Phase-shifting Technique Research Articles

Visual reconstruction of milling workpiece surface topography based on phase shifting and complementary gray code

When the surface texture of a workpiece is extremely fine, cameras struggle to accurately capture depth information, making conventional machine vision methods insufficient for achieving micrometer-scale three-dimensional surface reconstructions. To overcome this limitation, the study focuses on high-precision 3D reconstruction of the surface morphology of milled workpieces. Given the smoothness of milled surfaces, their susceptibility to overexposure, and the difficulty in extracting depth information from two-dimensional image pixels, the paper proposes a novel method that combines phase-shifting with complementary Gray code to achieve micrometer-level surface reconstruction. The superiority of this method over traditional phase-shifting techniques is demonstrated through comparisons of overall morphology, two-dimensional power spectral density (2D PSD), and the average deviations of sampled surfaces. Results show that the proposed method reduces the average relative error in surface deviations by 25.89% compared to traditional techniques. Furthermore, cross-sectional analyses reveal that the reconstructed point cloud surface more closely mirrors the actual peak-to-valley characteristics of the real surface. Experimental results confirm that this method effectively captures the surface features of milled workpieces, indicating broad potential for applications in precision manufacturing.

A low-power quadrature voltage-controlled oscillators with LC emitter degeneration phase shift technique

This paper introduces a novel phase-shifting technique for quadrature voltage-controlled oscillators (QVCOs) utilizing an LC emitter degeneration architecture. The proposed technique enables a phase shift of up to ±90°in the transconductance of the coupling path while also generating a negative input resistance. This innovative approach avoids phase ambiguity, mitigates the trade-off between phase noise and phase error, and substantially reduces QVCO power consumption. Moreover, compared to conventional capacitance emitter degeneration methods, the LC emitter degeneration structure has a lower equivalent input capacitance, expanding the QVCO’s frequency tuning range. The designed QVCO is implemented using a 180 nm SiGe BiCMOS technology, occupying a compact area of 0.037 mm2. Post-layout simulation evaluations under various process, voltage, and temperature (PVT) conditions validate the robustness and reliability of the design. Results indicate a phase noise of 102.7 dBc/Hz at a 1 MHz offset from a 22.1 GHz carrier, a frequency tuning range of 25.2%, a phase error of 0.9°, and a power consumption of 12 mW from a 1.1 V supply, achieving a figure of merit (FoM) of 178.8 dBc/Hz.

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.

Polarization-filterless polarization-sensitive polarization-multiplexed phase-shifting self-reference digital holography

I propose a phase-shifting self-reference digital holography technique in which both three-dimensional (3D) and polarization information is simultaneously obtained without any polarization filters. A Fourier-transform lens, a polarization beam splitter, and two phase-only spatial light modulators are used to simultaneously generate self-reference holograms with orthogonal polarization directions. 3D and polarization information is multiplexed in the recorded phase-shifted digital holograms and retrieved by applying polarization-selective phase-shifting interferometry and numerical refocusing. The validity of the proposed technique is experimentally demonstrated.

Implementation of a high-resolution micro-grating accelerometer using a subdivision interpolation technique

This paper proposes a subdivision interpolation technique for an optical accelerometer based on diffraction grating interferometry. The diffraction light intensity curve presents a sine shape with the increase of the acceleration. To address the issues of linearization signal processing across the entire range, a subdivision interpolation circuit is employed, in conjunction with a 90° phase shift and high-precision DC bias-voltage techniques, converting an analog signal with sinusoidal characteristics from the photodetector into standard incremental digital signals that vary linearly over the full range. The novel methodology, to the best of our knowledge, ensures that its performance is least affected by the phase imbalance, offset error, and amplitude mismatch induced by fabrication and alignment errors of the grating, achieving high-resolution digital signal output. The experiment results reveal that the optical accelerometer based on grating interferometry achieved a sensitivity of 85.2 V/g, a resolution of 137.6 µg, as well as a subdivision interpolation factor of 45. This work provides a significant guide for the development of high-resolution MOEMS accelerometers in practical applications.

Single-frame transmission and phase imaging using off-axis holography with undetected photons

Imaging with undetected photons relies upon nonlinear interferometry to extract the spatial image from an infrared probe beam and reveal it in the interference pattern of an easier-to-detect visible beam. Typically, the transmission and phase images are extracted using phase-shifting techniques and combining interferograms from multiple frames. Here we show that off-axis digital holography enables reconstruction of both transmission and phase images at the infrared wavelength from a single interferogram, and hence a single frame, recorded in the visible. This eliminates the need for phase stepping and multiple acquisitions, thereby greatly reducing total measurement time for imaging with long acquisition times at low flux or enabling video-rate imaging at higher flux. With this single-frame acquisition technique, we are able to reconstruct transmission images of an object in the infrared beam with a signal-to-noise ratio of 3.680±0.004\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3.680\\,\\pm \\,0.004$$\\end{document} at 10 frames per second, and record a dynamic scene in the infrared beam at 33 frames per second.

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.

3-level inverter based compensator for power quality enhancement using proposed Trianguzoidal PWM technique

In today’s scenario, the integration of a grid-connected load system with a hybrid energy system (HES) is encouraged to improve the reliability of the system. With the stunning rise in nonlinear loads in HES over the last two decades, the power quality (PQ) of the system has emerged as a paramount concern in contemporary times. The power quality problems include the injection of harmonics in the source current, low input power factor, poor voltage regulation, the burden of reactive power, etc. So, to mitigate these power quality problems in a single-phase distribution system, a 3-level Cascade H-bridge (CHB) inverter-based shunt active power filter (SAPF) is employed alongside a proposed Trianguzoidal pulse width modulation (TRZ PWM) strategy. The single-phase distribution system with SAPF is simulated in fixed and dynamic load conditions to check the system’s efficacy. The proposed PWM techniques for SAPF are compared with conventional PWM techniques, i.e., level shift, phase shift, and hybrid PWM techniques. Results indicate satisfactory performance of the proposed PWM techniques, exhibiting low harmonic distortion in source current, well within IEEE 519 limits, and high active filtering efficiency (AFE) compared to conventional PWM methods. Furthermore, this paper provides detailed comparisons of conventional and proposed PWM techniques in the context of active & reactive power supplied or delivered by load, source, and compensator, input power factor, harmonics in source or grid current, AFE, and individual harmonic components concerning fundamental component of source current.

High-speed lateral scanning white-light phase shift interferometry.

In this study, we present lateral scanning white light interferometry (LS-WLI), where phase-shifting algorithms are applied to inspect the topography of a large field of view (FOV) with high-speed measurements. At a point, the interference signal must be acquired with a specific condition to adapt the phase-shifting algorithm. This means that all points have two points, of which the phase difference is π/2, when the number of points acquired in a phase period is multiple of 4, despite increasing the data points in a period. Consequently, stretching the fringe spacing in LS-WLI facilitates the application of phase-shift techniques, thereby enhancing stage speed, even with a fixed camera speed. Using the proposed method, we can successfully obtain a laterally expended topographic image as 5.25 mm × 1.25 mm, where the step height of the microstructure is 140 nm.

Experimental investigation of bidirectional series resonant DC-DC converter in different operating modes

This paper presents a study of bidirectional series resonant DC/DC converter. The main operating modes of the converter with phase-shift control technique are observed. An experimental survey with a laboratory model of such type of converter working over the resonant frequency is made. The functionality of the studied device operating in a wide area of loading is demonstrated with waveforms of the main parameters. The conducted measurements are used to build the experimental output characteristics of the converter. A similarity of the experimental results with the theoretical are denoted, and the ability to achieve current source characteristics for the whole range of loading is proven. The possibility of the studied converter for operation both in forward and reverse modes of energy flow is proved, which positions the device as an appropriate variant for implementation in the storage system control area.

Measurement of space charge density distributions and dielectric resonance enhancement of beam deflection properties of KTN crystal

In recent years, potassium tantalum niobate (KTN) electro-optical deflection devices have gained considerable attention because of their notable advantages, such as large deflection angles, low operational voltage requirements, and compact dimensions. This study uses the phase-shifted interferometric optical path to characterize the influence of direct current (DC) voltage on charge density. An interferogram is acquired using the four-step phase-shifting technique, enabling the calculation of phase delays and deducing the variation in charge density. Experimental results demonstrate that the charge density near the cathode increases with an increase in DC voltage. Subsequently, we utilize the frequency dependence of the dielectric constant of the KTN crystal on the electric field. The dielectric constant can be enhanced when the characteristic frequency of the motion of the polar nanoscale region matches the frequency of the electric field. This field-induced enhancement effect improves the beam deflection performance of the KTN crystal. Application requirements in the field of high-speed random scanning can be realized through the mechanism of the KTN crystal co-acting with DC and alternating current electric fields.

Digital shearography for NDT: Study on a novel experiment based method for removing global deformation✰

Fringe patterns are typically produced as the results of traditional optical Nondestructive Evaluation (NDE) employing digital shearography. Structural flaws affect the response of the surrounding material to a certain loading, resulting in unique fringe patterns that are related to the local deformation. Smaller defect information, however, can be easily lost in the fringe pattern caused by global deformation during the flaw detection procedure. In order to improve the flaw detection capabilities of this technology, it is important to streamline the inspection process and to simplify the interpretation of the results. This study proposes a practical and effective methodology that experimentally removes fringe patterns caused by global deformation in digital shearography and only retains the defect information. For shearographic Non-Destructive Testing (NDT), two sets (3 or 4 images) of temporal phase-shifted interferograms under different loads P1 and P2 are recorded. This novel approach involves recording one additional set of temporal phase-shifted interferograms at a load between P1 and P2, e.g. P1’. Two phase maps of shearograms can be generated using the phase shift technique, corresponding to the two loads Δ2 = (P1’-P1) and Δ1 = (P2-P1), respectively. Because of the nondestructive nature of the testing, the magnitude of the loads P1 and P2 is small, and the 1st derivative of global deformation in the shearing direction of the test part is assumed to be linear. Therefore, a linear coefficient C based on the two shearograms can be determined. The information from global deformation is then removed by subtracting the shearogram generated with the small load Δ2 multiplied by the correlation coefficient C from the one obtained with the relatively large load Δ1. This technique is further improved by calculating a complete surface linear coefficient Cij, which improves the detail processing of the deformation of samples with complex geometry and mechanical properties. This technique is shown to effectively assess a wide range of structures, including aluminum specimens with prepared flaws and intricate composite laminates. The experimental findings demonstrate that the suggested technique improves the non-destructive testing capabilities of digital shearography, thereby simplifying defect detection and visualization.

Enhanced accuracy in 3D structured illumination microscopy through binary encoding with accelerated speed using sampling Moiré

Structured Illumination Microscopy (SIM) is widely recognized as a precise and stable technique for three-dimensional inspection. However, efficiently achieving precise results still poses a challenge to be addressed. This research paper presents significant advancements aimed at enhancing the precision and efficiency of the SIM system. We leverage the defocus sensitivity of binary fringes, which yields more accurate height mapping, reducing the error by an outstanding 5% to 20%. Additionally, we introduce a novel technique called sampling Moiré (SM) for modulation decoding from a single shot, resulting in a reduction of camera exposure time by (N−1)/N compared to the N-step phase shift technique and a minimum 20% reduction in error compared to the Fourier transform (FT). These advancements elevate the system's precision and increase efficiency, making SIM an even more powerful tool for high-quality three-dimensional (3D)inspections.

Fringe-based depth segmentation via minimum-fringe-period-based singular points extraction

In the field of machine vision, depth segmentation plays a crucial role in dividing targets into different regions based on abrupt changes in depth. Phase-shifting depth segmentation is a technique that extracts singular points to form segmentation lines by leveraging the phase-shifting invariance of singular points in different wrapped phase maps. This makes it immune to color, texture, and camera exposure. However, current phase-shifting depth segmentation techniques face challenges in the precision of segmentation. To overcome this issue, this paper proposes a singular points extraction technique by constructing a more comprehensive threshold with the help of the minimum period of the phase map. Taking full advantage of the proposed technique, mean-value points and order singular points are accurately filtered out, and the integrity of segmentation lines in high-curvature regions can be guaranteed. During optimization processing, the precision of segmentation is improved by employing a low-cost morphology-based optimization model. Simulation results demonstrate the segmentation accuracy reaches up to 98.58% even in a noisy condition. Experimental results on different objects indicate that the proposed method exhibits good generalization and robustness.

Large optoelectronic chromatic dispersion in PN-type silicon photodiodes and photovoltaic cells.

Optoelectronic chromatic dispersion (OED) is a significant source of effective chromatic dispersion in photodiodes. We present an experimental and theoretical study of OED in PN-type Si photodiodes and photovoltaic cells and report on a very large effective chromatic dispersion in these devices. As measured with the modulation phase-shift technique at a frequency of 4 kHz for these slow devices, the OED spectral sensitivity for a commercial Si photodiode is approx. 0.02 deg/nm in the 720-850 nm wavelength band and increases to 0.25 deg/nm at λ = 1µm. For a Si photovoltaic cell, the OED is approx. 0.09 deg/nm in this spectral region. These values translate into an effective chromatic dispersion parameter of approx. 1012ps/(n m ×k m) for these sub-millimeter device lengths, which is over eight orders of magnitude larger than high-dispersion materials such as chalcogenide glass. The enormous dispersion in these sub-millimeter sized silicon-based devices can be utilized for on-chip optoelectronic sensors such as wavelength monitoring and spectroscopy. The substantial OED of photovoltaic cells can be utilized for the characterization and optimization and new applications for optical sensing with these self-powered devices.

A novel hybrid model based on integrating RGB and YCrCb color spaces for demodulating the phase map of fibres using a color phase-shifting profilometry technique

In this paper, a refined color phase- shifting profilometry technique is suggested for accurate examining of the phase and optical features of polymeric fibres. It is based on combining the RGB and the YCrCb color spaces. The primary components of the suggested model (RGCb) are red (R), green (G), and blue chrominance (Cb). This model is considered an early study in combining color spaces to demodulate the phase map of the tested fibre. The suggested model enhances affects that arise from color crosstalk and chromatic aberration, especially in the blue color channel. The Pluta polarizing interference microscope is utilised for capturing RGB interference fringe pattern for polypropylene (PP) fibre. The wrapped and unwrapped phase maps of this fibre are demodulated via the traditional, the corrected RGB color phase shifting algorithms and the suggested RGCb model. For evaluating the accuracy of the suggested model, the contour line method is used. The obtained results confirm that the demodulated phase using the suggested RGCb model has the least standard deviation from the reference phase value compared to the other two algorithms. The validation of the suggested model for investigating the optical properties of drawn fibres with a high order of fringe shift is checked. Based on the demodulated phase maps from the suggested model, the 2.5D birefringence profile of a PP fibre is examined.

Large and tunable optoelectronic chromatic dispersion in PIN-type photodiodes.

It is known that PN-type photodiodes possess high optoelectronic chromatic dispersion (OED). Here we present a theoretical and experimental study of OED in PIN-type photodiodes. Applying the modulation phase-shift technique, a Ge PIN photodiode exhibits ∼0.5 deg/nm phase-shift sensitivity at 10 MHz modulation, corresponding to a dispersion of 1.4 ×109ps/(n m ×k m), many orders of magnitude larger than high-dispersion optical materials such as chalcogenide glass. A striking feature of the PIN device is the ability to tune the amount and sign of the OED through the bias voltage. Electronic tuning between -0.8 deg/nm and +0.5 deg/nm is shown. The PIN photodiode is an on-chip device possessing significant tunable dispersion for applications in optical sensing and spectroscopy.

NiO thickness measurement using a rectangular-type Sagnac interferometer as the material transport layer in a perovskite solar cell

This work aims to utilize a phase-shifting technique in a rectangular-type Sagnac interferometer (RTSI) to measure the thickness of a thin film of nickel (II) oxide (NiO) in an electron transport layer (ETL) in perovskite solar cell preparation. The NiO layer is deposited on a fluorine-doped tin oxide (FTO) glass substrate. In the RTSI setup, the signal output from the interferometer is divided into the reference and testing arms using a nonpolarizing beam splitter (NPBS). The balanced photodetectors then detect the signal, with the FTO/NiO layer placed in the testing arm and pure FTO in the reference arm. By analyzing the signal intensities at polarization settings of 0° to 180°, the phase shift and thickness of the NiO layer can be determined. The thickness values of FTO and NiO films obtained through three different phase-shifting algorithms of three-, four-, and five-steps are calculated. The obtained NiO thickness values are validated against scanning electron microscopy (SEM). Finally, by considering the NiO thickness value that exhibits the lowest percentage error compared to one from SEM, it is confirmed that the three-step algorithm is the most suitable scheme for obtaining intensities at 0°, 45°, and 90°. Therefore, the proposed setup shows promise as a replacement for SEM in thickness measurements.

Nanoscale surface metrology with a liquid crystal-based phase-shifting angular shearing interferometer.

In this Letter, a phase-shifting angular shearing interferometer has been proposed for the application in optical surface metrology (SM) by using a combination of a wedge-shaped liquid crystal (LC) cell and a polarization phase shifter. The demonstration of this angular shearing interferometer for step height measurement is accomplished with the help of a phase-shifting technique. Four phase-shifted interferograms produced by a geometrical phase shifter are subjected to a simplified Wiener deconvolution method, which resembles a simple analysis technique for shearing interferograms in comparison to alternative approaches. A simulation study has been conducted to validate the proposed technique. The experimental results show an accuracy of 5.56% for determining the step height, which also agrees with the results obtained by atomic force microscopy. Owing to the tunability of birefringence, the proposed LC-based angular shearing interferometry technique will be useful to control spatial resolution in optical metrology.

Effect of Polarization on Cross-Spectral Density Matrix

Coherence-polarization properties of different beams are experimentally measured in the far-field from the source and results are presented for incoherent sources with three different polarization features, such as unpolarized, diagonally polarized, and spatially depolarized. These results highlight the role of polarization tailoring on far-field coherence-polarization properties of the incoherent vector source. The effect of polarization on far-field coherence is analyzed using a beam cross-spectral density (CSD) matrix, and the role of polarization tailoring on the CSD matrix is demonstrated. Two-dimensional spatial distributions of all four elements of the CSD matrix are experimentally realized using a field-based interferometer with Sagnac geometry in combination with a four-step phase-shifting technique.