Phase-shifting Method Research Articles

Restoration of X-ray phase-contrast imaging based on generative adversarial networks

For light-element materials, X-ray phase contrast imaging provides better contrast compared to absorption imaging. While the Fourier transform method has a shorter imaging time, it typically results in lower image quality; in contrast, the phase-shifting method offers higher image quality but is more time-consuming and involves a higher radiation dose. To rapidly reconstruct low-dose X-ray phase contrast images, this study developed a model based on Generative Adversarial Networks (GAN), incorporating custom layers and self-attention mechanisms to recover high-quality phase contrast images. We generated a simulated dataset using Kaggle’s X-ray data to train the GAN, and in simulated experiments, we achieved significant improvements in Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM). To further validate our method, we applied it to fringe images acquired from three phase contrast systems: a single-grating phase contrast system, a Talbot-Lau system, and a cascaded grating system. The current results demonstrate that our method successfully restored high-quality phase contrast images from fringe images collected in experimental settings, though it should be noted that these results were achieved using relatively simple sample configurations.

Optimal Capacitance Design for IRS Aided Wireless Power Transfer for Sustainable IoT Communication

ABSTRACTIntelligent reflecting surface (IRS) is a cutting‐edge technique that can significantly improve wireless propagation. It can efficiently utilize wireless power transfer to enable sustainable Internet‐of‐Things (IoT) transmission by reconfiguring the incident signal from the active transmitter. However, the flexibility of capacitance tuning in the IRS system, which controls underlying reflections, is often overlooked. The effective capacitance design in the IRS system can provide a new degree of freedom in the IoT communication system, which can enable additional performance gain in the received power. To achieve this, a novel IRS circuital optimization model is proposed in this work. It incorporates various electrical parameters of the meta‐surface unit cell for improved IoT‐enabled communication. The proposed optimization model provides an optimal capacitance as a function of phase shift (PS), which is controlled by IRS, incident frequency, and other IRS electrical parameters. This optimal capacitance is then used to define the received power. The convexity of the optimization problem is proved, and the global optimal capacitance is obtained for received power maximization. Our simulations show that the proposed optimization model outperforms the existing constructive interference‐based optimal PS method, for which the capacitance is first calculated. Finally, the analytical results are numerically validated with several optimal design insights.

Sub-∘C-precision temperature imaging using phase-shift luminescence thermometry

Abstract This work explores the potential of luminescence thermometry to provide temperature imaging with high temperature resolution using the phase-shift method. Phosphor thermometry has been widely used for temperature imaging, especially with the decay-time method. However, the phase-shift method was rarely used. In this approach, excitation is modulated in time, and due to the temperature-dependent luminescence dynamics of the painted luminescent probe, the emission waveform is phase-shifted with respect to the excitation waveform. Initially, a parametric study was performed on the effect of excitation waveform frequency and shape, based on a millisecond-decay time phosphor. The study found that the best precision is achieved with a square waveform at a frequency such that the phase shift is π 4 at the target temperature. Then, this method was compared with the well-established decay-time method. Phase-shift method offered a three-fold improvement in temperature precision under identical peak excitation power. Finally, two-dimensional measurements were demonstrated on a temperature-controlled plate using a high speed CMOS camera, and an LED illumination. A temperature precision of 0.13 ∘C was obtained at a temporal resolution of 0.25 s and a spatial resolution of around 1 mm, due to a pre-processing binning of 7 by 7 pixels. This technique can be used as a robust alternative to infrared thermometry to probe the thermal processes with small temperature differences.

Three-dimensional polarimetric ptychography

A three-dimensional polarimetric ptychography (3D-PP) technique is proposed to reconstruct the residual stress distribution in optical elements in three dimensions by combining polarization imaging and a 3D ptychographic iterative engine (3D-PIE). 3D-PP mainly uses two orthogonal linear polarizers placed along the light direction to capture the photoelastic information within an optical element. Based on phase shift theory, a three-step phase shift method is proposed to record three dark field images, allowing for calculating the isometric line of residual stress within the optical element. This method enables the layer-by-layer measurement of residual stress within thick samples and assesses the distribution of residual stress along the detection axis, enhancing the precision of stress measurements.

Three-Frame Random Phase-Shifting Algorithm Based on VU Decomposition Method and Ellipse Fitting

Abstract To enhance the precision and robustness of the three-frame phase shift technique, a new three-frame random phase-shifting fringe pattern phase demodulation method that combines VU decomposition and ellipse fitting techniques without the need for pre-filtering is proposed. The proposed method first performs VU decomposition on the interferograms to establish two orthogonal components of the fringe pattern. Then, the ellipse fitting method is used to obtain the relevant ellipse coefficients, thereby achieving precise phase demodulation. This method does not require an accurate phase-shifting process, thereby relaxing the stringent requirements on the phase shifter. Compared with traditional algorithms, the proposed method performs better under conditions of non-uniform background intensity and modulation amplitude. Numerical simulation experiments demonstrate that the proposed method maintains good stability across 20 repeated tests. Within the SNR range of 30 to 50 dB, the RMSE of the suggested approach is approximately 0.006 rad. This proves the effectiveness of the algorithm and provides a new approach for the development of three-frame phase-shifting technology.

Dynamic phase measurement based on two-step phase-shifting interferometry with geometric phase grating

Abstract This paper proposes a novel dynamic 2-step phase-shifting interferometry method with a geometric phase grating and direct aberration-free object phase recovery algorithm. By exploring the amplitude-phase modulation property of the geometric phase grating, two-step phase-shifting interferograms with π / 2 phase shift can be obtained in a single shot through two kinds of spatial-multiplexing arrangements. Then the restriction on the background uniformity of the 2-step phase-shifting algorithms and the system aberration can be avoided simultaneously, based on the presented direct and fast object phase demodulation strategy with an object-free state recorded in advance, so an accurate object measurement result can be guaranteed. Accordingly, a detailed analysis of the theoretical model of error sources is conducted by taking the depolarization error of geometric phase grating and phase measurement model error into consideration, with a Least Squares Iteration optimization strategy established to further improve the measurement accuracy. Experiments on various types of phase objects, such as a photo-etched quartz substrate, the spatial light modulator, and a silicon chip, validate the effectiveness and accuracy of our method when compared with the reference phase obtained from 4-step temporal phase-shifting method. The dynamic phase measurement capability is demonstrated by exhibiting the evaporation process of alcohol droplet.

Single-pixel deep phase-shifting incoherent digital holography

Incoherent digital holography technology reduces the requirement for coherence of light sources, greatly expanding the application range of digital holography. In this paper, we designed a Multi-head attention single-pixel (MHASP) phase-shifting network for incoherent digital holography. The trained network has the capability to effortlessly predict three interferograms, encompassing phase shifts of 0, 2/3 π, and 4/3 π, solely from one-dimensional input data. Utilizing the conventional three-step phase-shifting method, we are able to effectively eliminate the DC and twin terms from the holographic reconstruction process, subsequently achieving a high-fidelity reconstruction facilitated by the employment of the back propagation algorithm. The comprehensive experimental findings clearly indicate that, beyond facilitating high-precision reconstruction, the introduced MHASP phase-shifting approach efficiently preserves 3D information through calibrating the back propagation distance, even when confronted with a reduced volume of holographic data. Furthermore, the introduced approach uses a network to replace the actual phase shift operation, which can better improve the utilization of object light energy. This approach not only circumvented the constraints posed by area array sensors but also facilitated high-fidelity imaging with minimal data volume, thereby expanding the horizons of incoherent digital holography applications in the realm of 3D imaging.

Efficient completely polarization-encoded binocular structured light 3D measurement method for metallic objects

In practical 3D measurement applications, stereo vision assisted with phase shift patterns is intensively studied and widely used for its high precision and excellent noise resilience. While aiming to improve matching efficiency, excessive projection patterns or unreliable algorithms may be introduced as a side effect. We propose a completely polarization-encoded phase shift (CPPS) method to overcome the above challenges. In our method, the Stokes parameter S1 of the polarization patterns is encoded. Compared to the traditional fringe patterns, our method can reduce the number of projected patterns to improve the measurement efficiency. Therefore, the exact constraints can be realized without additional patterns. Experimental results show that the CPPS method reduces the matching time by 76.6% while reducing the number of fringe patterns by half.

A spatial phase-shifting method for real-space wave reconstruction of off-axis electron holograms

The Fourier transform with a side-band filter is the well-established method for reconstructing off-axis fringe-type holograms due to its ease of implementation and fast processing. However, this method works in reciprocal space and requires inversion of a side-band sub-region, which can degrade the spatial resolution of reconstructed wave compared to the original hologram. We present a new method, the spatial phase-shifting (SPS) method, for real-space wave reconstruction of off-axis electron holograms. We describe the working principles of the SPS method in analogy to the temporal phase-shifting method. We conducted both hologram simulations and experiments to evaluate its applicability and effectiveness. We compared the wave reconstruction results of the SPS and the conventional Fourier transform method, highlighting the advantages of the newly proposed SPS method. Our results demonstrate that the proposed SPS method is particularly effective for real-space wave reconstruction of small-sized hologram, providing an alternative approach to off-axis type holography wave reconstruction.

Dynamic deformation measurement with 2-frame phase-shifting speckle interferometry based on speckle statistics and wavefront multiplexing.

Phase-shifting speckle interferometry could achieve full-field deformation measurement of rough surfaces. To meet the dynamic requirement and further improve the accuracy, a two-step synchronous phase-shifting measurement system is established based on the polarization-sensitive phase modulation ability of a liquid crystal spatial light modulator; by multiplexing the reference wavefront, an accurate phase shift is generated between two independent recording channels, and a common-path self-reference vortex interference structure is built for precise spatial registration. Meanwhile, according to the speckle statistical principle, a novel two-frame phase-shifting algorithm as well as a two-step spatial registration strategy is presented to strengthen the robustness of intensity and position differences caused by spatial-multiplexing; thereby, accurate transient deformation can be directly obtained from phase-shifting speckle interferograms recorded before and after deformation. The effectiveness and accuracy of the proposal are validated from the out-of-plane deformation measurement experiment by comparing with the traditional two-step and four-step phase-shifting methods. The dynamic ability is exhibited through reconstructing mechanical and thermal deformations across various application scenarios.

Simultaneous measurement of six displacement gradients using Digital Shearography

Optical methods show significant promise in accurately measuring all components of the displacement gradient tensor in three-dimensional space, excluding those related to depth measurement. However, dynamic measurements using Digital Shearography face challenges due to the complexity of acquiring sufficient phase information in one capture. This paper introduces a novel Digital Shearography system with triple beams and spatial phase shift capabilities. It allows simultaneous measurement of in-plane and out-of-plane phase distributions in a single image. Three laser beams, each with distinct wavelengths, are strategically positioned both horizontally and vertically to illuminate the object under test. Utilizing beam splitting and redirection, the system achieves dual shearing directions and captures shearograms using a 3CCD camera. Phase information extracted via the spatial phase-shift method enables determination of the six measurable displacement gradients and corresponding strain components. The manuscript provides a comprehensive explanation of the system’s theory, supported by experimental results, and explores potential applications.

Theory and application of robust linear phase-shift algorithm for phase-shift deflectometry method

Based on the polynomial theory, the error propagation characteristics of the widely used N-step discrete Fourier transform (N-DFT) phase-shift algorithm were analyzed via theoretical analysis, under the effect of Gamma distortion and phase detuning. The results showed that the N-DFT algorithm could not simultaneously suppress both types of error. A robust linear phase-shift (RLPS) algorithm was designed, the performance of the RLPS and 8-DFT algorithms in terms of spectral response, detuning robustness, and GS/N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${G}_{S/N}$$\\end{document} was briefly analysis by Manuel Servin method. The Simulation analysis and comparison of the results show that the RLPS algorithm could suppress both types of error simultaneously, which exhibited better stability and accuracy than N-DFT and exponential algorithms, particularly in gradient measurement stability, peak-to-valley (PV) and root-mean-square (RMS) error suppression. Moreover, a physical experiment apparatus was built to test unidirectionally inclined plane mirror and concave mirror using the RLPS, N-DFT, and exponential algorithms. The results showed that the RLPS algorithm could significantly improve the measurement stability and accuracy in the presence of detuning and without screen Gamma calibration.

Multi-layered medium ultrasonic phased array sparse TFM imaging based on self-adaptive differential evolution algorithm

Abstract Multilayer Composite material structures have been widely used in modern engineering fields. However, defects within these materials can adversely affect mechanical properties. Ultrasonic phased array total focusing method (TFM) imaging has advantages of high precision and dynamic focusing over the entire range, achieving significant progress in homogeneous medium detection. However, heavy computational burdens of multilayer structures lead to inefficient imaging. To address this issue, a sparse-TFM imaging algorithm using ultrasonic phased arrays suitable for multilayer media is proposed in this paper. This method constructs a fitness function with constraints such as main lobe width and sidelobe peak. Its objective is to obtain the distribution of sparse array element positions using an self-adaptive differential evolution algorithm. Subsequently, the delay time of each array element in multilayer media sparse TFM is calculated using the root mean square (RMS) principle and combined with amplitude weighting, the method corrects the imaging results. Compared with the Ray-based full-matrix capture and TFM method (Ray-based FMC/TFM), the RMS-based full-matrix capture and TFM (RMS-based FMC/TFM), and the phase shift method, the experimental and simulation results demonstrate that the proposed method significantly reduces the imaging data volume, improves computational efficiency, and maintains quantitative errors within 0.2 mm.

3D reconstruction with single-frame two-step phase-shift method based on orthogonal composite fringe pattern projection

Abstract In order to realize single-frame three-dimensional (3D) reconstruction, a single-frame two-step phase-shift method based on orthogonal composite pattern projection is proposed to solve the problem that the traditional N-step phase-shift profilometry needs multiple projections for 3D reconstruction. The orthogonal composite pattern uses only two carrier channels to reduce the spectrum overlapping influence on the demodulation accuracy of carrier and modulated fringes. A two-dimensional variational mode decomposition method is adopted to remove the background DC component of the sinusoidal fringe to overcome the mode overlap problem by controlling the size of the bandwidth. Thus, the two-step phase-shift method is applied to calculate the phases for 3D reconstruction. The experimental results show that, compared with the typical Fourier transform profilometry method, 3-step composite method and 2 + 1 composite method, the 3D reconstruction accuracy of the proposed method is improved by 49.1%,31.4% and 23.2% respectively according to mean absolute error, and by 73.0%, 58.4% and 56.8% respectively according to mean squared error as the evaluation index. Finally, the dynamic 3D reconstruction experiment demonstrates the good adaptability of dynamic 3D reconstruction.

A composite control method of PWM and phase shift for a three-level DC-DC converter

Abstract This research introduces a control strategy for the Three Level Active Half Bridge (TL-DAHB) DC-DC converter that integrates PWM combined with phase-shift control. This composite control method precisely regulates the output voltage by adjusting the phase-shift duty cycle between the input and output sides. Additionally, the application of the PWM control loop optimizes the duty cycle of the switches, effectively reducing the current stress on the converter during operation, improving transmission efficiency, and decreasing conduction losses of the switches. These enhancements boost the overall performance and the reliability of the converter. With its excellent voltage regulation capabilities and safety features, this converter is an ideal choice in the field of power conversion, especially in applications that demand high levels of stability and safety.

Absolute emission height determination of the radio emission components of PSR B2111+46 at multiple bands by relativistic phase shift method

Absolute emission height determination of the radio emission components of PSR B2111+46 at multiple bands by relativistic phase shift method

Frequency‐Bessel Transform Method for Multimodal Dispersion Measurement of Surface Waves From Distributed Acoustic Sensing Data

AbstractThe array‐based frequency‐Bessel transform method has been demonstrated to effectively extract dispersion curves of higher‐mode surface waves from the empirical Green's functions (EGFs) of displacement fields reconstructed by ambient noise interferometry. Distributed acoustic sensing (DAS), a novel dense array observation technique, has been widely implemented in surface wave imaging to estimate subsurface velocity structure in practice. However, there is still no clear understanding in theory about how to accurately extract surface‐wave dispersion curves directly from DAS strain (or strain rate) data. To address this, we extend the frequency‐Bessel transform method by deriving Green’s functions (GFs) for horizontal strain fields, making it applicable to DAS data. First, we test its performance using synthetic GFs and verify the correctness of extracted dispersion spectrograms with theoretical results. Then, we apply it to three field DAS ambient‐noise data sets, two recorded on land and one in the seabed. The reliability and advantages of the method are confirmed by comparing results with the widely used phase shift method. The results demonstrate that our extended frequency‐Bessel transform method is reliable and can provide more abundant and higher‐quality dispersion information of surface waves. Moreover, our method is also adaptable for active‐source DAS data with simple modifications to the derived transform formulas. We also find that the gauge length in the DAS system significantly impacts the polarity and value of extracted dispersion energy. Overall, our study provides a theoretical framework and practical tool for multimodal surface wave dispersion measurement using DAS data.

Experimental Study on the Reconstruction of a Light Field through a Four-Step Phase-Shift Method and Multiple Improvement Iterations of the Least Squares Method for Phase Unwrapping

Phase unwrapping technology can reflect the true phase information of an image, but it is affected by adverse factors such as noise, shadows, and fractures when extracting the true phase information of an object. Therefore, corresponding unwrapping algorithms need to be studied for different interference images. This paper summarizes and analyzes various phase unwrapping algorithms and ultimately selects the required method based on their advantages and disadvantages. Using the four-step phase-shift method to reconstruct the phase of the optical field and then combining it with the least squares method to unwrap the phase through multiple improvement iterations, the simulated collected interference fringe images are simulated using the MATLAB program to complete the phase unwrapping of the interference information field. Based on the analysis of the final experimental results, the reliability of this research method was verified.

Improved complementary gray code fourfold-N step phase-shifting method based on eliminating periodic spurious tones phase error

In the process of using the complementary Gray code fourfold-N step phase-shifting method, the wrapped phase has periodic spurious tones phase error after eliminating the phase difference and fusing. Therefore, this method still makes phase error during process. To solve this problem, an improved complementary Gray code fourfold-N step phase-shifting method is proposed in this paper. The proposed method does not add new projection images, it improves the method and eliminates the periodic spurious tones phase before fusing the wrapped phase. So the proposed method not only maintains the advantage of fourfold-N step phase-shifting method in improving measurement efficiency, but also effectively eliminates periodic spurious tones phase error and improves measurement accuracy. Experimental results show that compared with complementary Gray code fourfold-N step phase-shifting method, the measurement accuracy is increased by 6.16%; compared with complementary Gray code N-step phase-shifting method, the measurement accuracy is increased by 0.72% and the measurement efficiency is increased by 8.26%.

Single-frame fringe pattern analysis with synchronous phase-shifting based on polarization interferometry phase measuring deflectometry (PIPMD)

In the domain of phase measuring deflectometry (or fringe projection profilometry), utilizing only a single-frame fringe pattern to achieve high-precision three-dimensional reconstruction has emerged as a focal point of ongoing research. To achieve four-step phase-shifting demodulation from a single-frame fringe pattern, this paper proposes a Polarization Interferometry Phase Measuring Deflectometry (PIPMD). This method primarily relies on a Michelson polarization interferometry structure to produce projected polarization interference fringes, which are then captured by a polarization camera as modulated single-frame deformed fringe patterns. These single-frame fringe patterns enable pixelated four-step phase shifting with adjacent 2 × 2 pixel units. To validate the proposed method, a series of experiments has been conducted, including surface shape detection of a concave spherical mirror and an off-axis parabolic mirror, as well as dynamic deformation measurements of a deformable mirror. All experimental results consistently indicate that the polarization interference-based fringe projection technique can achieve synchronized phase-shifting demodulation of single-frame fringe patterns, thereby facilitating high-precision reconstruction of the fringe patterns captured in a single frame. This synchronous phase-shifting technique can overcome the influence of air disturbances in traditional four-step phase-shifting methods, thereby enhancing the accuracy of phase demodulation. Additionally, this polarization interference-based Phase Measuring Deflectometry exhibits promising application prospects in dynamic measurements.