Fitting the correlation function

The whole correlation function of the intensity of scattered light is usually determined from a single realization of the photocurrent. As a result, the values of the correlation function at different delay times are not statistically independent. A standard least-squares fitting procedure is not optimal for an analysis of such data. However, the benefits of mathematically rigorous but highly nonlinear and less stable methods are not known. We consider the test case of a Gaussian signal with a single-exponential correlation function without shot noise. In this case the fitting procedure, which is based on the maximum-likelihood principle for the observed signal, permits an analytical solution. We demonstrate that such a rigorous statistical analysis produces an approximately two times more-accurate result for the relaxation time than does the standard least-squares fit. This gain, however, is greatly reduced by the presence of shot noise, which introduces additional uncorrelated errors into the values of the correlation function.     

Effect of aerosol particle microstructure on cw Doppler lidar signal statistics

Analysis of signal statistical characteristics is carried out, and estimation errors of the radial wind velocity are calculated by use of numerical simulation of a cw Doppler lidar return, taking into account the atmospheric aerosol microstructure. It has been found that, at small sounded volume, the large particles contribute significantly to the scattered field. As a result the lidar return probability density function distribution can differ significantly from a Gaussian distribution. Neglect of the aerosol microstructure effect results in considerable underestimation of the error of cw Doppler lidar velocity estimates at small sounded volume.     

Tolerance of Spectral Estimation

A statistical expression for the mean square error of a spectrum estimation has been derived in terms of the variances and covariances of the amplitude and phase errors of a complex data sequence. No restrictions need be imposed on the magnitude of these variances and covariances. Numerical results have been systematically presented in graphs which illustrate the dependence of the spectrum error on the standard deviation and correlation distance of the amplitude and phase errors. It is shown that large phase error tends to dominate the spectrum error, and that large correlation distances worsen the spectrum error and sharpen its dependency on the frequency index. An expression to estimate the variance of frequency error has also been derived under the assumption of small phase errors. Numerical results are given, which demonstrate the linear dependency of the frequency error on the phase error and shows that a large correlation distance worsens the frequency error while a large number of samples reduces it.     

相关时延估计误差对测频误差的影响

声学多普勒测速技术采用宽带编码信号进行多普勒频移估计时会产生测频误差,该误差来源主要分为两种：（1）宽带信号频谱不对称;（2）相关时延存在估计误差。文章主要讨论相关时延估计误差对测频误差的影响,分析了其产生的原因以及该误差对测频误差的影响。忽略相关函数简化误差以及滤波后频点不对称,推导得到由相关时延估计误差导致的测频误差的解析式。进行了仿真和湖试数据分析,不同频移下的测频误差与理论测频误差一致,不同填充系数下的实际测速误差与理论测频误差变化趋势相同。该对比结果验证了相关时延估计误差会对测频误差产生影响,证明了由相关时延估计误差导致的测频误差的解析式可信。     

Generalized pointwise bias error bounds for response surface approximations

This paper proposes a generalized pointwise bias error bounds estimation method for polynomial‐based response surface approximations when bias errors are substantial. A relaxation parameter is introduced to account for inconsistencies between the data and the assumed true model. The method is demonstrated with a polynomial example where the model is a quadratic polynomial while the true function is assumed to be cubic polynomial. The effect of relaxation parameter is studied. It is demonstrated that when bias errors dominate, the bias error bounds characterize the actual error field better than the standard error. The bias error bound estimates also help to identify regions in the design space where the accuracy of the response surface approximations is inadequate. It is demonstrated that this information can be utilized for adaptive sampling in order to improve accuracy in such regions. Copyright © 2005 John Wiley & Sons, Ltd.     

Comments, with reply, on `Effect of various dither forms oquantization errors of ideal A/D converters' by M.F. Wagdy

In the above-titled paper (see ibid., vol.38, p.850-5, Aug. 1989), the effect of dithering on correlation (covariance) between the signal and the quantization error and on the spectrum of quantization errors was addressed. The commenter shows that for the evaluation of the correlation (or covariance) more effective methods exist, and the covariance between the signal and the quantization error can be easily made equal to zero with appropriate dithering. It is also pointed out that the mean value of the signal must be taken into account. Some misunderstandable statements on the error spectrum are stated precisely. The author replies that the commenter misunderstood the original paper and further amplifies his work in support of this assertion     

Correlation transfer equation for multiply scattered light modulated by an ultrasonic pulse

We develop a temporal correlation transfer equation (CTE) and a Monte Carlo algorithm (MC) for multiply scattered light modulated by an ultrasonic pulse propagating in an optically scattering medium, where the ultrasound field can be nonuniform and the medium can have spatially heterogeneous distribution of optical parameters. The CTE and MC can be used to obtain the time-varying specific intensity and the spatial distribution of the time-dependent power spectral density, respectively, of ultrasound-modulated light. We expect the CTE and MC to be applicable for estimation of contrast and resolution in a wide spectrum of conditions in ultrasound-modulated optical tomography of soft biological tissues.     

Correction of detector nonlinearity for the balloonborne Michelson Interferometer for Passive Atmospheric Sounding

The detectors used in the cryogenic limb-emission sounder MIPAS-B2 (Michelson Interferometer for Passive Atmospheric Sounding) show a nonlinear response, which leads to radiometric errors in the calibrated spectra if the nonlinearity is not taken into account. In the case of emission measurements, the dominant error that arises from the nonlinearity is the changing detector responsivity as the incident photon load changes. The effect of the distortion of a single interferogram can be neglected. A method to characterize the variable responsivity and to correct for this effect is proposed. Furthermore, a detailed error estimation is presented.     

Near-field intensity correlations of scattered light

We show that the two-point correlation function in the near field of scattered light is simply related to the scattered intensity distribution. We present a new, to our knowledge, optical scheme to measure the correlation function in the near field, and we describe a processing technique that permits the subtraction of stray light on a statistical basis. We present experimental data for solutions of latex spheres, and we show that this novel technique is a powerful alternative to static light scattering.     

Quantitative use of Rayleigh waves to locate and size subsurface holes

An ultrasonic inspection method is used to obtain the circumference of a subsurface hole and the depth of the hole below the surface. A pitch-catch Rayleigh wave transducer set-up was used to launch a Rayleigh surface wave at the flaw and to capture and record the scattered waves. The frequency spectrum of the scattered waves can be used to obtain the depth of the hole. The ligament of material between the hole and the surface is sent into resonance, and this feature can be extracted from the scattered waves' frequency spectrum. The frequency is a function of the ligament length; thus the hole depth can be obtained. The circumference of the hole is found from a time of flight measurement. A Rayleigh wave is formed that travels around the hole's surface. The length of time required for the wave to travel around the hole is a measure of the circumference.     

全相位频谱校正技术在水声通信中的应用研究

多普勒效应是影响水下移动通信性能的主要因素,准确估计多普勒频移对提高通信系统可靠性具有重要意义。在进行离散频谱分析时,时域非整周期截断会造成频域能量的泄漏,导致频谱估计精度降低。全相位频谱分析具有良好的抑制频谱泄漏特性及相位不变性。仿真验证了全相位频谱校正技术相对于传统频谱校正技术在估计性能上的优势,并在此基础上探讨了全相位频谱校正技术在水声通信中的应用。采用全相位频谱校正技术进行多普勒频移估计,进而进行多普勒补偿以降低通信系统误码率。仿真结果表明,全相位频谱校正技术能够实现高精度多普勒频移估计,从而提高水下移动通信系统的可靠性。     

Theory of Light Scattering by Amorphous Absorbing Media

The present paper studies the determination of structural statistics of amorphous absorbing media from the distribution of intensity of scattered light. Assuming a gaussian distributed inhomogeneity, the form of the correlation function for absorbing materials is discussed. Furthermore, the relationship between the correlation function and the scattered intensity is established in both the Fresnel and Fraunhofer regions. The first Born approximation is discussed, as well as the difficulties in solving the inverse statistical problem due to the complex nature of the permittivity.     

Number Fluctuations of Polydisperse Scatterers

The intensity statistics of incoherently detected light scattered from fluctuating numbers of polydisperse scatterers undergoing brownian motion are discussed. General formulae are developed for the normalized moments of the intensity distribution and normalized intensity correlation functions. A relationship between the variance of any finite duration measurement of a normalized moment and the higher-order correlation functions is also obtained. This error is evaluated up to the fourth normalized moment. Theoretical moments and errors are then compared with measurements on polydisperse polystyrene latex samples. Although agreement between theory and experiment is good, it is clear that any measurement of polydispersity by this technique can be only relative.     

Scattering effects at near-wall flow measurements using Doppler global velocimetry

Doppler global velocimetry (DGV) is considered to be a useful optical measurement tool for acquiring flow velocity fields. Often near-wall measurements are required, which is still challenging due to errors resulting from background scattering and multiple-particle scattering. Since the magnitudes of both errors are unknown so far, they are investigated by scattering simulations and experiments. Multiple-particle scattering mainly causes a stochastic error, which can be reduced by averaging. Contrary to this, background scattering results in a relative systematic error, which is directly proportional to the ratio of the background scattered light power to the total scattered light power. After applying a correction method and optimizing the measurement arrangement, a subsonic flat plate boundary layer was successfully measured achieving a minimum wall distance of 100 μm with a maximum relative error of 6%. The investigations reveal the current capabilities and perspectives of DGV for near-wall measurements.     

Multiple-scattering effects on infrared scattering measurements used to characterize droplet size and volume fraction distributions in diesel sprays

We quantify the maximum error due to multiple-scattering effects for an infrared scattering droplet izing technique. Errors in Sauter mean diameters (SMDs) and liquid volume fractions were estimated lased on experimentally determined polarization properties of the scattered light. Light that is multiply scattered from spherical particles becomes randomly polarized, whereas singly scattered light from a spherical particle contains no cross-polarization scattering component. Therefore measurement of the cross-polarization component (in this case parallel) of the scattering signal is a measure of the multiply scattered light. A ratio of parallel to perpendicular polarized scattered light was experimentally determined and used to calculate an error due to multiple scattering. The infrared scattering measurements and polarization measurements used to quantify the multiple-scattering errors were applied to a typical diesel spray that was injected into three different background conditions: a room ambient condition; a room-temperature, high-pressure condition; and a combusting condition. Droplet SMD, liquid volume fraction, and multiple-scattering errors were determined for a number of locations within the spray; results indicate that the combusting case is negligibly affected by multiple scattering. However, the room ambient case exhibited notable errors due to multiple scattering near the centerline of the spray, and the high-pressure case demonstrated susceptibility to multiple scattering throughout all regions investigated. It is important to note, however, that multiple-scattering errors in many cases translate into relatively small effects on the reported droplet sizes.     

Spatial correlations between chromophores in thin films by femtosecond hyper-Rayleigh scattering

Femtosecond hyper-Rayleigh scattering has been used to probe the spatial orientational fluctuations between nonlinear optical chromophores as dopants in spincoated polymer films. The fluctuation in the second-order incoherently scattered light intensity upon translating the sample is indicative of the degree of spatial correlation between the chromophores. The decay of the autocorrelation function of this fluctuating signal is characterized by a spatial correlation length. Electric-field poling of chromophores is shown to increase this length. The temporal characteristics of this correlation length have been studied and compared with relaxation times, obtained with coherent second-harmonic generation. This correlation length decays much faster than the second-harmonic intensity. The difference in relaxation time between the incoherent and the coherent process is explained by translational diffusion of free volume over the wavelength and over the coherence length, respectively.     

合成孔径声呐时延估计误差校正改进算法

由相位解缠错误造成的时延估计误差会严重降低合成孔径声呐时延估计的精度。现有的时延估计误差校正算法采用二次函数作为时延的拟合模型,该模型在距离向近端和远端处不符合时延空变规律,拟合误差较大且无法估计载体的横荡和升沉运动。针对该问题,文章提出一种改进的时延估计误差校正算法,利用时延的距离空变函数代替二次函数作为拟合模型。数值仿真和实验结果表明,相较于参考算法,改进算法校正时延估计误差的效果更好、速度更快,同时还能准确地估计载体的横荡和升沉运动。运动补偿结果显示了改进算法能较好地提升成像质量。     

Modal iterative estimation in linear models with unimodal errors and non-grouped and grouped data collected from different sources

In this paper we introduce an iterative estimation procedure based on conditional modes suitable to fit linear models when errors are known to be unimodal and, moreover, the dependent data stem from different sources and, consequently, may be either non-grouped or grouped with different classification criteria. The procedure requires, at each step, the imputation of the exact values of the grouped data and runs by means of a process that is similar to the EM algorithm with normal errors. The expectation step has been substituted with a mode step that avoids awkward integration with general errors and, in addition, we have substituted the maximisation step with a natural one which only coincides with it when the error distribution is normal. Notwithstanding the former modifications, we have proved that, on the one hand, the iterative estimating algorithm converges to a point which is unique and non-dependent on the starting values and, on the other hand, our final estimate, being anM-estimator, may enjoy good stochastic asymptotic properties such as consistency, boundness inL ₂, and limit normality. Research partially founded by Ministry of Education and Culture, Spain. Grant SEC99-0402     

基于时延估计的海底线阵阵形估计方法研究

阵形估计是水听器阵列应用中的关键问题,基于时延估计的阵形估计方法比基于传感器测量和基于匹配场处理的方法具有更强的适应性和较高的精度。针对浅海水听器阵列中水平长线阵存在的纵向相关振荡现象引起的不能简单以某一阵元为基准求相对时延的问题,充分利用了阵元信号的高相关性,提出了基于子阵时延的阵形估计方法,针对子阵间时延估计误差向阵端累积的问题,该方法以时延估计的克拉美罗界为依据提出了合理的子阵方式,在一定程度上减小了误差传递。对已有海试数据阵形估计处理的结果表明,相对于单源固定间距方法和未分子阵的双源时延估计方法,基于子阵时延的阵形估计方法满足阵元间距的约束,有较好的空间谱特性,减小了阵形估计误差,对长水听器阵列的应用及阵形估计具有较大应用价值。