On the determination of the properties of a medium from its reflection coefficient

This thesis demonstrates how the parameters of a slightly non-homogeneous medium can be derived approximately from the reflection coefficient.

Two types of media are investigated. The first is described by the one-dimensional wave equation, the second by the more complex Timoshenko beam equation. In both cases, the media are assumed to be infinite in extent, with the media parameters becoming homogeneous as the space variable approaches positive or negative infinity.

Much effort is placed in deriving properties of the reflection coefficient for both cases. The wave equation is considered primarily to introduce the techniques used to investigate the more complex Timoshenko equation. In both cases, an approximation is derived for one of the medium parameters involving the reflection coefficient.

Precision of quasi-optical null-balanced bridge techniques for transmission and reflection coefficient measurements

The precision of quasioptical null-balanced bridge instruments for transmission and reflection coefficient measurements at millimeter and submillimeter wavelengths is analyzed. A Jones matrix analysis is used to describe the amount of power reaching the detector as a function of grid angle orientation, sample transmittance/reflectance and phase delay. An analysis is performed of the errors involved in determining the complex transmission and reflection coefficient after taking into account the quantization error in the grid angle and micrometer readings, the transmission or reflection coefficient of the sample, the noise equivalent power of the detector, the source power and the post-detection bandwidth. For a system fitted with a rotating grid with resolution of 0.017 rad and a micrometer quantization error of 1 μm, a 1 mW source, and a detector with a noise equivalent power 5×10−9 W Hz−1/2, the maximum errors at an amplitude transmission or reflection coefficient of 0.5 are below ±0.025.

Viscosity measurement of Newtonian liquids using the complex reflection coefficient

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

P3L-3 Viscosity measurement of Newtonian liquids using the complex reflection coefficient

This work presents the implementation of the ultrasonic shear reflectance method for viscosity measurement of Newtonian liquids using wave mode conversion from longitudinal to shear waves and vice-versa. The method is based on measuring the complex reflection coefficient (magnitude and phase) at a solid-liquid interface. Viscosity measurements were made in the range from 1 to 3.5MHz at 22.5°C for automotive oil (SAE40) and at 15°C for olive oil. Moreover, measurements of the olive oil were also conducted in the range from 15 to 30°C at 3.5MHz. The experimental results agree with those provided by a rotational viscometer. © 2006 IEEE.

Experimental study of the complex reflection coefficient of shear waves from the solid-liquid interface

The determination of the reflection coefficient of shear waves reflected from a solid-liquid interface is an important method in order to study the viscoelastic properties of liquids at high frequency. The reflection coefficient is a complex number. While the magnitude measurement is relatively easy and precise, the phase measurement is very difficult due to its strong temperature dependence. For that reason, most authors choose a simplified method in order to obtain the viscoelastic properties of liquids from the measured coefficient. In this simplified method, inconsistent viscosity results are obtained because pure viscous behavior is assumed and the phase is not measured. This work deals with an effort to improve the experimental technique required to measure both the magnitude and phase of the reflection coefficient and it intends to report realistic values for oils in a wide range of viscosity (0.092 - 6.7 Pa.s). Moreover, a device calibration process is investigated in order to monitor the dynamic viscosity of the liquid.

Ultrasonic densitometer using a multiple reflection technique

This work presents recent improvements in a density measurement cell with a double-element transducer that can eliminate diffraction effects. A new mechanical design combined with the use of more appropriate materials has resulted in better parallelism between interfaces, more robust assembly, and chemical resistance. A novel method of signal processing, named energy method, is introduced to obtain the reflection coefficient, reducing sensitivity to noise and improving accuracy. The measurement cell operation is verified both theoretically, using an acoustic wave propagation model, and experimentally, using homogeneous liquids with different densities. The accuracy in the density measurement is 0.2% when compared with the measurements made with a pycnometer.

Wave reflection at the end of a waveguide supported by a nonlinear spring

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Reflection of solar wind hydrogen from the lunar surface

The solar wind continuously flows out from the Sun and directly interacts with the surfaces of dust and airless planetary bodies throughout the solar system. A significant fraction of solar wind ions reflect from an object's surface as energetic neutral atoms (ENAs). ENA emission from the Moon was first observed during commissioning of the Interstellar Boundary Explorer (IBEX) mission on 3 December 2008. We present the analysis of 10 additional IBEX observations of the Moon while it was illuminated by the solar wind. For the viewing geometry and energy range (> 250 eV) of the IBEX-Hi ENA imager, we find that the spectral shape of the ENA emission from the Moon is well-represented by a linearly decreasing flux with increasing energy. The fraction of the incident solar wind ions reflected as ENAs, which is the ENA albedo and defined quantitatively as the ENA reflection coefficient RN, depends on the incident solar wind speed, ranging from ~0.2 for slow solar wind to ~0.08 for fast solar wind. The average energy per incident solar wind ion that is reflected to space is 30 eV for slow solar wind and 45 eV for fast solar wind. Once ionized, these ENAs can become pickup ions in the solar wind with a unique spectral signature that reaches 3vSW. These results apply beyond the solar system; the reflection process heats plasmas that have significant bulk flow relative to interstellar dust and cools plasmas having no net bulk flow relative to the dust.

Wave reflection at a stent

A simple analytical expression has been derived to calculate the characteristics of a wave that reflects at a stent implanted in a uniform vessel. The stent is characterized by its length and the wave velocity in the stented region. The reflected wave is proportional to the time derivative of the incident wave. The reflection coefficient is a small quantity of the order of the length of the stent divided by the wavelength of the unstented vessel. The results obtained coincide with those obtained numerically by Charonko et al. The main simplifications used are small amplitude of the waves so that equations can be linearized and that the length of the stent is small enough so that the values of the wave functions are nearly uniform along the stent. Both assumptions hold in typical situations.

Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

Power transfer and mode transitions in low-frequency inductively coupled plasmas

Operation and mode jumps in low-frequency (500 kHz) radio-frequency inductively coupled plasmas are investigated. The discharge is driven by a flat inductive coil which can excite the electrostatic (E) and electromagnetic (H) discharge modes. The power transfer efficiency and mode transition behavior are studied. It is found that the power reflection coefficient as a function of the input power is minimal in the vicinity of the mode transitions and exhibits hysteresis, which is also observed when the operating gas pressure is varied.

Field and potential around local scatterers in thin metal films studied by scanning tunneling potentiometry

We report the direct observation of electrochemical potential and local transport field variations near scatterers like grain boundaries, triple points, and voids in thin platinum films studied by scanning tunneling potentiometry. The field is highest at a void, followed by a triple point and a grain boundary. The local transport field near a void can even be four orders of magnitude higher than the macroscopic field, indicating that the void is the most likely place for an electromigration induced failure. The field build up for a particular type of scatterer depends on the grain connectivity. We estimate an average grain boundary reflection coefficient for the film from the temperature dependence of its resistivity.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Measurement of the acoustical impedance of a black box at low frequencies using a shorter impedance tube

For the experimental evaluation of the acoustical impedance of a termination by the impedance-tube method at low frequencies, the length of the impedance tube is a problem. In the present paper, the method of exact analysis of standing waves developed by the authors for the stationary medium as well as for mean flow, has been extended for measurement of the acoustical impedance of a termination at low frequencies. The values of the tube attenuation factor and the wave number at the low frequency of interest are established from the experiment conducted, with the given impedance tube, at a higher frequency. Then, exciting the tube at the desired low frequency it is sufficient to measure sound pressure at three differenct locations (not necessarily the minima) in order to evaluate reflection coefficient and hence the impedance of the termination at that frequency.

Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.