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.

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.

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.

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.

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.

The Magnetic Anisotropy and Complete Phase Diagram of CuFeO2 Measured in a Pulsed High Magnetic Field up to 75 T

The magnetization behavior of a CuFeO2 single crystal grown by the floating zone technique is investigated with a pulsed high magnetic field. We observe a series of field-induced multi-step-like transitions with hysteresis, of which the critical magnetic fields are temperature-dependent and show anisotropy. By using a pulsed high magnetic field up to 75 T, the magnetization behavior shows that the critical transition magnetic fields of spin- flip/flop shift to lower field regions with an increase in temperature. According to the magnetization curves, a complete magnetic phase diagram is depicted.

A novel high precision Doppler frequency estimation method based on the third-order phase-locked loop

In deep space exploration,many engineering and scientific requirements require the accuracy of the measured Doppler frequency to be as high as possible.In our paper,we analyze the possible frequency measurement points of the third-order phase-locked loop(PLL)and find a new Doppler measurement strategy.Based on this finding,a Doppler frequency measurement algorithm with significantly higher measurement accuracy is obtained.In the actual data processing,compared with the existing engineering software,the accuracy of frequency of 1 second integration is about 5.5 times higher when using the new algorithm.The improved algorithm is simple and easy to implement.This improvement can be easily combined with other improvement methods of PLL,so that the performance of PLL can be further improved.

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.

Wavefront measurement of a multilens optical system based on phase measuring deflectometry

Usually,a multilens optical system is composed of multiple undetectable sublenses.Wavefront of a multilens optical system cannot be measured when classical transmitted phase measuring deflectometry[PMD] is used.In this study,a wavefront measuring method for an optical system with multiple optics is presented based on PMD.A paraxial plane is used to represent the test multilens optical system.We introduce the calibration strategy and mathematical deduction of gradient equations.Systematic errors are suppressed with an N-rotation test.Simulations have been performed to demonstrate our method.The results showing the use of our method in multilens optical systems,such as the collimator and single-lens reflex camera lenses show that the measurement accuracy is comparable with those of interferometric tests.

Research on ambiguity resolution aided with triple difference

The ambiguity resolution in the field of GPS is investigated in detail. A new algorithm to resolve the ambiguity is proposed. The algorithm first obtains the floating resolution of the ambiguity aided with triple difference measurement. Decorrelation of searching space is done by reducing the ambiguity covariance matrix＇s dimension to overcome the possible sick factorization of the matrix brought by Z-transformation. In simulation, the proposed algorithm is compared with least-squares ambiguity decorrelation adjustment （LAMBDA）. The result shows that the proposed algorithm is better than LAMBDA because of lesser resolving time, which approximately reduces 20% resolving time. Thus, the proposed algorithm adapts to the high dynamic real-time applications.

A convenient look-up-table based method for the compensation of non-linear error in digital fringe projection

Although the structured light system that uses digital fringe projection has been widely implemented in three-dimensional surface profile measurement, the measurement system is susceptible to non-linear error. In this work, we propose a convenient look-up-table-based （LUT-based） method to compensate for the non-linear error in captured fringe patterns. Without extra calibration, this LUT-based method completely utilizes the captured fringe pattern by recording the full-field differences. Then, a phase compensation map is established to revise the measured phase. Experimental results demonstrate that this method works effectively.