New representation of the multimode phase shifting operator and its application

Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the mnltimode coordinate-momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the rnultimode phase shifting operator.

2D PHASE SHIFTING AND LOGICAL MOIRE USED IN FRINGES ANALYSIS

Phase Shifting And Logical Moire (PSALM) is a kind of computer image processing method which can be used in phase measurement and to obtain the shape, deformation and strain distribution of an object.This paper presents the structure and working procedure of a 2D phase measurement PSALM2D program and its application. When analyzing moire interferometric fringes,we can obtain 2D distribution of displacement and strain.When it is used in reflection moire we can measure the slope of a specimen.Satisfactory visualization and quantitative results are given by PSALM2D.

A NEW ALGORITHM FOR ELIMINATING PHASE-SHIFT ERROR IN PHASE SHIFTING INTERFEROMETRY

The effect of phaseshift error in phase shifting interferometry is investigated. A new algorithm with two sets of 4 samples for eliminating phase shift error is presented. The computer simulation and experiment result show that the phase shift offset should be π when the algorithm is used, and this algorithm has gotten better result than the original 4 sample algorithm.

Diagnosing ratio of electron density to collision frequency of plasma surrounding scaled model in a shock tube using low-frequency alternating magnetic field phase shift

A non-contact low-frequency(LF)method of diagnosing the plasma surrounding a scaled model in a shock tube is proposed.This method utilizes the phase shift occurring after the transmission of an LF alternating magnetic field through the plasma to directly measure the ratio of the plasma loop average electron density to collision frequency.An equivalent circuit model is used to analyze the relationship of the phase shift of the magnetic field component of LF electromagnetic waves with the plasma electron density and collision frequency.The applicable range of the LF method on a given plasma scale is analyzed.The upper diagnostic limit for the ratio of the electron density(unit:m^(-3))to collision frequency(unit:Hz)exceeds 1×10^(11),enabling an electron density to exceed 1×10^(20)m^(-3)and a collision frequency to be less than 1 GHz.In this work,the feasibility of using the LF phase shift to implement the plasma diagnosis is also assessed.Diagnosis experiments on shock tube equipment are conducted by using both the electrostatic probe method and LF method.By comparing the diagnostic results of the two methods,the inversion results are relatively consistent with each other,thereby preliminarily verifying the feasibility of the LF method.The ratio of the electron density to the collision frequency has a relatively uniform distribution during the plasma stabilization.The LF diagnostic path is a loop around the model,which is suitable for diagnosing the plasma that surrounds the model.Finally,the causes of diagnostic discrepancy between the two methods are analyzed.The proposed method provides a new avenue for diagnosing high-density enveloping plasma.

Error-CompensatingFive-SamplePhase-Shifting Algorithm Based on Phase-Shift Error Estimation

A new error compensating five sample phase shifting algorithm which is insensitive to phase shift error is proposed to retrieve the phase distribution of a fringe pattern. It includes two steps. First, the linear phase shift error is estimated using four sample images. Then, the phase distribution is calculated with error corrected by using the phase shift error estimated in the first step. As the equations of error estimation and phase calculation are simple, this new algorithm is practical as well as effective. Computer simulations were carried out to verify the effectiveness of the algorithm. Results of two other well known error compensating algorithms are also presented, which show the new algorithm is the least sensitive to phase shift error.

Method for rapid measuring retardation of a quarter-wave plate based on simultaneous phase shifting technique

A method for rapid measuring retardation of a quarter-wave plate based on simultaneous phase shifting technique is presented. The simultaneous phase shifting function is realized by an orthogonal grating, a diaphragm, an analyzer array, and a 4-quadrant detector. The intensities of the light beams from the four analyzers with different azimuths are measured simultaneously. The retardation of the quarter-wave plate is obtained through the four light intensity values. In this method, the major axis position of the quarter-wave plate need not intensity fluctuation of light be determined in advance source. The feasibility of the In addition, the measured result is free of the method is verified by the experiments.

Discrete Phase Shifts Control and Beam Selection in RIS-Aided MISO System via Deep Reinforcement Learning

Reconfigurable intelligent surface(RIS)for wireless networks have drawn lots of attention in both academic and industry communities.RIS can dynamically control the phases of the reflection elements to send the signal in the desired direction,thus it provides supplementary links for wireless networks.Most of prior works on RIS-aided wireless communication systems consider continuous phase shifts,but phase shifts of RIS are discrete in practical hardware.Thus we focus on the actual discrete phase shifts on RIS in this paper.Using the advanced deep reinforcement learning(DRL),we jointly optimize the transmit beamforming matrix from the discrete Fourier transform(DFT)codebook at the base station(BS)and the discrete phase shifts at the RIS to maximize the received signal-to-interference plus noise ratio(SINR).Unlike the traditional schemes usually using alternate optimization methods to solve the transmit beamforming and phase shifts,the DRL algorithm proposed in the paper can jointly design the transmit beamforming and phase shifts as the output of the DRL neural network.Numerical results indicate that the DRL proposed can dispose the complicated optimization problem with low computational complexity.

Three-step self-calibrating generalized phase-shifting interferometry

An accurate and fast three-step self-calibrating generalized phase-shifting interferomertry(SGPSI) is proposed. In this approach, two new phase-shifting signals are constructed by the difference interferograms normalization and noise suppressing, then the unknown phase shift between the two difference phase-shifting signals is estimated quickly through searching the minimum coefficient of variation of the modulation amplitude, a limited number of pixels are selected to participate in the search process to further save time, and finally the phase is reconstructed through the searched phase shift. Through the reconstruction of phase map by the simulation and experiment, and the comparison with several mature algorithms, the good performance of the proposed algorithm is proved, and it eliminates the limitation of requiring more than three phase-shifting interferograms for high-precision SGPSI. We expect this method to be widely used in the future.

Shaped Offset Quadrature Phase Shift Keying Based Waveform for Fifth Generation Communication

Fifth generation(5G)wireless networks must meet the needs of emerging technologies like the Internet of Things(IoT),Vehicle-to-everything(V2X),Video on Demand(VoD)services,Device to Device communication(D2D)and many other bandwidth-hungry multimedia applications that connect a huge number of devices.5G wireless networks demand better bandwidth efficiency,high data rates,low latency,and reduced spectral leakage.To meet these requirements,a suitable 5G waveform must be designed.In this work,a waveform namely Shaped Offset Quadrature Phase Shift Keying based Orthogonal Frequency Division Multiplexing(SOQPSK-OFDM)is proposed for 5G to provide bandwidth efficiency,reduced spectral leakage,and Bit Error Rate(BER).The proposed work is evaluated using a real-time Software Defined Radio(SDR)testbed-Wireless open Access Research Platform(WARP).Experimental and simulation results show that the proposed 5G waveform exhibits better BER performance and reduced Out of Band(OOB)radia-tion when compared with other waveforms like Offset Quadrature Phase Shift Key-ing(OQPSK)and Quadrature Phase Shift Keying(QPSK)based OFDM and a 5G waveform candidate Generalized Frequency Division Multiplexing(GFDM).BER analysis shows that the proposed SOQPSK-OFDM waveform attains a Signal to Noise Ratio(SNR)gain of 7.2 dB at a BER of 10�3,when compared with GFDM in a real-time indoor environment.An SNR gain of 8 and 6 dB is achieved by the proposed work for a BER of 10�4 when compared with QPSK-OFDM and OQPSK-OFDM signals,respectively.A significant reduction in OOB of nearly 15 dB is achieved by the proposed work SOQPSK-OFDM when compared to 16 Quadrature Amplitude Modulation(QAM)mapped OFDM.

Model on picometer-level light gravitational delay in the GRACE Follow-On-like missions

Laser interferometry plays a crucial role in laser ranging for high-precision space missions such as GRACE(Gravity Recovery and Climate Experiment)Follow-On-like missions and gravitational wave detectors.For such accuracy of modern space missions,a precise relativistic model of light propagation is required.With the post-Newtonian approximation,we utilize the Synge world function method to study the light propagation in the Earth’s gravitational field,deriving the gravitational delays up to order c^(−4).Then,we investigate the influences of gravitational delays in three inter-satellite laser ranging techniques,including one-way ranging,dual one-way ranging,and transponder-based ranging.By combining the parameters of Kepler orbit,the gravitational delays are expanded up to the order of e^(2)(e is the orbital eccentricity).Finally,considering the GRACE Follow-On-like missions,we estimate the gravitational delays to the level of picometer.The results demonstrate some high-order gravitational and coupling effects,such as c^(−4)-order gravitational delays and coupling of Shapiro and beat frequency,which may be non-negligible for higher precision laser ranging in the future.

Beamforming Design for IRS-and-UAV-Aided Two-Way Amplify-and-Forward Relay Networks in Maritime IoT

In this paper,an intelligent reflecting surface(IRS)-and-unmanned aerial vehicle(UAV)-assisted two-way amplify-and-forward(AF)relay network in maritime Internet of Things(IoT)is proposed,where ship1(S1)and ship2(S2)can be viewed as data collecting centers.To enhance the message exchange rate between S1 and S2,a problem of maximizing minimum rate is cast,where the variables,namely AF relay beamforming matrix and IRS phase shifts of two time slots,need to be optimized.To achieve a maximum rate,a low-complexity alternately iterative(AI)scheme based on zero forcing and successive convex approximation(LC-ZF-SCA)algorithm is presented.To obtain a significant rate enhancement,a high-performance AI method based on one step,semidefinite programming and penalty SCA(ONSSDP-PSCA)is proposed.Simulation results show that by the proposed LC-ZF-SCA and ONS-SDP-PSCA methods,the rate of the IRS-and-UAV-assisted AF relay network surpass those of with random phase and only AF relay networks.Moreover,ONS-SDP-PSCA perform better than LC-ZF-SCA in aspect of rate.

Transmit Power Minimization for IRS-Assisted NOMA-UAV Networks

The flexibility of unmanned aerial vehicles(UAVs)allows them to be quickly deployed to support ground users.Intelligent reflecting surface(IRS)can reflect the incident signal and form passive beamforming to enhance the signal in the specific direction.Motivated by the promising benefits of both technologies,we consider a new scenario in this paper where a UAV uses non-orthogonal multiple access to serve multiple users with IRS.According to their distance to the UAV,the users are divided into the close users and remote users.The UAV hovers above the close users due to their higher rate requirement,while the IRS is deployed near the remote users to enhance their received power.We aim at minimizing the transmit power of UAV by jointly optimizing the beamforming of UAV and the phase shift of IRS while ensuring the decoding requirement.However,the problem is non-convex.Therefore,we decompose it into two sub-problems,including the transmit beamforming optimization and phase shift optimization,which are transformed into second-order cone programming and semidefinite programming,respectively.We propose an iterative algorithm to solve the two sub-problems alternatively.Simulation results prove the effectiveness of the proposed scheme in minimizing the transmit power of UAV.

The Aharonov-Bohm Effect: An Exploration of Quantum Interference and Electromagnetic Potentials

The AB(Aharonov-Bohm)effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle’s wave function,even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect,an electron beam is split into two paths,with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams,the vector potential A associated with the magnetic flux Φ through the solenoid induces a phase shift in the electron’s wave function.This phase shift,quantified by △φ=qΦ/hc,manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED(quantum electrodynamics),where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems,beyond its classical role.This article outlines the AB effect,including its theoretical framework,experimental observations,and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.

Applications of Wavelet Analysis in Differential Propagation Phase Shift Data De-noising

Using numerical simulation data of the forward differential propagation shift （ΦDP） of polarimetric radar,the principle and performing steps of noise reduction by wavelet analysis are introduced in detail.Profiting from the multiscale analysis,various types of noises can be identified according to their characteristics in different scales,and suppressed in different resolutions by a penalty threshold strategy through which a fixed threshold value is applied,a default threshold strategy through which the threshold value is determined by the noise intensity,or a ΦDP penalty threshold strategy through which a special value is designed for ΦDP de-noising.Then,a hard-or soft-threshold function,depending on the de-noising purpose,is selected to reconstruct the signal.Combining the three noise suppression strategies and the two signal reconstruction functions,and without loss of generality,two schemes are presented to verify the de-noising effect by dbN wavelets：（1） the penalty threshold strategy with the soft threshold function scheme （PSS）; （2） the ΦDP penalty threshold strategy with the soft threshold function scheme （PPSS）.Furthermore,the wavelet de-noising is compared with the mean,median,Kalman,and finite impulse response （FIR） methods with simulation data and two actual cases.The results suggest that both of the two schemes perform well,especially when ΦDP data are simultaneously polluted by various scales and types of noises.A slight difference is that the PSS method can retain more detail,and the PPSS can smooth the signal more successfully.

Adaptive compensating method for Doppler frequency shift using LMS and phase estimation

The novel compensating method directly demodulates the signals without the carrier recovery processes, in which the carrier with original modulation frequency is used as the local coherent carrier. In this way, the phase offsets due to frequency shift are linear. Based on this premise, the compensation processes are： firstly, the phase offsets between the baseband neighbor-symbols after clock recovery is unbiasedly estimated among the reference symbols; then, the receiving signals symbols are adjusted by the phase estimation value; finally, the phase offsets after adjusting are compensated by the least mean squares （LMS） algorithm. In order to express the compensation processes and ability clearly, the quadrature phase shift keying （QPSK） modulation signals are regarded as examples for Matlab simulation. BER simulations are carried out using the Monte-Carlo method. The learning curves are obtained to study the algorithm＇s convergence ability. The constellation figures are also simulated to observe the compensation results directly.

PLL DEMODULATION TECHNIQUE FOR M-RAY POSITION PHASE SHIFT KEYING

The paper presents a kind of transmission system which employs M-ary Position Phase Shift Keying(MPPSK) to send data and Phase Locked Loop(PLL) based techniques for data retrieve.With a single PLL, MPPSK demodulation is achieved, as well as carrier recovery and symbol synchronization.Firstly, MPPSK modulation method is briefly introduced.2PPSK's PSD expression is given with its optimization result.Orthogonal Phase Detector(PD) and static threshold are used for the purpose of wider phase range and simplicity in demodulation.The data rate is alterable, which is 4.65 kbps for 2PPSK and 9.3 kbps for 4PPSK in the paper.Then some indicative comparisons in Signal to Noise Ratio Symbol Error Rate(SNR-SER) are made among 2PPSK, 3PPSK and 4PPSK, of which 4PPSK has proved to be optimal in ten slots each symbol conditions.And finally, it is demonstrated by system simulations that lower than 10-4 Symbol Error Rate(SER) performance can be obtained at 13 dB symbol SNR.

Carrier phase shifted SPWM based on current sourced multi-modular converter for active power filter

A novel current-source active power filter (APF) based on multi-modular converter with carrier phase-shifted SPWM (CPS-SPWM) technique is proposed. With this technique, the effect of equivalent high switching frequency con-verter is obtained with low switching frequency converter. It is very promising in current-source APF that adopt super-conducting magnetic energy storage component.

Fluctuations of optical phase of diffracted light for Raman–Nath diffraction in acousto–optic effect

The Raman–Nath diffraction in acousto–optic effect was studied theoretically and experimentally in the paper. Up to now, each order of diffracted light in Raman–Nath diffraction was still considered simply to be just frequency-shifted and to be a plane wave. However, we find that the phase and frequency shifts occur simultaneously and individually in Raman–Nath diffraction. The findings demonstrate that, in addition to the frequency shift, the optical phase of each order of diffracted light is also shifted by the sound wave and fluctuates with the sound wave and is related to the location in the acoustic field from which the diffracted light originates. As a result, the wavefront of each order of diffracted light is modulated to fluctuate spatially and temporally with the sound wave. Obviously, these findings are significant for applications of Raman–Nath diffraction in acousto–optic effect because the optical phase plays an important role in optical coherence technology.

Multiple phase detector of M-ary phase shift keying symbols in code division multiple access systems

A novel iterative technique, the phase descent search detection was proposed. This technique constrained the solution （PDS） algorithm, for M-ary phase shift keying （M-PSK） symbols to have a unit magnitude and it was based on coordinate descent iterations where coordinates were the unknown symbol phases. The PDS algorithm, together with a descent local search （also implemented as a version of the PDS algorithm）, was used multiple times with different initializations in a proposed multiple phase detector; the solution with the minimum cost was then chosen as the final solution. The simulation results show that for highly loaded multiuser scenarios, the proposed technique has a detection performance that is close to the single-user bound. The results also show that the multiple phase detector allows detection in highly overloaded scenarios and it exhibits near-far resistance. In particular, the detector has a performance that is significantly better, and complexity that is significantly lower, than that of the detector based on semi-definite relaxation.

Round-Robin Differential Phase Shift with Heralded Single-Photon Source

Round-robin differential phase shift （RRDPS） is a novel quantum key distribution protocol which can bound information leakage without monitoring signal disturbance. In this work, to decrease the effect of the vacuum component in a weak coherent pulses source, we employ a practical decoy-state scheme with heralded singlephoton source for the RRDPS protocol and analyze the performance of this method. In this scheme, only two decoy states are needed and the yields of single-photon state and multi-photon states, as well as the bit error rates of each photon states, can be estimated. The final key rate of this scheme is bounded and simulated over transmission distance. The results show that the two-decoy-state method with heralded single-photon source performs better than the two-decoy-state method with weak coherent pulses.