Search Results (35)

Dynamic visual cryptography (DVC) can be formulated as a discrete-time reconstruction problem for time-averaged moiré fringes generated by oscillatory transformations of periodic gratings. When implemented on digital display hardware, the continuous oscillatory motion must be realized through discrete frames, which may prevent correct reconstruction of higher-order time-averaged fringes due to refresh-rate limitations. In this work, mathematical criteria are derived to ensure the reliable reconstruction of higher-order time-averaged moiré fringes under finite refresh rate constraints. Harmonic, stochastic, and rectangular temporal waveforms are examined within a unified framework based on the number of frames per oscillation period and the discrete structure of the resulting time-averaged intensity distribution. Stochastic waveforms are shown to not guaranty reproducible fringe formation. For harmonic modulation with a 240 Hz display refresh rate and a 50 Hz oscillation frequency, only four full frames per period are obtained, which is insufficient to reconstruct the third time-averaged moiré fringe requiring at least sixteen frames per period. Rectangular waveforms satisfy the derived reconstruction conditions when the pitch of the grating, the oscillation amplitude, and the resolution of the rendered grating meet explicit constraints. These results establish quantitative parameter bounds for a mathematically consistent software-based DVC implementation on digital displays. Full article

Distortion is a key parameter affecting the imaging performance of lenses. In this study, we propose a testing method based on detector Nyquist sampling of image data to achieve high-precision measurements of the distortion distribution of lenses. The distribution patterns of distortions in horizontal and vertical directions can be obtained by analyzing the distribution patterns of Moiré fringes in images under Nyquist sampling conditions and using phase-shift algorithms. The distortion-distribution characteristics of the lens are then calculated using distortion formulas. This method is characterized by high testing accuracy and sampling resolution. The image-plane distortion distribution exhibited a consistent linear trend when the object-plane position varied within a limited spatial range. Furthermore, the proposed method achieved a magnification deviation factor repeatability accuracy of approximately ±108 nm/cm and third-order distortion-measurement accuracy of approximately ±108 nm/cm³. This method enables a high-precision distortion evaluation of conventional industrial imaging lenses. Full article

Ground-based remote sensing of seismic and geophysical displacements remains a major challenge due to environmental hazards, signal attenuation, and practical deployment limitations of traditional seismometers. In this study, we present a detailed design, implementation, and performance evaluation of a Moiré-based apparatus for remote ground displacement measurement. The system operates by detecting fringe shifts formed between a fixed and a displaced grating, with displacement magnified through controlled angular superposition. We systematically assess each component of the system, including telescope optics, imaging sensors, and grating configurations, to optimize spatial resolution, contrast, and robustness under varying environmental conditions. A digital approach for fringe generation was employed, allowing controlled magnification and improved sensitivity without the need for physical alignment of dual gratings. Indoor experiments under low-turbulence conditions validated the system’s capability to detect displacements as small as $50 \mathrm{\mu }\mathrm{m}$. Subsequent outdoor trials at different distances demonstrated successful measurement of both square-wave and seismic-like displacements despite increased atmospheric turbulence and wind. The results confirm the system’s ability to perform real-time, long-range, non-contact displacement monitoring with high accuracy and resilience to environmental variability. This study establishes a foundation for the application of Moiré-based sensing in challenging field conditions, including volcanic and seismic zones. Full article

Raster-stereography and Moiré Fringe Topography are widely recognized as effective techniques for surface screening. Traditionally, these methods have been applied in various medical and clinical contexts, such as assessing human body symmetry, analyzing spinal deformities, evaluating scapular positioning, and predicting trunk-related abnormalities. Both techniques have proven to be reliable tools for examining the human body surface and identifying health-related issues. However, in these techniques, line grids projected onto non-uniform surfaces often break or distort, complicating curvature detection. Capturing and digitizing these distortions through photographymeans further reducing accuracy due to low contrast between background and projected lines. In this paper, we present a modified, i.e., dotted-based, approach to Moiré Fringe Topography construction, offering a simpler, more accurate, and efficient method for recording human body surface curvatures. The proposed technique significantly reduces the complexity of the data acquisition process while maintaining precision in surface analysis. A Single-Photon Avalanche Diode (SPAD) image sensor was used to capture the Moiré patterns. Full article

This paper proposes a grating Moiré fringe signal compensation method based on Variational Mode Decomposition (VMD) to address signal errors in grating encoders. VMD decomposes Moiré fringe signals into multiple amplitude-modulated and frequency-modulated components, and realizes noise compensation through parameter optimization and signal reconstruction. The Multi-Strategy Particle Swarm Optimization (MSPSO) enhances optimization performance via adaptive inertia weight adjustment and chaotic perturbation, solving the problems of mode mixing or over-decomposition caused by blind parameter selection in traditional VMD. A hardware-software co-design test system based on ZYNQ FPGA is developed, which optimally allocates tasks between the Processing System and Programmable Logic, resolving issues of large data volume and long computation time in traditional systems. The compensation scheme provides excellent signal processing performance. The experimental tests on random periodic signals, triangular waves and square waves with different duty cycles have demonstrated the robustness of this scheme. After compensation, the output signal exhibits excellent sinuosity and orthogonality, with harmonic components and noise in the frequency domain almost negligible. It provides a practical solution for high-precision measurement in ultra-precision machining, semiconductor manufacturing, and automated control. Full article

To investigate the radiation stability of the intermetallic in PH 13–8 Mo steel, precipitates with different sizes were generated and then the samples are irradiated with 400 keV Fe⁺ at room temperature with maximum damage up to 8 dpa. The pre- and post-irradiation samples are examined with selected area electron diffraction (SAED), scanning transmission electron microscopy (STEM) and Energy Dispersive Spectroscopy (EDS). Before the irradiation, B2 NiAl precipitates are uniformly distributed in matrix with increased sizes of 2.5, 4.9 and 8.1 nm. After the irradiation, the intensity of SAED superlattice pattern of B2 NiAl with 8.1 nm diminishes rather than disappeared in the remaining samples, indicating that the ordered B2 structure of NiAl precipitates of smaller size are mostly destroyed. EDS results proves that no elemental diffusion took place between the precipitates and matrix. Moiré fringes are found to be located beside dissolved precipitates attributed to radiation-enhanced diffusion. This work will provide advice for the material design of other intermetallic strengthened alloys especially in nuclear applications. Full article

This work employs moiré interferometry to investigate the influence of sintering temperature and sandblasting on the optical and mechanical properties of magnesium aluminate spinel (MgAl₂O₄). S25CRX14 Spinel pellets were fabricated via Spark Plasma Sintering (SPS) at 1300 °C, 1350 °C, and 1400 °C. The sintered samples were subsequently analyzed before and after sandblasting. Moiré interferometry, a non-destructive and contactless technique based on the superposition of tow linear transmission gratings, has proven particularly suitable for detecting micro-defects in transparent materials. The analysis of moiré fringes provided essential insights into the presence and size of defects, enabling accurate quality assessment without altering the samples. Its high spatial resolution, allowed the detection of even low-contrast defects. The results confirmed that the sintering temperature and sandblasting significantly influenced the mechanical and optical properties of the S25CRX14 spinel samples. The specimens sintered at 1350 °C exhibited the highest light transmission and the superior hardness. In contrast, the samples sintered at 1400 °C showed a notable degradation in their optical and mechanical properties. In conclusion, the pellets sintered at 1350 °C demonstrated the most favorable overall performance. This study confirms that moiré interferometry is a straightforward, accurate, and highly effective method for evaluating transparent ceramics, with very low implementation costs. Full article

Long bone fractures are breaks or cracks in a long bone of the body typically caused by trauma like a fall, sport injury, accidents etc. This study investigates the effectiveness of experimental methods for fast and safe healing of long bone fractures in humans, highlighting both their advantages and disadvantages, respectively finding the most effective and safe methods for evaluating the types of fixators that can be used in the consolidation of fractured long bones. As for the preliminary data, numerical methods and applied mathematics were used to address this problem. After collecting of preliminary data there were performed a series of experimental analysis as follows: Electrical Strain Gauges (ESGs); the Moiré Fringes method; Photo-Elasticity, with the particular technique thereof, the so-called Photo-Stress method; Holographic Interferometry (HI); Speckle Pattern Interferometry (ESPI) and Shearography; and Video Image Correlation (VIC), which is also called Digital Image Correlation (DIC). By analyzing different methods, the following two methods resulted to be widely applicable, namely, ESG and DIC/VIC. The findings highlight the net advantages regarding the objective choice of these types of fixators, thereby contributing to a possible extension of these approaches for the benefit of medical surgical practice Full article

This study introduces a novel, low-cost, and non-invasive method for characterizing the surface profile of transparent objects using double digital fringe projection (DDFP). By projecting dual sinusoidal patterns that generate a Moiré effect and applying a frequency-domain Gaussian filter, the system isolates relevant data for accurate phase recovery through the isotropic quadrature transform (IQT). Experimental validation with plastic and acrylic samples confirms the method’s high spatial resolution and robustness against ambient noise. Unlike traditional systems, this technique avoids coherent light sources and complex hardware, improving its accessibility for academic and industrial use in transparent surface metrology. Full article

The remote sensing of seismic waves in challenging and hazardous environments, such as active volcanic regions, remains a critical yet unresolved challenge. Conventional methods, including laser Doppler interferometry, InSAR, and stereo vision, are often hindered by atmospheric turbulence or necessitate access to observation sites, significantly limiting their applicability. To overcome these constraints, this study introduces a Moiré-based apparatus augmented with active convolved illumination (ACI). The system leverages the displacement-magnifying properties of Moiré patterns to achieve high precision in detecting subtle ground movements. Additionally, ACI effectively mitigates atmospheric fluctuations, reducing the distortion and alteration of measurement signals caused by these fluctuations. We validated the performance of this integrated solution through over 1900 simulations under diverse turbulence intensities. The results illustrate the synergistic capabilities of the Moiré apparatus and ACI in preserving the fidelity of Moiré fringes, enabling reliable displacement measurements even under conditions where passive methods fail. This study establishes a cost-effective, scalable, and non-invasive framework for remote seismic monitoring, offering transformative potential across geophysics, volcanology, structural analysis, metrology, and other domains requiring precise displacement measurements under extreme conditions. Full article

Alignment systems are core subsystems of lithography, which directly affect the overlay accuracy of the lithography process. The Moiré fringe-based alignment method has the advantages of high precision and low complexity. However, the precision of this method is highly sensitive to variations in the gap between the wafer and the mask. To enhance the performance of Moiré fringe-based alignment, this paper proposes a novel method in which the multi-wavelength approach is used to enhance the imaging depth of focus (DOF). We use a multi-wavelength light to illuminate the alignment marks on the wafer and mask, which is combined with different sources. Then, we use the improved phase analysis algorithm to analyze the contrast of the Moiré fringe and calculate the Moiré fringe displacement. Experiments show that, in an alignment range of 1000 μm, the effective DOF can exceed 400 μm. It is evidenced that the accuracy of the Moiré fringe alignment is unaffected and remains at the nanometer level. Otherwise, with parameter optimization, the alignment DOF is expected to be further extended. Full article

The Talbot wavemeter has attracted widespread attention from researchers in recent years due to its advantages of miniaturization and low cost. However, the impact of varying incident conditions caused by factors such as alignment has remained a challenge for spectral retrieval. This paper first derives the influence of different incident conditions on the interference pattern based on Fresnel diffraction and verifies the derivation through simulations. We propose a method to address the impact of incident conditions on the interference pattern. By adding a grating with a different periodicity in front of the detector, Moiré fringes are generated in the periodicity dimension, increasing the fringe period and thus enlarging the tolerance for angular misalignment. Finally, we constructed a Talbot wavemeter based on a double-grating structure, achieving a spectral resolution of 9 nm at 360 nm. This method provides a reference for the future development of a high-precision, high-resolution Talbot wavemeter. Full article

This paper proposes an improved algorithm based on the phase extraction of the Moiré fringe for wafer-mask alignment in nanoimprint lithography. The algorithm combines the strengths of the two-dimensional fast Fourier transform (2D-FFT) and two-dimensional window Fourier filtering (2D-WFF) to quickly and accurately extract the fundamental frequencies of interest, eliminate noise in the fundamental frequency band by using the threshold of the local spectrum, and effectively suppress spectral leakage by using a Gaussian window with outstanding sidelobe characteristics while overcoming their limitations, such as avoiding the time-consuming parameter adjustment. The phase extraction accuracy determines the misalignment measurement accuracy, and the alignment accuracy is enhanced to the nanometer level, which is 15.8% and 6.6% higher than 2D-FFT and 2D-WFF, respectively. The results of simulations and experiments confirm the feasibility and rationality of the algorithm. Full article

A highly robust dual-frequency hierarchical temporal phase unwrapping (DHTPU) based on the novel spatial computer-generated Moiré profilometry (SCGMP) is proposed. The method requires only three patterns: a high-frequency fringe to provide robust surface information, a multi-period low-frequency fringe to eliminate the 2π-phase ambiguities, and a flat pattern to remove the average intensity of the two fringes. In decoding, different from traditional Moiré profilometries that rely on spectrum filters, SCGMP only employs spatial-domain calculations to extract the wrapped phase, thereby preserving more detailed information. Furthermore, we fully explore SCGMP’s capability to significantly alleviate phase ambiguity and provide an algorithm to determine the maximum measurable height range for a fixed system, enabling the direct extraction of the continuous basic phase from the multi-period low-frequency fringe. Consequently, the proposed basic phase exhibits an enhanced signal-to-noise ratio, compared to the traditional basic phase derived from the single-period fringes, effectively releasing the high-frequency restriction in the traditional DHTPU. The experimental results verify that the proposed DHTPU method has considerable accuracy and great potential for high-speed measurements, due to there being only three shots required. Full article

Overlay accuracy, one of the three fundamental indicators of lithography, is directly influenced by alignment precision. During the alignment process based on the Moiré fringe method, a slight angular misalignment between the mask and wafer will cause the Moiré fringes to tilt, thereby affecting the alignment accuracy. This paper proposes a leveling strategy based on the DQN (Deep Q-Network) algorithm. This strategy involves using four consecutive frames of wafer tilt images as the input values for a convolutional neural network (CNN), which serves as the environment model. The environment model is divided into two groups: the horizontal plane tilt environment model and the vertical plane tilt environment model. After convolution through the CNN and training with the pooling operation, the Q-value consisting of n discrete actions is output. In the DQN algorithm, the main contributions of this paper lie in three points: the adaptive application of environmental model input, parameter optimization of the loss function, and the possibility of application in the actual environment to provide some ideas. The environment model input interface can be applied to different tilt models and more complex scenes. The optimization of the loss function can match the leveling of different tilt models. Considering the application of this strategy in actual scenarios, motion calibration and detection between the mask and the wafer provide some ideas. To verify the reliability of the algorithm, simulations were conducted to generate tilted Moiré fringes resulting from tilt angles of the wafer plate, and the phase of the tilted Moiré fringes was subsequently calculated. The angle of the wafer was automatically adjusted using the DQN algorithm, and then various angles were measured. Repeated measurements were also conducted at the same angle. The angle deviation accuracy of the horizontal plane tilt environment model reached 0.0011 degrees, and the accuracy of repeated measurements reached 0.00025 degrees. The angle deviation accuracy of the vertical plane tilt environment model reached 0.0043 degrees, and repeated measurements achieved a precision of 0.00027 degrees. Moreover, in practical applications, it also provides corresponding ideas to ensure the determination of the relative position between the mask and wafer and the detection of movement, offering the potential for its application in the industry. Full article