Comparison of Rectangular and Polar Quantizers in Digital Holography

Complex amplitude encoded in any digital hologram must undergo quantization, usually in either polar or rectangular format . In this paper these two schemes are compared under the constraints and conditions inherent in digital holography . For Fourier transform holograms when the spectrum is levelled through phase coding, the rectangular format is shown to be optimal . In the absence of phase coding, and also if the amplitude spectrum has a large dynamic range, the polar format may be preferable .

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.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Effect of surface tension on the mode selection of vertically excited surface waves in a circular cylindrical vessel

Singular perturbation theory of two-time-scale expansions was developed in inviscid fluids to investigate patternforming, structure of the single surface standing wave, and its evolution with time in a circular cylindrical vessel subject to a vertical oscillation. A nonlinear slowly varying complex amplitude equation, which involves a cubic nonlinear term, an external excitation and the influence of surface tension, was derived from the potential flow equation. Surface tension was introduced by the boundary condition of the free surface in an ideal and incompressible fluid. The results show that when forced frequency is low, the effect of surface tension on the mode selection of surface waves is not important. However, when the forced frequency is high, the surface tension cannot be neglected. This manifests that the function of surface tension is to cause the free surface to return to its equilibrium configuration. In addition, the effect of surface tension seems to make the theoretical results much closer to experimental results.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.

强散射体产生的像面散斑对比度与随机表面及成像系统关系的研究

We study the statistical properties of the image speckles produced by strong-scattering objects in the 4f optical imaging system. Using the generic expression of the complex amplitude of speckles and the approximation of the double-exponential function, we first obtain the ensemble average of the speckle intensity. Then we derive the variance of the speckle intensity based on the rotational transformation of the real and imaginary parts of the complex amplitude of speckles. We finally obtain the expression for the contrast of the. speckles, which is explicitly related to the statistical parameters of random surface and to the parameters of the imaging system. Our results are an obvious improvement compared with those reported in the literature, where the relations including such implicit quantities as the average size of the scattering grains of the random surface and the number of scattering grains are usually used. The results of this paper would be helpful for the characterization of random surface by speckle contrast.

Theoretical investigations of experimental gravitation

This thesis has two basic themes: the investigation of new experiments which can be used to test relativistic gravity, and the investigation of new technologies and new experimental techniques which can be applied to make gravitational wave astronomy a reality.

Advancing technology will soon make possible a new class of gravitation experiments: pure laboratory experiments with laboratory sources of non-Newtonian gravity and laboratory detectors. The key advance in techno1ogy is the development of resonant sensing systems with very low levels of dissipation. Chapter 1 considers three such systems (torque balances, dielectric monocrystals, and superconducting microwave resonators), and it proposes eight laboratory experiments which use these systems as detectors. For each experiment it describes the dominant sources of noise and the technology required.

The coupled electro-mechanical system consisting of a microwave cavity and its walls can serve as a gravitational radiation detector. A gravitational wave interacts with the walls, and the resulting motion induces transitions from a highly excited cavity mode to a nearly unexcited mode. Chapter 2 describes briefly a formalism for analyzing such a detector, and it proposes a particular design.

The monitoring of a quantum mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. Chapter 3 reviews the standard techniques for monitoring the oscillator; and it introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator.

The standard method for monitoring the oscillator is the "amplitude- and-phase" method (position or momentum transducer with output fed through a linear amplifier). The accuracy obtainable by this method is limited by the uncertainty principle. To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well-known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak force, but which cannot provide good accuracy in determining its precise time-dependence. Chapter 3 considers extensively a new type of quantum nondemolition measurement - a "back-action-evading" measurement of the real part X₁ (or the imaginary part X₂) of the oscillator's complex amplitude. In principle X₁ can be measured arbitrarily quickly and arbitrarily accurately, and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force.

Chapter 3 describes explicit gedanken experiments which demonstrate that X₁ can be measured arbitrarily quickly and arbitrarily accurately, it considers approximate back-action-evading measurements, and it develops a theory of quantum nondemolition measurement for arbitrary quantum mechanical systems.

In Rosen's "bimetric" theory of gravity the (local) speed of gravitational radiation v_g is determined by the combined effects of cosmological boundary values and nearby concentrations of matter. It is possible for v_g to be less than the speed of light. Chapter 4 shows that emission of gravitational radiation prevents particles of nonzero rest mass from exceeding the speed of gravitational radiation. Observations of relativistic particles place limits on v_g and the cosmological boundary values today, and observations of synchrotron radiation from compact radio sources place limits on the cosmological boundary values in the past.

洛仑兹脉冲光束的复振幅包络解和复解析信号解的比较研究

使用复振幅包络表示式和复解析信号表示式推导了洛仑兹脉冲光束的传输公式．通过具体数值计算对脉冲光束的复振幅包络解和复解析信号解在不同带宽时的传输进行了对比研究．数值结果表明脉冲光束为窄带时，在传输方向轴中心的一定范围内两种解是一致的，而对于宽带脉冲光束，复振幅包络解在轴中心较近的距离即表现出奇异性，复解析信号解才是符合物理意义的表示式．由数值计算得出了选择脉冲光束研究方法的条件，并从所得公式对复振幅包络解出现奇异性的现象进行了解释．

窄带和宽带双曲正割脉冲光束的解析传输式

从近轴波动方程出发推导了窄带和宽带双曲正割脉冲光束的解析传输公式。通过数值计算比较了分别采用复振幅包络(CAE)表示式和复解析信号(CAS)表示式得到的脉冲光束，得出了选择脉冲光束研究方法的条件。结果表明复振幅包络表示式得到的解会存在空间奇异性，使光束出现不符合物理意义的非光束行为。对于宽带光束，复振幅包络解的奇异点的位置距离轴中心较近，使复包络解不能正确表示脉冲光束，而对于奇异点位置远离轴中心的窄带光束，对脉冲光束产生的影响可以忽略。因此，窄带脉冲光束可以采用复振幅包络和复解析信号两种表示式来研究，而对

Spatiotemporal behaviors and singularity of ultrashort pulsed Elegant Hermite-Gaussian beams

Analytical propagation expressions of ultrashort pulsed Elegant Hermite-Gaussian beams are derived and spatiotemporal properties of the pulses with different transverse modes are studied. Singularity of the complex amplitude envelope solution of the pulses obtained under slowly varying envelope approximation is analyzed in detail. The rigorous analytical solution of the pulse is deduced and no singularity emerges in the solution. The obtained results indicate that the transverse mode affects not only the spatiotemporal properties but also the singularity of the pulses. Time delay of the off-axis maximum intensity is more obvious and the singularity is located nearer to the z-axis for the pulse with higher transverse modes. (C) 2007 Elsevier GmbH. All rights reserved.

Channel modelling for MIMO systems

Systems equipped with multiple antennas at the transmitter and at the receiver, known as MIMO (Multiple Input Multiple Output) systems, offer higher capacities, allowing an efficient exploitation of the available spectrum and/or the employment of more demanding applications. It is well known that the radio channel is characterized by multipath propagation, a phenomenon deemed problematic and whose mitigation has been achieved through techniques such as diversity, beamforming or adaptive antennas. By exploring conveniently the spatial domain MIMO systems turn the characteristics of the multipath channel into an advantage and allow creating multiple parallel and independent virtual channels. However, the achievable benefits are constrained by the propagation channel’s characteristics, which may not always be ideal. This work focuses on the characterization of the MIMO radio channel. It begins with the presentation of the fundamental results from information theory that triggered the interest on these systems, including the discussion of some of their potential benefits and a review of the existing channel models for MIMO systems. The characterization of the MIMO channel developed in this work is based on experimental measurements of the double-directional channel. The measurement system is based on a vector network analyzer and a two-dimensional positioning platform, both controlled by a computer, allowing the measurement of the channel’s frequency response at the locations of a synthetic array. Data is then processed using the SAGE (Space-Alternating Expectation-Maximization) algorithm to obtain the parameters (delay, direction of arrival and complex amplitude) of the channel’s most relevant multipath components. Afterwards, using a clustering algorithm these data are grouped into clusters. Finally, statistical information is extracted allowing the characterization of the channel’s multipath components. The information about the multipath characteristics of the channel, induced by existing scatterers in the propagation scenario, enables the characterization of MIMO channel and thus to evaluate its performance. The method was finally validated using MIMO measurements.

Polyphase Implementation of Non-recursive Comb Decimators for Sigma-Delta A/D Converters

In a sigma-delta analog to digital (A/D) As most of the sigma-delta ADC applications require converter, the most computationally intensive block is decimation filters with linear phase characteristics, the decimation filter and its hardware implementation symmetric Finite Impulse Response (FIR) filters are may require millions of transistors. Since these widely used for implementation. But the number of FIR converters are now targeted for a portable application, filter coefficients will be quite large for implementing a a hardware efficient design is an implicit requirement. narrow band decimation filter. Implementing decimation In this effect, this paper presents a computationally filter in several stages reduces the total number of filter efficient polyphase implementation of non-recursive coefficients, and hence reduces the hardware complexity cascaded integrator comb (CIC) decimators for and power consumption [2]. Sigma-Delta Converters (SDCs). The SDCs are The first stage of decimation filter can be operating at high oversampling frequencies and hence implemented very efficiently using a cascade of integrators require large sampling rate conversions. The filtering and comb filters which do not require multiplication or and rate reduction are performed in several stages to coefficient storage. The remaining filtering is performed reduce hardware complexity and power dissipation. either in single stage or in two stages with more complex The CIC filters are widely adopted as the first stage of FIR or infinite impulse response (IIR) filters according to decimation due to its multiplier free structure. In this the requirements. The amount of passband aliasing or research, the performance of polyphase structure is imaging error can be brought within prescribed bounds by compared with the CICs using recursive and increasing the number of stages in the CIC filter. The non-recursive algorithms in terms of power, speed and width of the passband and the frequency characteristics area. This polyphase implementation offers high speed outside the passband are severely limited. So, CIC filters operation and low power consumption. The polyphase are used to make the transition between high and low implementation of 4th order CIC filter with a sampling rates. Conventional filters operating at low decimation factor of '64' and input word length of sampling rate are used to attain the required transition '4-bits' offers about 70% and 37% of power saving bandwidth and stopband attenuation. compared to the corresponding recursive and Several papers are available in literature that deals non-recursive implementations respectively. The same with different implementations of decimation filter polyphase CIC filter can operate about 7 times faster architecture for sigma-delta ADCs. Hogenauer has than the recursive and about 3.7 times faster than the described the design procedures for decimation and non-recursive CIC filters.

Reduction of vestigial sideband effects due to multipath transmission in terrestrial broadcast television

In terrestrial television transmission multiple paths of various lengths can occur between the transmitter and the receiver. Such paths occur because of reflections from objects outside the direct transmission path. The multipath signals arriving at the receiver are all detected along with the intended signal causing time displaced replicas called 'ghosts' to appear on the television picture. With an increasing number of people living within built up areas, ghosting is becoming commonplace and therefore deghosting is becoming increasingly important. This thesis uses a deterministic time domain approach to deghosting, resulting in a simple solution to the problem of removing ghosts. A new video detector is presented which reduces the synchronous detector local oscillator phase error, caused by any practical size of ghost, to a lower level than has ever previously been achieved. From the new detector, dispersion of the video signal is minimised and a known closed-form time domain description of the individual ghost components within the detected video is subsequently obtained. Developed from mathematical descriptions of the detected video, a new specific deghoster filter structure is presented which is capable of removing both inphase (I) and also the phase quadrature (Q) induced ghost signals derived from the VSB operation. The new deghoster filter requires much less hardware than any previous deghoster which is capable of removing both I and Q ghost components. A new channel identification algorithm was also required and written which is based upon simple correlation techniques to find the delay and complex amplitude characteristics of individual ghosts. The result of the channel identification is then passed to the new I and Q deghoster filter for ghost cancellation. Generated from the research work performed for this thesis, five papers have been published. D

Relativistic three-body model for final state interaction in D+ → K-π+π+ decay

A challenge in mesonic three-body decays of heavy mesons is to quantify the contribution of re-scattering between the final mesons. D decays have the unique feature that make them a key to light meson spectroscopy, in particular to access the Kn S-wave phase-shifts. We built a relativis-tic three-body model for the final state interaction in D+ → K -π+π+ decay based on the ladder approximation of the Bethe-Salpeter equation projected on the light-front. The decay amplitude is separated in a smooth term, given by the direct partonic decay amplitude, and a three-body fully interacting contribution, that is factorized in the standard two-meson resonant amplitude times a reduced complex amplitude that carries the effect of the three-body rescattering mechanism. The off-shell reduced amplitude is a solution of an inhomogeneous Faddeev type three-dimensional integral equation, that includes only isospin 1/2 K -π+ interaction in the S-wave channel. The elastic K-π+ scattering amplitude is parameterized according to the LASS data[1]. The integral equation is solved numerically and preliminary results are presented and compared to the experimental data from the E791 Collaboration[2, 3] and FOCUS Collaboration[4, 5].

XRF data, magnetic susceptibility, greyscale values and revised depths of sediments from ODP Leg 154 sites

The distinctly cyclic sediments recovered during ODP Leg 154 played an important role in constructing the astronomical time scale and associated astro(bio)chronology for the Miocene, and in deciphering ocean-climate history. The accuracy of the timescale critically depends on the reliability of the shipboard splice used for the tuning and on the tuning itself. New high-resolution colour- and magnetic susceptibility core scanning data supplemented with limited XRF-data allow improvement of the stratigraphy. The revised composite record results in an improved astronomical age model for ODP Site 926 between 5 and 14.4 Ma. The new age model is confirmed by results of complex amplitude demodulation of the precession and obliquity related cycle patterns. Different values for tidal dissipation are applied to improve the fit between the sedimentary cycle patterns and the astronomical solution. Due to the improved stratigraphy and tuning, supported by the results of amplitude demodulation, the revised time scale yields more reliable age estimates for planktic foraminiferal and calcareous nannofossil events. The results of this study highlight the importance of stratigraphy for timescale construction.