Phase Decorrelation Research Articles

Allan Variance Computed in Space Domain: Definition and Application to InSAR Data to Characterize Noise and Geophysical Signal.

The Allan variance was introduced 50 years ago for analyzing the stability of frequency standards. In addition to its metrological interest, it may be also considered as an estimator of the large trends of the power spectral density (PSD) of frequency deviation. For instance, the Allan variance is able to discriminate different types of noise characterized by different power laws in the PSD. The Allan variance was also used in other fields than time and frequency metrology: for more than 20 years, it has been used in accelerometry, geophysics, geodesy, astrophysics, and even finances. However, it seems that up to now, it has been exclusively applied for time series analysis. We propose here to use the Allan variance on spatial data. Interferometric synthetic aperture radar (InSAR) is used in geophysics to image ground displacements in space [over the synthetic aperture radar (SAR) image spatial coverage] and in time thanks to the regular SAR image acquisitions by dedicated satellites. The main limitation of the technique is the atmospheric disturbances that affect the radar signal while traveling from the sensor to the ground and back. In this paper, we propose to use the Allan variance for analyzing spatial data from InSAR measurements. The Allan variance was computed in XY mode as well as in radial mode for detecting different types of behavior for different space-scales, in the same way as the different types of noise versus the integration time in the classical time and frequency application. We found that radial Allan variance is the more appropriate way to have an estimator insensitive to the spatial axis and we applied it on SAR data acquired over eastern Turkey for the period 2003-2011. Spatial Allan variance allowed us to well characterize noise features, classically found in InSAR such as phase decorrelation producing white noise or atmospheric delays, behaving like a random walk signal. We finally applied the spatial Allan variance to an InSAR time series to detect when the geophysical signal, here the ground motion, emerges from the noise.

The effects of phase decorrelation on the dynamics of the bump-on-tail instability

The dynamics of the bump-on-tail instability has been studied. The novelty of the work is the analysis of how the bump-on-tail dynamics is affected by an extrinsic stochastisation of the phase of the wave-particle interaction; here referred to as phase decorrelation. For this purpose, a nonlinear Monte Carlo model has been developed. When the characteristic time scale for macroscopic phase decorrelation becomes shorter than time scales of nonlinear wave-particle dynamics, the system may be described quasilinearly, with the phase decorrelation being replaced by a quasilinear diffusion coefficient in particle energy. A purely quasilinear Monte Carlo model, which is typically less computationally demanding than the fully nonlinear description due to the reduced dimensionality of phase space, has been developed for comparison. In this paper, parameter regimes, where the nonlinear and the quasilinear descriptions quantitatively agree on a macroscopic level, have been investigated, using combined theoretical and numerical analyses. Qualitative effects on the macroscopic dynamics by the presence of phase decorrelation and/or by structures of the energy distribution function in the proximity of the wave-particle resonance are also studied.

Multi-functional angiographic OFDI using frequency-multiplexed dual-beam illumination.

Detection of blood flow inside the tissue sample can be achieved by measuring the local change of complex signal over time in angiographic optical coherence tomography (OCT). In conventional angiographic OCT, the transverse displacement of the imaging beam during the time interval between a pair of OCT signal measurements must be significantly reduced to minimize the noise due to the beam scanning-induced phase decorrelation at the expense of the imaging speed. Recent introduction of dual-beam scan method either using polarization encoding or two identical imaging systems in spectral-domain (SD) OCT scheme shows potential for high-sensitivity vasculature imaging without suffering from spurious phase noise caused by the beam scanning-induced spatial decorrelation. In this paper, we present multi-functional angiographic optical frequency domain imaging (OFDI) using frequency-multiplexed dual-beam illumination. This frequency multiplexing scheme, utilizing unique features of OFDI, provides spatially separated dual imaging beams occupying distinct electrical frequency bands that can be demultiplexed in the frequency domain processing. We demonstrate the 3D multi-functional imaging of the normal mouse skin in the dorsal skin fold chamber visualizing distinct layer structures from the intensity imaging, information about mechanical integrity from the polarization-sensitive imaging, and depth-resolved microvasculature from the angiographic imaging that are simultaneously acquired and automatically co-registered.

25-Gb/s OFDM 60-GHz Radio Over Fiber System Based on a Gain Switched Laser

A 25-Gb/s OFDM 60-GHz radio over fiber (RoF) transmission system employing a gain switched DFB laser for millimeter-wave generation is demonstrated. Transmission performance below the 7% FEC limit is achieved over 50 km of fiber initially by employing precompensation. This precompensation overcomes phase noise caused by the optical phase decorrelation induced by chromatic dispersion on the two optical channels separated by 60 GHz. An externally injected gain switched laser is subsequently employed to eradicate the need for the precompensation, thus reducing phase noise and increasing the tolerance to the induced time delay between the optical tones. Transmission performance below the 7% limit is achieved over 25 km of fiber with 2-m wireless transmission in this case.

Comparisons of the nonlinear and the quasilinear model for the bump-on-tail instability with phase decorrelation

The dynamics of discrete global modes in a toroidal plasma interacting with an energetic particle distribution is studied, and in particular when the dynamics of the system using the nonlinear and quasilinear descriptions are macroscopically similar. The dynamics can be described with a nonlinear bump-on-tail model in a two-dimensional phase space of particles. A Monte Carlo framework is developed for this model with an included decorrelation of the wave- particle phase, which is used to model extrinsic stochastisation of the wave-particle interactions. From this description, a quasilinear version of the model is also developed, which is described by a diffusive process in energy space due to the added phase decorrelation. Due to the reduced dimensionality of phase space, the quasilinear description is typically less computationally demanding than the nonlinear description. The purpose of the studies is to find conditions when a quasilinear model sufficiently describes the same phenomena of the wave-plasma interactions as a nonlinear model does. Via numerical and theoretical parameter studies, regimes where the two models overlap macroscopically are found. These regimes exist above a given threshold of the strength of the decorrelation, where coherent phase space structures are destroyed on time scales shorter than characteristic time scales of nonlinear particle motion in phase space close to the wave-particle resonance. Specifically for the quasilinear model, a theoretical value of the time scale of quasilinear flattening is derived and numerically verified.

Chromatic Dispersion-Induced Optical Phase Decorrelation in a 60 GHz OFDM-RoF System

We propose and demonstrate a 25-Gb/s 16-quadrature amplitude modulation orthogonal frequency division multiplexing 60-GHz radio over fiber transmission system based on a gain-switched optical comb source. The impact of the phase noise caused by the optical phase decorrelation due to the chromatic dispersion is theoretically studied and experimentally investigated by employing a high linewidth comb source and transmitting over a 50-km standard single-mode fiber reel. A time delay precompensation is deployed based on the study of phase noise in order to reduce the phase noise impact, and thereby improve system performance.

Analysis of image formation in optical coherence elastography using a multiphysics approach.

IMAGE FORMATION IN OPTICAL COHERENCE ELASTOGRAPHY (OCE) RESULTS FROM A COMBINATION OF TWO PROCESSES: the mechanical deformation imparted to the sample and the detection of the resulting displacement using optical coherence tomography (OCT). We present a multiphysics model of these processes, validated by simulating strain elastograms acquired using phase-sensitive compression OCE, and demonstrating close correspondence with experimental results. Using the model, we present evidence that the approximation commonly used to infer sample displacement in phase-sensitive OCE is invalidated for smaller deformations than has been previously considered, significantly affecting the measurement precision, as quantified by the displacement sensitivity and the elastogram signal-to-noise ratio. We show how the precision of OCE is affected not only by OCT shot-noise, as is usually considered, but additionally by phase decorrelation due to the sample deformation. This multiphysics model provides a general framework that could be used to compare and contrast different OCE techniques.

Coupling of GPS/GNSS and radar interferometric data for a 3D surface displacement monitoring of landslides

Persistent scatterer interferometry (PSI) is capable of millimetric measurements of ground deformation phenomena occurring at radar signal reflectors (persistent scatterers, PS) that are phase coherent over a period of time. However, there are also limitations to PSI; significant phase decorrelation can occur between subsequent interferometric radar (InSAR) acquisitions in vegetated and low-density PS areas. Here, artificial amplitude- and phase-stable radar scatterers may have to be introduced. I2GPS was a Galileo project (02/2010–09/2011) that aimed to develop a novel device consisting of a compact active transponder (CAT) with an integrated global positioning system (GPS) antenna to ensure millimetric co-registration and a coherent cross-reference. The advantages are: (1) all advantages of CATs such as small size, light weight, unobtrusiveness and usability with multiple satellites and tracks; (2) absolute calibration for PSI data; (3) high sampling rate of GPS enables detection of abrupt ground motion in 3D; and (4) vertical components of the local velocity field can be derived from single-track InSAR line-of-sight displacements. A field trial was set to test the approach at a potential landslide site in Potoska planina, Slovenia to evaluate the applicability for operational monitoring of natural hazards. Preliminary results from the trial highlight some of the key considerations for operational deployments in the field. Ground motion measurements also allowed an assessment of landslide hazard at the site and demonstrated the synergies between InSAR and GPS measurements for landslide applications. InSAR and GPS measurements were compared to assess the consistency between the methods from the slope mass movement detection aspect.

A three-dimensional sorting reliability algorithm for coastline deformation monitoring, using interferometric data

The paper focusses on three-dimensional (3-D) coastline deformation using interferometric synthetic aperture radar data(InSAR). Conventional InSAR procedures were implemented on three repeat passes of ENVISAT ASAR data. Furthermore, the three-dimensional sorting reliabilities algorithm (3D-SRA) were implemented with the phase unwrapping technique. Subsequently, the 3D-SRA was used to eliminate the phase decorrelation impact from the interferograms. The study showed that the performance of the InSAR method using the 3D-SRA algorithm, is better than the conventional InSAR procedure. In conclusion, the integration of the 3D-SRA, together with phase unwrapping, can produce accurate 3-D coastline deformation information.

Monte-Carlo model for nonlinear interactions of Alfvén eigenmodes with energetic ions

A Monte-Carlo model for interactions between a single Alfvén eigenmode and energetic ions in a tokamak is presented. A phenomenological decorrelation of the wave-particle phase is introduced to mimic decorrelation by collisions or by other waves. Analysis is dedicated to how the strength of the phase decorrelation affects the nonlinear wave-particle interactions. Several of the phenomena that have been observed in some earlier models describing the nonlinear dynamics of Alfvén eigenmodes have been verified, such as the growth and saturation of the wave mode amplitude giving rise to a localized flattening of the distribution function, as well as the generation of coherent structures in the distribution function. The degree of phase decorrelation is shown to have a strong effect on the dynamics of the Alfvén eigenmode excitation.

Ultrasound modulation of coherent light in a multiple-scattering medium: experimental verification of nonzero average phase carried by light

We demonstrate the phase fluctuation introduced by oscillation of scattering centers in the focal volume of an ultrasound transducer in an optical tomography experiment has a nonzero mean. The conditions to be met for the above are: (i) the frequency of the ultrasound should be in the vicinity of the most dominant natural frequency of vibration of the ultrasound focal volume, (ii) the corresponding acoustic wavelength should be much larger than , a modified transport mean-free-path applicable for phase decorrelation and (iii) the focal volume of the ultrasound transducer should not be larger than 4 – 5 times . We demonstrate through simulations that as the ratio of the ultrasound focal volume to increases, the average of the phase fluctuation decreases and becomes zero when the focal volume becomes greater than around ; and through simulations and experiments that as the acoustic frequency increases from 100 Hz to 1 MHz, the average phase decreases to zero. Through experiments done in chicken breast we show that the average phase increases from around 110° to 130° when the background medium is changed from water to glycerol, indicating that the average of the phase fluctuation can be used to sense changes in refractive index deep within tissue.

SYNTHETIC APERTURE RADAR INTERFEROMETRY FOR DIGITAL ELEVATION MODEL OF KUWAIT DESERT – ANALYSIS OF ERRORS

Abstract. Using different combinations of 29 Advanced Synthetic Aperture Radar (ASAR) images, 43 Digital Elevations Models (DEM) were generated adopting SAR Interferometry (InSAR) technique. Due to sand movement in desert terrain, there is a poor phase correlation between different SAR images. Therefore, suitable methodology for generating DEMs of Kuwait desert terrain using InSAR technique were worked out. Time series analysis was adopted to derive the best DEM out of 43 DEMs. The problems related to phase de-correlation over desert terrain are discussed. Various errors associated with the DEM generation are discussed which include atmospheric effects, penetration into soil medium, sand movement. The DEM of Shuttle Radar Topography Mission (SRTM) is used as a reference. The noise levels of DEM of SRTM are presented.

Three-Dimensional Coastal Geomorphology Deformation Modelling Using Differential Synthetic Aperture Interferometry

This work presents a new approach for three-dimensional (3D) coastal deformation simulation using differential synthetic aperture interferometry (DInSAR). In doing so, conventional InSAR procedures are implemented to three repeat passes of RADARSAT-1 SAR fine mode data (F1). Further, the DInSAR method is implemented with the phase unwrapping technique. Consequently, DInSAR is used to eliminate the phase decorrelation impact from the interferograms. The study shows the accurate performance of DInSAR with a root mean square error of 0:02 ±0:21 m and 90% confidence intervals. In conclusion, the DInSAR technique produces an accurate 3D coastal geomorphology reconstruction

Ionospheric Artifacts in Simultaneous L-Band InSAR and GPS Observations

Phase artifacts in interferometric synthetic aperture radar (InSAR) images frequently degrade the interpretability of the phase and correlation signatures of terrain. Often, these distortions are attributed to spatially variable ionospheric propagation delays at two different SAR acquisition times. We present here L-band InSAR data from Iceland, California, and Hawaii. The California and Hawaii interferograms show no significant ionospheric artifacts, while the Iceland interferogram shows a maximum misregistration of three pixels in the azimuth direction, which leads to severe phase decorrelation artifacts in the InSAR image. We relate the misregistration of complex pixels seen in the interferograms to the gradient of the ionospheric total electron content (TEC) observed by global positioning system (GPS) data and confirm that indeed the phase artifacts in the Iceland interferogram are due to dispersive ionospheric propagation rather than other decorrelation factors such as neutral atmospheric delays. We develop a method to measure the spatial TEC variation at synthetic aperture length scales using dual-frequency GPS carrier phase data. We solve for the GPS data ambiguities using a low-resolution ionosphere reference derived from either available ionospheric observations or the GPS carrier phase data themselves. GPS observations show directly the level of ionospheric variability, and the spatial TEC gradient as observed by GPS predicts the misregistration of complex pixels in interferograms in all three areas. This confirmation of the cause of the image artifacts suggests that they can be routinely corrected from the InSAR data alone, provided that the sensor measures the change in TEC along the radar swath.

Convective and diffusive ULF wave driven radiation belt electron transport

[1] The process of magnetospheric radiation belt electron transport driven by ULF waves is studied using a 2-D ideal MHD model for ULF waves in the equatorial plane including day/night asymmetry and a magnetopause boundary, and a test kinetic model for equatorially mirroring electrons. We find that ULF wave disturbances originating along the magnetopause flanks in the afternoon sector can act to periodically inject phase space density from these regions into the magnetosphere. Closely spaced drift-resonant surfaces for electrons with a given magnetic moment in the presence of the ULF waves create a layer of stochastic dynamics for L-shells above 6.5–7 in the cases examined, extending to the magnetopause. The phase decorrelation time scale for the stochastic region is estimated by the relaxation time for the diffusion coefficient to reach a steady value. This is found to be of the order of 10–15 wave periods, which is commensurate with the typical duration of observed ULF wave packets in the magnetosphere. For L-shells earthward of the stochastic layer, transport is limited to isolated drift-resonant islands in the case of narrowband ULF waves. We examine the effect of increasing the bandwidth of the ULF wave driver by summing together wave components produced by a set of independent runs of the ULF wave model. The wave source spectrum is given a flat-top amplitude of variable width (adjusted for constant power) and random phase. We find that increasing bandwidth can significantly enhance convective transport earthward of the stochastic layer and extend the stochastic layer to lower L-shells.

Extended focus high-speed swept source OCT with self-reconstructive illumination

We present a Bessel beam illumination FDOCT setup using a FDML Swept Source at 1300 nm with up to 440 kHz A-scan rate, and discuss its advantages for structural and functional imaging of highly scattering samples. An extended focus is achieved due to the Bessel beam that preserves its lateral extend over a large depth range. Furthermore, Bessel beams exhibit a self-reconstruction property that allows imaging even behind obstacles such as hairs on skin. Decoupling the illumination from the gaussian detection increases the global sensitivity and enables dark field imaging. Dark field imaging is useful to avoid strong reflexes from the sample surface that adversely affect the sensitivity due to the limited dynamic range of high speed 8 bit acquisition cards. In addition the possibility of contrasting capillaries with high sensitivity is shown, using inter-B-scan speckle variance analysis. We demonstrate intrinsic advantages of the extended focus configuration, in particular the reduction of the phase decorrelation effect below vessels leading to improved axial vessel definition.

Effects of diffraction by ionospheric electron density irregularities on the range error in GNSS dual‐frequency positioning and phase decorrelation

It can be important to determine the correlation of different frequency signals in L band that have followed transionospheric paths. In the future, both GPS and the new Galileo satellite system will broadcast three frequencies enabling more advanced three frequency correction schemes so that knowledge of correlations of different frequency pairs for scintillation conditions is desirable. Even at present, it would be helpful to know how dual‐frequency Global Navigation Satellite Systems positioning can be affected by lack of correlation between the L1 and L2 signals. To treat this problem of signal correlation for the case of strong scintillation, a previously constructed simulator program, based on the hybrid method, has been further modified to simulate the fields for both frequencies on the ground, taking account of their cross correlation. Then, the errors in the two‐frequency range finding method caused by scintillation have been estimated for particular ionospheric conditions and for a realistic fully three‐dimensional model of the ionospheric turbulence. The results which are presented for five different frequency pairs (L1/L2, L1/L3, L1/L5, L2/L3, and L2/L5) show the dependence of diffractional errors on the scintillation index S4 and that the errors diverge from a linear relationship, the stronger are scintillation effects, and may reach up to ten centimeters, or more. The correlation of the phases at spaced frequencies has also been studied and found that the correlation coefficients for different pairs of frequencies depend on the procedure of phase retrieval, and reduce slowly as both the variance of the electron density fluctuations and cycle slips increase.

Phase locking a fiber laser array via diffractive coupling

We demonstrate phase locking of a linear array of seven fiber lasers via diffractive coupling. Coupling between the lasers is achieved by a common output coupler positioned at a quarter Talbot distance from the lasers. The output beams are anti-phase locked with a measured far-field fringe contrast of 82%, and their total output power is higher than that obtained when the lasers operate individually. We measure an exponential phase decorrelation between distant lasers in the array, and discuss its fundamental limitation on scalability of this and similar local coupling methods.

V/UHF space radars: Spatial phase decorrelation of transionospheric signals in the equatorial region

[1] The spatial decorrelation of V/UHF signals by equatorial ionospheric turbulence is studied using 150 and 400 MHz signals transmitted from low-earth-orbiting beacon satellites. The signals are monitored on a linear array of spaced antennas located on Ascension Island, and processed coherently to determine the cross-correlations of the phases of the received signals. Analyzing signals from the low-inclination satellite C/NOFS has provided an opportunity to investigate the correlation variations in and out of scintillating structures. As a necessary step, the geometrical component of the phase difference between antennas has been accurately removed by adjusting the satellite orbital information using the measured phases. In order to unambiguously measure the spatial phase correlation without any temporal effects, the phase cross-correlation was calculated as the cross-correlation function of time-synchronized signals. As expected, the VHF signals were more affected by scintillation than the UHF signals. When the signal propagated through patches of strong scintillation, the VHF signal became completely uncorrelated over an ionospheric distance of 130 m, while over the same distance the UHF phase correlation decreased to 0.55. The time-synchronized technique limited the spatial variations assessed to east-west distances of ∼300 m. To extend this range, a novel ‘phase reconstruction’ technique was developed to link arrays of samples together. In the absence of scintillation the measured decorrelation distance is ∼10 km at both frequencies, but with increasing scintillation, the decorrelation distance falls to ∼100 m at VHF and 300 m at UHF. A clear relation between the decorrelation distance of the measured phase and S4 is observed and a simple empirical model has been derived.

Detailed rockslide mapping in northern Norway with small baseline and persistent scatterer interferometric SAR time series methods

Rockslides have a high socioeconomic and environmental importance in many countries. Norway is particularly susceptible to large rockslides due to its many fjords and steep mountains. One of the most dangerous hazards related with rock slope failures are tsunamis that can lead to large loss of life. It is therefore very important to systematically identify potential unstable rock slopes. Traditional landslide monitoring techniques are expensive and time consuming. Differential satellite interferometric synthetic aperture radar (InSAR) is an invaluable tool for land displacement monitoring. Improved access to time series of satellite data has led to the development of several innovative multitemporal algorithms. Small baseline (SB) methods are based on combining and inverting a set of unwrapped interferograms that are computed with a small perpendicular baseline in order to reduce spatial phase decorrelation. Another well proven technique is the persistent scatterer interferometric method (PSI) that is based on analysis of persistent point targets. In this paper, we apply both approaches to study several rockslide sites in Troms County in the far north of Norway. Moreover, we take the opportunity to address the difference and similarities between the SB and the PSI multitemporal InSAR methods for displacement studies in rural terrain.