Estimation Of Phase Shift Research Articles

Phase reconstruction by phase shift estimation with reliable parameter minimization

Abstract Achieving a balance between accuracy and speed in phase reconstruction is a challenging problem. In phase-shifting interferometry, increasing the speed by reducing the number of phase shifts while maintaining high accuracy is highly desirable. We propose an accurate and efficient two-step phase reconstruction method utilizing random phase shift. This method directly estimates the phase shift through reliable parameter minimization, allowing for easy and precise phase reconstruction. Simulations and experiments demonstrate the superior performance of our method across various scenarios, outperforming well-known two-step phase-shifting algorithms. We expect this paper to provide a general and powerful tool for phase reconstruction.

Two-step differential phase-shifting phase retrieval using generative adversarial network

Phase-shifting interferometry (PSI) is a high-accuracy optical measurement technique which requires accurate phase-shift estimation or sufficient phase-shifting interferograms to ensure phase-retrieval accuracy. Therefore, obtaining the highest phase retrieval accuracy from fewer interferograms remains a challenge. Based on this, we propose a two-step differential phase-shifting phase retrieval method using generative adversarial network, which can achieve higher phase-retrieval accuracy from two arbitrary phase-shifting interferograms, compared to representative two-step arbitrary phase-shifting phase retrieval methods. A phase retrieval generative adversarial network (PR-GAN) which can be trained with artificial training data for phase retrieval from experimental interferograms is employed. Experimental results demonstrate that accurate phase results can be obtained, even when the phase shift is approximately π or the fringe number is relatively small.

Two-step phase shifting algorithm based on cost function minimization

A computationally efficient phase shift estimation algorithm is proposed for two-step phase-shifting interferometry based on a cost function minimization technique. The proposed method can accurately estimate the phase shift over a wide range resulting in reliable phase estimation. Due to the analytical solution offered by the proposed method, its computational efficiency is found to be higher than the existing state-of-art methods. While the performance of some methods is user-defined parameter-dependent, the proposed method is non-parametric and user-independent. The accuracy of phase shift and subsequent phase estimation using the proposed algorithm is found to be maximum around phase shift of π/2rad which further decreases for the phase shift values closer to 0rad and πrad. The experimental results demonstrate the practical applicability of the proposed method.

Better Heisenberg Limits, Coherence Bounds, and Energy-Time Tradeoffs via Quantum Rényi Information.

An uncertainty relation for the Rényi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form RMSE≥f(α)/(⟨N⟩+12), bounding the root mean square error of any estimate of a random optical phase shift in terms of average photon number, where f(α) is maximised for non-Shannon entropies. Related simple yet strong uncertainty relations linking phase uncertainty to the photon number distribution, such as ΔΦ≥maxnpn, are also obtained. These results are significantly strengthened via upper and lower bounds on the Rényi mutual information of quantum communication channels, related to asymmetry and convolution, and applied to the estimation (with prior information) of unitary shift parameters such as rotation angle and time, and to obtain strong bounds on measures of coherence. Sharper Rényi entropic uncertainty relations are also obtained, including time-energy uncertainty relations for Hamiltonians with discrete spectra. In the latter case almost-periodic Rényi entropies are introduced for nonperiodic systems.

Low-cost, microcontroller-based phase shift measurement system for a wireless power transfer prototype

Seeking to characterize and mitigate the adverse effects of misalignment in WPT applications, we present the design and construction of a low-cost wireless charger prototype and a novel phase-shift measurement system. The first is built using a half-bridge inverter and antennas with series-series compensation, while a microcontroller (Teensy 4.1) supplies high-frequency PWM signals. The measurement system comprises high-speed operational amplifiers and an exclusive OR gate. A resistor was used as load. On the other hand, the maximum power transfer efficiency occurs at the resonance frequency, nevertheless, this depends physically on the geometry of the coupling system. Using a 3D-printed displacement system, we created controlled vertical misalignments between the coils, thereby obtaining variations in the resonance frequency of the system and consequently, producing a proportional phase shift between the voltage and current waves of the transmitting antenna. As the experimental results demonstrate, the measurement system can process this high-frequency signal for the phase shift estimation and subsequently use it as a control variable in a proportional-integral controller, which adjusts the operation frequency of the system and brings it back to optimal conditions. This precise yet inexpensive implementation could find its application in EVs and biomedical devices’ efficient wireless chargers.

Phase Retardation Analysis in a Rotated Plane-Parallel Plate for Phase-Shifting Digital Holography.

In this paper, we detail a phase-shift implementation in a rotated plane-parallel plate (PPP). Considering the phase-shifting digital holography application, we provide a more precise phase-shift estimation based on PPP thickness, rotation, and mutual inclination of reference and object wavefronts. We show that phase retardation uncertainty implemented by the rotated PPP in a simple configuration is less than the uncertainty of a traditionally used piezoelectric translator. Physical experiments on a phase test target verify the high quality of phase reconstruction.

Quantum Fisher information bounds on precision limits of circular dichroism

Circular dichroism (CD) is a widely used technique for investigating optically chiral molecules, especially for biomolecules. It is thus of great importance that these parameters be estimated precisely so that the molecules with desired functionalities can be designed. In order to surpass the limits of classical measurements, we need to probe the system with quantum light. We develop quantum Fisher information matrix (QFIM) for precision estimates of the circular dichroism and the optical rotary dispersion for a variety of input quantum states of light. The Cramer-Rao bounds, for all four chirality parameters are obtained, from QFIM for (a) single photon input states with a specific linear polarization and for (b) NOON states having two photons with both either left polarized or right polarized. The QFIM bounds, using quantum light, are compared with bounds obtained for classical light beams i.e., beams in coherent states. Quite generally, both the single photon state and the NOON state exhibit superior precision in the estimation of absorption and phase shift in relation to a coherent source of comparable intensity, especially in the weak absorption regime. In particular, the NOON state naturally offers the best precision among the three. We compare QFIM bounds with the error sensitivity bounds, as the latter are relatively easier to measure whereas the QFIM bounds require full state tomography. We also outline an empirical scheme for estimating the measurement sensitivities by projective measurements with single-photon detectors.

Two-step phase extraction and random phase shift estimation in phase-shifting profilometry based on least-squared optical flow method

Phase shifting profilometry normally requires at least three-frame fringe patterns to extract the phase of objects. In the dynamic measurement field, it is desirable to reduce the number of fringe patterns and eliminate the phase-shifting error caused by the moving of the test object between fringe patterns. In the field of interferometry, the optical flow technique is an outstanding two-step phase reconstruction method. However, the accuracy of the optical flow (OF) algorithm is limited by the residual background intensity and approximation operation as well as noise. In this paper, a phase reconstruction method based on the optical flow algorithm and two-frame least square algorithm (OF&LSA) is proposed to alleviate the phase error caused by the above problems. The proposed method is employed in dynamic phase-shifting profilometry to achieve 2-frame phase reconstruction. The simulation and experiment results verify that the proposed OF&LSA improves the phase accuracy of OF algorithm significantly, and it also performs better than the 3-step phase shifting method in our dynamic measurement experiment.

Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox

The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.

Deep learning-based nonlinear phase shift estimation in coherent optical communication systems

In this paper, a convolutional neural network (CNN) based algorithm is proposed for the estimation of nonlinear phase shift (NLPS) in coherent optical communication systems. Simulations show that the mean relative errors (MREs) of the estimated NLPS will be less than 5.0%, 2.0% and 1.0% as the optical signal-to-noise ratio (OSNR) is larger than 18 dB, 22 dB and 27 dB, respectively. Furthermore, we numerically investigate the NLPS estimation scheme for signals with data rates of 56Gbit/s, 70Gbit/s and 112Gbit/s respectively, and the MRE analysis shows that the proposed algorithm is insensitive to the variation of data rates in the PDM-QPSK systems.

Two-Step Phase-Shifting Algorithm Based on the Quadratic Spatial Filtering of Interferograms

By using the quadratic spatial filtering (QSF) operation of interferograms, we propose a fast and accurate phase retrieval algorithm in 2-step phase-shifting interferometry (PSI), in which both the interference signal separation and blind phase shift estimation can be realized. Compared with the existed 2-step PSI algorithms, the proposed QSF algorithm reveals two advantages: First, when the background intensity is not accurately estimated, which is a serious problem in 2-step PSI, the distortion of the retrieved phase can be released. Second, there is no requirement about the fringe density of interference pattern, reflecting the phase shift estimation can be realized even if the fringes density is sparse. The former is a valuable solution to reduce most significant errors in 2-step PSI, and the latter makes the accuracy robust against different fringe patterns. Both the simulation and experimental results demonstrate the excellent performance of the proposed QSF algorithm.

Effects of motion on correlations of pulse-echo ultrasound signals: Applications in delay estimation and aperture coherence.

The correlation between two pulse-echo ultrasound signals is used to achieve a wide range of ultrasound techniques, such as Doppler imaging and elastography. Prior theoretical descriptions of pulse-echo correlations were restricted to stationary scatterers. Here, a theory for the correlation of moving scatterers is presented. An expression is derived for the correlation of two pulse-echo signals with arbitrary transmit and receive apertures acquired from a medium undergoing bulk motion using the Fresnel approximation. The derivation is shown to coincide with prior derivations in the absence of scatterer motion. The theory was compared against simulations in applications of phase-shift estimation and aperture coherence measurements. The phase-shift estimate and jitter were accurately predicted under axial and transverse motion for focused transmit apertures and for sequential and interleaved synthetic transmit apertures. The theory also accurately predicted how motion affects the correlation coefficient between receive aperture elements for a synthetic transmit aperture. The presented theory provides a framework for analyzing the correlations of arbitrary pulse-echo configurations for applications in which scatterer motion is expected.

Influence of low power consumption on IEEE 802.15.4 in wireless networks performance

IEEE 802.15.4 standard defines both media access control (MAC) and physical (PHY) layer protocols for low power consumption, low peak data rate, and low cost applications. Nowadays the most important feature of IEEE 802.15.4 is maximizing battery life. This paper is focusing how to achieve low average power consumption through assuming that the amount of data transmitted is short and that it is transmitted infrequently so as to keep a low duty cycle. The outcomes demonstrate that the phase shift estimation of Offset quadrature phase-shift keying (OQPSK) modulation has no impact on bit error rate (BER) if it is identical in the transmitter as same as in the receiver.

AF-Net: A Convolutional Neural Network Approach to Phase Detection Autofocus

It is important for an autofocus system to accurately and quickly find the in-focus lens position so that sharp images can be captured without human intervention. Phase detectors have been embedded in image sensors to improve the performance of autofocus; however, the phase shift estimation between the left and right phase images is sensitive to noise. In this paper, we propose a robust model based on convolutional neural network to address this issue. Our model includes four convolutional layers to extract feature maps from the phase images and a fully-connected network to determine the lens movement. The final lens position error of our model is five times smaller than that of a state-of-the-art statistical PDAF method. Furthermore, our model works consistently well for all initial lens positions. All these results verify the robustness of our model.

Phase estimation based on inverse weak-value using a monochromatic light source

Weak-value measurement (WVM) technique, especially the linear WVM technique, has been proved to be useful in high precision metrology. However, the phase shift to be measured is strictly dominated by the input meter, such as the light wavelength and the space position, which are the basic elements of the linear WVM regime. In this work, an inverse WVM technique using a monochromatic light source is presented to achieve precise estimation of the wavelength-independent phase shift. The theoretical analysis in sensitivity and precision indicates that the inverse WVM technique is more applicable to wavelength-independent phase estimation, as compared to the typical linear WVM technique. Furthermore, two possible experimental designs based on the inverse WVM technique are proposed, which may promote the practical applications of this technique in precision metrology.

Accurate phase-shift estimation for fringe-pattern profilometry.

Fringe-pattern profilometry (FPP) has been widely used for phase reconstruction. It involves the use of phase shifting for phase retrieval. Phase-shift errors can affect the accuracy of phase reconstruction, and limited studies have been dedicated to studying phase-shift errors due to experimental, human, or environmental factors. We propose a simple and yet accurate phase-shift estimation method. Our study shows that the method is able to accurately estimate the actual phase shifts used in the FPP technique. The proposed method can find its applications in FPP and other phase shifting-based three-dimensional imaging techniques.

Dynamic of quantum Fisher information and quantum interferometric power in multipartite coherent states

We examine the role of quantum correlations, contained multipartite Glauber coherent states, in enhancing the precision in the estimation of an unknown phase shift. We give the explicit form of quantum Fisher information in even and odd multipartite coherent states. Two different pairing schemes are considered to evaluate the sensitivity of the probe state to the phase shift for some relevant local Hamiltonians. Also, a particular interest is dedicated to the derivation of the quantum interferometric power which quantifies the amount of non-classical correlations. This quantum correlations quantifier is compared with the original quantum discord built upon von Neumann entropy and we discuss the effects of quantum correlations in quantum metrology protocols. In addition, the dynamics of quantum Fisher information about a dephasing channel is studied. In order to illustrate our results, we examine the situation involving tripartite coherent states to determine the sensitivity of the probe state when the first qubit is driven by an arbitrary local Hamiltonian.

Real-time motion-induced-error compensation in 3D surface-shape measurement.

Object motion can introduce unknown phase shift and thus measurement error in multi-image phase-shifting methods of fringe projection profilometry. This paper presents a new method to estimate the unknown phase shifts and reduce the motion-induced error by using three phase maps computed over a multiple measurement sequence and calculating the difference between phase maps. The pixel-wise estimation of the motion-induced phase shifts permits phase-error compensation for non-homogeneous surface motion. Experiments demonstrated the ability of the method to reduce motion-induced error in real-time, for shape measurement of surfaces with high depth variation, and moving and deforming surfaces.

Fast and robust phase-shift estimation in two-dimensional structured illumination microscopy

A method of determining unknown phase-shifts between elementary images in two-dimensional Structured Illumination Microscopy (2D-SIM) is presented. The proposed method is based on the comparison of the peak intensity of spectral components. These components correspond to the inherent structured illumination spectral content and the residual component that appears from wrongly estimated phase-shifts. The estimation of the phase-shifts is carried out by finding the absolute maximum of a function defined as the normalized peak intensity difference in the Fourier domain. This task is performed by an optimization method providing a fast estimation of the phase-shift. The algorithm stability and robustness are tested for various levels of noise and contrasts of the structured illumination pattern. Furthermore, the proposed approach reduces the number of computations compared to other existing techniques. The method is supported by the theoretical calculations and validated by means of simulated and experimental results.

Average labour productivity dynamics over the business cycle

An unobserved components model is used to analyse the cyclicality of average labour productivity in Australia since 1980. The model includes a direct estimate of phase shift so that the lead or lag of cycles relative to output can be determined. Average labour productivity is found to be countercyclical with output and employment and lagging the cycle in output by about six quarters. The observations are consistent with a theoretical model in which employment adjustment costs are falling due to lower turnover in employment. A more flexible labour market allows greater variation in employment relative to variation in output which tends to make productivity more countercyclical. The model is also used to determine the relative importance of the intensive and extensive margins of labour supply by examining fluctuations in both employment rates and average hours per worker. The full-time employment rate is significantly procyclical and lagging output as expected. The part-time employment rate is countercyclical, suggesting that there is some substitution of part time for full-time workers during economic downturns. At the intensive margin, average hours are procyclical, but they make a smaller contribution to the cyclicality of productivity than the employment rate.