This paper introduces a novel technique for achieving three-dimensional detection of optical element surface defects by applying the transport of intensity equation (TIE) to the reconstruction of scattered light intensity distributions. A TIE-based model is developed to simulate the intensity and phase distributions of scattered light fields, with the reconstructed dimensions of corresponding surface defects used to verify the feasibility of the method. In addition, the limitations of conventional fast Fourier transform (FFT) solvers are addressed using an improved strategy that avoids zeroes and minima, simplifies the computational process, and ensures convergence, thereby achieving efficient, high-precision phase recovery. Finally, an experimental system was constructed to empirically validate the effectiveness of the proposed method, which accurately reconstructed the phase distributions of surface defects and reliably determined their spatial dimensions.

Lateral shear interferometry is a high-precision wavefront detection technique that achieves self-interference by utilizing lateral displacement of the same wavefront in space, effectively mitigating the influence of reference surface errors and achieving high measurement accuracy. However, the accuracy of obtaining the two key parameters-shear amount and shear angle-directly impacts the final detection results. Achieving high-precision acquisition of these parameters is crucial for enhancing system performance. Currently, mainstream methods primarily rely on edge detection and image segmentation of the interferogram, estimating shear parameters through rectangular or circular fitting. However, such methods are highly sensitive to interferogram quality and may produce significant errors when edge transitions are unclear or spots are uneven. To address these issues, this paper proposes a shear parameter acquisition method driven by the second derivative of the autocorrelation function (ACF-SD), that directly leverages the overall structure of the interferogram, fully utilizing its periodicity and symmetry information to effectively avoid acquisition errors caused by edge deficiencies or spot degradation. This method demonstrates high robustness and applicability in simulation and experimental validation, providing a new approach for parameter calibration in transverse shear interferometry and significantly expanding its application prospects in optical detection.

To address the challenge of inaccurate wavefront reconstruction caused by excessively dense interference fringes, this paper proposes an interferogram-driven method for large-gradient wavefront reconstruction. In this method, the interferogram serves as the optimization target, while the Zernike polynomial coefficients are treated as the optimization variables. By constructing an iterative optimization framework using the structural similarity index (SSIM) as the evaluation metric, the particle swarm optimization (PSO) algorithm is employed to iteratively update the Zernike coefficients. This process drives the simulated interferogram to gradually converge toward the target interferogram, thereby achieving the reconstruction of large-gradient wavefront. Simulation and experimental results demonstrate that, as long as the interferometric modulation has not undergone complete collapse and no dark regions appear in the interferogram, the proposed method can achieve accurate reconstruction of large-gradient wavefronts. The reconstructed surface shape obtained by this method is highly consistent with that measured by a ZYGO interferometer, with the absolute PV and RMS surface errors better than lambda/50 and lambda/200, respectively, verifying the accuracy and reliability of the proposed approach.

The core of multi-spectral radiation thermometry lies in determining the object’s emissivity. However, existing methods generally suffer from issues such as low accuracy and poor applicability. This paper establishes a relevant mathematical model and constraint conditions based on Planck’s radiation law and multi-objective constraint optimization theory. By integrating the particle swarm optimization (PSO) and JAYA algorithms, the proposed approach addresses the tendency of PSO to get trapped in local optima and the slower convergence speed of the JAYA algorithm. Simulation experiments conducted under four different wavelength and emissivity models at a true temperature of 2,000 K demonstrate that the PSO-JAYA method achieves a retrieval error of only 0.8 % and significantly improves retrieval speed. The method exhibits notable advantages in both retrieval accuracy and efficiency, confirming its reliability for practical applications.

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.

Aiming at the problems of low efficiency and lengthy scanning paths of traditional two-step methods in surface defect detection of large-aperture optical components, this paper proposes an improved detection technique integrating hierarchical clustering and ant colony algorithm. First, after preliminary grid scanning, image preprocessing (median filtering, Otsu binarization, and morphological operations) is performed to extract defect coordinate information. Then, hierarchical clustering is adopted to group spatially adjacent defects into the minimum number of field-of-view-compliant sub-apertures without presetting cluster numbers. Finally, the ant colony algorithm transforms sub-aperture traversal into a traveling salesman problem (TSP) to generate the globally optimal scanning path. Experimental verification shows that the proposed method reduces the scanning distance to 1/5 and the detection time to 1/6 of the traditional method while maintaining equivalent detection accuracy (error < 5%). This study realizes efficient and high-precision defect detection when defects are in a discrete state during the second-step precise scanning, providing a practical solution for large-aperture optical component inspection. (c) 2026 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.

In lateral shearing interferometry, the presence of edge discretization and weak gradient variations in shear interferograms affects the accurate determination of effective interference regions and the calculation of shear parameters, thereby influencing wavefront reconstruction accuracy. Existing algorithms impose stringent requirements on interferogram quality and are prone to feature misidentification under low-contrast or noisy conditions. To address this issue, this study proposes a hybrid data-driven InterferoNet deep learning framework. By combining large-scale simulated interferograms with a limited number of real experimental interferograms for model training, this method achieves high-precision segmentation between interference and non-interference regions in shear interferograms. The resulting segmentation mask can be directly used to determine the effective interference region, while the shear parameters are obtained through least-squares circle fitting of the segmented mask. The identified interference region and calculated shear parameters are then applied to the wavefront reconstruction algorithm to reconstruct the phase of the test object. Experimental results demonstrate that the proposed method maintains stable segmentation performance for interferograms affected by noise, low contrast, or edge discretization, effectively identifies interference regions, and achieves subpixel-level accuracy in shear parameter determination, significantly improving wavefront reconstruction precision.

In Frequency-Shifting Digital Holographic Microscopy (FSDHM), tilted illumination causes positional distortions in spectral sub-apertures, significantly reducing the accuracy of super-resolution phase reconstruction without precise correction. We propose a novel method for high-precision super-resolution phase reconstruction. By analyzing the complex amplitude distribution of the original image across spatial, fractional fourier, and fourier domains, a fractional - frequency domain position mapping model was established. We convert the spectral synthetic aperture problem into the fractional domain, thereby avoiding the limitations of indistinct spectral structural features. Exploiting spatial features of the original image in the fractional domain for feature extraction and matching, this method maps fractional domain offsets back to the frequency domain, enabling precise correction and synthesis of spectral sub-apertures. Simulations and experiments demonstrate sub-aperture positional distortion correction with errors below 1/4 pixel, improving accuracy by 72.9% over conventional FSDHM and achieving super-resolution phase reconstruction by a factor of 1.71. We confirm the method’s applicability to biological pathology samples. It significantly reduces reliance on mechanical control precision and supports flexible frequency-shifting operations with arbitrary offsets. We anticipate that our work offers a viable new tool for applications requiring the non-destructive evaluation of cells or pathological samples, as well as high-precision industrial inspection tasks.

Frequency-shifting digital holographic microscopy (FSDHM) is an emerging technique that offers nondestructive, non-contact, super-resolution imaging in three dimensions. However, a broad application of this technology has been limited by lengthy acquisition times and complex control setups. To overcome these challenges, we propose a novel technique termed sparse aperture-based frequency-shifting digital holographic microscopy (SA-FSDHM). In this process, we introduce a general sparse aperture strategy for diverse samples and develop a reconstruction algorithm based on spectrum compensation. This process includes an analysis of the diffraction characteristics of fine object structures and the complex amplitude spectra of off-axis holograms, which led to a reduction in the number of images required for acquisition from N to (N + 1)/2. This approach achieves high-quality phase reconstruction at the same level as FSDHM while requiring fewer holograms, effectively resolving trade-offs between data acquisition volumes and reconstruction resolution. SA-FSDHM also improves experimental efficiency without the need for complex or expensive control devices. As such, the proposed technique is particularly suitable for applications requiring both high resolution and rapid acquisition, such as live cell imaging and wafer defect detection, thereby providing a novel solution for efficient super-resolution 3D imaging.

In lateral shearing interferometry for aspheric surface measurement, the nonuniform fringe density distribution caused by zonal curvature variations degrades wavefront reconstruction accuracy. To address this issue, this paper proposes a fused multi-shear wavefront reconstruction method for aspheric measurement. First, the test aspheric wavefront is partitioned into annular subzones based on the wavefront slope principle, while ensuring fringe resolvability at the zone edges, optimal shear amounts are matched to each zone to acquire appropriate interferograms. Specifically, a smaller shear amount is used in the high curvature zone to reduce the stripe density, and a larger shear amount is used in the low curvature zone to increase the data volume. After phase extraction and unwrapping are performed for the sheared interferograms of each annular subzone, differential Zernike polynomials are employed to independently reconstruct the wavefront for each annular subzone, and multi-shear wavefront fusion algorithm model is established to achieve full-aperture measurement through local surface. Experimental results demonstrate that this method effectively resolves the inherent limitation of conventional single-shear approaches in simultaneously measuring high and low curvature zones, significantly improves fringe pattern resolvability, and provides a viable approach for enhancing the measurement precision of aspheric surfaces.

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 (MAE) for wafer rotational position correction is 0.048 degrees, with a root-mean-square error of 0.053 degrees. For probe mark depth measurement, comparison with white-light interferometry yields a MAE of 0.08 mu m 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.

A bifocal interference confocal microscopy system (BICMS) is proposed in which bifocal lenses are used to overcome the tradeoff between high resolution and long working distance, which cannot be achieved simultaneously in devices with small numerical apertures (NAs). In this work, a bifocal lens is introduced in the proposed system to ensure signals (generating the interference) originate from the same point on the surface of the object to be measured. The annular interference region generated by the bifocal lenses can be used to sharpen the width of the central bright spot. This reduces the full width at half maximum for the normalized lateral intensity point spread function, thereby improving the stability, anti-disturbing capabilities, and lateral resolution. A theoretical analysis (using a wavelength of 632.8 nm and an objective NA of 0.1) demonstrated BICMS improved the lateral resolution of the confocal microscope from 2.34 mu m to 1.33 mu m, which is 1.7 times that of a CMS; in the case of NA = 0.2, BICMS improved the lateral resolution of the confocal microscope from 1.24 mu m to 0.92 mu m, which is 1.3 times that of the CMS. As such, the proposed system is bringing the possibility of a wide range of applications for high-resolution confocal microimaging systems.

This paper explores a multi-directional (multiple directional) shearing synchronous polarization phase-shifting interferometer that utilizes a birefringent crystal displacer. This design effectively mitigates nonlinear issues and environmental influences commonly encountered in synchronous phase-shifting interferometry. Additionally, it enables the acquisition of shear wavefront information from multiple directions. By solving for the coefficients of the measured wavefront using multi-directional differential wavefront data, the system performs coefficient fitting to reconstruct the wavefront. The characteristics of crystal birefringence beam modulation, phase grating diffraction, and the polarization phase-shifting array for synchronous phase-shifting interferometry are investigated, based on the specific implementation methods of multi-directional shearing and synchronous polarization phase-shifting. The preprocessing method for the multi-directional shearing phase-shifting interferogram is then presented, followed by a detailed explanation of the spatial position registration technique for the shearing interferogram and the calculation method for the shear amount. The interferometer’s construction system was experimentally tested using a spherical optical component, and the results were compared with those obtained from ZYGO to verify its accuracy and testing reliability.

To address the problem of inaccurate shear estimation caused by insufficient interferogram quality, this paper proposes a phase-driven shear correction method that effectively enhances the accuracy of wavefront reconstruction. The method treats the phase extracted from the actual interferogram as the optimization target and regards the shear amount as the variable. By iteratively updating the shear amount, the simulated phases corresponding to different shear amounts progressively approach the actual phase, thereby achieving simultaneous optimization of shear estimation and wavefront reconstruction. To validate the proposed approach, interferograms with varying shear amounts were simulated, and the method was applied to correct the shear amount. The results demonstrate that the method consistently converges to the actual shear amount under different shearing conditions and significantly enhances reconstruction accuracy. Experimental results demonstrate that, compared to traditional methods, the proposed method reduces the peak-to-valley deviation from the ZYGO reference from 0.0454λ to 0.0255λ, thereby fully verifying its accuracy and reliability.

Optical components are extensively used in aerospace, microelectronic equipment, precision optical measurement, laser optics and other fields. Surface defects on optical components can significantly impact system performance, necessitating specialized detection methods. However, technical challenges persist in achieving high-resolution, high-precision and efficient optical surface defect detection. To address this, we propose an improved YOLOv8-based object recognition algorithm. By incorporating the BRA attention mechanism into YOLOv8’s backbone network, multi-scale feature maps are processed to enhance adaptability to complex scenarios. Simultaneously, replacing the feature fusion module with the Context-GuideFPN module enables contextual guidance and adaptive adjustments during multi-scale feature integration without excessive computational overhead. Experimental results on our high-quality microscopic dark-field image dataset demonstrate that the enhanced BACG-YOLOv8 achieves excellent performance in optical component defect detection. The optimized network accurately extracts defect details, particularly demonstrating refined edge feature extraction while effectively suppressing noise interference. This significantly reduces detection errors and improves defect extraction accuracy.

To our knowledge, a novel synchronous multi-wavelength interferometric technique is introduced. The aspherical surface profile is measured by focusing a multi-wavelength beam at various positions along the optical axis using a dispersive lens, thereby generating a series of spherical waves with varying curvatures. A comprehensive analysis of the operational mechanism of dispersive lenses in aspherical surface metrology is conducted, culminating in the design principles for their axial focal points. This approach significantly enhances measurement efficiency and accuracy while minimizing mechanical movement errors compared to the conventional annular sub-aperture method. Moreover, the integration of dispersive lenses streamlines system design, reduces the complexity of system modeling, and facilitates the development of a more precise digital twin model for subsequent error correction.

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.

Phase information in single exposure images is often lost for specimens with non-uniform transmittance. To address this issue, we propose a multi-exposure image fusion phase enhancement technique for holographic images. In this process, exposure time is varied to acquire 11 groups of four-step phase-shifted holographic images from a common sampling area. The resulting images are then decomposed using a wavelet transform. Maximum phase information from the low-frequency regions and regional features from the high-frequency regions were employed to avoid discontinuities in subsequent reconstructions, caused by regional truncation. Holographic images were then obtained after multi-exposure image fusion using a wavelet fusion method. Corresponding phase information was acquired by reconstructing fused holographic images using a four-step phase shifting technique. Experimental results showed that for specimens with non-uniform transmittance, this approach increased information entropy by 4.2%, edge density by 5%, and contrast by 3.8%, in comparison with the single-exposure digital holography phase reconstruction method. This result suggests that clarity and information content are improved, thereby enhancing the reconstructed phase.

To address the issue of inaccurate calculation of shear quantity and shear angle in lateral shear interferograms due to their discretely distributed edges and unclear gradient changes, this paper proposes a high-precision computation method for key parameters. First, it enhances the clarity of interferogram edges and suppresses internal fringe noise interference by computing the spatial modulation transfer function (MTF) of lateral shear interferograms. Building on this, an improved GrabCut algorithm is employed to iteratively segment the interferogram region from the background, overcoming issues with edge recognition errors caused by insignificant gradient features in interferogram images. Finally, shear quantity and shear angle are computed using effective interferogram edge extraction and circular fitting constraint algorithms, thereby reducing fitting errors or failures due to matrix singularity. Simulation results show that the shear quantity error is within 0.09 pixels, and the shear angle error is within 0.18°. Experimental results indicate that when using a parallel polarized beam splitter with a standard shear ratio of 0.1 for measurement, the shear ratio error is within 0.01 units. When the obtained data are used for wavefront reconstruction, the PV and RMS calculation accuracies are approximately λ/50 and λ/78 (λ=632.8nm), respectively, outperforming mainstream algorithms. This demonstrates that the proposed method maintains excellent performance and effectiveness even in complex scenarios with high-precision requirements.

In lateral shearing interferometry, the discretely distributed edges and weak gradient variations in shearing interferograms can adversely affect the accurate calculation of shear parameters, consequently degrading wavefront reconstruction precision. To address this issue, this study proposes a TransUNet-based transfer learning method for shear parameter calculation. First the model pre-trained with simulated interferograms to learn fringe characteristics, then the model fine-tunes with limited real experimental data to overcome the scarcity of real interferograms. The model can achieve precise four-class segmentation of interferograms (background, two non-interference regions, and interference fringes), building upon the segmentation results, least-squares circle fitting algorithm is applied to simultaneously accomplish shear parameter calculation and wavefront center localization. Experimental validation demonstrates that the proposed method maintains excellent computational precision and automation levels even under noisy and weak-gradient conditions, while the shear parameters calculated by our method achieve significantly higher accuracy in wavefront reconstruction than existing mainstream algorithms.