Systematic Phase Errors Research Articles

Phase amplification in optical interferometry with weak measurement

Improving the phase resolution of interferometry is crucial for high-precision measurements of various physical quantities. Systematic phase errors dominate the phase uncertainties in most realistic optical interferometers. Here we propose and experimentally demonstrate a weak measurement scheme to considerably suppress the phase uncertainties by the direct amplification of phase shift in optical interferometry. Given an initial ultra-small phase shift between orthogonal polarization states, we observe the phase amplification effect with a factor of 388. Our weak measurement scheme provides a practical approach to significantly improve the interferometric phase resolution, which is favorable for precision measurement applications.

Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm

The origin of the Finite Grid Instability (FGI) is studied by resolving the dynamics in the 1D electrostatic Particle-In-Cell (PIC) model in the spectral domain at the single particle level and at the collective motion level. The spectral fidelity of the PIC model is contrasted with the underlying physical system or the gridless model. The systematic spectral phase and amplitude errors from the charge deposition and field interpolation are quantified for common particle shapes used in the PIC models. It is shown through such analysis and in simulations that the lack of spectral fidelity relative to the physical system due to the existence of aliased spatial modes is the major cause of the FGI in the PIC model.

Neural network calibration of a snapshot birefringent Fourier transform spectrometer with periodic phase errors.

Systematic phase errors in Fourier transform spectroscopy can severely degrade the calculated spectra. Compensation of these errors is typically accomplished using post-processing techniques, such as Fourier deconvolution, linear unmixing, or iterative solvers. This results in increased computational complexity when reconstructing and calibrating many parallel interference patterns. In this paper, we describe a new method of calibrating a Fourier transform spectrometer based on the use of artificial neural networks (ANNs). In this way, it is demonstrated that a simpler and more straightforward reconstruction process can be achieved at the cost of additional calibration equipment. To this end, we provide a theoretical model for general systematic phase errors in a polarization birefringent interferometer. This is followed by a discussion of our experimental setup and a demonstration of our technique, as applied to data with and without phase error. The technique's utility is then supported by comparison to alternative reconstruction techniques using fast Fourier transforms (FFTs) and linear unmixing.

Rapid extraction of the phase shift of the cold-atom interferometer via phase demodulation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11174249 and 61475139), the Ministry of Science and Technology of China (Grant No. 2011AA060504), the National Basic Research Program of China (Grant No. 2013CB329501), and the Fundamental Research Funds for the Central Universities, China (Grant No.

Generally, the phase of the cold-atom interferometer is extracted from the atomic interference fringe, which can be obtained by scanning the chirp rate of the Raman lasers at a given interrogation time T. If mapping the phase shift for each T with a series of measurements, the extraction time is limited by the protocol of each T measurement, and therefore increases dramatically when doing fine mapping with a small step of T. Here we present a new method for rapid extraction of the phase shift via phase demodulation. By using this method, the systematic shifts can be mapped though the whole interference area. This method enables quick diagnostics of the potential cause of the phase shift in specific time. We demonstrate experimentally that this method is effective for the evaluation of the systematic errors of the cold atomic gravimeter. The systematic phase error induced by the quadratic Zeeman effect in the free-falling region is extracted by this method. The measured results correspond well with the theoretic prediction and also agree with the results obtained by the fringe fitting method for each T.

THE 2014 ALMA LONG BASELINE CAMPAIGN: AN OVERVIEW

A major goal of the Atacama Large Millimeter/submillimeter Array (ALMA) is to make accurate images with resolutions of tens of milliarcseconds, which at submillimeter (submm) wavelengths requires baselines up to ~15 km. To develop and test this capability, a Long Baseline Campaign (LBC) was carried out from September to late November 2014, culminating in end-to-end observations, calibrations, and imaging of selected Science Verification (SV) targets. This paper presents an overview of the campaign and its main results, including an investigation of the short-term coherence properties and systematic phase errors over the long baselines at the ALMA site, a summary of the SV targets and observations, and recommendations for science observing strategies at long baselines. Deep ALMA images of the quasar 3C138 at 97 and 241 GHz are also compared to VLA 43 GHz results, demonstrating an agreement at a level of a few percent. As a result of the extensive program of LBC testing, the highly successful SV imaging at long baselines achieved angular resolutions as fine as 19 mas at ~350 GHz. Observing with ALMA on baselines of up to 15 km is now possible, and opens up new parameter space for submm astronomy.

Effects of systematic phase errors on optimized quantum random-walk search algorithm**Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).

This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover’s algorithm.

Phase retrieval from carrier frequency interferograms: reduction of the impact of space-variant disturbances

Phase “extraction” by using temporal phase shifting is sensitive to vibrations and drifts, producing systematic phase errors periodic withtwice the fringe frequency. This error source may be avoided by evaluating only single carrier frequency interferograms, which makesthe procedure immune against vibrations and drifts provided that the integration time is short enough to freeze the fringe pattern.However, the phases extracted from single interferograms in this way often show local irregularities depending on the mean phase of theinterference pattern. Such local phase irregularities are caused by local disturbances in the light path like specks and dust particles onthe optical components of the interferometer. Moreover, since digitized data are gathered, there is a nonlinear processing step involvedwhich is also responsible for the generation of such irregularities. Here, it is proposed to use a set of suitably combined phase-rampedinterferograms to reduce phase dependent irregularities. The proposed averaging technique also reduces edge ringing effects known fromFourier evaluation procedures. Since the imaging optics also contributes to the phase to be measured when tilted wavefronts are used,calibration is mandatory. The calibrated state is only valid if strict rules considering fringe number per diameter as well as the position of the wedge in the interferometer are maintained in the measuring process.

Channel balancing algorithm in multichannel wide‐area surveillance systems

Channel balancing is one of the crucial steps to obtain a satisfactory result in multichannel moving target detection. Therefore many algorithms have been proposed to realise channel balancing in multichannel synthetic aperture radar (SAR)-ground moving target indication (GMTI) systems, such as an adaptive two-dimensional calibration algorithm, linear fitting algorithm and eigen-decomposition algorithm. However, all of these aforementioned algorithms have some small defects in certain conditions, when used in the real data of multichannel wide area surveillance (WAS)–GMTI systems. The small defects can increase the false alarm probability, which is undesirable in moving target detection. In this study, after the detailed analysis about the interference phase in the wide-area surveillance mode, a novel channel balancing algorithm is proposed to perform channel balancing in multichannel WAS–GMTI systems. The new algorithm mainly concentrates on the balancing of systematic azimuthal phase errors. The effectiveness of the proposed algorithm is demonstrated when compared with other typical channel balancing algorithms in Monte Carlo simulations and real data processing.

Si wire array waveguide grating with stray light reduction scheme fabricated by ArF excimer immersion lithography

A Si wire arrayed waveguide grating designed to reduce the noise and transmission peak width and avoid systematic phase error generated at the curved waveguides is reported. A slab waveguide structure to remove stray light is used. 200 GHz spacing 16 channel devices were fabricated by ArF immersion. An improved crosstalk of −23 dB was obtained.

Super-resolution scanning laser microscopy through virtually structured detection

High resolution microscopy is essential for advanced study of biological structures and accurate diagnosis of medical diseases. The spatial resolution of conventional microscopes is light diffraction limited. Structured illumination has been extensively explored to break the diffraction limit in wide field light microscopy. However, deployable application of the structured illumination in scanning laser microscopy is challenging due to the complexity of the illumination system and possible phase errors in sequential illumination patterns required for super-resolution reconstruction. We report here a super-resolution scanning laser imaging system which employs virtually structured detection (VSD) to break the diffraction limit. Without the complexity of structured illumination, VSD provides an easy, low-cost and phase-artifact free strategy to achieve super-resolution in scanning laser microscopy.

Minimizing electrostatic charging of an aperture used to produce in-focus phase contrast in the TEM

Microfabricated devices designed to provide phase contrast in the transmission electron microscope must be free of phase distortions caused by unexpected electrostatic effects. We find that such phase distortions occur even when a device is heated to 300 °C during use in order to avoid the formation of polymerized, carbonaceous contamination. Remaining factors that could cause unwanted phase distortions include patchy variations in the work function of a clean metal surface, radiation-induced formation of a localized oxide layer, and creation of a contact potential between an irradiated area and the surround due to radiation-induced structural changes. We show that coating a microfabricated device with evaporated carbon apparently eliminates the problem of patchy variation in the work function. Furthermore, we show that a carbon-coated titanium device is superior to a carbon-coated gold device, with respect to radiation-induced electrostatic effects. A carbon-coated, hybrid double-sideband/single-sideband aperture is used to record in-focus, cryo-EM images of monolayer crystals of streptavidin. Images showing no systematic phase error due to charging are achievable under conditions of low-dose data collection. The contrast in such in-focus images is sufficient that one can readily see individual streptavidin tetramer molecules. Nevertheless, these carbon-coated devices perform well for only a limited length of time, and the cause of failure is not yet understood.

최소 자승법을 이용한 고해상도 밀리미터파 탐색기의 비선형 위상 오차의 추정

본 논문 연구에서는 고해상도 레이더 탐색기에 쓰이는 FMICW(Frequency Modulated Interrupted Continuous Wave) 또는 FMCW(Frequency Modulated Continuous Wave) 시스템의 비선형 특성에 의해서 발생되는 거리 해상도(range resolution) 성능 저하 현상을 보상하기 위하여, 하드웨어의 비선형 위상 오차 성분을 다양한 진폭, 위상을 가지는 사인함수와 랜덤 성분으로 모델링하고, 이를 추정할 수 있는 신호 처리 알고리즘을 새롭게 제안하였다. 이 방법은 알고 있는 거리에 위치한 두 개의 기준점 목표물(point target)로부터 각각 측정된 두 개의 IF 신호를 연립방정식화하여 희소 선형식(sparse linear equation)을 세우고, 최소 자승법(least squares) 관점에서 최적 해로서의 비선형 오차 성분을 추정하는 방법으로써 추정된 비선형 오차 성분은 비선형 오차 특성 보상을 위한 사전 왜곡(predistortion) 기법을 위해 사용될 수 있다. In this thesis, to compensate the sweep nonlinearity occurring in the high resolution radar system using FMICW or FMCW, the method of the estimation of the nonlinearity is proposed. The nonlinear phase component caused by the nonlinear characteristic of the radar system is modelled as a linear combination of the sinusoidal functions consisting of various magnitudes and phases(systematic nonlinear phase error) and a random component(stochastic nonlinear phase error). From two IF signals that are measured respectively independently for two reference point targets lying in different distances which are known, a sparse linear equation is made and solved by least squares method to estimate the nonlinear phase component. The estimated component can be used for predistortion method to compensate the sweep nonlinearity.

Improved arrayed-waveguide-grating layout avoiding systematic phase errors

We present a detailed description of an improved arrayed-waveguide-grating (AWG) layout for both, low and high diffraction orders. The novel layout presents identical bends across the entire array; in this way systematic phase errors arising from different bends that are inherent to conventional AWG designs are completely eliminated. In addition, for high-order AWGs our design results in more than 50% reduction of the occupied area on the wafer. We present an experimental characterization of a low-order device fabricated according to this geometry. The device has a resolution of 5.5 nm, low intrinsic losses (< 2 dB) in the wavelength region of interest for the application, and is polarization insensitive over a wide spectral range of 215 nm.

Phase error compensation method using smoothing spline approximation for a three-dimensional shape measurement system based on gray-code and phase-shift light projection

A novel phase error compensation method is presented for the reduction of phase error and shape waviness for a three-dimensional shape measurement system based on gray-code and phase-shift light projection. The phase error is mainly caused by the nonsinusoidality of projected phase-shift patterns. According to the system's phase-distribution properties, the proposed method adopts smoothing spline approximation to precisely extract the specific system phase error from the reference phase. This specific system phase error can be used to compensate the object phase during measures. The experimental results show that this compensation can reduce the shape waviness by 70%. In addition the residual object phase error is reduced by a smoothing procedure based on smoothing spline approximation. This procedure shows a 65% reduction in the residual shape waviness.

Cluster states from imperfect global entanglement

The cluster state, the highly entangled state that is the central resource for one-way quantum computing, can be efficiently generated in a variety of physical implementations via global nearest-neighbor interactions. In practice, a systematic phase error is expected in the entangling process, resulting in imperfect cluster states. We present a stochastic measurement technique to generate large perfect cluster states and other graph states with high probability from imperfect cluster states even when their initial entanglement is weak.

Technique for correcting systematic phase errors during fibre Bragg grating inscription

A simple technique for correcting systematic phase errors introduced during the holographic inscription of fibre Bragg gratings is presented. The technique involves characterising the fabrication errors associated with the phase mask and writing medium (i.e. the fibre). This is accomplished by measuring the phase of the coupling coefficient of a weak, uniform ‘trace grating’ written in the fibre. This phase is then used to generate a phase-corrected profile by combining the inverse of the measured phase with the phase of a target grating&apos;s profile. The trace grating is then overwritten with the stronger phase-corrected grating. Using this technique, a dual phase-shifted grating has been fabricated successfully and the overall phase error in reduced by a factor of 13.

Reconstruction of DEMs From ERS-1/2 Tandem Data in Mountainous Area Facilitated by SRTM Data

A new approach is presented in this paper to produce Digital Elevation Model (DEM) in mountainous areas with steep slope using ERS-1/2 tandem data. In order to reduce the impact of phase errors on the Interferometric Synthetic Aperture Radar (InSAR)-generated DEM, an external DEM such as that from Shuttle Radar Topography Mission (SRTM) is utilized in this approach. The proposed algorithm includes two steps: The first step is to model and remove phase trends with a linear regression analysis before converting phase to height; the second step is to filter unreliable height points before interpolating the DEM from the InSAR height map. The critical points are the following: 1) determining the one-to-one correspondence between the interferogram and the SRTM DEM before knowing the InSAR-derived elevation values and 2) estimating the elevation range of every pixel from SRTM DEM. To solve the first problem, an iteratively geocoding algorithm is performed. A DEM interpolation error model solves the second one. For InSAR data processing, the SRTM DEM is not only usable for modeling systematic phase errors but also for filtering gross height errors. The experiments in Zhangbei and the Three Gorges areas in China show that our approach has improved the accuracy of the resulting DEMs significantly without any ground control points.

Measurement uncertainty estimation in real experimental conditions of ultrasonic interferometer manometer established at NPL, India

The National Physical Laboratory, India, has established an ultrasonic interferometer manometer (UIM) as a primary standard in the barometric pressure region. This paper reports the results of the measurement uncertainty of the UIM evaluated under experimental conditions at each pressure point through a software developed and integrated with the existing operating software program. Through the operating software program, an initial estimate of column length using time-of-flight and four predefined ultrasonic frequencies with the help of an exact fractions algorithm is made, but the final pressure is calculated from the measurements made at multiple frequencies. At a particular pressure point, 44 measurements are made at different frequencies, covering two full circles (fringes). The mean of these 44 measurements is taken as the measured pressure to minimize the uncertainty contribution due to systematic phase error. In the present uncertainty evaluation, the standard deviation of this mean is taken into account in estimating the measurement uncertainty in real experimental conditions. The uncertainty thus estimated has been compared with that uncertainty, evaluated theoretically, as per ISO Guide to the Expression of Uncertainty in Measurements. This experimental determination of measurement uncertainty has helped us in making further improvements in the measurement accuracy of the UIM, especially at low-pressure measurements.

Application of ZPETC based least-beat and non-ripple control in precision linear motor displacement system

To make the output response of the control system of precision linear motor displacement system (PLMDS) accu- rately track the input instructions and to eliminate the adverse influences introduced by the load disturbance and the cut- ting-force fluctuation from direct drive, a zero phase error tracking control (ZPETC) scheme based on least-beat and non-ripple control in PLMDS is proposed for the application to the CNC turning of non-circular cross-section part, which can eliminate the system phase error caused by the unstable zeros and enhance the system response rate as well. Simulation re- sults show that this method can effectively improve the system tracking performance. The steady-state sinusoidal signal track- ing error of the system can reach up to ±0.5 μm with rapid and accurate step response. Compared with general control strate- gies of PLMDS, this method increases the system tracking ac- curacy and possesses fine anti-disturbance ability, which is endowed with the potential for wide application.

A bang-bang PLL employing dynamic gain control for low jitter and fast lock times

Bang-bang phase detector based PLLs are simple to design, suffer no systematic phase error, and can run at the highest speed a process can make a working flip-flop. For these reasons designers are employing them in the design of very high speed Clock Data Recovery (CDR) architectures. The major drawback of this class of PLL is the inherent jitter due to quantized phase and frequency corrections. Reducing loop gain can proportionally improve jitter performance, but also reduces locking time and pull-in range. This paper presents a novel PLL design that dynamically scales its gain in order to achieve fast lock times while improving jitter performance in lock. Under certain circumstances the design also demonstrates improved capture range. This paper also analyses the behaviour of a bang-bang type PLL when far from lock, and demonstrates that the pull-in range is proportional to the square root of the PLL loop gain.