Temporally Modulated Phase Retrieval Method for Weak Temporal Phase Measurement of Laser Pulses

We propose a simple iterative algorithm based on a temporally movable phase modulation process to retrieve the weak temporal phase of laser pulses. This unambiguous method can be used to achieve a high accuracy and to simultaneously measure the weak temporal phase and temporal profile of pulses, which are almost transform- limited. A detailed analysis shows that this iterative method has valuable potential applications in the charac- terization of pulses with weak temporal phase.

Bunch-length measurement at a bunch-by-bunch rate based on time–frequency-domain joint analysis techniques and its application

This paper presents a new technique for measuring the bunch length of a high-energy electron beam at a bunch-by-bunch rate in storage rings.This technique uses the time–frequency-domain joint analysis of the bunch signal to obtain bunch-by-bunch and turn-by-turn longitudinal parameters,such as bunch length and synchronous phase.The bunch signal is obtained using a button electrode with a bandwidth of several gigahertz.The data acquisition device was a high-speed digital oscilloscope with a sampling rate of more than 10 GS/s,and the single-shot sampling data buffer covered thousands of turns.The bunch-length and synchronous phase information were extracted via offline calculations using Python scripts.The calibration coefficient of the system was determined using a commercial streak camera.Moreover,this technique was tested on two different storage rings and successfully captured various longitudinal transient processes during the harmonic cavity debugging process at the Shanghai Synchrotron Radiation Facility(SSRF),and longitudinal instabilities were observed during the single-bunch accumulation process at Hefei Light Source(HLS).For Gaussian-distribution bunches,the uncertainty of the bunch phase obtained using this technique was better than 0.2 ps,and the bunch-length uncertainty was better than 1 ps.The dynamic range exceeded 10 ms.This technology is a powerful and versatile beam diagnostic tool that can be conveniently deployed in high-energy electron storage rings.

An improved phase measurement method of integrated pulse profile for pulsar

Integrated profile is one of the basic characteristic of X-ray pulsar. Gaussian function fit is used to model the components of X-ray pulsar profile, and it is combined with Poisson distribution model of X-ray pulsar to analyze Cramer-Rao low bound （CRLB） of phase, phase rate estimation and relation between CRLB and profile components. Then, a time domain method using minimum entropy is proposed for profile phase and phase rate estimation, and its effectiveness is explained using simulation examples.

On the temperature characteristics of phase measurement in homodyne fiber interferometer

Different from the traditional way of using piezoelectric （PZT）phase shifter to measure phase difference, a new method is designed to calculate it between signals in the two arms of a homodyne fiber interferometer. A simple homodyne fiber interferometer system is then established to measure the interference photoeurrent and the photocurrents from the two fiber arms generated by the signal power on a temperature control plat. The homodyne fiber interferometer system is composed of fiber and sensitive to the variation of temperature. Thus, is necessary to study the temperature characteristics in the phase measurement of homodyne fiber interferometer. The experimental results show that the variation of the phase difference of signals in the two fiber arms is proportional to the variation of temperature.

High accuracy amplitude and phase measurements based on a double heterodyne architecture

In the digital low level RF （LLRF） system of a circular （particle） accelerator, the RF field signal is usually down converted to a fixed intermediate frequency （IF）. The ratio of IF and sampling frequency determines the processing required, and differs in various LLRF systems. It is generally desirable to design a universally compatible architecture for different IFs with no change to the sampling frequency and algorithm. A new RF detection method based on a double heterodyne architecture for wide IF range has been developed, which achieves the high accuracy requirement of modern LLRF. In this paper, the relation of IF and phase error is systematically analyzed for the first time and verified by experiments. The effects of temperature drift for 16 h IF detection are inhibited by the amplitude and phase calibrations.

Entanglement-free determination of pretilt angles of twisted nematic liquid-crystal cells by phase measurement

Because of low cost, fast response time, and high light transmittance, thin-film-transistor （TFT） driven twisted nematic （TN） liquid-crystal displays （LCDs） have been widely used in calculators, computer screens, and cell phones. The pretilt angle of the TN medium within the TFT-TN panel affects not only its response times and view- ing angles but also the light-leakage positions of fringed- field-induced disclination lines within pixels of theTFT-TN panel.

Differential evolution-based optimal placement of phase measurement unit considering measurement redundancy

Phase measurement unit(PMU)is the key equipment for electric power system,which has been used to monitor and control power grid.But it is too expensive to deploy on each bus.So,we need to investigate how to deploy PMU to satisfy our observation requirements with minimum PMU numbers.This problem is called the optimal PMU placement(OPP).In this paper,we employ differential evolution(DE)algorithm to solve the OPP problem.Our optimization target is to make the power grid completely observable with maximum redundancy and minimum number of PMU.The proposed method is tested on IEEE 14-bus system,IEEE 30-bus system and IEEE 57-bus system respectively with considering the zero injection.

Phase-only Correlation Measurement with Computer-controlled LCD and CCD Image Processing System

Using computer-controlled liquid crystal display (LCD) as an image processor and a CCD camera as a detector, phase-only correlation measurement is performed with the aid of joint transform correlation method (JTC). This computer -controlled LCD-CCD image processing system may be a powerful tool for defect detection, position control and pattern recognition. It enables new possibilities in analog real-time image processing. This is of great interest in microelectronic manufacturing today and in the future.

The holographic reconstructing algorithm and its error analysis about phase-shifting phase measurement

Phase-shifting measurement and its error estimation method were studied according to the holographic principle.A function of synchronous superposition of object complex amplitude reconstructed from N-step phase-shifting through one integral period(N-step phase-shifting function for short)was proposed.In N-step phase-shifting measurement,the interferograms are seen as a series of in-line holo-grams and the reference beam is an ideal parallel-plane wave.So the N-step phase-shifting function can be obtained by multiplying the interferogram by the original reference wave.In ideal conditions,the proposed method is a kind of synchro-nous superposition algorithm in which the complex ampli-tude is separated,measured and superposed.When error exists in measurement,the result of the N-step phase-shifting function is the optimal expected value of the least-squares fitting method.In the above method,the N+1-step phase-shifting function can be obtained from the N-step phase-shifting function.It shows that the N-step phase-shifting function can be separated into two parts:the ideal N-step phase-shifting function and its errors.The phase-shifting errors in N-steps phase-shifting phase measurement can be treated the same as the relative errors of amplitude and intensity under the understanding of the N+1-step phase-shifting function.The difficulties of the error estimation in phase-shifting phase measurement were restricted by this error esti-mation method.Meanwhile,the maximum error estimation method of phase-shifting phase measurement and its formula were proposed.

A Portable Analog Lock-In Amplifier for Accurate Phase Measurement and Application in High-Precision Optical Oxygen Concentration Detection

A portable analog lock-in amplifier capable of accurate phase detection is proposed in this paper. The proposed lock-in amplifier, which uses the dual-channel orthometric signals as the references to build the xy coordinate system, can detect the relative phase between the input and x-axis based on trigonometric function. The sensitivity of the phase measurement reaches 0.014degree, and a detection precision of 0.1 degree is achieved. At the same time, the performance of the lock-in amplifier is verified in the high precision optical oxygen concentration detection. Experimental results reveal that the portable analog lock-in amplifier is accurate for phase detection applications. In the oxygen sensing experiments, 0.058% oxygen concentration resulted in 0.1 degree phase shift detected by the lock-in amplifier precisely. In addition, the lock-in amplifier is small and economical compared with the commercial lock-in equipments, so it can be easily integrated in many portable devices for industrial applications.

Single-Shot Measurement of Transient Phase Shift Induced by Laser Wake

Based on the frequency-to-time mapping relation of the linearly chirped pulse, the temporal phase shift induced by a laser-excited wake in a helium gas jet is measured using a chirped-pulse spectral interferometry with ～ 140 fs resolution over a temporal region of I ps in a single shot. In this measurement, the image of the wake is obtained with one-dimensional spatial resolution and temporal resolution limited only by the bandwidth and chirp of the pulse. The ＇bubbles＇ feature of the wake structure, along with multiple wakes excited by the main lobe and the side lobe of a laser focal-spot, is captured simultaneously.

Recent Progress of Full‑Field Three‑Dimensional Shape Measurement Based on Phase Information

Full-field three-dimensional(3D)measurement technology based on phase information has become an indispensable part of geometric dimension measurement in modern scientific research and engineering applications.This field has been developing and evolving for the study of highly reflective phenomena,diffuse reflections,and specular surfaces,and many novel methods have emerged to increase the speed of measurements,enhance data accuracy,and broaden the robustness of the system.Herein,we will discuss the latest research progress in full-field 3D shape measurement based on phase information systematically and comprehensively.First,the fundamentals of 3D shape measurement based on phase information are introduced,namely,phase-shifting and transform-based methods.Second,recent technological innovations are highlighted,including increases in measurement speed and automation and improvements in robustness in complex environments.In particular,the challenges faced by these technological advances in solving highly dynamic,composite surface measurement problems are presented,i.e.,with multiexposure techniques proposed for high dynamics that extend the dynamic range of the camera to reduce the effects of overexposure but increase the cost of time and have high hardware requirements,fringe adaptive techniques that overcome light variations but are computationally complex,and multipolarized camera techniques that reduce the effects of light variations but are sensitive to the light source.Third,the phase-shifting method combined with coding is proposed to improve the measurement speed,but the accuracy is slightly reduced.Deep learning techniques are proposed to cope with measurements in complex environments,but the dataset computation process is cumbersome.Finally,future research directions are suggested,and the challenges are presented.Overall,this work provides a reference for researchers and engineers.

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.

Analysis and optimization of distance measurement in MATLAB/SIMULINK model

Based on the basic principle of Time-Of-Flight cameras,a novel MATLAB/SIMULINK model is proposed to measure phase delay of a modulated light signal which represents the distance from camera to object. Subsequently,by discussing influence factors of phase measurement,it is found that the integration time,the sampling time,and the aliasing effect have important effect on improving the accuracy of phase measurement. Interestingly,by analyzing different integration time and sampling time, it is found that the best integration time and sampling time are 0.05 ms and 10 ns,respectively. In this case(i.e.,in absence of the aliasing effect),the variation range of the distance error is between 1 mm and 11 mm in the interval of one period. Especially,under the consideration of the aliasing effect,the average value of distance error is half of that in absence of the aliasing effect. This improves the accuracy of the distance measurement greatly.

COMPACT PHASE GRATING INTERFERENCE SENSOR FOR MICRO-DISPLACEMENT

On the basis of existing techniques, a compact micro-displacement sensor of phase grating interference （PGI） is described, which adopts cylindrical hologram diffraction grating as the calibration standard. The optical principle of the sensor is explained, and the relation between the grating motion displacement and the phase shift of interference stripes is deduced. The improvement of the integral structure and the method of photoelectric signal processing are described in detail. With the software system based on the virtual instrument development platform Labwindows/CVI and other hardwares such as the precision displacement worktable, the surfaces of typical parts are measured and the characterization results are given. The sensor has wide measuring range and high resolution, its sensitivity and resolution being independent of the wavelength of the incident light. The vertical measuring range is 0-6 mm, and the vertical resolution is 0.005μm. The experimental results show that the sensor can be used to measure and characterize the surface topography parameters of the plane and curved surface.

Phase Properties of Nonlinear Coherent States

Using the Pegg-Barnett formalism we study the phase probability distributions and the squeezing effects of measured phase operators in the nonlinear coherent states introduced by R.L. de Matos Filho and W. Vogel to describe the center-of mass motion of a trapped ion and the q-coherent states. Moreover, we have obtained the completeness relation of nonlinear coherent states and proved that the q-Fock state \n>(q) introduced in many papers is, in fact, the usual Fock state.

Fluctuations and Squeezing for Measured Phase Operators of the J-C Model in the Kerr Medium

By using the theory of measured phase operator proposed by Barnett and Pegg, dynamic properties of the phase of a field are studied. The time evolution and squeezing of measured phase operators of a coherent field interacting with a two-level atom in the cavity with or without the Kerr medium are investigated. The influences of virtual cavity field on squeezing of measured phase operator are studied. Our numerical results show that the squeezing effects are clearly influenced by Kerr medium parameters, the field intensity, and the detuning. Moreover, the influence of the virtual-photon field makes more quantum noise in the evolution of measured phase operators. Key words Jaynes-Cummings model (JCM) - Kerr medium - measured phase operator - squeezing - virtual photon PACS 2001 4250Dv

Higher-Order Fluctuations and Measured Phase Operators in the Squeezed Thermal States

We study the higher order fluctuations and squeezing of quadrature operators in the squeezed thermal states. In terms of measured phase operators, we discuss the fluctuations and squeezing of phases in these states. We conclude that the condition of higher order squeezing for quadrature components of the field is order independent and the fluctuations of measured phase operators are temperature independent.

Properties of Phase and Their Evolutions in Damped Odd and Even Coherent States

The properties of measured phase operators in damped odd and even coherent states have been studied. The fluctuations associated with measured phase and their squeezing in these states are investigated. The phase properties in damped superposition coherent states are considered too with the help of measured phase operators. These fluctuations and their squeezing are affected by damping and evolve with time elapsing.

Design of IREDM System with a DSP Phase Detector

The design and realization of a new generation of infra-red electronic distance measurement (IR EDM) system are presented.A DSP(Digital Signal Process) phase detector based on high speed analog-to-digital converter and DSP technique has been designed,in order to improve the precision and reliability of IR EDM system.As a result,the EDM system developed with a DSP phase detector has a precision of 3 mm in the measuring range of 2 km.