described in the article.

Synchronous Detection to Reduce Offsets in Focus Error of an Optical Pickup Unit

The optical pickup unit (OPU) is an optical assembly, which is used for reading and writing digital optical disks. It consists of a laser diode, quadrant photodetector, and other optical components to maintain focus. This arrangement of the laser and photodetector is very similar to those in expensive equipment, such as atomic force microscopes, used for nanoscale metrology. Many researchers have hence investigated the use of an OPU to design low-cost alternatives. However, these nonstandard uses of an OPU are challenging since the OPU has originally been optimized to sense reflections from the highly reflecting surface of an optical disk. In this work, we present a new synchronous detection-based method that improves the performance of the OPU in measuring the reflection from poorly reflecting substrates. This method utilizes the high bandwidth of both the laser and photodetector of the OPU. We excite the laser with a pulsed input and look for a signal at the pulsing frequency in the output from the OPU. This signal is further processed through a phase-sensitive detector. We show that this method reduces the offsets in the measurement and allows us to make effective use of a higher gain to measure the reflection from substrates with poor reflectivity.

대면적 레이저 직접묘화 공정에서 비점수차 자동초점 기술 연구

We developed an astigmatic autofocus optics and a control unit which were implemented in a direct laser writing system for a large area patterning process. The autofocus module is comprised of a collimated laser, a quadrant photodiode, an astigmatic lens, and a few polarizing optics. This system has a 0.526 V/μm focus error signal resolution in the 50x objective lens and a surface tracking capability of under 1 mm/s XY translation stage speed. In this study, we conducted a patterning experiment using SU-8 photocurable resist on a silicon wafer to study the accuracy of the astigmatic autofocus system. We highlighted some features of this system for future improvement.

Reducing field depth: annular Hadamard masks.

For optically narrowing field depth, we explore the use of annular masks that are coded with the elements of Hadamard matrices. We show that with no further reduction of light throughput, these annular masks can enhance the influence of focus error on the modulation transfer functions (MTF). We report numerical evaluations of the irradiance point spread functions (PSFs), their associated MTFs, and of some digitally generated images. For complementing our assessments, we evaluate the Fisher information of these Walsh-Hadamard, annular masks. We suggest an optical technique for breaking 3-D scenes into several 2-D sliced frames by translating out-of-focus images into background noise.

The Effect of adding First Order Aberrations To Third Order Aberrations on Point Spread Function for Triangular Aperture

In this work, Point Spread Function (PSF) for triangular aperture was studied, in case of ideal optical system, also in case of presence first order aberrations )focal error and tilt aberration) and third order aberrations (spherical ,coma, and astigmatism aberrations) individually, and for the same values of aberration factor )W=0.1λ …..0.5 λ ) for angle of rotation (ѱ =0). First order aberrations were added to third order aberrations, to obtain the best balance and to reduce the curve width of the (PSF), and to increase the Strehl ratio, like adding a tilt aberration to the coma aberration and adding focal error to spherical aberration and astigmatism aberration. There are some aberrations effects impact negatively on point spread function, such as focal error with coma aberration and tilt aberration with spherical aberration.

Performance-Based Active Wafer Clamp Design for Wafer Heating Effects in EUV Lithography

To improve overlay and focus errors in lithographic applications, an active wafer clamp (AWC) concept is proposed. Using this concept, mechanical actuators deform the wafer to compensate thermally induced deformations. In [1] a localized feedforward (FF) control algorithm for the AWC concept was introduced. In this paper we aim to improve this algorithm and discuss practical implications for the design of an AWC concept, motivated by the optimal performance that can be achieved using the FF control scheme. This leads to a design, where the actuators are placed below the clamping electrode, and 3-degree-of-freedom (DOF) actuators can be reduced to 2-DOF actuators with negligible performance loss. Considering the fact that the AWC concept contains tens of thousands of actuators, this leads to a significant reduction. Finally, other methods are presented to further reduce the computational complexity to control the AWC.

Tilting high-intensity focused ultrasound phased array to augment the focal steering range for treatment of uterine fibroids

Phased arrays are increasingly employed in clinical high-intensity focused ultrasound (HIFU) systems for treatment of uterine fibroids. However, the electronic steering range of current phased arrays is insufficient to cover a symptomatic uterine fibroid. This study proposes a method to augment the focal steering range for HIFU treatment of uterine fibroids. Geometric focus can be shifted by tilting HIFU phased array around two orthogonal axes with a rotating platform, and both rotating angles can be adjusted up to 15° with tilt radius of 277 mm according to the shift of geometric focus. A three-layer (skin, fat and muscle) tissue model was used as the beam propagation path. The acoustic fields with and without tilting HIFU phased array were characterized by numerical simulation and hydrophone measurement. Focal accuracy was evaluated in phantoms and targeting areas were ablated in in vivo pigs’ thighs. In combination with the electronic focal steering, the steering range in the focal plane has been augmented to ±53 mm from ±6 mm. In the phantoms, the mean focal error has been increased from 0.2 mm to 0.9 mm with the geometric focus shift ranged from 10 mm to 40 mm. In vivo experimental results have proved that it is safe and effective to ablate the 25 mm × 25 mm square area. Tilting the HIFU phased array is feasible to safely augment the focal steering range, which can potentially improve the efficacy of HIFU treatment.

Analysis of focal length error in torsion angle measurement system

Analysis of focal length error in torsion angle measurement system

Focusing and Frequency Smoothing for Arbitrary Arrays With Application to Speaker Localization

The coherent signal subspace method (CSSM) enables the direction-of-arrival (DoA) estimation of coherent sources with subspace localization methods. The focusing process that aligns the signal subspaces within a frequency band to its central frequency is central to the CSSM. Within current focusing approaches, a direction-independent focusing approach may be more suitable for reverberant environments since no initial estimation of the sources' DoAs is required. However, these methods use integrals over the steering function, and cannot be directly applied to arrays around complex scattering structures, such as robot heads. In this article, current direction-independent focusing methods are extended to arrays for which the steering function is available only for selected directions, typically in a numerical form. Spherical harmonics decomposition of the steering function is then employed to formulate several aspects of the focusing error. A case of two coherent sources is studied and guidelines for the selection of the frequency smoothing bandwidth are suggested. The performance of the proposed methods is then investigated for an array that is mounted on a robot head. The focusing process is integrated within the direct-path dominance (DPD) test method for speaker localization, originally designed for spherical arrays, extending its application to arrays with arbitrary configurations. Finally, experiments with real data verify the feasibility of the proposed method to successfully estimate the DoAs of multiple speakers under real-world conditions.

Non-contact method of thickness measurement for a transparent plate using a laser auto-focus scanning probe

In this paper we propose a novel non-contact method of thickness measurement for a transparent plate using a laser auto-focus scanning (LAFS) probe. Through the analysis of the focus error signal (FES) from the actual specimen's upper and lower surface reflectances, a measurement model is introduced to find the best focus position on the corresponding surface of the transparent plate. Thus, the thickness of a specimen can be obtained. Herein, the LAFS probe measurement characteristics by auto-searching the FES method can be analyzed, which can then realize non-contact measurement and focus detection of micro-displacements. Therefore, we have successfully designed a low-cost, high-precision auto-focusing thickness measurement system with linear piezoelectric nano-positioning. To verify the proposed method, some transparent specimens were evaluated, and the thicknesses were rapidly and successfully measured. Experiments confirm the validity of the proposed system, and the results show that the method is effective for the thickness measurement of transparent plates.