Ailing Tian

Single-shot lateral shearing interferometry enables the acquisition of a composite interferogram containing both x - and y -direction shearing interference fringes in a single exposure using a polarization camera. However, accurately separating the fringe phases corresponding to different shearing directions remains challenging. To address this issue, a fringe phase separation method based on the two-dimensional continuous wavelet transform (2D-CWT) is proposed. A complex analytic signal is first constructed to eliminate phase ambiguity, followed by multi-scale and multi-directional decomposition using a Morlet wavelet. Ridge features are then enhanced by local maximum sparsification, and a sequential ridge extraction strategy incorporating neighborhood constraints is employed to identify the ridges corresponding to the x - and y -direction shearing fringes, from which the respective wrapped phases are recovered. Simulation and experimental results demonstrate that the proposed method effectively separates the fringe phases under spectral aliasing conditions without requiring large amounts of training data. Compared with the Fourier transform method, it achieves higher separation accuracy and stronger robustness, providing an effective solution for composite shearing fringe separation.

： In wafer probe card electrical testing, anomalies such as probe mark offset and excessive depth represent critical bottlenecks that compromise testing stability and accuracy.To tackle this challenge, a digital holographic detection method based on spectral angular constraints is proposed, achieving unified real-time in-situ monitoring across the front-and back-ends of the entire probe card testing process. The method analyzes the spatial and frequency domain distribution characteristics of the wafer to construct a spatial-frequency rotation mapping model. By applying angular constraints to the original image spectrum of the hologram, high-precision correction of wafer rotational misalignment is achieved, thereby substantially reducing the risk of probe mark offset. Simultaneously, the same optical system is utilized to perform real-time reconstruction of three-dimensional probe mark surface topography and extraction of key parameters such as probe mark depth. Based on the measured three-dimensional topography data, a detailed analysis of probe mark morphological features and their formation mechanisms is conducted. Experimental results demonstrate that the mean absolute error for wafer rotational position correction is 0.048°, with a root-mean-square error of 0.053°. For probe mark depth measurement, comparison with white-light interferometry yields a mean absolute error of 0.08μm and a relative error of 1.46%. This method provides an efficient, accurate, and non-contact metrological solution for probe card testing in advanced semiconductor processes, thereby facilitating further research and practical applications of related testing technologies.

Lateral shearing interferometry is an effective method for directly measuring the depth gradient of aspherical surfaces. To address the low phase reconstruction accuracy resulting from the fact that lateral shear interferometers typically obtain only two sets of wavefront data in a single orthogonal direction, which leads to fewer sampling points, this paper presents an aspherical surface measurement method based on birefringent crystals and multi-directional lateral shearing phase-shifting interferometry. This method overcomes nonlinear issues and environmental influences during phase-shifting interferometry, captures shear wavefront data in multiple directions, and reconstructs the surface by solving for the wavefront coefficients using multi-directional differential wavefront information. It also reduces system random errors, improving surface reconstruction accuracy. We propose a multi-directional lateral shearing synchronous phase-shifting interferometry technique for measuring aspherical surfaces. The methodology includes multi-directional shearing, synchronous phase-shifting, crystal birefringence modulation, phase grating diffraction, and polarization phase-shifting arrays. An experimental system was built to test aspherical surface samples, and aspherical surface measurements were conducted on a surface with a 90 mm diameter, 606 mm vertex curvature radius, and a quadratic conic coefficient of −1. The deviation of the measured aspherical surface from the optimal spherical surface was obtained, and the initial deviation of the ideal aspherical surface from the optimal spherical surface was calculated using the ray tracing method. The repeated measurement results were consistent with those from the ZYGO interferometer’s self-collimation method, with an RMS deviation better than λ/100. The experiment demonstrated the effectiveness, repeatability and measurement stability of the multi-directional lateral shearing interferometry system for measuring aspherical surfaces.

To overcome the limitations of phase sampling points in testing aspherical surface wavefronts using traditional interferometers, we propose a high-spatial-resolution method based on multi-directional orthogonal lateral shearing interferometry. In this study, we provide a detailed description of the methodology, which includes the theoretical foundations and experimental setup, along with the results from simulations and experiments. By establishing a relational model between the multi-directional differential wavefront and differential Zernike polynomials, we demonstrate high-spatial-resolution wavefront reconstruction using multi-directional orthogonal lateral shearing interferometry. Theoretical calculations and simulations of aspherical surface wavefront testing are followed by experimental verification on an aspherical surface with a known asphericity. Comparing the measurement results with those from the LuphoScan profilometer, we achieve a relative measurement error with an RMS precision better than λ/100.

A novel preprocessing method based on a modified U-NET is proposed for single interference fringes. The framework is constructed by introducing spatial attention and channel attention modules to optimize performance. In this process, interferometric fringe maps with an added background intensity, fringe amplitude, and ambient noise are used as the input to the network, which outputs fringe maps in an ideal state. Simulated and experimental results demonstrated that this technique can preprocess single interference fringes in ~1 microsecond. The quality of the results was further evaluated using the root mean square error, peak signal-to-noise ratio, structural similarity, and equivalent number of views. The proposed method outperformed U-NET, U-NET++, and other conventional algorithms as measured by each of these metrics. In addition, the model produced high-quality normalized fringes by combining objective data with visual effects, significantly improving the accuracy of the phase solutions for single interference fringes.

The mirror component is one of the most critical components in the space remote sensing payload, and the performance of its support essentially determines the imaging quality of the system. Mirror components need to have high face shape accuracy, high reliability, and high stability. In this paper, taking the square mirror with the size of 550 mm × 450 mm as an example, we chose the Ultra-Low-Expansion Glass (Corning) as the mirror blank material, and through in-depth research on the principle of the three-point backside support and the engineering realization, we designed a three-point backside flexible support structure applied to the space mirror component. The design results were testified by simulation analysis; the results showed that with the mirror’s weight of 13.2 kg, the surface density can reach 48.5 kg/m². For each gravity acceleration of 1 g, within the temperature range from 16 to 24 °C, carrying a forced displacement of 5 μm, the RMS value of the mirror component can reach 1/55λ (λ = 632.8 nm), which meets the requirement of high face shape accuracy of the mirror component in space. Finally, the mechanical test was carried out on the assembled mirror component, and the intrinsic frequencies of three directions of the mirror component were obtained through the test: 173.8 Hz, 176.4 Hz and 271.5 Hz, respectively. The changes of the mirror and its support structure were all less than 5″ after the 8 g sinusoidal vibration test and the 5.66 g random vibration test, which indicates that the flexible support structure meets the requirements of the high reliability of the space remote sensing loads and the high accuracy of the space mirror component. It shows that the flexible support structure meets the high reliability and high stability requirements of space remote sensing loads. The theoretical data and test results in this research can provide theoretical references for mirror components of the same size and type.

For a fiber optic gyroscope, thermal deformation of the fiber coil can introduce additional thermal-induced phase errors, commonly referred to as thermal errors. Implementing effective thermal error compensation techniques is crucial to addressing this issue. These techniques operate based on the real-time sensing of thermal errors and subsequent correction within the output signal. Given the challenge of directly isolating thermal errors from the gyroscope’s output signal, predicting thermal errors based on temperature becomes necessary. To establish a mathematical model correlating the temperature and thermal errors, this study measured synchronized data of phase errors and angular velocity for the fiber coil under various temperature conditions, aiming to model it using data-driven methods. However, due to the difficulty of conducting tests and the limited number of data samples, direct engagement in data-driven modeling poses a risk of severe overfitting. To overcome this challenge, we propose a modeling algorithm that effectively integrates theoretical models with data, referred to as the TD-model in this paper. Initially, a theoretical analysis of the phase errors caused by thermal deformation of the fiber coil is performed. Subsequently, critical parameters, such as the thermal expansion coefficient, are determined, leading to the establishment of a theoretical model. Finally, the theoretical analysis model is incorporated as a regularization term and combined with the test data to jointly participate in the regression of model coefficients. Through experimental comparative analysis, it is shown that, relative to ordinary regression models, the TD-model effectively mitigates overfitting caused by the limited number of samples, resulting in a substantial 58% improvement in predictive accuracy.

In this paper, we propose a measurement method of micro-optical elements with parallel phase-shifting digital holographic phase imaging. This method can record four phase-shifting holograms with a phase difference of π/2 in a single shot and correct the pixel mismatch error of the polarization camera using a bilinear interpolation algorithm, thereby producing high-resolution four-step phase-shifting holograms. This method reconstructs the real phase information of the object to be measured through a four-step phase-shifting algorithm. The reproduced image eliminates the interference of zero-order images and conjugate images, overcoming the problem that traditional phase-shifting digital holography cannot be measured in real time. A simulation analysis showed that the relative error of this measurement method could reach 0.0051%. The accurate surface topography information of the object was reconstructed from an experimental measurement through a microlens array. Multiple measurements yielded a mean absolute error and a mean relative error for the vertical height of the microlens array down to 5.9500 nm and 0.0461%, respectively.

For a fiber optic gyroscope, thermal deformation of the fiber coil can introduce additional ther-mal-induced phase errors, commonly referred to as thermal errors. Thermal error compensation techniques are effective means of addressing this issue. The principle behind these techniques involves real-time sensing of thermal errors and correcting them within the output signal. Since it is challenging to directly separate thermal errors from the output signal of the fiber optic gyro-scope, it is necessary to predict thermal errors based on temperature. To establish a mathematical model between temperature and thermal errors, this paper measured synchronized data of phase errors and angular velocity for the fiber coil under different temperature conditions and aimed to model it using data-driven methods. Due to the difficulty of conducting tests and the limited number of data samples, an algorithm called TD-model modeling is proposed to address the issue of overfitting, which can reduce the model's generalization ability. First, a theoretical analysis of the phase errors caused by thermal deformation of the fiber coil is performed. Subsequently, the critical parameters, such as the thermal expansion coefficient, are determined, and a theoretical model is established. Finally, the theoretical analysis model is incorporated as a regularization term and combined with the test data to jointly participate in the regression of model coefficients. Through experimental comparative analysis, it is shown that, relative to ordinary regression models, the TD-model effectively mitigates overfitting caused by the limited number of samples, leading to a 58% improvement in predictive accuracy.