Trace Distortion Research Articles

Enhanced perturbation measurement range chirped pulse ϕ-OTDR for distributed static measurements using feedback frequency-shift compensation technology

Chirped-pulse phase-sensitive optical time-domain reflectometry (CP-ϕOTDR) is a newly developed distributed optical fiber sensing (DOFS) technology that can measure physical quantities across the length of optical fiber. The measurement of perturbations as strain or temperature changes is performed by comparing the time domain trace of Rayleigh backscattered (RBS) light with a reference trace. However, large strain or temperature fluctuations or laser frequency noises necessitate frequent updates of the reference, and short-term change measurements must be integrated to obtain absolute strain or temperature, which introduces a 1/f noise component due to the combination of noise with each cumulative change. In this study, we propose a novel CP-ϕOTDR system based on frequency-shift compensation (FSC) technology. This system utilizes real-time feedback control of the central frequency of the incident laser to compensate for time domain trace distortion caused by large perturbations. It overcomes the limitations associated with the total chirp bandwidth and eliminates the 1/f noise component by obviating the need for frequent updates of the reference trace. The measuring range for perturbations is only limited to the wavelength range supported by the integrated optical devices, typically on the order of nanometers, corresponding to at least tens of Kelvin in temperature fluctuations or hundreds of micro-strains. To validate the effectiveness, we conducted a temperature measurement experiment involving a 1 K variation, which is about 90 times the maximum measurable perturbation that the original CP-ϕOTDR system can demodulate with the reference unchanged. The results demonstrate that the FSC method significantly expands the perturbation measurement range of the CP-ϕOTDR system.

Rate Entropy Function

We consider the rate entropy function, which is the infimum of average mutual information with conditional entropy distortion constraint. Conditional entropy distortion is actually the expected distortion of logarithmic loss. It can be regarded a generalized distortion since it does not satisfy non-negativity. Like rate distortion function, the rate entropy function is essentially a variation problem with no general solution. So we propose three methods to construct a particular solution. Accordingly, closed-form expressions of rate entropy function for the uniform source and several additive sources are derived. Particularly, neither squared error nor magnitude error distortion exists for the Cauchy source due to the absence of first-order and higher-order moments, but the entropy distortion does. Entropy distortion varies depending on the source. For Gaussian sources, entropy distortion is equivalent to squared error distortion. In the case of vector Gaussian sources, entropy distortion is equivalent to the determinant of error covariance matrix, which is different from both covariance matrix distortion and trace distortion.

Strain measurement range enhanced chirped pulse φ-OTDR for distributed static and dynamic strain measurement based on random fiber grating array

A high-performance distributed sensing system based on a random fiber grating array (RFGA) and multi-frequency database demodulation (MFDD) method for strain induced delay time measurement is demonstrated. It enables a wide measurement range for both static and dynamic strain sensing. The proposed MFDD method can enlarge the strain measurement range, since the large strain variation induced time domain trace distortion could be compensated for by laser initial frequency changes. Furthermore, a random fiber grating made with embedded large random refractive index changes along the single-mode fiber could provide a stable reflection with a wide reflection spectrum range. Such a structure successfully improves the time delay measurement precision and achieves a large tuning range, as demonstrated by the database in which a set of pre-recorded undisturbed reflected Rayleigh traces form RFGA at various laser frequencies. Ultimately, a dynamic strain with a peak-to-peak value of 12.5µε at a vibration frequency of 50 Hz is accurately reconstructed when the pulse repetition rate is 1 kHz, which was not detected using a conventional chirped pulse phase-sensitive optical frequency domain reflectometers. The maximum measurable strain variation of about 12.5µε represents a factor of 3 improvement. This number is limited by a pre-recorded frequency scanning range of RFGA response in the database.

Design rules for optimizing unipolar coded Brillouin optical time-domain analyzers.

The performance of unipolar unicolor coded Brillouin optical time-domain analysis (BOTDA) is evaluated based on both Simplex and Golay codes. Four major detrimental factors that limit the system performance, including decoded-gain trace distortion, coding pulse power non-uniformity, polarization pulling and higher-order non-local effects, are thoroughly investigated. Through theoretical analysis and an experimental validations, solutions and optimal design conditions for unipolar unicolor coded BOTDA are clearly established. First, a logarithmic normalization approach is proposed to resolve the linear accumulated Brillouin amplification without distortion. Then it is found out that Simplex codes are more robust to pulse power non-uniformity compared to Golay codes; whilst the use of a polarization scrambler must be preferred in comparison to a polarization switch to mitigate uncompensated fading induced by polarization pulling in the decoded traces. These optimal conditions enables the sensing performance only limited by higher-order non-local effects. To secure systematic errors below 1.3 MHz on the Brillouin frequency estimation, while simultaneously reaching the maximum signal-to-noise ratio (SNR), a mathematical model is established to trade-off the key parameters in the design, i.e., the single-pulse Brillouin amplification, code length and probe power. It turns out that the optimal SNR performance depends in inverse proportion on the value of maximum single-pulse Brillouin amplification, which is ultimately determined by the spatial resolution. The analysis here presented is expected to serve as a quantitative guideline to design a distortion-free coded BOTDA system operating at maximum SNR.

Coherent BOTDA Using Phase- and Polarization-Diversity Heterodyne Detection and Embedded Digital Signal Processing

We have proposed and experimentally demonstrated a configuration of coherent BOTDA using optical phase-and polarization-diversity heterodyne detection and embedded digital signal processing (DSP). With the unwanted probe sideband and Rayleigh scattered noise eliminated by stable electrical filtering, the in-phase and quadrature-phase heterodyne sensing signals in both x- and y-polarizations are received by the phase-and polarization-diversity coherent receiver with independent local light, and processed by the subsequent embedded DSP. The embedded DSP algorithms are designed to recover the baseband BOTDA trace for sensing and remove the intermediate frequency noise (both amplitude and phase noise) to avoid trace distortion. A spatial resolution of ~3 m and temperature accuracy of ±0.3 °C have been achieved over 40-km sensing distance. The configuration, compatible with the detection scheme of optical coherent communication systems, is potential for future high-speed coherent BOTDA with real-time DSP designed to satisfy different requirements.

Rate Region of the Vector Gaussian CEO Problem With the Trace Distortion Constraint

We establish a new extremal inequality, which is further leveraged to give a complete characterization of the rate region of the vector Gaussian CEO problem with the trace distortion constraint. The proof of this extremal inequality hinges on a careful analysis of the Karush-Kuhn-Tucker necessary conditions for the non-convex optimization problem associated with the Berger-Tung scheme, which enables us to integrate the perturbation argument by Wang and Chen with the distortion projection method by Rahman and Wagner.

Experimental and theoretical demonstration of validity and limitations in fringe-resolved autocorrelation measurements for pulses of few optical cycles

Using 3.6- and 5.3-fs pulses, we demonstrated theoretically and experimentally that fringe-resolved autocorrelation (FRAC) traces are distorted by bandwidth limitations of the second-harmonic generation (SHG) in 10-microm-thick, type I ss-BaB2O4 for pulses shorter than sub-5 fs. In addition, detailed numerical analysis of the SHG showed that the optimum crystal angle where the FRAC trace distortion becomes minimum is in disagreement not only with the phase-matching angle but also with the angle where the FRAC signal intensity becomes maximum. Furthermore, the apparent pulse duration measured at a nonoptimum angle was confirmed to become shorter than that of its transform-limited pulse, in excellent agreement with the calculated result.

Experimental Studies of bed topography and flow patterns in large‐amplitude meanders: 2. Mechanisms

Large‐amplitude river meanders develop multiple scour holes within a single bend that are observed to be part of overlapping shingle bars (Whiting and Dietrich, this issue). These bars, having wavelengths near 4 channel widths, consist of a pool along the outer concave bank and a depositional lobe along the inner convex bank. The development of multiple pools and lobes within a bend has been shown to cause localized bank erosion and channel trace distortion expressed as planform asymmetry and compound heads. In this second paper we describe experiments designed specifically to test hypotheses that propose multiple pools to be the result of an overshoot phenomenon, to be a consequence of an alternate bar‐like instability, or to develop from a flow/planform instability. Although our experiments favor the hypothesis that multiple bars in bends of large amplitude arise from an alternate bar‐like instability, experiments conducted over an immobile flat bed also reveal longitudinal oscillations in flow that may arise in these long bends. This secondary effect interacts with shingle bars to amplify pool expression at particular points along the channel.

Effects of trap levels in single-photon optical time-domain reflectometry: evaluation and correction

Single photon detectors used in optical time-domain reflectometry (OTDR) suffer from carrier trapping phenomena. It is shown that trapping effects can result in a severe OTDR trace distortion, and that accurate measurements of trap releases open the way to the correction of the OTDR data. A simple procedure for offline correction of the experimental traces is presented. Its applicability range is analyzed, using a Monte Carlo program which simulates the actual OTDR experiments. A great improvement of signal-to-noise ratio in single-photon OTDR is expected by exploiting the technique. Requirements for the electronics to be used for these measurements are discussed. >

Address tracing of parallel systems via TRAPEDS

Trace-driven simulation is an important aid in performance analysis of computer systems. Capturing address traces to use in these simulations, however, is a difficult problem for parallel processor architectures. A technique termed TRAPEDS modifies executable code (at the assembly language level) to dynamically collect the address trace from executing code. TRAPEDS has recently been implemented on both a hypercube multicomputer and a shared-memory multiprocessor. Particular attention is focused on strategies for efficiently and accurately collecting traces from both classes of parallel machines. The iPSC/2 hypercube multicomputer implementation traces both user and system code, and performs simulation on-the-fly to avoid large storage costs. Strategies are detailed for mitigating address trace distortion when collecting operating system traces. The Encore Multimax multiprocessor implementation uses a timer-based approach to reflect the interleaving of the processor traces and stores the traces to disc. Time and space overhead results are presented for both TRAPEDS implementations. Experimental cache simulation results derived from iPSC/2 address traces are presented to illustrate the importance of tracing operating system references.

THE BLOCK MOVE SUM NORMAL MOVEOUT CORRECTION

A new normal moveout technique designated Block Move Sum (BMS) is described. In theory it better approximates the ideal inverse NMO process than do currently utilized techniques. Data blocks are corrected as units thus eliminating trace stretching and reducing trace distortion. The proposed correction and two common production methods are applied to both synthetic and real data and compared. Crosscorrelations calculated from synthetic seismogram data suggest the BMS method creates the least signal distortion. For field CDP data, the BMS does improve signal resolution for events at early times.

Some New Aspects of High-Speed Oscillography

From a consideration of the mechanism of the cathode-ray oscillograph at very high speeds it is shown, in Part I, that conventional deflection systems do not fully realize the possibilities of the cathode-ray tube. By a modification of the shape of the deflector-plates it is theoretically possible, under suitable conditions, to expand the time-scale obtainable with a given time-base generator up to infinity. This gain is obtained at the expense of definition, but brightness is not affected. Relativistic considerations are shown to be irrelevant. The geometry of the deflected electron beam is examined, and an expression derived relating the shape of the effective time-base voltage wave-form, the time-scale, and the shape of the Y-plates. Part II examines some practical factors ignored in the analysis of Part I. These cause various forms of trace distortion, which are classified as (i) intermodulation effects, (ii) mismatching distortion, (iii) transit-time effects, (iv) defocusing and equivalent effects. Possible ways of overcoming a number of these difficulties are described. Some have already been employed with success, but others have not yet been followed up.