Phase Measurement Noise Research Articles

Multipass wide-field phase imager.

Advances in optical imaging always look for an increase in sensitivity and resolution among other practicability aspects. Within the same scope, in this work we report a versatile interference contrast imaging technique, with high phase sensitivity and a large field-of-view of several mm2. Sensitivity is increased through the use of a self-imaging non-resonant cavity, which causes photons to probe the sample in multiple rounds before being detected, where the configuration can be transmissive or reflective. Phase profiles can be resolved individually for each round thanks to a specially designed single-photon camera with time-of-flight capabilities and true pixels-off gating. Measurement noise is reduced by novel data processing combining the retrieved sample profiles from multiple rounds. Our protocol is especially useful under extremely low light conditions as required by biological or photo-sensitive samples. Results demonstrate more than a four-fold reduction in phase measurement noise, compared to single round imaging, and values close to the predicted sensitivity in case of the best possible cavity configuration, where all photons are maintained until n rounds. We also find good agreement with the theoretical predictions for low number of rounds, where experimental imperfections would play a minor role. The absence of a laser or cavity lock-in mechanism makes the technique an easy to use inspection tool.

Effectiveness of null time-delay interferometry channels as instrument noise monitors in LISA

We present a study of the use and limits of the time-delay interferometry null channels for in-flight estimation of the Laser Interferometer Space Antenna instrumental noise. The paper considers how the two main limiting noise sources, test-mass acceleration noise and interferometric phase measurement noise, propagate through different time-delay interferometry channels: the Michelson combination $X$ that is the most sensitive to gravitational waves, then the less-sensitive combinations $\ensuremath{\alpha}$, and finally the null channel $\ensuremath{\zeta}$. We note that the null channel $\ensuremath{\zeta}$, which is known to be equivalent to any null channel, not only has a reduced sensitivity to the gravitational waves, but also features a larger degree of cancellation of the test mass acceleration noise relative to the interferometry noise. This severely limits its use in quantifying the low-frequency instrumental noise in the Michelson $X$ combination, which is expected to be dominated by acceleration noise. However, we show that one can still use in-flight noise estimations from $\ensuremath{\zeta}$ to put an upper bound on the considered noises entering in the $X$ channel, which allows one to distinguish them from a strong stochastic gravitational wave background.

A New Instantaneous Method for Attitude Determination Using GPS Phase Measurement

This article proposes a new algorithm for attitude determinations using GPS phase signals. The proposed method is an instantaneous method along with the small-angle assumption. Different from the existing methods, this method uses a newly defined performance index “BDOP” to determine search sequences for different satellite signals, phase measurement noise, and baseline geometry to define the search space and ambiguity candidates’ properties determined in previous search steps to reduce the search space for the subsequent searches. Consequently, the proposed method reduces the computation time and improves the attitude determination accuracy. The proposed method is verified both by numerical simulations and experiments. Simulation results indicate that the computation time of the proposed method is 0.01 s, the success rate 85%, and the angle estimation accuracy less than 1° when three antennas are installed 1 m apart, receiving GPS signals from five satellites, and the standard deviation of the phase measurement noise of 0.5 cm. In experiments, we verify the algorithms using a homemade three-antenna GPSR and a three-axis gimbal platform. The three antennas are installed 0.5 m apart and receive GPS signals from six satellites. The angle estimation error is less than 2° when the platform rotates in three axes simultaneously. In that experimental setup, the angle estimation degenerates at the large platform angles due to the signal interference from the ground effect and gimbal platform geometry.

Experimental scheme and noise analysis of weak-light phase locked loop for large-scale intersatellite laser interferometer.

In the current space gravitational wave (GW) detection, satellites are separated by millions of kilometers. As a result, watts of laser from one satellite is attenuated to the picowatt level at the other end due to the Gaussian beam divergence and the finite aperture of the telescope. Establishing an effective interferometry with such weak-light is a major challenge. The key is to enhance the weak-light while preserving its phase information, which carries the actual GW signal. This can be accomplished by employing an optical phase-locked loop (PLL) to lock the phase of a local oscillator (LO) laser to the weak-light and then sending the power-amplified LO back to the interferometer on the other satellite. Although shot-noise-limited performance of the picowatt level weak-light PLL has been achieved for high frequencies, it remains elusive for frequencies below 0.1Hz. Here, we propose a three-step experimental scheme to identify the main noise sources of the weak-light PLL, which turn out to be the low-frequency phase measurement noise, the weak-light shot noise, and the laser phase noise. In this paper, the first step experiment result shows that the out-loop phase noise can be suppressed to a level less than 6 × 10-6 rad/√Hz from 6 mHz to 1Hz by first using the special pilot-tone technique in the PLL to directly reduce the sampling time jitter noise in the digital phasemeter. The out-loop phase noise is mainly limited by the signal amplitude variation and differential time jitter noise of the reference clock.

Robust RFID Localization in Multipath With Phase-Based Particle Filtering and a Mobile Robot

This work revisits particle filtering RFID localization methods, solely based on phase measurements. The reader is installed on a low-cost robotic platform, which performs autonomously (and independently from the RFID reader) open source simultaneous localization and mapping (SLAM). In contrast to prior art, the proposed methods introduce a weight metric for each particle-measurement pair, based on geometry arguments, robust to phase measurement noise (e.g., due to multipath). In addition, the methods include the unknown constant phase offset as a parameter to be estimated. No reference tags are employed, no assumption on the tags' topology is assumed and special attention is paid for reduced execution time. It is found that the proposed phase-based localization methods offer robust performance in the presence of multipath, even when the tag phase measurements are variable in number and sporadic. The methods can easily accommodate a variable number of reader antennas. Mean absolute 3D localization error in the order of 24 cm for RFID tags in a library was shown, even though the system did not exploit excessive bandwidth or any reference tags. As a collateral dividend, the proposed methods also offer a concrete way to classify the environment as multipath-rich or not.

Sampling Frequency Fluctuations of the Sensors and Software SPIDAR Ground Penetrating Radar: Impact on Probing Passive Surface Acoustic Wave Delay Lines for Pollution Sensing

In the context of the subsurface pollutant detection using cooperative targets probed by ground penetrating RADAR (GPR), we assess the sampling frequency stability of the instrument as needed to make sure any time delay variation between echoes is associated with subsurface chemical detection and not with instrument drift. Thanks to surface acoustic wave (SAW) transducers designed as GPR cooperative targets, the sampling frequency of the sensors and Software SPIDAR GPR control unit is characterized for short- and long-term sampling rate stabilities. The long-term stability of the instrument is below the phase measurement noise of the SAW cooperative target. However, short-term (within each trace) phase fluctuations are observed, hinting at short-term stroboscopic delay synthesis artifacts. Having demonstrated the stability of the baseline, we demonstrate gas-phase pollutant detection in the subsurface environment using GPR interrogation of a SAW sensor functionalized with a dedicated coating for reacting with hydrogen sulfide. Finally, for onsite long-term monitoring, an embedded vector network analyzer is shown to exhibit sufficient stability and the targeted performance for this measurement by recovering the time-domain response through the inverse Fourier transform of the frequency swept characterization of the sensor.

Low-noise and high-sensitivity Φ-OTDR based on an optimized dual-pulse heterodyne detection scheme.

In this paper, a novel phase-sensitive optical time-domain reflectometry ($\Phi $Φ-OTDR) based on the optimized dual-pulse heterodyne detection scheme (DHDS) is proposed, which is designed to implement distributed vibration sensing with low phase noise and high sensitivity. The optimized DHDS employs an unbalanced interferometer to separate a light pulse into dual probe pulses so that they are generated by the laser at the same time. This ensures that the measurement sensitivity of a phase-interrogation-based $\Phi $Φ-OTDR can be improved simply by increasing the space interval of the dual probe pulses while the phase noise of the $\Phi $Φ-OTDR does not deteriorate. In addition, the proposed DHDS utilizes only one acousto-optic modulator (AOM) to shift the frequencies of the dual probe pulses so as to eliminate the effects of frequency shift jitters, and thus guarantees low phase noise level of a $\Phi $Φ-OTDR. The distributed vibration sensing performances of the $\Phi $Φ-OTDR with the proposed DHDS are theoretically and experimentally studied in terms of multi-event signal restoration and phase noise level. The proposed approach solves the contradiction between the measurement sensitivity and phase noise of a $\Phi $Φ-OTDR and promotes the $\Phi $Φ-OTDR to the applications of distributed weak vibration sensing.

An assessment of wide-lane ambiguity resolution methods for multi-frequency multi-GNSS precise point positioning

We assess the time-to-first-fix (TTFF) and the ambiguity fixing rate of two PPP wide-lane ambiguity resolution (WL-AR) methods, namely the geometry-based and ionospheric-free (GB-IF) method, and the geometry-free and ionospheric-free (GF-IF) method. First, an optimal GF-IF WL linear combination is selected based on the ratio between the code and carrier phase measurement noise (). Then, the relation between ambiguity variance and satellite geometry in the GB-IF WL-AR is investigated. Both simulated and real data from 31 GNSS stations over 37 consecutive days in 2017 were used. Numerical results show that the GF-IF WL-AR method has shorter TTFF and higher ambiguity fixing rate compared to the GB-IF method when . However, when , the GB-IF method outperforms the GF-IF method. Depending on RT values used, 2–10 min would be required to resolve the WL ambiguities when using GNSS measurements with one second sampling rate.

Kalman filter-based phase estimation of continuous-variable quantum key distribution without sending local oscillator

Phase estimation is one of the crucial procedures in continuous-variable quantum key distribution without sending local oscillator (LLO-CVQKD), aiming at compensating the phase drift in post-processing. To decrease the phase noise caused by the phase drift and measurement error, we propose Kalman filter-based phase noise estimation of LLO-CVQKD, which involves the measurements and filtering through exploiting the small amplitude reference pulses, achieving the accurate phase noise estimation. Simulation results indicate that Kalman filter-based phase noise estimation is capable of reducing measurement error and phase noise, while increasing the secret key rate by 7 times.

High-efficiency squeezed light generation for gravitational wave detectors

The engineering of strongly squeezed vacuum states of light is a key technology for the reduction of quantum noise in gravitational wave detectors. We report on the observation of up to 12.0 dB squeezed vacuum states of light at the wavelength of 1064 nm in the frequency band from 10 Hz to 100 kHz. This is the strongest squeezing reported to date within this detection band. The squeezed states were generated in a half-monolithic, standing-wave cavity optical parametric amplifier, which was resonant for the fundamental and harmonic light fields. We chose appropriate reflectivities to obtain a significant reduction of the required pump power, which was 8.6 mW only. Our analysis revealed that the residual measurement phase noise was smaller than 3.5 mrad rms and that the squeezed light source provided up to 14 dB of squeezing for a downstream application. The experiment was electronically stabilized in all relevant degrees of freedom, demonstrating the applicability of the linear, doubly resonant cavity topology for current and future gravitational wave detectors.

Initial Assessment of the LEO Based Navigation Signal Augmentation System from Luojia-1A Satellite.

A low Earth orbiter (LEO)-based navigation signal augmentation system is considered as a complementary of current global navigation satellite systems (GNSS), which can accelerate precise positioning convergence, strengthen the signal power, and improve signal quality. Wuhan University is dedicated to LEO-based navigation signal augmentation research and launched one scientific experimental satellite named Luojia-1A. The satellite is capable of broadcasting dual-frequency band ranging signals over China. The initial performance of the Luojia-1A satellite navigation augmentation system is assessed in this study. The ground tests indicate that the phase noise of the oscillator is sufficiently low to support the intended applications. The field ranging tests achieve 2.6 m and 0.013 m ranging precision for the pseudorange and carrier phase measurements, respectively. The in-orbit test shows that the internal precision of the ephemeris is approximate 0.1 m and the clock stability is 3 × 10−10. The pseudorange and carrier phase measurement noise evaluated from the geometry-free combination is about 3.3 m and 1.8 cm. Overall, the Luojia-1A navigation augmentation system is capable of providing useable LEO navigation augmentation signals with the empirical user equivalent ranging error (UERE) no worse than 3.6 m, which can be integrated with existing GNSS to improve the real-time navigation performance.

Note: A new method for directly reducing the sampling jitter noise of the digital phasemeter.

The sampling jitter noise is one non-negligible noise source of the digital phasemeter used for space gravitational wave detection missions. This note provides a new method for directly reducing the sampling jitter noise of the digital phasemeter, by adding a dedicated signal of which the frequency, amplitude, and initial phase should be pre-set. In contrast to the phase correction using the pilot-tone in the work of Burnett, Gerberding et al., Liang et al., Ales et al., Gerberding et al., and Ware et al. [M.Sc. thesis, Luleå University of Technology, 2010; Classical Quantum Gravity 30, 235029 (2013); Rev. Sci. Instrum. 86, 016106 (2015); Rev. Sci. Instrum. 86, 084502 (2015); Rev. Sci. Instrum. 86, 074501 (2015); and Proceedings of the Earth Science Technology Conference (NASA, USA, 2006)], the new method is intrinsically additive noise suppression. The experiment results validate that the new method directly reduces the sampling jitter noise without data post-processing and provides the same phase measurement noise level (10-6 rad/Hz1/2 at 0.1 Hz) as the pilot-tone correction.

Photonic-Delay Line Cross Correlation Method Based on DWDM for Phase Noise Measurement

A dual photonic-delay line cross-correlation method for phase noise measurement of microwave signal based on dense wavelength division multiplexing (DWDM) is proposed and experimentally demonstrated. The kilometer-long delay fiber is used together by the two mutually independent channels through the DWDM technology, which makes it easier to get the same delay between two channels. And it reduces the cost of the system by reducing the use of several kilometers of fiber and a Mach-Zendher modulator. Then, it uses variable optical fiber delay lines to replace the electronic phase shifters and a broader operation bandwidth can be obtained. A lower phase noise floor has been obtained by more averaging of the cross-correlation spectrum. In the experiments, the phase noise of a 10-GHz microwave signal has been measured accurately. A large operation bandwidth of 4-11 GHz is achieved and a measurement phase noise floor of -152.6 dBc/Hz at 10 kHz offset at 10 GHz in a 20 μs delay measurement system is realized by averaging 100 times.

Integrated GPS + BDS instantaneous medium baseline RTK positioning: Signal analysis, methodology and performance assessment

BDS system has become regionally operational and it is expected that it will reach its full operational status in the next few years. Therefore application of fully operational GPS system together with dynamically developing BDS is of interest for scientific, navigation and land surveying communities. In the first part the study demonstrates an analysis of measurement noise for both aforementioned systems. In the second part the mathematical and stochastic models of combined multi-GNSS medium range RTK positioning were presented. Furthermore, the performance assessment of single-epoch multi-baseline positioning was analyzed. The analysis of dispersion of undifferenced pseudorange observations caused by noise and multipath effect has confirmed slightly higher precision of code observations on the first in respect to second frequency for both systems. Moreover, the more detailed analysis suggests that in the case of strong ionospheric disturbances the internal smoothing of code measurements can be a source of their strong discrepancies. Due to the medium length of baselines (∼40km) the investigation of phase measurement noise was executed using triple differenced data. Generally it has shown the similar level of discrepancies for both systems. Only for geostationary BDS satellites one can observe measurable increase of noise. The quality assessment of instantaneous multi-baseline RTK (Real Time Kinematic) positioning based on single GPS or BDS systems, as well as on combined multi-GNSS observations, was evaluated simulating different observing conditions with terrain obstacles. The performance assessment of combined GPS and BDS precise relative positioning has proved the advantage of multi-GNSS positioning especially in harsh observing conditions. The usage of observational data from both systems allowed instantaneous positioning even with high elevation mask.

Application of the full spectrum inversion algorithm to simulated airborne GPS radio occultation signals

Abstract. With a GPS receiver on board an airplane, the airborne radio occultation (ARO) technique provides dense lower-tropospheric soundings over target regions. Large variations in water vapor in the troposphere cause strong signal multipath, which could lead to systematic errors in RO retrievals with the geometric optics (GO) method. The spaceborne GPS RO community has successfully developed the full-spectrum inversion (FSI) technique to solve the multipath problem. This paper is the first to adapt the FSI technique to retrieve atmospheric properties (bending and refractivity) from ARO signals, where it is necessary to compensate for the receiver traveling on a non-circular trajectory inside the atmosphere, and its use is demonstrated using an end-to-end simulation system. The forward-simulated GPS L1 (1575.42 MHz) signal amplitude and phase are used to test the modified FSI algorithm. The ARO FSI method is capable of reconstructing the fine vertical structure of the moist lower troposphere in the presence of severe multipath, which otherwise leads to large retrieval errors in the GO retrieval. The sensitivity of the modified FSI-retrieved bending angle and refractivity to errors in signal amplitude and errors in the measured refractivity at the receiver is presented. Accurate bending angle retrievals can be obtained from the surface up to ∼ 250 m below the receiver at typical flight altitudes above the tropopause, above which the retrieved bending angle becomes highly sensitive to the phase measurement noise. Abrupt changes in the signal amplitude that are a challenge for receiver tracking and geometric optics bending angle retrieval techniques do not produce any systematic bias in the FSI retrievals when the SNR is high. For very low SNR, the FSI performs as expected from theoretical considerations. The 1 % in situ refractivity measurement errors at the receiver height can introduce a maximum refractivity retrieval error of 0.5 % (1 K) near the receiver, but the error decreases gradually to ∼ 0.05 % (0.1 K) near the surface. In summary, the ARO FSI successfully retrieves the fine vertical structure of the atmosphere in the presence of multipath in the lower troposphere.

Accurate phase-shift velocimetry in rock

Spatially resolved Pulsed Field Gradient (PFG) velocimetry techniques can provide precious information concerning flow through opaque systems, including rocks. This velocimetry data is used to enhance flow models in a wide range of systems, from oil behaviour in reservoir rocks to contaminant transport in aquifers. Phase-shift velocimetry is the fastest way to produce velocity maps but critical issues have been reported when studying flow through rocks and porous media, leading to inaccurate results. Combining PFG measurements for flow through Bentheimer sandstone with simulations, we demonstrate that asymmetries in the molecular displacement distributions within each voxel are the main source of phase-shift velocimetry errors. We show that when flow-related average molecular displacements are negligible compared to self-diffusion ones, symmetric displacement distributions can be obtained while phase measurement noise is minimised. We elaborate a complete method for the production of accurate phase-shift velocimetry maps in rocks and low porosity media and demonstrate its validity for a range of flow rates. This development of accurate phase-shift velocimetry now enables more rapid and accurate velocity analysis, potentially helping to inform both industrial applications and theoretical models.

Radio-interferometric tracking using fault-tolerant phase unwrapping

A novel radio-interferometric measurement method for tracking applications is proposed. Fixed radio transceiver nodes are used to generate interferometric signals, allowing the tracking of a moving object equipped with a radio receiver. Low-frequency phase measurements of the interferometric signals are processed by the proposed simultaneous phase unwrapping algorithm, and then the real-time position estimates are calculated. The performance of the tracking system is analyzed by simulations and real measurements, indicating that the proposed method tolerates well substantial measurement phase noise and even sporadic large measurement errors.

Resolving phase measurement ambiguity in presence of coloured noise

Recovering a distance from ambiguous phase measurements observed at multiple signal frequencies involves the estimation of both integer and scalar quantities simultaneously. The problem is optimally addressed by existing methods only when the measurement noise is IID. A noise ‘whitening’ procedure is derived with a least-square estimation structure inherent to the Lattice method proposed previously which thus extends this Lattice-based algorithm to cope with coloured phase measurement noise in an optimal manner demonstrated via simulation.

Method of excess fractions with application to absolute distance metrology: theoretical analysis

The method of excess fractions (EF) is well established to resolve the fringe order ambiguity generated in interferometric detection. Despite this background, multiwavelength interferometric absolute long distance measurements have only been reported with varying degrees of success. In this paper we present a theoretical model that can predict the unambiguous measurement range in EF based on the selected measurement wavelengths and phase noise. It is shown that beat wavelength solutions are a subset of this theoretical model. The performance of EF, for a given phase noise, is shown to be equivalent to beat techniques but offers many alternative sets of measurement wavelengths and therefore EF offer significantly greater flexibility in experimental design.

Short and zero baseline analysis of GPS L1 C/A, L5Q, GIOVE E1B, and E5aQ signals

Stochastic properties of GNSS range measurements can accurately be estimated using a geometry-free short and zero baseline analysis method. This method is now applied to dual-frequency measurements from a new field campaign. Results are presented for the new GPS L5Q and GIOVE E5aQ wideband signals, in addition to the GPS L1 C/A and GIOVE E1B signals. As expected, the results clearly show the high precision of the new signals, but they also show, rather unexpectedly, significant, slowly changing variations in the pseudorange code measurements that are probably a result of strong multipath interference on the data. Carrier phase measurement noise is assessed on both frequencies, and finally successful mixed GPS-GIOVE double difference ambiguity resolution is demonstrated.