Precise Phase Measurements Research Articles

Automated acquisition of vast numbers of electron holograms with atomic-scale phase information.

An automated acquisition system for collecting a large number of electron holograms, to improve the statistical precision of phase analysis, was developed. A technique for shifting the electron beam in combination with stage movement allows data to be acquired over a wide area of a TEM-specimen grid. Undesired drift in the hologram position, which may occur during the hologram acquisition, can be corrected in real time by automated detection of the interference-fringe region in an image. To demonstrate the usefulness of the developed automated hologram acquisition system, gold nanoparticles dispersed on a carbon foil were observed with a 1.2-MV atomic resolution holography electron microscope. The system could obtain 1024 holograms, which provided phase maps for more than 500 nanoparticles with a lateral resolution of 0.14nm, in just 1h. The observation results revealed an anomalous increase in mean inner potential for a particle size smaller than 4nm. The developed automated hologram acquisition system can be applied to improve the precision of phase measurement by averaging many phase images, as demonstrated by single particle analysis for biological entities. Moreover, the system makes it possible to study electrostatic potential of catalysts and other functional nanoparticles at atomic resolution.

A Phase Calibration Method for Millimeter-Wave Up-Converter Using Electro-Optic Sampling

A phase measurement method using electro-optic sampling of millimeter-wave 4-tone signals is presented for phase calibration of frequency converters. Phase lock loop (PLL) circuits with high comparison frequencies of 2.6 and 15 GHz are used to synchronize the millimeter-wave 4-tone signal with a short optical pulse for low-jitter equivalent time sampling. A 4-tone separate detection method using a lock-in amplifier is applied for precise phase measurement with high frequency resolution. In addition, a phase-correction scheme using 4-tone signals with different frequency spacings is introduced for wideband phase calibration. The error vector magnitude (EVM) of the 10.2-Gbaud quadrature phase shift keying (QPSK) signal with 292.5-GHz carrier frequency is evaluated to confirm the effectiveness of the wideband phase calibration.

Mitigation of ionospheric scintillation effects on GNSS precise point positioning (PPP) at low latitudes

Global navigation satellite systems (GNSS) underpin a number of modern life activities, including applications demanding positioning accuracy at the level of centimetres, such as precision agriculture, offshore operations and mining, to name a few. Precise point positioning (PPP) exploits the precision of the GNSS signal carrier phase measurements and may be used to provide the high accuracy positioning needed by these applications. The Earth’s ionosphere is critical in PPP due to its high variability and to disturbances such as scintillation, which can affect the satellite signals propagation and thereby degrade the positioning accuracy, especially at low latitudes, where severe scintillation frequently occurs. This manuscript presents results from a case study carried out at two low latitude stations in Brazil, where a dedicated technique is successfully applied to mitigate the scintillation effects on PPP. The proposed scintillation mitigation technique improves the least square stochastic model used for position computation by assigning satellite and epoch specific weights based on the signal tracking error variances. The study demonstrates that improvements in the 3D positioning error of around 62–75% can be achieved when applying this technique under strong scintillation conditions. The significance of the results lies in the fact that this technique can be incorporated in PPP to achieve the required high accuracy in real time and thus improve the reliability of GNSS positioning in support of high accuracy demanding applications.

Quantitative phase imaging based on simple Michelson-type lateral shearing interferometry with rotational right-angle prisms.

By using a kind of simple Michelson-type lateral shearing interferometry, in this paper, the precise quantitative phase measurement of transparent microscopic objects is realized successfully. For this interferometry, on the basis of the fundamental structure of the traditional Michelson interferometer, the two plane mirrors are replaced with two ordinary right-angle prisms. In the beginning, the ridges of the two right-angle prisms are set to align with the optical axis and be in the vertical direction. Subsequently, to achieve the lateral shear, one of these two right-angle prisms is rotated around its ridge. Furthermore, the goal to obtain more lateral shear can be achieved by introducing a bigger rotating angle or rotating another prism simultaneously. In addition, owing to the simple structure of the Michelson interferometer and the inexpensive optical components used, the system is compact, portable, easy to operate, and low cost. The experimental results show the practicability of this system.

A High Precision Time Synchronization Method for Smart Grid based on Beidou Satellite System

With the rapid development of power grid and the large-scale application of automation equipment in power station, the requirement of high precision time synchronization for power system production and control is rapid growth. The accuracy of time synchronization for power system is an important basis to guarantee power network operation control and fault analysis, and a fundamental guarantee to improve power network accident analysis and stability control. In order to ensure that the automatic device receives accurate time synchronization signal, time monitoring and application schemes of different technical routes are studied in this paper. It is proposed that the precise monitoring based on the direct measurement of Beidou can realize high precision time monitoring and synchronization, better guarantee the accuracy of time synchronization between power equipment, ensure the precision of phase measurement, line fault location and time sequence recording of power system, and provide technical support for the stable and reliable operation of power system.

Phase sensitivity of a Mach-Zehnder interferometer with single-intensity and difference-intensity detection

Interferometry is a widely-used technique for precision measurements in both classical and quantum contexts. One way to increase the precision of phase measurements, for example in a Mach-Zehnder interferometer (MZI), is to use high-intensity lasers. In this paper we study the phase sensitivity of a MZI in two detection setups (difference intensity detection and single-mode intensity detection) and for three input scenarios (coherent, double coherent and coherent plus squeezed vacuum). For the coherent and double coherent input, both detection setups can reach the quantum Cramer-Rao bound, although at different values of the optimal phase shift. The double coherent input scenario has the unique advantage of changing the optimal phase shift by varying the input power ratio.

Laser Interferometer for Space Gravitational Waves Detection and Earth Gravity Mapping

The idea of using space laser interferometer to measure the relative displacement change between two satellites has been considered for space gravitational waves detection and Earth gravity filed mapping in recent years. Some investigations on the key issues of laser interferometer in our working team have been presented in this paper. An on-ground laser interferometer prototype used for the demonstration of satellite-to-satellite ranging has been constructed, which is equipped with phasemeter, laser pointing modulation and laser phase-locking control. The experimental results show that path-length measurement sensitivity of the laser interferometer reaches 200 pm/√ Hz, and phase measurement precision achieves 2π × 10− 5 rad/√ Hz, and laser pointing modulation precision is better than 80 nrad/√ Hz, and laser phase-locking control precision attains 2π × 10− 4 rad/√ Hz within the frequency regime of 1 mHz–1 Hz. All of these demonstrate that the proposed laser interferometer has very promising feasibility to meet the requirement of the Taiji, TianQin and Space Advanced Gravity Measurement (SAGM) missions which are put forward by Chinese scientists.

Adiabatic Mach–Zehnder interferometer in a dipolar spin-1 condensate

We propose and analyze a realizable scheme for performing a Heisenberg-limited Mach–Zehnder interferometry with a dipolar spin-1 condensate. Based upon adiabatic processes of sweeping the transverse magnetic field, we demonstrate a perfect phase transition, which accomplishes the beam splitter, phase shifter and recombiner as for a Mach–Zehnder interferometer. The attractive dipolar interaction ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. We also study the spin squeezing of the state generated in the beam splitter and show that the spin squeezing exhibits an extremum near the critical point of phase transition.

Noise suppression in inverse weak value-based phase detection

We examine the effect of different sources of technical noise on inverse weak value-based precision phase measurements. We find that this type of measurement is similarly robust to technical noise as related experiments in the weak value regime. In particular, the measurements considered here are robust to additive Gaussian white noise and angular jitter noise commonly encountered in optical experiments. Additionally, we show the same techniques used for precision phase measurement can be used with the same technical advantages for optical frequency measurements.

Singular Spectrum Based Smoothing of GNSS Pseudorange Dynamics

Traditional approach towards precise point positioning in a single frequency global navigation satellite system (GNSS) receiver is to combine the precise but ambiguous carrier phase measurements with noisy but unambiguous code delay measurements to get a better estimate of the pseudorange dynamics. However, ionosphere divergence error and cycle slips limit the efficacy of this approach especially in harsh propagation scenarios. We propose a new approach that utilizes only code delay measurements to get the same level of accuracy as from the traditional approach. The proposed approach is based on extracting the principle components from the singular spectrum of windowed code delay measurements. The simulation results, supported by real GNSS data analysis, indicate improved accuracy and enhanced robustness against noise and propagation impairments with respect to traditional approach.

Uncovering common misconceptions in GNSS Precise Point Positioning and its future prospect

Within the last decade, GNSS Precise Point Positioning (PPP) has generated unprecedented interest among the GNSS community and is being used for a number of scientific and commercial applications today. Similar to the conventional relative positioning technique, PPP could provide positioning solutions at centimeter-level precision by making use of the precise carrier phase measurements and high-accuracy satellite orbits and clock corrections provided by, for example, the International GNSS Service. The PPP technique is attractive as it is computationally efficient; it eliminates the need for simultaneous observations at both the reference and rover receivers; it also eliminates the needs for the rover receiver to operate within the vicinity of the reference receiver; and it provides homogenous positioning quality within a consistent global frame anywhere in the world with a single GNSS receiver. Although PPP has definite advantages for many applications, its merits and widespread adoption are significantly limited by the long convergence time, which restricts the use of the PPP technique for many real-time GNSS applications. We provide an overview of the current performance of PPP as well as attempt to address some of the common misconceptions of this positioning technique--considered by many as the future of satellite positioning and navigation. Given the upcoming modernization and deployment of GNSS satellites over the next few years, it would be appropriate to address the potential impacts of these signals and constellations on the future prospect of PPP.

Focus on test, measurement, and materials

Focus on test, measurement, and materials

Phase measurement accuracy in noise waveform synthetic aperture radar

Detection of small changes in natural formations and human-made constructions is a promising application of synthetic aperture radar (SAR). This paper deals with a specific radar, which is a ground-based SAR using noise waveform. Being fully coherent, SAR provides both phase and amplitude information for every pixel in the mapped area. This gives rise to the possibility of comparing phases between the images taken from the same position at different times in order to extract information about the changes that have occurred between subsequent radar measurements. Such a technique, called coherent change detection (CCD), allows changes of a subwavelength size to be detected. The use of a noise waveform for sounding ensures high electromagnetic compatibility and interference immunity. Moreover, it enables long integration time in the detection stage. However, the random nature of probing signals used in noise radars leads to randomness of the output signals and the preservation of residual fluctuation in the images generated. This random residual, along with external noise, influences the overall accuracy of the phase measurement in noise radar. In this paper, the theoretical and experimental investigation of this specific influence of noise on the precision of phase measurements is presented. The theoretical part of the paper is focused on the estimation of the Cramer-Rao lower bound for the phase measurements using both statistical theory and geometrical interpretation of complex signals. In the experimental part, these findings are verified with dedicated measurements of a metallic sphere displacement, carried out with the help of a ground-based noise waveform SAR.

Photon-counting 1.0 GHz-phase-modulation fluorometer.

We have constructed an improved version of a photon-counting phase-modulation fluorometer (PC-PMF) with a maximum modulation frequency of 1.0 GHz, where a phase domain measurement is conducted with a time-correlated single-photon-counting electronics. While the basic concept of the PC-PMF has been reported previously by one of the authors, little attention has been paid to its significance, other than its weak fluorescence measurement capability. Recently, we have recognized the importance of the PC-PMF and its potential for fluorescence lifetime measurements. One important aspect of the PC-PMF is that it enables us to perform high-speed measurements that exceed the frequency bandwidths of the photomultiplier tubes that are commonly used as fluorescence detectors. We describe the advantages of the PC-PMF and demonstrate its usefulness based on fundamental performance tests. In our new version of the PC-PMF, we have used a laser diode (LD) as an excitation light source rather than the light-emitting diode that was used in the primary version. We have also designed a simple and stable LD driver to modulate the device. Additionally, we have obtained a sinusoidal histogram waveform that has multiple cycles within a time span to be measured, which is indispensable for precise phase measurements. With focus on the fluorescence intensity and the resolution time, we have compared the performance of the PC-PMF with that of a conventional PMF using the analogue light detection method.

Measurement errors in entanglement-assisted electron microscopy

The major resolution-limiting factor in cryoelectron microscopy of unstained biological specimens is radiation damage by the very electrons that are used to probe the specimen structure. To address this problem, an electron microscopy scheme that employs quantum entanglement to enable phase measurement precision beyond the standard quantum limit has recently been proposed {[}Phys. Rev. A \textbf{85}, 043810{]}. Here we identify and examine in detail measurement errors that will arise in the scheme. An emphasis is given to considerations concerning inelastic scattering events because in general schemes assisted with quantum entanglement are known to be highly vulnerable to lossy processes. We find that the amount of error due both to elastic and inelastic scattering processes are acceptable provided that the electron beam geometry is properly designed.

Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system

BeiDou regional navigation satellite system (BDS) also called BeiDou-2 has been in full operation since December 27, 2012. It consists of 14 satellites, including 5 satellites in Geostationary Orbit (GEO), 5 satellites in Inclined Geosynchronous Orbit (IGSO), and 4 satellites in Medium Earth Orbit (MEO). In this paper, its basic navigation and positioning performance are evaluated preliminarily by the real data collected in Beijing, including satellite visibility, Position Dilution of Precision (PDOP) value, the precision of code and carrier phase measurements, the accuracy of single point positioning and differential positioning and ambiguity resolution (AR) performance, which are also compared with those of GPS. It is shown that the precision of BDS code and carrier phase measurements are about 33 cm and 2 mm, respectively, which are comparable to those of GPS, and the accuracy of BDS single point positioning has satisfied the design requirement. The real-time kinematic positioning is also feasible by BDS alone in the opening condition, since its fixed rate and reliability of single-epoch dual-frequency AR is comparable to those of GPS. The accuracy of BDS carrier phase differential positioning is better than 1 cm for a very short baseline of 4.2 m and 3 cm for a short baseline of 8.2 km, which is on the same level with that of GPS. For the combined BDS and GPS, the fixed rate and reliability of single-epoch AR and the positioning accuracy are improved significantly. The accuracy of BDS/GPS carrier phase differential positioning is about 35 and 20 % better than that of GPS for two short baseline tests in this study. The accuracy of BDS code differential positioning is better than 2.5 m. However it is worse than that of GPS, which may result from large code multipath errors of BDS GEO satellite measurements.

Optimal multi-photon phase sensing with a single interference fringe

Quantum entanglement can help to increase the precision of optical phase measurements beyond the shot noise limit (SNL) to the ultimate Heisenberg limit. However, the N-photon parity measurements required to achieve this optimal sensitivity are extremely difficult to realize with current photon detection technologies, requiring high-fidelity resolution of N + 1 different photon distributions between the output ports. Recent experimental demonstrations of precision beyond the SNL have therefore used only one or two photon-number detection patterns instead of parity measurements. Here we investigate the achievable phase sensitivity of the simple and efficient single interference fringe detection technique. We show that the maximally-entangled “NOON” state does not achieve optimal phase sensitivity when N > 4, rather, we show that the Holland-Burnett state is optimal. We experimentally demonstrate this enhanced sensitivity using a single photon-counted fringe of the six-photon Holland-Burnett state. Specifically, our single-fringe six-photon measurement achieves a phase variance three times below the SNL.

Fundamental limits on the digital phase measurement method based on cross-correlation analysis

Ultra-precision phase measurement is a key technology for state-of-the-art laser interferometry. In this paper we present a fully digital phase measurement method based on cross-correlation analysis, and analyze the measurement errors caused by sampling quantization, intrinsic white noise and non-integral-cycle sampling. The last error source results in a cyclic error that has not been reported ever. We used a high-performance data acquisition system to carry out the cross-correlation-based phase measurement, and obtained a noise level of 1.2 × 10(-6) rad/Hz(1/2)[commercial at]1 Hz. Moreover, the cyclic phase error of about 10(-2) rad/Hz(1/2), caused by non-integral-cycle sampling, had been observed. In order to demonstrate the application of this precision phase measurement method, an ultra-precision heterodyne laser interferometer, consisting of digital phase measurement system and ultra-stable optical bench, was constructed for displacement measurement. The experimental results showed that a measurement resolution of 63 pm had been achieved.

Research on the Sampling Frequency’s Range to Improve the Precision of All-Phase FFT Phase Measurement

To improve the precision of all-phase FFT (apFFT for short) phase measurement, this paper takes full advantages of the basic properties of apFFT spectral analysis and deduce the distribution range of sampling frequency. And through simulation experiment, this deduced range is verified. Moreover this paper points that, in contrast to the case of FFT, apFFT can acquire the high precision of phase measurement in a relatively wide range, which means that the hardware cost can be reduced. Therefore the proposed research is of both high theoretic value and of high engineering significance.

Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer

A nonlinear interferometer uses nonlinear elements as beam splitters to split and to recombine optical waves for interference. As a result, the interference fringe size has a nonlinear dependence on the intensity of the field for phase sensing and leads to an enhanced phase signal. In this paper, a practical scheme of nonlinear interferometry for precision phase measurement is analyzed with parametric amplifiers as the nonlinear beam splitters. It is found that the signal due to phase shift is enhanced by a factor of the amplification gain as compared to a linear interferometer with the same phase-sensing light intensity while the quantum noise is kept at the vacuum level, thus, effectively increasing the signal-to-noise ratio (SNR) beyond the standard quantum limit. Furthermore, the scheme is not as sensitive to the detection loss as the linear scheme with a squeezed state for noise reduction. However, losses inside the interferometer limit the enhancement factor in SNR. We apply the concept to a Michelson interferometer but with parametric amplifiers involved for gravitational-wave detection. We find that effective power is increased by the gain of the amplifiers without actually increasing the cycling power inside the interferometer. Furthermore, the full benefits with squeezed input and variational output or the combination of a quantum nondemolition interferometer for sensitivity beyond the standard quantum limit apply here with even better results. Such a nonlinear interferometer will find wide applications in precision measurements.