Encapsulation is a critical step in semiconductor manufacturing, providing chips with a stable and protected operational environment through integration into compatible external structures. High-precision and non-destructive surface morphology measurement of transparent encapsulated devices is essential, as it enables early detection of latent defects, supports process optimization, and ensures long-term device reliability. However, conventional white light interferometric microscopy faces inherent limitations when applied to encapsulated samples. Existing optical-path compensation schemes offer only restricted compensation ranges, and even small residual mismatches between the encapsulation layer and the compensation glass can introduce monochromatic aberrations and chromatic dispersion. These residual errors degrade fringe contrast, distort the recovered phase, and can ultimately lead to failure in reconstructing surface morphology. To address these challenges, we propose a dual-arm differential adjustable compensation strategy for white light interferometric microscopy. The method is designed to address the thickness mismatch and material dispersion when measuring encapsulated microstructures. The system incorporates two independently adjustable compensators: a plate compensator inserted into the test arm and a pair of wedge plates placed in the reference arm. The wedge plates provide a thickness adjustment range from 4.8 mm to 5.2 mm enabling the system to realize a continuously adjustable compensation range. The two compensators form a continuously adjustable configuration capable of correcting up to 400 mu m of thickness deviation. This design supports stable compensation for encapsulation thicknesses from 0 mm to 5.2 mm. A 2.5 & times; Michelson-type interferometric objective is employed in order to conveniently separate monochromatic aberrations from chromatic dispersion, thereby enabling a focused investigation of dispersion-induced phase distortions and the effectiveness of the proposed compensation strategy. Theoretical modelling and numerical simulations were conducted to assess the feasibility and robustness of the proposed compensation strategy. The modelling incorporated the spectral characteristics of the light source, the refractive-index dispersion of the encapsulation materials, and the numerical aperture of the interferometric objective. A detailed quantitative analysis was carried out to evaluate the influence of light-source bandwidth, the intensity ratio between the two interferometric arms, and residual thickness mismatch on the achievable fringe contrast. The results highlight the necessity of incorporating adjustable wedge plates to achieve continuous and precise dispersion compensation. Based on the simulation outcomes, acceptable tolerance ranges for the residual mismatch were derived, providing practical design guidelines for implementing adjustable dispersion compensation in interferometric microscopy platforms. Experimental validation was conducted using three representative classes of samples to verify the measurement accuracy and system stability. In addition to validating measurement accuracy, these experiments were also designed to evaluate the long-term operational stability of the compensation mechanism, especially under varying encapsulation thicknesses. First, a Bruker RM1722 roughness standard was used to evaluate surface roughness under encapsulation. The dynamic adjustment of the wedge plates in the reference arm effectively preserved high-contrast fringes. The encapsulated sample exhibited an arithmetic average roughness of (0.63 +/- 0.003) nm, which closely matched the value of (0.61 +/- 0.004) nm for the unpackaged sample. Second, a standard SHS-23008 step height specimen was measured beneath a 1 mm K9 cover plate to simulate the encapsulation condition. The reconstructed step height was (9.272 +/- 0.021) mu m, demonstrating both the accuracy of the compensation method and the robustness of the phase retrieval process. Finally, the technique was applied to TO-packaged photodiodes to characterize the surface morphology of the encapsulated chip region. The arithmetic mean height and root mean square height of the surface were 3.855 nm and 3.892, respectively, indicating the good fabrication quality. These comprehensive results confirm that the proposed dual-arm differential adjustable interferometric method is feasible, reliable, and highly accurate for characterizing the surface morphology of transparent encapsulated microstructures. The demonstrated performance establishes the method as an effective and practical solution for high-precision, non-contact morphology evaluation of transparent encapsulated devices.

Objective Dynamic optical profilometers, due to their vibration-resistant design, are widely used in critical applications such as in-situ real-time measurement in machining workshops and inspection of large-aperture optical lenses. However, their unique phase-shifting mechanism-based on polarization cameras-renders them highly sensitive to polarization variations along the optical path, where non-ideal polarization states can introduce substantial measurement errors. While existing studies primarily address error correction in discrete polarization components (e. g., quarter-wave plates and polarizers) using the Lissajous ellipse transformation method, polarization errors within the Linnik-type polarization microscopic interference objective-the core component of dynamic profilometers-remain insufficiently studied. Notably, as the key optical element, internal polarization errors in the Linnik objective can directly compromise the accuracy of surface topography measurements. Owing to its distinctive non-common-path configuration, measurement precision is limited not only by wavefront mismatch between the paired microscope objectives but also by polarization asymmetry, which has emerged as a critical bottleneck. This study establishes a polarization error propagation model through theoretical analysis of polarization state evolution within the interference objective, systematically elucidating the formation mechanisms and manifestations of polarization errors. The findings are expected to provide theoretical support for improving the measurement accuracy of dynamic optical profilometers. Methods This study utilized a custom-built Linnik-type polarization interference objective system. Using Mueller matrix analysis, an experimental optical path was established to measure and compute the polarization parameters-specifically phase retardation and polarization azimuth-of the dual microscope objectives via a polarization camera. Each objective's polarization characteristics were modeled as a waveplate defined by its fast and slow axes and associated phase retardation (Fig. 2), enabling the construction of a global-waveplate dual coordinate system. With this waveplate coordinate system as a reference, the measured polarization parameters were integrated into Jones matrices to streamline the derivation process. Through Jones matrix analysis of light propagation within the interference objective, a polarization error propagation model was developed. This model not only provides the theoretical formulation of polarization-induced errors but also identifies phase retardation and polarization azimuth deviations-induced by polarization aberrations in the objective -as critical factors influencing topography measurement accuracy. Experimental validation was performed at two levels: calibration tests using quarter-wave plates to verify model accuracy, and comparative tests against a commercial white-light interferometer (Veeco NT9100) to demonstrate the reliability and stability of the correction method. Results and Discussions Experimental results demonstrate high consistency in the measured phase retardation and polarization azimuth angles between the two objectives, with minimal deviations in polarization parameters: the phase retardation difference remains within 10 degrees , while the polarization azimuth angle exhibits less variation than phase retardation (Fig. 7). In the quarter-wave plate validation experiment (Fig. 5), the measured phase retardation introduced by the test sample was 3.146 rad. This excellent agreement between experimental and calculated results conclusively validates the polarization error model. Error compensation experiments were subsequently conducted on a smooth surface following the established correction procedure. As illustrated in the comparative results, the corrected measurements from the dynamic optical profilometer show excellent agreement with the reference topography obtained via white-light interferometry (Veeco NT9100). The relative error in surface roughness Sa decreased from 90% to 15%, with a significant improvement in overall topography fidelity (Fig. 9). For stability testing, repeated measurements were performed on a standard roughness silicon wafer using both white-light interferometry and the dynamic optical profilometer. The white-light interferometer yielded an average S-a value of 0.283 nm with a standard deviation of 0.022 nm, corresponding to data fluctuations within +/- 0.033 nm. In contrast, the dynamic optical profilometer produced an average S-a of 0.292 nm with a standard deviation of 0.014 nm and fluctuations within +/- 0.02 nm (Fig. 11). These comparative results confirm the superior measurement stability of the dynamic optical profilometer. Conclusions This study proposes a polarization error correction method for Linnik-type polarization interference objectives based on differential polarization analysis using dual objectives. Through Mueller matrix modeling, the disparity in polarization characteristics between the two microscope objectives was quantified. The established error propagation model revealed a symmetric distribution of polarization errors at an azimuth angle alpha =45 degrees , providing theoretical insight into the error mechanism inherent in interference objectives. Subsequently, a validation experiment on polarization error was conducted using a quarter-wave plate. The experimental results show strong consistency with the theoretical polarization error transfer model. Furthermore, comparative error correction experiments were performed on an existing dynamic optical profiler. After correction, the deviation of the surface topography Sa value from the mean measured by a white-light interferometer (Veeco NT9100) was less than 0.028 nm, with a standard deviation of only 0.014 nm. These results confirm the feasibility and repeatability of the proposed method. It should be noted that, due to experimental constraints, this study did not include comparative analysis of polarization errors across objectives with different numerical apertures, which may affect the model's universality in diverse optical systems. Future work will focus on developing a hierarchical correction method based on numerical aperture characteristics, leveraging parametric modeling to enhance calibration efficiency and accuracy across varied optical configurations.

The surface roughness of a hypodermic needle critically influences puncture performance, yet its quantitative relationship with puncture force lacks sufficient characterization and validation. In this study, a controlled gradient of surface roughness (Sa = 0.244-0.500 mu m) was established by polishing needle bevels, and an integrated framework was developed to couple surface metrology with puncture mechanics. To ensure accurate surface characterization, a filtering strategy based on the instrument metrological characteristics and sample surface features (IMSF) was proposed for optimizing scanning white light interferometry (SWLI) measurements. Additionally, an automatic puncture feature extraction (APFE) method was developed to quantify puncture force by extracting the initial slope of force-displacement curves. Under a fixed insertion angle, puncture force exhibited a clear nonlinear dependence on roughness, which a quadratic model accurately described. This quadratic correlation was further validated across five distinct insertion angles (30 degrees-90 degrees), each yielding high coefficients of determination (R-2 > 0.96). Two-way ANOVA further confirmed significant main effects of angle, roughness and their interaction, validating the model's robustness across different conditions. To account for manufacturing feasibility, a composite evaluation function Psi(Sa) was proposed, integrating normalized puncture slope with an inverse roughness-based machining difficulty index. Analysis of Psi(Sa) identified a consistent platform region in the range of Sa approximate to 0.30-0.40 mu m, offering stable puncture performance while minimizing production complexity. These findings identify a roughness range that balances functional performance and manufacturability effectively, providing a validated and practical guideline for optimizing needle surface texture in medical device production.

Low-coherence scanning interferometry (LCSI) is a widely used technique for high-precision three-dimensional (3D) surface topography measurement. However, the measurement accuracy and efficiency of existing methods are significantly constrained by the sampling interval and the uniformity of the sampling positions. To address this issue, this paper proposes a global adaptive low-pass filtering (GALF) method. Instead of relying on ground-truth height values or reference envelopes, the proposed method combines actual sampling position information with an ideal interferometric model to construct a comprehensive objective function based on envelope morphological similarity. This objective function enables adaptive optimization of the cutoff frequency and filter order, thereby improving envelope extraction and three-dimensional surface reconstruction under non-uniform undersampling conditions. Simulation and experimental results demonstrate that, for step samples with heights on the order of tens of micrometers, even when the sampling interval is increased to 19 times the Nyquist interval and exhibits a non-uniform deviation of ±0.2 μm, the proposed method can constrain the height measurement error and the reconstructed surface waviness to within 1% and 0.5 μm, respectively, while maintaining high computational efficiency (topography reconstruction completed in approximately 10 s). Furthermore, the method can reliably reconstruct complex surfaces, such as microchannels and bumps, under low signal-to-noise ratio conditions. These results indicate that the GALF method provides a practical and robust solution for high-precision three-dimensional surface measurement under sparse and non-uniform sampling conditions.

Abstract Metalens arrays hold great promise for compact light-field imaging systems owing to their compactness and wavefront shaping capabilities. However, their fixed focal lengths fundamentally limit depth-of-field modulation and axial scanning, restricting their adaptability to diverse light-field imaging scenarios. Here, we demonstrate adaptive light-field imaging using a varifocal Alvarez metalens array. The array is composed of two closely bonded metasurfaces, each patterned with 24 × 20 cubic-phase sub-regions. Through relative lateral displacement, the Alvarez metalens array achieves continuous focal length tuning from 3.33 mm to 4.50 mm. Integrated into a plenoptic imaging system, the proposed metalens array enables dynamic focusing and an expanded depth range. We further introduce a MultiLensFusion algorithm that combines these multi-focus captures into high-resolution, all-in-focus renderings. This work offers a compact and versatile platform for next-generation light-field imaging systems with dynamically tunable optical response.

Piston errors between isolated regions remain a major obstacle in segmented phase unwrapping. We propose a robust phase unwrapping method based on phase gradient-domain reconstruction and the least-squares algorithm. The approach reconstructs and bridges segmented phase islands in the gradient domain, providing a continuous gradient field for subsequent unwrapping. To ensure robustness under varying noise conditions, an adaptive dual-domain filtering strategy is introduced. A Noise Index (NI) is defined to quantify the density of gradient outliers, enabling dynamic switching between gradient-domain filtering and a cascaded complex-domain and gradient-domain filtering scheme. In addition, a residual iterative process is employed to correct local phase errors. Numerical simulations and experimental validations confirm that the proposed method successfully eliminates piston errors among phase islands, maintains accurate global phase reconstruction under various obscuration and noise conditions, and achieves high computational efficiency, thereby providing a reliable and practical solution for optical interferometric applications.

With the rapid development of precision manufacturing, semiconductor lithography, and aerospace engineering, ultra-precision machining and metrology have placed higher demands on micro-displacement measurement systems that combine nanometer-level precision with high-bandwidth real-time performance. In dynamic, high-speed motion scenarios, such systems not only need to achieve extremely high resolution but also provide low-latency data processing at high sampling rates. As a fundamental technology in modern length metrology, laser interferometry has inherent advantages in terms of accuracy and stability. However, traditional software-based processing architectures rely on CPUs and sequential execution models, often encountering severe computational bottlenecks when processing high-speed interferometric signals. These limitations make it difficult to simultaneously meet the conflicting demands of large measurement range, high resolution, and real-time detection. To overcome these challenges, this paper proposes a single-frequency laser displacement measurement system based on FPGA, which integrates an FPGA platform and a high-performance point-by-point phase calculation algorithm. By transferring the signal processing algorithm from software to a dedicated hardware logic platform and employing parallel computing and a pipelined approach, the system significantly improves real-time performance while maintaining nanometer-level measurement accuracy. First, this paper establishes a four-channel orthogonal laser interferometry structure and develops a real-time phase demodulation method based on the phase difference between adjacent sampling points. By introducing phase jump correction and cumulative phase compensation mechanisms, the algorithm effectively solves the problems of phase unwrapping ambiguity and displacement direction discrimination under high-speed motion conditions, thereby ensuring the continuity and robustness of displacement measurement. Meanwhile, to analyze the impact of non-ideal optical elements on nonlinear errors, this paper constructs a systematic error model using Jones matrix theory. This model quantitatively analyzes the effects of waveplate angle misalignment and Polarization Beam Splitter (PBS) splitting ratio imbalance on the interference signal, revealing their roles in introducing DC offset, amplitude mismatch, and non-orthogonality between orthogonal channels. Based on this analysis, this paper designs a vector-based error compensation algorithm to correct these defects, thereby significantly improving phase linearity and overall measurement accuracy. Based on the proposed algorithm, a complete experimental test platform was established, and a host-computer-based multi-threaded displacement measurement software was developed to evaluate the system performance. Experimental results demonstrate that, within a measurement range of 200 mu m, the system achieves a statistical measurement accuracy better than 10 nm while supporting millisecond-level data update rates, thereby validating the effectiveness and practicality of the proposed method. Based on the validated theoretical and software framework, this paper further develops an FPGA hardware system integrating a high-speed multi-channel ADC to comprehensively enhance real-time processing capabilities. By employing a fully pipelined architecture and dedicated parallel processing units, key algorithms such as error compensation and phase demodulation are transformed into hardware logic. This hardware-oriented design ensures stable and predictable computational latency, which is crucial for real-time measurement. Experimental comparisons show that the results of the FPGA-based hardware processing are in high agreement with the results of the host multi-threaded software algorithm, with a Root Mean Square Error (RMSE) of only 9.16 nm and statistical accuracy consistently maintained within 10 nm. Real-time performance evaluation further validates the advantages of the proposed system. The initial processing latency is reduced to 10.4 mu s, and the displacement data update cycle reaches 100 ns. Therefore, the system can reconstruct complete micrometer-level motion trajectories in real time within 1 millisecond, representing a significant performance improvement compared to traditional CPU-based processing architectures. These performance characteristics make the system particularly suitable for applications such as high-speed motion, dynamic vibration monitoring, and real-time feedback control. In summary, this paper proposes a laser interferometric real-time displacement measurement system by deeply integrating a point-by-point phase demodulation algorithm and FPGA-based hardware acceleration technology. This system simultaneously achieves high precision, high stability, and ultra-fast real-time performance. It provides a reliable and high-performance metrology solution for closed-loop motion control, dynamic vibration analysis, and nanometer-level precision positioning in ultra-precision engineering applications, demonstrating significant practical value and broad application prospects.

Accurate determination of both spatial period and height is essential for grating characterization using coherence scanning interferometry (CSI), particularly when the lateral period measurement limit of the CSI system and the grating height is smaller than the illumination wavelength. The accuracy of both grating period and height measurements are significantly constrained by the combined effects of limited lateral resolution and edge-induced interferometric signal superposition. In this paper, we propose a method that combines dark field geometry guidance with model-assisted interferometric processing to enable accurate grating characterization under resolution-limited conditions without modifying the existing hardware. Dark field imaging enhances edge localization rather than the intrinsic optical resolution of the system, thereby enabling subpixel grating-edge localization and geometric referencing. In simulation, the grating period estimation achieves an error below ±2%. Subsequently, the accurately localized grating edge geometry is incorporated into Fourier-domain analysis under the guidance of a Fourier-optics-based interferometric signal formation model, through which redundant superposed interferometric components induced by grating edges are effectively identified and eliminated, thereby enabling more reliable grating height calculation from the conditioned interferometric signal. Finally, the grating surface topography is reconstructed using a standard envelope-based CSI algorithm. As a representative validation, experiments on a Bruker step height standard demonstrate that the proposed combination of dark field geometry guidance and model-assisted interferometric processing achieves accurate step width estimation and effectively eliminates redundant interferometric components in the vicinity of step edges. In addition, measurements performed on the PTB RS-N resolution standard, which contains gratings with different spatial periods, further validate the robustness of the proposed method. Experimental results show that the proposed method improves both grating period determination and grating height measurement under resolution-limited conditions. For a grating with a 2 µm period, the proposed method reduces the signed relative height error of the reconstructed profile from 5.6% to 0.3% compared with conventional median filtering.

The topographic spatial resolution in microscopic interferometry is constrained by its optical resolution. This study presents a novel Linnik-type microscopic interferometry system that incorporates full-field annular radially polarized (RP) illumination to enhance system response in both imaging and topographic reconstruction near the diffraction-limit frequency. Unlike previous studies that rely on point-scanning configurations to exploit the tight focusing properties of RP light, full-field RP illumination is realized via a two-stage relay system integrating a spatial light modulator (SLM) and a vortex retarder (VR). This transition from point-scanning to full-field implementation improves measurement efficiency while preserving resolution advantages. System response is evaluated through numerical analyses of Modulation Transfer Function (MTF) and Instrument Transfer Function (ITF) under differently modulated illumination. Experimental validation using various amplitude and phase objects yields full-field microscopic images and 3D surface topographies via coherence scanning interferometry (CSI). Results demonstrate that structures previously indistinguishable under conventional illumination, such as 2293 cycles/mm line pairs and 2500 cycles/mm phase gratings, become clearly distinguishable in both intensity images and reconstructed topographies. Furthermore, Siemens star measurements reveal enhanced system response and more isotropic performance. These findings confirm the advantages of using full-field annular RP light in interferometric microscopy for high-resolution metrology.

Objective Transparent optical components require accurate, quantitative characterization of transmitted wavefronts and nanoscale height steps. While the Mach-Zehnder interferometer is a classical platform for such metrology, we propose a polarization-multiplexed Mach-Zehnder interferometer in which the phase shifts are produced by rotating a spiral phase plate (SPP). Two orthogonal polarization channels respectively carry the intrinsic SPP phase and the composite phase of the SPP and the sample, enabling single-sequence phase separation and minimizing repeated actuation. Key challenges addressed include the diffraction associated with the SPP's central singularity and step edges and the spatial non-uniformity of phase steps under rotation. Our objective is to demonstrate accurate, robust recovery of the sample phase and transmitted wavefront on a transparent step plate and to quantify agreement with a commercial Fizeau interferometer. Methods The system adopts a Mach-Zehnder layout with polarization multiplexing and a motorized SPP in the reference arm. A four-step rotational phase-shifting interferometry (PSI) sequence is executed while the two interferometric paths are combined and imaged on a polarization camera so that s/p channels are recorded simultaneously (Fig. 3). To suppress artifacts from the SPP's central singularity and etched step, we use a non-center incidence strategy: a ring-shaped effective aperture is selected by radial sampling of the SPP, and the rotational angles are chosen to minimize the deviation from the target pi /2 step within the ring (Fig. 5). Following channel demultiplexing and analytical decoupling, we obtain the wrapped SPP/sample phase, then perform a single phase-unwrapping step and convert optical path difference to height. System cavity phase is calibrated prior to inserting the sample (Fig. 9). The test object is a transparent step plate with a nominal height of 139 nm. Repeated measurements and cross-validation are performed against a 4 inch Zygo Fizeau interferometer on the same field (Fig. 11 and Fig. 12). Results and Discussions The proposed scheme enables simultaneous acquisition of the SPP-only phase and the composite sample/SPP phase within one rotational sequence, avoiding repeated phase shifts and reducing temporal drift. The non-center incidence selection yields higher fringe visibility and visibly suppresses ring-like diffraction artifacts in the imaging domain, improving edge fidelity in the vicinity of the height discontinuity. On a 4.8 mm & times; 4.8 mm field, the average measured step height over ten trials is 137.2 nm versus the nominal 139 nm, corresponding to a 1.29% deviation. The transmitted wavefronts (upper and lower surfaces) reconstructed by our method agree with the Zygo results with absolute deviations smaller than 0.011 in peak-to-valley (PV) value and 0.0021 in root-mean-square (RMS) value (Fig. 11 and Fig. 12). These outcomes confirm the method's accuracy and reproducibility for transparent samples with weak reflectivity and small phase excursions. In addition, by applying interpolation and resampling, the resolution of the experimental data (Fig. 11) and the Zygo laser interferometer data (Fig. 12) is unified. Subtracting the two datasets after resolution matching yields the transmitted wavefront error (Fig. 13), whose maximum absolute value is 0.021, consistent in magnitude with the simulation results. Wavefront measurement errors caused by SPP quality defects are limited. In the future, the wavefront measurement errors can be further reduced by replacing the SPP with a high-precision SPP to improve measurement accuracy. Overall, the method delivers high-accuracy transmitted-wavefront metrology without piezo stages or wavelength-tuning sources and with minimal mechanical actuation (only SPP rotation) while keeping the optical setup compact. Conclusions This paper proposes a rotational phase-shifting method based on orthogonal polarization multiplexing for high-accuracy measurement of the phase and transmitted wavefront of transparent samples. The method does not rely on high-precision phase-shifting devices such as piezoelectric stages or tunable lasers. The phase shift is achieved solely by rotating an SPP, resulting in a simple structure capable of stable and continuous phase shifting. By encoding the SPP's intrinsic phase and the phase combined with the sample into two orthogonally polarized interference beams, the two sets of phase information can be synchronously separated and extracted. Simulations indicate that the quality of the SPP has a limited effect on phase-shifting measurement errors, and future use of a high-precision SPP can further reduce measurement errors. The feasibility and accuracy of the method are validated experimentally. For a transparent step sample with a nominal step height of 139 nm, the mean error of ten measurements using the proposed method is 1.29% relative to the nominal value. Compared with measurements from a Fizeau laser interferometer, the absolute deviations of the PV and RMS values of the transmitted wavefronts on the upper and lower step surfaces are less than 0.011 and 0.0021, respectively, and the absolute wavefront error is below 0.021, demonstrating high consistency and accuracy. In summary, the proposed method provides a novel approach for phase-shifting measurements and shows promising applicability and practical value in phase and transmitted-wavefront characterization of transparent optical components.

Low-coherence scanning interferometry (LCSI) is capable of high-precision 3D surface topography measurement. However, when measuring a millimeter-scale step surface, traditional methods are often limited by excessive measurement time and high computational load. This paper proposes a prior-knowledge-assisted adaptive variable-rate sampling strategy combined with polynomial regression fitting (APRF). The method adaptively adjusts the scanning rate and sampling interval according to the step height (0.1-1.5 mm) to control the acquisition time within 0.5 s. Meanwhile, for non-uniform undersampled interference signals, the APRF algorithm is employed to rapidly reconstruct the interference envelope and obtain the 3D topography of the sample. Experiments demonstrate that under a scanning speed of 7.5 mm/s, a sampling interval 100 times the Nyquist interval, and a positional scanning non-uniformity of +/- 1.0 mu m, the proposed method completes the measurement of a 1.5 mm multi-step sample within 10 s, achieving accuracy improvements of more than fourfold and twofold over the centroid and Gaussian fitting methods, respectively. These findings comprehensively demonstrate the effectiveness, robustness, and practical superiority of the proposed approach for high-speed inspection of large-scale specimens.

Non-destructive and accurate characterization of high aspect ratio (HAR) and composite micro-trenches is critical for advanced microfabrication but remains a major challenge. Conventional coherence scanning interferometry (CSI), while widely adopted, suffers from low signal-to-noise ratio (SNR) and limited lateral resolution when applied to HAR and composite microstructures. Here, we present Fourier ptychographic coherence scanning interferometry (FP-CSI), the first transmissive CSI modality that integrates the aperture synthesis strategy of Fourier ptychographic microscopy with the quantitative phase-resolved capability of interferometry. FP-CSI enables robust three-dimensional morphology reconstruction with enhanced SNR and improved lateral resolution, without reliance on iterative phase retrieval. We demonstrate accurate measurements of a HAR micro-trench (300 μm depth, 30:1 aspect ratio) and micro-electro-mechanical system (MEMS) devices (aspect ratios 6:1–20:1). FP-CSI achieves lateral resolution up to the incoherent diffraction limit and maintains this performance even at trench bottoms. Owing to its fidelity, robustness, and non-destructive operation, FP-CSI provides a powerful new metrology platform for next-generation semiconductor inspection, precision manufacturing, and emerging micro-optoelectronic systems. A transmissive Fourier ptychographic coherence scanning interferometry method provides accurate 3D morphology measurements of high aspect ratio and composite micro-trenches, enhancing both the signal-to-noise ratio and lateral resolution.

From integrated optical circuits to long-haul fiber-optic networks,most photonic devices and communication systems rely on low-loss optical fibers.One of the key parameters affecting the transmission performance of optical fibers is their refractive index distribution,which determines characteristics such as insertion loss,propagation modes,and bandwidth of optical fibers.However,internal defects within the fiber can cause scattering or absorption of the optical signal during transmission,leading to attenuation and leakage of the output optical signal.Therefore,accurately and rapidly measuring the refractive index distribution and internal defects of optical fibers is of great significance for the optimization of fiber structure design and quality monitoring.Currently,the main methods for measuring the refractive index of optical fibers include the refractive near-field method,atomic force etching method,focusing method,thin-film interferometry,and transverse interferometry.Among these,transverse interferometry based on microscopic imaging requires no pre-treatment of the fiber.The fiber can be directly immersed in a matching liquid to achieve rapid,non-destructive measurement of the three-dimensional refractive index of the fiber.Therefore,this paper aims to construct a transverse interferometric system to reconstruct the three-dimensional refractive index distribution of optical fibers,enabling the detection of internal geometric structures and defects within the fiber.Based on the method of microscopic interferometry,this paper designs a cylindrical lens system for fiber measurement that effectively compensates for imaging astigmatism and proposes a high-precision transmissive transverse microscopic interferometric tomography system and method based on the cylindrical lens.First,a fiber simulation model was established based on the Finite Difference Time Domain(FDTD)theory for simulation verification.The results showed that the refractive index reconstruction error was extremely small,verifying the feasibility of the measurement method.Secondly,regarding the selection of the refractive index matching liquid in the experiment,the refractive index distribution of the fiber was reconstructed through single-direction projection to determine the optimal refractive index difference between the matching liquid and the fiber cladding.On this basis,three-dimensional refractive index tomographic reconstruction experiments were conducted on both multimode and single-mode fibers,and the results were compared with those obtained using a spherical lens.The results showed that the measurement error of the fiber core diameter using the cylindrical lens system was reduced by a factor of 10,and all measured values were within the given error range.Furthermore,the fiber defect detection experiment results indicated that the size,shape,and location of internal fiber defects could be identified through the reconstruction of the three-dimensional refractive index distribution of the fiber.

Objective White light interferometers are typically equipped with interference microscopes of various magnifications to meet the topography measurement needs for different scenarios.Low-magnification interferometric microscopes have a large field of view and a small numerical aperture(NA),enabling them to capture low-frequency information from the sample's surface topography and measure macro-scale structures.High-magnification interference microscopes have a small field of view but a large NA,providing higher lateral resolution and a higher cutoff frequency.These are ideal for detecting microscopic topography parameters with high-frequency features in fine structures.Compared to low-magnification interference microscopes,the larger NA allows for the collection of returning light beams at steeper angles,facilitating the detection of sharper slopes and providing more accurate surface topography measurements for curved samples.To simultaneously characterize both the micro-topography features and macro-scale features in the measured topography data,the conventional method involves performing a stitching scan across the lateral range using a high-magnification interference microscope and then fusing multiple sets of measurement data.However,fine microstructures are not evenly distributed across the sample surface,and there are regions with low-frequency features between microstructures that do not require high-resolution detection.Including these low-frequency regions in the stitching and fusion process can reduce detection efficiency.To mitigate this,a more efficient approach can be adopted by considering the characteristics of various magnifications of interference microscopes in white light interferometers.This approach involves conducting targeted detection of local areas that reflect micro-topography features,while simultaneously meeting the requirement to capture macro-scale features.The fusion of macro-scale and micro-topography features into a single dataset helps improve efficiency. Methods The multi-magnification data fusion technology of white light interferometers integrates topography data from different magnification interference microscopes into a unified dataset,thus enhancing the comprehensiveness of topographic feature parameters in the fused data.In this paper,we introduce two techniques,surface fitting and wavelet decomposition fusion.After evaluating the advantages and disadvantages of these methods,we propose a strategy for fusing topography data from various magnification interference microscopes in white light microscopy interferometry based on frequency filtering.The process begins with normalized cross-correlation(NCC)and normalized iterative closest point(NICP)to achieve sub-pixel level registration of the data sets.During the subsequent data fusion stage,based on multi-porous wavelet decomposition,we analyze the cut-off frequency for each magnification microscope,which provides theoretical support for wavelet decomposition and fusion strategies.This ultimately results in a more comprehensive data fusion approach. Results and Discussions Our fusion method fully leverages the advantages of the low-magnification interference microscope's large field of view and the high NA and resolution of the high-magnification interference microscope.We apply this method in fusion experiments for topography data from various surface structures.The first sample surface contains multiple convex arrays.By retaining the periodic information in the data measured by the low NA interference microscope,the curvature feature parameters are refined using high NA interference microscope data through fusion.As a result,the relative errors for the period and curvature radius of the subunits in the final fused data decrease by 1.34 percentage points and 6.00 percentage points,respectively.The second sample is a step-type structure with multiple cylinders arranged on the surface according to a specific pattern.The low-magnification interference microscope can measure the overall periodic arrangement of the structure.After fusing the high-resolution data from the step structure measured by the high-magnification interference microscope,various topography feature parameters can be simultaneously characterized.In the final fusion result,the relative error compared to the scanning electron microscope(SEM)measurement data is 0.419%. Conclusions In this paper,we propose a fusion method that decomposes topography data from various magnification interference microscopes,fuses the sub-data with the same frequency components,and retains the feature information from each dataset.The experiment,which includes two samples with different features,demonstrates how the proposed fusion method can extend the slope measurement range of the low-magnification interference microscope,reduce measurements,and improve the efficiency of the white light interferometer in analyzing both macro-and micro-topography feature parameters simultaneously.The broad applicability of this fusion method for handling various feature samples has been validated,further enhancing the functionality of white light interferometers.The multi-magnification fusion strategy proposed in this paper can be applied not only in white light interferometers but also to topography data obtained from various detection methods.It offers an effective data processing and characterization solution for instruments that integrate multiple measurement technologies,thus enhancing their capabilities.

The performance of large-aperture telescopes of segmented mirrors is primarily determined by the co-phase metrics among segmented mirrors. This paper proposes a novel method, based on polarization-multiplexing multi-wavelength dynamic interferometry, to measure co-phase errors of segmented mirrors. This method merges two light sources into the orthogonally polarized beams serving as test and reference beams. These beams are regrouped before being recorded, allowing two polarization cameras to respectively record the interferograms at different wavelengths. Consequently, this approach enables simultaneous work for two light sources in a single optical path without crosstalk. By integrating spatial phase shifting, two polarization cameras each capture four phase-shifted interferograms in a single shot. The analysis of error amplification due to environmental disturbance demonstrated the superior environmental insensitivity capability of the proposed method. The feasibility of the proposed method was validated using the experimentally constructed interferometer, which adjusted the piston error of the two segmented mirrors from 40.6 mu m to 9.73 nm. This approach minimizes errors caused by environmental disturbance and eliminates the need for high-speed response hardware and their mutual synchronization, offering an effective and economical solution for addressing co-phase errors in largeaperture telescopes of segmented mirrors.

In coherence scanning interferometry (CSI) for high-aspect-ratio (HAR) micro-structures, modulation aberrations induced by trench hinder accurate measurement on their bottom. In order to solve this problem, current methods primarily address single trenches or trench arrays with the same depth by active correcting modulation aberrations. However, many sensor microstructures comprise composite trenches (CT) of varying sizes. Existing approaches lack the ability to dynamically and accurately compensate modulation aberrations during vertical scanning as they vary with CT geometry, limiting high-precision topography reconstruction. What we believe to be a novel method is proposed that dynamic compensation of modulation aberration induced by HAR CT via backpropagation neural network algorithm (DC-BPA) for topography measurement in this paper. The method strategy includes pre-scan to rapidly determine linewidth and depth of tested CT via edge recognition and calculation of Vollath function for auto-focusing near bottom of CT, and deduce the modulation aberrations of each trench using the backpropagation neural network algorithm (BPA) according to determined linewidth and depth, and finally achieve whole coherence vertical scanning through dynamic compensation for each trench of entire CT. Experimental measurements is realized for two kinds of HAR CT samples with depths ranging from 90μm to 130μm. The topography results demonstrate that the proposed method effectively corrects modulation aberrations of CT and gathers scanning interference images with high signal-to-noise ratio near bottom of trench. The results of topography are good agreement with them of scanning electron microscopy. The maximum absolute deviations of linewidth are 0.46μm and 0.41μm, while the maximum depth absolute deviations are 0.54μm and 0.67μm, respectively for two above kinds of samples.

Low-coherence scanning interferometry (LCSI) is a high-precision method for 3D surface topography measurement. However, the non-uniform spatial distribution of sampling points and the size of sampling intervals jointly constrain the measurement accuracy and efficiency of existing methods. To address this issue, this paper proposes an envelope centroid localization method based on sinc function interpolation (ECS). By exploiting the structural similarity between the sinc function and the distribution of low-coherence interference signals, the ECS method compensates for non-uniform and sparse vertical scan sampling points in the characteristic regions of the interference envelope via interpolation. This approach effectively mitigates information loss caused by insufficient sampling and variations in the sampling interval, thereby achieving a better balance between measurement accuracy and efficiency. Under conditions of extremely sparse sampling (sampling interval reaching 17 times the Nyquist interval) and non-uniform sampling intervals (sampling intervals difference up to ±0.2 µm), the proposed method improves measurement accuracy by more than 300% compared to the traditional center of mass (COM) method and peak fitting (PF) method. The reconstructed surface waviness is maintained at around 0.05 µm. These results verify the effectiveness of the proposed method in processing sparse and non-uniform sampling data in LCSI.

A multi-aberration evaluation function is proposed based on the confocal conic mirrors, aiming to search for the optimal starting-point of unobscured four-mirror reflective imagers. Typical aberrations in the off-axis confocal conic system are quantitatively calculated, and the multi-aberration evaluation function is subsequently established to determine the optimal initial structure. Off-axis aberrations such as astigmatism, coma, and field curvature in the initial structure are simultaneously constrained through the proposed evaluation function. An off-axis four-mirror scanning-type space camera is presented as example, where a multi-aberration evaluation function is formulated based on design specifications. Particle swarm optimization algorithm is applied to find the optimal solution, resulting in a confocal conic configuration with excellent on- and off-axis imaging performance. Then, freeform surfaces are further introduced to optimize and expand field of view (FOV). An off-axis four-mirror space camera is realized with an entrance pupil diameter (EPD) of 200 mm, an F-number of 4, a FOV of 4° × 24°, and working band covering the visible and near-infrared (NIR) wavelengths, which also achieves high-quality imaging.

Lateral resolving power is a critical performance metric in coherence scanning interferometry (CSI) for characterizing surface form and texture. Pupil modulation enhances lateral resolving power by reducing the Airy disk size within the point spread function (PSF). In modern metrology, the instrument transfer function (ITF) serves as a comprehensive metric for evaluating lateral resolving power. This study presents an extended Fourier optics model integrated for CSI to simulate surface topography measurements, in which the ITF can be computed for various central obscuration ratios, taking the step-height surface as the sample. Under linear response conditions, the ITF is approximately equal to the corresponding modulation transfer function (MTF) at each central obscuration ratio. Comparisons of the MTF across different central obscuration ratios indicate that pupil modulation enhances the ITF in the high spatial frequency range. As an example, direct measurement of the ITF on a step-height surface validates the accuracy of our model predictions, while experiments with a Siemens star further demonstrate that pupil modulation improves topographic spatial resolution at high spatial frequencies.

In this Letter, we present what we believe to be a novel technique for robust, high-precision measurement of buried microstructures in wafer-level packaging, termed active wavefront-compensatory coherence scanning interferometry (AWC-CSI). By combining high numerical aperture (NA) optics with a deformable mirror for active aberration correction and a dispersion-matched compensation plate in the reference arm, AWC-CSI significantly enhances signal fidelity and signal-to-noise ratio under encapsulating layers. Experimental validation on packaged micro-electromechanical systems (MEMS) devices and resolution targets demonstrated an average topographic lateral resolution of approximately 0.95 μm under encapsulation layers ranging from 100 μm to 300 μm in thickness, with a system optical resolution of 0.89 μm. These results confirm its effectiveness for high-precision inspection and its potential for advanced packaging process optimization.