Reflectometry Signals Research Articles

Simulation of Electron Density Profile Reconstruction on Ultrashort-Pulse Reflectometry

For the reconstruction of electron density profiles in the Sustained Spheromak Physics Experiment plasma, ultrashort-pulse reflectometry signals are numerically generated solving a one-dimensional wave equation by means of the central difference scheme. The signals cover an O-mode cutoff frequency range of 33–93 GHz. The lower frequencies (6–18 GHz) of a chirped waveform are up-converted to higher frequencies using four mixers. The reflected signals are down-converted to the lower frequency signals, thereby permitting band-pass filters to compute the time delays of different frequency components. A variety of density profiles are assumed to examine the performance of density profile reconstruction.

마이크로파 Reflectometry의 산란 신호 응답 특성

시간 지연이나 위상 지연과 같은 레이다 기법을 기반으로 하는 마이크로파 reflectometry를 비균질 매질의 밀도 특성을 조사하기 위한 비파괴 검사 장치로 응용하기 위한 시스템 특성을 연구하였다. 특히 마이크로파 reflectometry를 플라즈마 연구 분야에 응용하기 시작한 것은 비교적 최근의 일로서 그 활용도가 점차 증가하고 있는데, 마이크로파 reflectometry로 비균질 매질을 조사하기 위해서는 대상에 따른 시스템의 하드웨어 구성이 최적화되어야 하며, 시스템에서의 신호 응답 특성이 이해되어야만 전체적인 시스템 해법을 제공하는 것이 된다. 마이크로파 reflectometry를 이용하여 진단하는 대상인 플라즈마의 특성에 따른 시스템의 구성을 설명하고, 파동수 및 밀도 섭동에 관한 시스템의 특성을 실험적으로 조사하기 위한 장치를 설명하였다. 마이크로파 reflectometry의 신호는 대부분의 전자기파 에너지가 반사되는 지역에서 기인하는 cutoff 신호와 교란 신호와의 상호 작용으로 발생하는 산란 신호로 구성된다. 이 논문에서는 마이크로파 reflectometry의 산란 신호 특성을 실험적 방법으로 조사한 결과를 제시하며, 1차원 파동방정식을 이용한 수치 해석적 결과와 비교 분석하였고, cutoff 신호 특성과도 비교하였다. The characteristics of microwave reflectometry, which is based on the technologies of FM radar and is applied as a non-invasive method to examine the properties including density distribution of inhomogeneous media, is investigated. The microwave reflectometry system requires not only an optimized system hardware but as well as the understanding of system response from the media under test in order to provide the system solution describing the object under test quantitatively. The introduction of microwave reflectometry especially in the area of applied plasma physics has been relatively new and the number of usage is found to be increasing gradually. The experimental method to characterize the microwave system as a device to examine the properties of plasma is explained. The microwave reflectometry signals consist of the cutoff signals which originate from the region where most of the reflected power comes from and the scattered signals which result as an interaction of the microwave and the density perturbations. This paper describes the experimental results of the scattered signal from the microwave reflectometry, such as the wavenumber dependence and the sensitivity on density perturbation, and the comparison of the characteristics with those from the numerical simulations and those from the cutoff signals.

GaN property evolution at all stages of MOVPE Si/N treatment growth

AbstractAn investigation of MOVPE GaN growth on sapphire (0001) using Si/N treatment is reported. The growth was monitored in situ He‐Ne laser reflectometry. By fitting the reflectivity signal, we derived expressions for the refractive index variation of both sapphire substrate and GaN as a function of the temperature. The morphological and optical property evolutions of the layer at all the growth stages were studied by atomic force microscopy (AFM) and transmittance measurements. A good agreement between AFM images and laser reflectometry signal is obtained. During the island growth and coalescence as clearly revealed by AFM images of the GaN layers, the transmittance signal evolves from featureless characteristic to a signal with regular oscillations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulations of a spatially resolved reflectometry signal from a highly scattering three-layer medium applied to the problem of glucose sensing in human skin

The possibility of using spatially resolved reflectometry (SRR) at a wavelength of 820 nm to detect changes in the optical properties of a highly scattering layered random medium simulating a biological tissue caused by changes in the glucose level is analysed. Model signals from a three-layer biological tissue phantom consisting of two skin layers and a blood layer located between them are obtained by the Monte-Carlo method. It was assumed that variations in the glucose level induce variations in the optical parameters of the blood layer and the bottom skin layer. To analyse the trajectories of photons forming the SRR signal, their scattering maps are obtained. The ratio of the photon path in layers sensitive to the glucose level to the total path in the medium was used as a parameter characterising these trajectories. The relative change in the reflected signal caused by a change in the glucose concentration is analysed depending on the distance between a probe radiation source and a detector. It is shown that the maximum relative change in the signal (about 7%) takes place for the source — detector separation in the range from 0.3 to 0.5 mm depending on the model parameters.

Measurements localization in poloidal correlation reflectometry

In the present paper the localization of poloidal correlation reflectometry (PCR) is treated analytically for arbitrary density and turbulence profiles. The 3D WKB approach is used to calculate the fluctuation reflectometry signal and the PCR cross correlation function produced by long-scale turbulence. The study is performed in cylindrical geometry correctly accounting for the plasma curvature effects. The probing wave propagation is described in paraxial approximation accounting for the refraction and diffraction effects. The obtained explicit expressions for the PCR characteristics can be used for determination of the turbulence level and the velocity distribution from the experimental data for arbitrary density profiles.

Characterization of Alfvén cascades on the JET tokamak using a multi-channel O-mode reflectometer diagnostic

A multi-channel reflectometer diagnostic probing the mid-plane plasma in the O-mode polarization is routinely used for detection of Alfvén eigenmodes (AEs) on the JET tokamak. The AEs are observed on the spectrogram of the homodyne signal reflected by the inner wall when the probing frequency is higher than the maximum of the plasma frequency (interferometry regime). In particular the time and frequency resolution of the Alfvén cascades (ACs) is better from this technique than from any other diagnostic. We show here that knowing the shape of the density fluctuations induced by an AC, the level of these density fluctuations can also be inferred from the phase fluctuations of the reflectometry signal.

Efficient reconstruction of dispersive dielectric profiles using time domain reflectometry (TDR)

Abstract. We present a numerical model for time domain reflectometry (TDR) signal propagation in dispersive dielectric materials. The numerical probe model is terminated with a parallel circuit, consisting of an ohmic resistor and an ideal capacitance. We derive analytical approximations for the capacitance, the inductance and the conductance of three-wire probes. We couple the time domain model with global optimization in order to reconstruct water content profiles from TDR traces. For efficiently solving the inverse problem we use genetic algorithms combined with a hierarchical parameterization. We investigate the performance of the method by reconstructing synthetically generated profiles. The algorithm is then applied to retrieve dielectric profiles from TDR traces measured in the field. We succeed in reconstructing dielectric and ohmic profiles where conventional methods, based on travel time extraction, fail.

장거리 광선로 감시용 1625 nm OTDR 신호 증폭을 위한 효율적인 Extended L-band Erbium-doped Fiber Amplifier

Optical Time Domain Reflectometry를 이용하여 수백 km 이상의 장거리 광통신망을 감시하기 위해서는 감시광을 증폭시켜야한다. 본 논문에서는 1625 nm OTDR 감시광을 증폭시키기 위해 fiber Bragg grating과 band pass filter를 이용하여 이득과 잡음지수를 각각 5.1 dB 그리고 0.9 dB 향상시킨 2단 구조의 Extended L-band EDFA를 제안하였다. 제안된 Extended L-band EDFA의 1625 nm 대역의 신호 이득은 16.3 dB이고 잡음지수는 7.1 dB였다. We have designed an extended L-band Erbium-doped fiber amplifier to amplify 1625 nm optical time domain reflectometry signal for a long distance monitoring system. The proposed amplifier has a dual-stage structure without an isolator. Gain improvement of 5.1 dB has been achieved by adding a fiber Bragg grating and a narrow band pass filter. As a result, the 16.3 dB gain and 7.1 dB noise figure has been successfully accomplished.

Laser‐reflectometry monitoring of the GaN growth by MOVPE using SiN treatment: study and simulation

AbstractThe SiN treatment of the sapphire substrate for GaN growth induces a spectacular effect on the in situ reflectometry monitoring signal. Different growth modes are observed. The evolution of the reflectometry signal is simulated by the scattering theory approximation. The point‐by‐point analysis reveals that the roughness (rms) increases in the first region where the growth mode is dominated by the formation of isolated and three‐dimensional hillocks. The rms attains a maximum value exceeding that authorized by the Rayleigh criteria. Another approach based on the effective medium approximation is used to simulate the entire reflectometry signal evolution. An effective refractive index and a growth rate profile are determined. The results obtained are in accordance with the observations done by the in situ ellipsometry monitoring. We have also studied the evolution of the defined recovery time as a function of the SiH4 flow rate and the SiN duration. Based on the concept of a nano‐epitaxial mask, induced by the SiN treatment of the sapphire surface, we have proposed a schematic model of the GaN growth that explains the recovery‐time behavior. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Time domain reflectometry of glass beads/magnetite mixtures: A time and frequency domain study

The measurements of the time domain reflectometry (TDR) signal propagating along a coaxial probe, filled with dry mixtures of glass beads and magnetite, are analyzed for deriving the attenuation factor α and the bandwidth. Samples with different percentages (5%–25%) of magnetite are considered. The α values are obtained by two different methods: (i) wave amplitude at the second reflection, (ii) electromagnetic parameters and widths of the passing bands. The two methods provide consistent α values within the experimental uncertainties. The agreement supports the possibility of measuring the attenuation factor from the second TDR reflection, for anhydrous samples similar to the investigated mixtures.

Spatially resolved water content profiles from inverted time domain reflectometry signals

We present a method for extracting spatially resolved water content profiles θ(x) from a two‐wire time domain reflectometry (TDR) probe. The profile θ(x) is represented in terms of the dielectric εr(x) and ohmic σ(x) properties in the longitudinal direction of the TDR probe. We solve the inverse problem iteratively by combining a one‐dimensional time domain solution of the transmission line equations and a genetic optimization method. The method is capable of finding the global optimum in a complicated error landscape without initial assumptions, except physically reasonable limits. The method utilizes both the position and the magnitude of the TDR signal. We analyze water content profiles from laboratory measurements and demonstrate that the achievable spatial resolution can be made as low as 2 cm and even smaller. The present implementation of the numerical code demonstrates the practical feasibility of spatially resolved water content profiles.

Simulation of amplitude and phase variations induced by magnetic islands with turbulence on reflectometry signals

Reflectrometry is influenced by plasma perturbations and turbulence, making the understanding of how signals are affected by such phenomena of prime importance. In this work we look at the effect magnetic islands with turbulence have on the amplitude and phase of reflectometry signals. For this purpose we resort to a two-dimensional finite difference time domain code and use a turbulence model based on experimental data. We investigate the possibility of occurrence of destructive interference due to a chain of islands and the role turbulence plays. The simulation of an island with turbulence present at the resonant surface q=2, with dimensions of the same order of magnitude as the phenomena observed on ASDEX Upgrade on Tore Supra, is also done with results which are in agreement with experimental observations.

On the use of the analytic signal to retrieve the phase from broadband reflectometry signals

A comparison is carried out between the phase derivative of broadband reflectometry signals, which are cosine signals calculated from a given electron-density profile according to the model that underlies the functioning of broadband reflectometers, and the phase derivative of the corresponding analytic signals. A class of density profiles commonly employed to model high-temperature plasmas is considered, for which it is shown that the two phase derivatives agree well, except for some oscillatory behavior at the beginning and ending of the signals. Gibbs’ phenomenon, associated with the practical calculation of the analytic signal is identified as the cause of this effect. The reconstructed density profiles are shown to be practically unaffected by the oscillations, which are averaged out upon integration, leading to good agreement with the original density profiles.

Two-dimensional linear theory of radial correlation reflectometry diagnostics

The two-dimensional linear theory of radial correlation reflectometry applicable for the case of low turbulence level, when the probing line is observable in the spectrum of reflected wave, is developed. It is shown that the small angle scattering in the plasma volume makes a significant contribution to the fluctuation reflectometry signal complicating the turbulence correlation length measurements. The conditions under which the cut off backscattering plays the dominant role and the correlation length estimation is possible are discussed.

Small-angle scattering and spatial resolution of fluctuation reflectometry: comparison of 2D analytical theory with numerical calculations

Three methods to study the effect of density fluctuations on the reflected signal, based on a 2D full-wave analysis and Born approximation numerical and analytical calculations, are developed. The explicit analytical expression for the signal produced by an island-like perturbation running in poloidal direction is obtained and shown to be in nice agreement with results of numerical techniques for small level density perturbations. It is shown, both numerically and analytically, that due to small-angle scattering effects, fluctuations far from the cut-off layer may produce a significant and, in some realistic cases, dominant response. The conditions under which the fluctuation reflectometry signal is generated only in the cut-off vicinity are given.

On a variational approach to the extraction of quadratures from broadband reflectometry signals

A variational method is employed to retrieve the phase from broadband reflectometry signals. The method yields the so-called in-phase and quadrature components of a signal (the signal quadratures in short), by stipulating that these should have the smallest possible amount of functional variation, whereby the signal carrier frequency is also recovered as a by-product. The variational approach is based on the reasonable assumption that, for given data, the quadratures are expected to be as slow as possible, as they contain the slow modulations of amplitude and phase, while rapid variations are accounted for by the carrier frequency. The advantages and shortcomings of the variational method are discussed, and a pertinent comparison with the analytic signal—recently proposed as a means to extract the phase from broadband reflectometry signals—is also carried out. The application of the variational method to the reflectometry problem is shown to yield results that are similar to those obtained via the analytic signal. The difference is not significant, especially if detailed measurements are not required, but only averaged ones.

Turbulence and beam size effects on reflectometry measurements

A two-dimensional code based on the WKB (Wenzel–Kramers–Brillouin) approximation is used to simulate reflectometry measurements in plasmas with turbulence. In this work we aim to understand, first the role of turbulence in the determination of density profiles with reflectometry and, second, the ability of reflectometry techniques to give reliable information on the characteristics of the turbulence itself. The effects on the profile determination of a rotating turbulence structure with nonperpendicular reflection are analyzed. The influence of the turbulence level, fluctuation wavelengths and antenna beam size on the density profile determination has been studied in static plasma with perpendicular launching. The code has been used to simulate correlation measurements. The results show the correlation of the reflectometry signals for different turbulence parameters. Errors in the correlation length increase when two-dimensional effects become important, though the homodyne signal works better than the phase. The correlation simulations also show the way for new methods to determine the group delay and therefore the density profile.

Optical time-domain reflectometry of bent plastic optical fibers

Optical time-domain reflectometry (OTDR) signals of step-index plastic optical fibers (POF's) and graded-index POF's were measured with a laser diode and an avalanche photodiode. When bent step-index and graded-index POF's were used, the OTDR signal behavior differed. The OTDR signal of the bent graded-index POF's had a step that corresponds to a curvature loss, but the step-index POF's had a spike signal at a bend, which indicated the occurrence of backscattering. The peak intensity was proportional to the square of the curvature. The refractive-index variation of the bent step-index POF's was measured, and the dependence of the peak intensity on the curvature was shown to agree with that predicted by the scattering from the refractive-index perturbation.

Two-dimensional full-wave simulation of microwave reflectometry on Alcator C-Mod

A new two-dimensional full-wave code has been developed to simulate ordinary (O) mode reflectometry signals caused by plasma density fluctuations. The code uses the finite-difference time-domain method with a perfectly matched layer absorption boundary to solve Maxwell’s equations. Huygens wave sources are incorporated to generate Gaussian beams. The code has been used to simulate the reflectometer measurement of the quasicoherent mode (60–250 kHz) associated with enhanced Dα (EDA) H modes in the Alcator C-Mod tokamak. It is found that an analysis of the realistic experimental layout is essential for the quantitative interpretation of the mode amplitude.

Calculation of in situ soil water content profiles from TDRsignal traces

The authors present a numerical one-dimensional model which computesthe soil water content profile, along transmission line probes, fromtime-domain reflectometry signal traces recorded with a reflectometer (TDR).Taking a discrete time-domain approach, they first developed a directiterative model which computes simulated signal traces from the dielectricconstant distribution of the propagation medium. The results tallied well withsignal traces recorded in simple cases. The inverse model was developed in asecond stage, to compute water content distribution along the transmissionline probes from a reflected signal trace. The results are shown both forcontrolled media and field conditions and are compared to direct water contentmeasurements. Filtering of the reflection coefficients had to be incorporatedto compensate for the high sensitivity to noise of the iterative computationand the simplicity of the propagation hypothesis. The inverted profiles arevery close to the direct measurements, validating this model for measurementsin low loss soils.