Reluctance actuators (RAs) excel in ultraprecision motion stages because of their high force density. However, high-fidelity force tracking control is significantly hindered by complex coupled nonlinearities, including variable-gap flux linkage, hysteresis, eddy currents, and flux leakage. Accurate inverse modeling is indispensable for counteracting these effects to enable precise control. Existing identification methods typically rely on additional sensing equipment and off-machine fixtures. Moreover, the sensitivity of model parameters to mover–stator position renders off-machine calibration vulnerable to reassembly errors. This paper proposes a comprehensive hybrid-driven inverse modeling and sensorless on-machine identification framework. First, an integrated analytical structure unifying multisource nonlinearities into a hybrid-driven model that ensures physical interpretability and high accuracy is presented. Second, a sensorless in situ identification strategy calibrates parameters without auxiliary metrology, hardware disassembly, or manual adjustments. By designing specific control laws and trajectories, the method utilizes only inherent displacement feedback to decouple and identify complex nonlinearities in situ. Consequently, the inverse model evolves from a coarse nominal classical lumped-parameter representation into a high-precision hybrid-driven model. Multiple force and motion control experiments are designed to demonstrate the proposed method’s repeatability and advantages over existing methods, verifying its effectiveness in enhancing high-precision feedforward controller performance and further approaching the accuracy limit, thereby aiding RA control research.

A high thrust-to-weight ratio imposes stricter requirements on thermal barrier coating for gas turbine blades. High-entropy pyrochlore oxides are particularly attractive due to their excellent performance. In this paper, a series of high-entropy oxides with the general formula La-2(Yb0.25(1-x)Y0.25(1-x)ZrxNb0.25(1-x)Ta0.25(1-x))(2)O-7 (x = 0 similar to 0.3) were designed and fabricated, and their phase composition, microstructure, and key properties were investigated. With increasing Zr4+ content, the phase composition transitions from a mixture of pyrochlore and secondary phase to a dual-phase pyrochlore, and finally to single-phase high-entropy pyrochlore oxides. Single-phase HEPOs La-2(Yb0.25(1-x)Y0.25(1-x)ZrxNb0.25(1-x)Ta0.25(1-x))(2)O-7 (x = 0.2 similar to 0.3) possess low thermal conductivity, a high coefficient of thermal expansion, and excellent high-temperature phase stability. Specifically, La-2(Yb0.1875Y0.1875Zr0.25Nb0.1875Ta0.1875)(2)O-7 exhibits a thermal conductivity as low as 0.96 W/(m & centerdot;K), and a coefficient of thermal expansion of 9.8 & times; 10(-6) K-1. After 120 h of heat treatment at 1450 degrees C, its grain growth rate is only 11.69%. These properties indicate that La-2(Yb0.1875Y0.1875Zr0.25Nb0.1875Ta0.1875)(2)O-7 has great potential for applications in the field of thermal barrier coating.

The pursuit of high lithography throughput necessitates dual-stage reticle systems that can achieve high scanning acceleration and long strokes, while maintaining nanometric positioning accuracy. Reluctance actuators (RAs) are considered ideal candidates for next-generation motion systems due to their high-force densities. However, conventional dual-stage control strategies predominantly employ a primary-secondary following mode, which strictly limits the relative displacement between the coarse and fine stages. This prevents the system from exploiting the nonlinear force surge capability of RAs with small air gaps, bottlenecking the overall system acceleration at the saturation limit of the coarse stage. To overcome this, a synergistic framework integrating nonlinear trajectory planning with a decoupled control architecture is proposed. This approach surpasses physical acceleration limits by optimizing the relative displacement to exploit the variable-gap force gain of the RA and breaking traditional kinematic constraints via decoupled control. Furthermore, a supporting in situ parameter identification method for RAs in a closed-loop dual-stage environment is developed to meet the stringent modeling accuracy requirements. Experimental validation demonstrates an acceleration improvement of up to 36.2% in the scanning acceleration. This is achieved without additional hardware costs, and while maintaining tracking errors below 10 nm during scanning. Overall, a novel approach is offered for high-performance lithography stage design.

Reluctance actuators (RAs) have been widely adopted in high-acceleration precision electromechanical systems such as lithography reticle stages due to their high thrust density and compact configuration. For system-level RA design, a multi-physics methodology balancing computational flexibility and predictive accuracy is essential to address bidirectional actuator-structure interactions. Current RA design methodologies predominantly focus only on electromagnetic performance optimization while neglecting thermal constraints in precision systems, particularly the thermal impact on external structures during continuous operation. To address this challenge, this paper proposes a bidirectional co-optimization framework integrating data-driven and physics-based approaches. Firstly, a high-fidelity structure-thermal surrogate model, neural network-LPTN hybrid network (NNLN), that synergizes data-driven and physics-based modeling approaches is proposed. This hybrid architecture achieves high-precision scalable thermal modeling while preserving physical interpretability, enabling dynamic coupling with external thermal models and effectively resolving the inherent trade-off between accuracy and scalability in conventional approaches, demonstrating over 50

Abstract. Laser interferometers and grating interferometers based on optical interferometry are widely used in displacement measurement of precision machining and testing equipment, such as the measurement system of integrated circuit equipment, due to their high precision, noncontact, and large dynamic measurement range. The ghost reflection in optical elements may lead to the periodic nonlinear error of the interferometer and also reduce alternating current/direct current. We propose a general method for automatic ghost reflection interface identification. It can analyze the influence weight of ghost reflection for each interface of any interferometer. In addition, the manufacturing cost of the interferometer is effectively reduced by optimization algorithms that enable ghost reflection avoidance in the interferometer design. Experimental results prove the influence weight of ghost reflection at different positions in the interferometer and provide the parameter selection of the most suitable interface reflection of the interferometer.

To accommodate the stage with large motion range and large rotating operation tolerance, a quad-pass homodyne interferometer without beam walk-off (BWO) is presented in this article. Based on the design that the measuring beam (MB) retraces the path of the incident beam, the system is immune to the inclination angle of the measured mirror (MM). The proposed optical structure eliminates BWO to improve fringe contrast, which is superior to the existing double-pass interferometers. Meanwhile, based on the characteristic of inclination immunity, the polarization leakage is isolated from the detector to effectively eliminate the periodic nonlinear error (PNL). A multichannel phase shift module (MCPSM) based on the spatial phase delay not only effectively improves the compactness of the interferometer but also can effectively suppress the PNL caused by the ghost reflection after combining with the multiple measurement signals algorithm. The interferometer is verified by simulations and experiments. In the experiments, the large rotating operation tolerance (±40 mrad) can be achieved. The residual PNL of each order is 1 pm/ $\surd $ Hz.

The periodic nonlinear error (PNL) caused by the high-order optical crosstalk of the homodyne interferometer with high optical subdivisions cannot be perfectly compensated by the ellipse fitting correction algorithm. In this paper, we focus on the PNL and propose a method to suppress it. In the method, the core idea of the multiple measurement signals algorithm is to eliminate the redundant items in the signals through the linear combination of six signals with the certain phase differences. Practical schemes for signals generation are also described in detail. The method is verified by simulations and experiments. In the experiments, the method proposed suppresses PNL at the order of 100 pm/root Hz compared with direct ellipse fitting correction algorithm (at the order of 1 nm/ root Hz).

In this paper, a correction undersampling unwrapping algorithm based on phase estimation is proposed. On the basis of direct unwrapping algorithm and the compensation period, the algorithm compensates the phase jump caused by undersampling. The calculation of compensation period is based on motion continuity and phase estimation. Meanwhile, integer ambiguity correction module avoids the accumulated phase error. The proposed algorithm is verified by simulations, which shows that the algorithm has high feasibility and accuracy, and can be applied to realize the displacement measurement of the undersampled homodyne interferometer.

To meet the needs of high speed measurement on hardware, undersampling technique is applied to displacement measurement homodyne interferometer. For orthogonal undersampled signals, the phase to be measured cannot be solved by arctangent function and original unwrapping algorithm. In this paper, a corresponding algorithm is proposed to measure the phases of the undersampled signals in practical conditions. The algorithm is a combination of the original phase solving algorithm and the compensation period. In the algorithm, the phase estimation and the error parameter model based on least square fitting are used to iteratively solve the desired phase. The proposed method is verified by simulations and experiments, and results demonstrate the high feasibility and accuracy of the algorithm.

面向浸没式光刻机双工件台的超精密位置测量应用需求,提出了一种超精密空间分离式外差利特罗平面光栅编码器位移测量系统.给出了测量系统的原理与方案设计、系统各部件的设计及制造、编码器测量原理推导及实验验证等.所设计平面光栅编码器位移测量系统的相位卡的细分率为4096,测量分辨率为x50 pm/z25 pm.实验结果表明:该平面光栅位移测量系统可实现x向和z向位移的同时测量,z向运动行程为±1 mm,满足光刻机双工件台的垂向调焦需求;Rx/Ry/Rz单轴转动或三轴联合转动极限转角为±1.5 mrad时,交流信号质量仍然满足测量要求,光刻机双工件台的Rx/Ry/Rz的调平转动满足需求.所设计的平面光栅编码器位移测量系统能够实现光刻机双工件台相应的测量功能且具有较高的性能指标.

Based on the spatial phase delay of beams, a displacement measurement method is proposed for homodyne interferometers. In this method, two detectors are arranged in the interference spot to collect signals. Based on the algorithm of least squares fitting the parameters of the ellipse equation, the relative phase of the signals is solved to calculate the displacement. The proposed method uses optical fiber bundles for beam reception, which is more compact in structure than the traditional quadrature phase calculation method, and eliminates polarization mixing. The spatial delay phase in the method can be any unknown constant, which makes it more applicable in practice. The feasibility of this method is verified by ZEMAX simulations and experiments. The experimental results show that the 3 sigma of errors without the effect of power noise and vibration is 7.2 nm. (C) 2022 Society of Photo-Optical Instrumentation Engineers (SPIE)

Grating interferometers that use large two-dimensional grating splice modules for performing wide-range measurements have significant advantages for identifying the position of the wafer stage. However, the manufacturing process of large two-dimensional grating splice modules is very difficult. In contrast to existing redundant designs in the grating line dimension, we propose a novel interferometric reading head with a redundant design for obtaining wide-range displacement measurements. This interferometric reading head uses a one-dimensional grating splice module, and it was observed to be compatible with two orthogonal gratings. We designed a grating interferometer system composed of four reading heads to achieve a wide range of measurements and verified it using ZEMAX simulation. By conducting experiments, we were able to verify the compatibility of the reading head with gratings possessing different grating line directions; the measurement noise was found to be less than 0.3 nm.

A method for measuring the relative phases (RPs) among the three beams in the case of homodyne three-beam interference (TBI) is proposed and verified by the ZEMAX simulation in this paper. The method requires that the interference beams are not on the same plane, that is, any two of the three beams interfere at an angle in different planes. Based on the phase delay of the beam in space, the inclined beams have different phases at different positions within the beams' range. By arranging the photodetector array within the interference area, the RPs can be calculated using the intensity of the interference light received by specific photodetector units. The application of the algorithm for the displacement measurement of the homodyne three-beam interferometer (TBIR) has been verified by simulation. The beam number of three-beam interference is one less than that of two two-beam interference when measuring two relative phases. Compared with the two-beam interferometer, the TBIR applied to two-degree-of-freedom displacement measurement is more compact in structure due to the more compact phase measurement components.

In this paper, the errors of the displacement measurement interferometer with multi-mode fiber-coupled delivery are analyzed when the fibers are disturbed. Simulation results show that the characteristic frequency of the measurement error is consistent with that of disturbance, and the error has higher order frequency components. The experiments are designed for the effect of fringe contrast on the measurement error. The experimental results show that the measurement error is rather sensitive to the interference angle between the measurement arm and the reference arm in the multi-mode fibers, but not to the irradiance ratio of the measurement arm and the reference arm. In an interferometer with multimode fiber, the interference angle between the measurement arm and the reference arm needs to be restricted. This conclusion provides a theoretical basis for designing an interferometer measurement system with interference angle that is adaptive to wider application.

Grating interferometry is an environmentally stable displacement measurement technique that has significant potential for identifying the position of the wafer stage. A fast and precise algorithm is required for real-time calculation of six degrees-of-freedom (DOF) displacement using phase shifts of interference signals. Based on affine transformation, we analyze diffraction spot displacement and changes in the internal and external effective optical paths of the grating interferometer caused by the displacement of the wafer stage (DOWS); then, we establish a phase shift-DOWS model. To solve the DOWS in real time, we present a polynomial approximation algorithm that uses the frequency domain characteristics of nonlinearities to achieve model reduction. The presented algorithm is verified by experiment and ZEMAX simulation.

We present a three-degrees-of-freedom laser interferometer based on differential wavefront sensing with a wide angular measurement range. To obtain measurement signals with a high AC/DC ratio and improve the linearity of differential wavefront sensing in a wide range angular displacement measurement, a fiber bundle instead of a quadrant photodiode is applied to receive the interference light. Meanwhile, a decoupled algorithm with quadratic correction derived by the ray tracing method and kinematic analysis is detailed in the case of the wide range angular displacement. The simulation and experimental results prove that the laser interferometer with the proposed structure could realize hundreds of microradian range of angular displacement measurement, which are expanded in the differential wavefront sensing.

In the displacement measurement of the wafer stage in lithography machines, signal quality is affected by the relative angular position between the encoder head and the grating. In this study, a two-degree-of-freedom fiber-coupled heterodyne grating interferometer with large operating range of rotation is presented. Fibers without fiber couplers are utilized to receive the interference beams for high-contrast signals under the circumstances of large angular displacement and ZEMAX ray tracing software simulation and experimental validation have been carried out. Meanwhile, a reference beam generated inside the encoder head is adopted to suppress the thermal drift of the interferometer. Experimental results prove that the proposed grating interferometer could realize sub-nanometer displacement measurement stability in both in-plane and out-of-plane directions, which is 0.246 nm and 0.465 nm of 3σ value respectively within 30 s.

Geometric self-calibration of the grating interferometer system is essential to improve the displacement measurement accuracy of the wafer stage, and the error analysis is critical for geometric self-calibration. The self-calibration idea based on the self-consistency of a redundant system and the step-by-step self-calibration method of the grating interferometer system for the wafer stage are briefly introduced. The error sources destroying the self-consistency of the geometric mathematical model are analyzed and transformed into the phase shift errors caused by nongeometric errors. The relationship between the accuracy of the model after self-calibration and the phase shift errors is established by fitting the simulation data and can be used as a basis for the design and accuracy budget of the self-calibration process of the grating interferometer system for the wafer stage.

超精密平面光栅编码器位移测量技术是32～7 nm节点浸没式光刻机的核心技术.通过分析浸没式光刻机平面光栅位置系统的需求和布局,提出了光刻机专用超精密平面光栅编码器的基本需求.针对现有的光栅编码器,开展了基本测量光路方案、相位探测方案、分辨率增强光路方案、离轴/转角允差光路方案、死程误差抑制光路方案的综述分析,提出了现有设计方案面向光刻机应用所需要解决的关键问题.面向亚纳米级测量精度的需求,针对光栅编码器的仪器误差,对周期非线性误差、死程误差、热漂移误差和波前畸变误差进行了综述分析,提出了平面光栅编码器实现亚纳米精度所需要解决的关键问题.本综述为光刻机专用超精密平面光栅编码器的研制提供了参考.