Experimental study of the effects of pulsed Doppler sample volume size and position on the Doppler spectrum

With a pulsed Doppler system, the recorded Doppler spectrum is expected to vary depending upon the sample volume size relative to the diameter of the vessel, the position of the sample volume in the vessel and the velocity profile. In the in vitro experiments described in this paper, the velocity profile was kept constant by using steady parabolic flow in a flow model. As the Doppler sample volume size and position were changed, the maximum variations of quantitative measurements from the Doppler spectrum were determined. The maximum, mean and mode frequencies and spectral broadening index (SBI) were affected by the position of the sample volume but to a lesser degree by its length (1.5-5.0 mm) relative to the 9.5 mm beam path length across the tube. When the centre of the Doppler sample volume was moved within the central 25% of the tube, the maximum variations were as follows: maximum frequency 3-5%, mean frequency 8-9%, mode frequency 8-9% and SBI 16-18%, where the range indicates the effect of increasing the sample volume size. Based on these results obtained under steady flow conditions in vitro, it is concluded that quantification of pulsed Doppler spectra may be feasible if the sample volume is positioned within the central 25% of the vessel.     

Pulsed Doppler flow-line spectrum for focused transducers with apodized apertures.

The properties of the single flow-line Doppler spectrum using pulsed wave (PW) ultrasound is studied on the basis of previously developed spectral theory for transducers with apodized apertures. It has been shown previously that the spectral width of Doppler signals from a sample volume in low velocity-shear flow is independent of the sample volume depth but that is not true for the spectra from the individual streamlines. The work presented here on the Doppler flow-line spectrum shows that its width should be invariant with flow-line location, if the sample volume depth is fixed. At the same time, for a transducer operating in PW mode not only the Doppler spectral width depends on the sample volume depth, but also the modal Doppler frequency shift changes with flow-line displacement in the illuminating field except if the sample volume centre and the beam focus coincide. The variation of modal Doppler frequency shift is the more explicit manifestation of the effect of wavefront curvature increasing for lines and sounding depths distant from the focal point. The values of the Doppler shift and spectral bandwidth are reported taking account of beam diffraction and variations in its geometry due to focusing.     

Correlation functions and power spectra of Doppler response signals in ultrasonic medical applications

Ultrasound Doppler methods are widely used in clinical practice as prospective investigational tool to study the vascular system and soft biological tissues. Meanwhile, the most general relationship between the power Doppler spectra, spectral characteristics of the scattering fluctuations and the probing ultrasound field parameters for some clinical implementations are still unexplored. Based upon the continuum model of scattering inhomogeneities, a set of the closed-form expressions for the correlation functions and the spectra of Doppler response of soft tissues and blood have been derived. The influence of the correlation among inhomogeneities and the diffusion processes on the Doppler power spectra formed by stationary flows have been examined. Computer simulations of Doppler spectra were performed for different values of correlation radius and diffusion coefficient. With simulation results the effects of the correlation among inhomogeneities and the diffusion processes on the spectral width and mean frequency are established and discussed in respect to turbulent flows. Closed-form expressions for correlation functions and Doppler spectra for the vibrational sonoelastography technique for visualizing malignant tumors in tissues have been derived. Based on the peculiarities of the obtained Doppler spectra, it is shown that the differentiation of soft tissues with respect to the amplitude value of constrained oscillations is feasible. The expressions were derived for the cases of non-stationary accelerated blood movement. It has been found that the frequency dependence reveals solely at a finite time of observation and depends on the initial phase of the accelerated movement.     

Flow spectra from spectral power density calculations for pulsed Doppler

Range gated pulsed Doppler can be used to make localized velocity measurements within a blood vessel. Both the transducer and the sample volume are of finite size, and this prohibits the measurement of velocity at a point. A spectral flow profile can be created by stepping a sufficiently small sample volume across the lumen of a vessel. However no such set of spectra will correspond directly to the true velocity profile. In this study we developed a systematic theoretical treatment which allows Doppler spectral power density (SPD) functions to be calculated under a very wide range of conditions. Simulated flow spectra were created from sets of these spectra. The model is based on the beam intensity weighted volume method and incorporates, through the idea of a spread function, Guidi's individual flow line spectrum. Our method can be applied for different spread functions; with beam profiles which are uniform, Gaussian or arbitrarily narrow (needle beam); with range gated sample volumes which can be maximal (CW-type) or minimal (PW-type); and for beams which intersect the flow tube axis, or are off centre. Under all conditions we find the spread function parameter k, equal to the ratio of the central Doppler shift to half the bandwidth, plays a key role. After formulating the model analytically, we sought simplifications to allow results to be obtained from simple, practical formulae. Spread and unspread SPD functions are in most cases given as single integrals which contain measurable physical parameters and can be easily evaluated numerically. Model results are presented for flow spectra of parabolic flow, illustrating the interplay between different factors in determining the appearance of spectral flow profiles.     

啁啾脉冲高斯光束在大气湍流中的传输特性北大核心CSCD

基于广义惠更斯-菲涅耳原理,推导出啁啾脉冲高斯光束在湍流大气中传输的光谱解析表达式,并对解析表达式进行了数值仿真。结果表明:啁啾参数越大,光源谱宽越宽;当光源相对谱宽大于0.336时,轴上点光谱产生蓝移;湍流使得轴上点光谱的相对频移量减小,相对频移量随源光谱宽的增大而非线性增大;增大光束束腰半径可减小湍流对光谱频移、光束展宽的影响。     

Effect of deviation from plane wave conditions on the Doppler spectrum from an ultrasonic blood flow detector.

Deviation from plane wave conditions within the ultrasound beam of a Doppler blood flow detector leads to a non-linear relationship between the phase angle of the back-scattered signal and the scatterer position. This in turn leads to frequency modulation of the Doppler signal and an increase in the Doppler spectrum width. The relationship between the ultrasound beam and the observed signal spectrum has been investigated by employing a computer-based model of the ultrasound field which enabled the calculation of: 1, pressure (amplitude and phase angle) field distributions from plane disc and focused transducers with unapodized and apodized aperture field distributions; 2, the Doppler signal from a scatterer moving through the field; and 3, the spectrum of this signal. The increase in spectral width resulting from deviations from plane wave conditions was calculated by comparing this spectrum with that of the signal from which frequency modulation had been removed.     

Spectral power density calculations for pulsed Doppler

Range-gated pulsed Doppler can be used to make localized velocity measurements within a blood vessel. A spectral flow profile can be created by stepping a sufficiently small sample volume across the lumen, but no set of spectra will correspond directly to the true velocity profile. Spectral flow profiles are affected by a complex interplay between different sources of spectral broadening. In this study we developed a systematic theoretical method which allows spectral power density functions to be calculated under a very wide range of conditions, and used it to obtain simulated flow spectra. The model was formulated analytically. It is based on the weighted-volume approach and incorporates, through the concept of a spread function, the intrinsic spectral broadening associated with a focused transducer. It can be applied for arbitrary values of the spread parameter; for non-uniform beam profiles; with maximal (continuous wave-type) or minimal (pulse wave-type) range-gated sample volumes; and for beams that intersect the flow tube axis, or are off centre. Results are presented for a Gaussian beam and parabolic flow. Simulated spectral flow profiles are given which illustrate how a profile's appearance can be altered by the different sources of spectral broadening.     

Quantitative retinal-blood flow measurement with three-dimensional vessel geometry determination using ultrahigh-resolution Doppler optical coherence angiography

Retinal blood flow quantification by retinal vessel segmentation with Doppler optical coherence angiography is presented. Vessel diameter, orientation, and position are determined in an en face vessel image and two representative cross-sectional flow images of the vessel. Absolute blood flow velocity is calculated with the help of the measured Doppler frequency shift and determined vessel angle. The volumetric flow rate is obtained with the position and the region of the vessel lumen. The volumetric blood flow rate of retinal arteries before and after a bifurcation is verified in a healthy human eye.     

光脉冲在密度随时间,空间变化的等离子体中的传播

本文定量地研究了光脉冲在密度随时间上升的等离子体中的频率上移,以及在密度随空间上升的等离子体中的脉宽压缩。通过求解波动方程,得到了描述光脉冲的时空演变特征的解析表达式,并在此基础上就脉冲形状、峰值位置、传播速度、脉冲宽度及光子数守恒等问题进行了讨论。     

对称零面积变换结合L-M拟合自动识别重叠光谱峰

Raman光谱分析中,由于仪器光谱分辨率的限制和复杂的目标成分,经常存在着谱峰重叠现象。容易导致谱峰参数提取乃至样品成分分析错误,更为现场光谱的自动分析处理增加了难度。重叠光谱峰的识别已成为现场光谱学处理的难点,针对这个问题,建立了一套自动识别重叠谱峰的方法：以多个高斯峰的组合作为重叠光谱解析模型,首先以对称零面积变换寻峰方法确定高斯峰的个数和初步的峰位、峰高、宽度参数,并以Levenberg-Marquardt方法对获得的初始高斯峰参数进行拟合优化,最终获得各个独立谱峰的拟合参数。对该方法进行了测试,其中以仿真数据进行的算法实验证明,对称零面积变换寻峰获得的初始参数与真实值较为接近,在此基础上进行的参数优化收敛速度快,对峰参数的提取可获得较高的准确度;以具有不同信噪比的实测Raman光谱数据进行的算法实验证明,该方法可以适用于信噪比在较大范围变化的信号,但对信噪比过低的实测信号则容易产生虚假峰和漏峰。研究证明,以对称零面积变换寻峰结合L-M拟合自动识别重叠光谱峰的方法具有一定的实用价值。     

基于希尔伯特变化的微小振动激光多普勒信号处理

为了实现对固体目标微小振动参数的测量,建立了微小振动的激光多普勒信号模型。采用希尔伯特数字运算,将激光多普勒振动信号的即时信号采样转化为信号的谱采样。通过频谱计算得到每个振动周期中瞬时频率的平均数,应用差值采样序列积分计算得到振动频率,最后根据振动信号频率变化与振幅的关系得到振幅。采用希尔伯特方法对实验测试结果进行处理验证,并分析了误差来源。实验结果表明：实验测量目标的振动振幅约为1.85×10-4m,转动的圆频率约为170 Hz。因此,应用希尔伯特变换方法处理测量的目标微小振动信号,获取目标运动的参数是可行的。     

Effect of frequency dependent processes on pulsed Doppler sample volume

The change in the frequency spectrum of ultrasound pulses as a result of frequency dependent attenuation and scatter is known to alter the spectrum of Doppler signals from blood flow parallel to the beam axis. It is shown here that the change in pulse shape accompanying this pulse spectrum change as a result of these processes, together with the velocity dispersion accompanying frequency dependent attenuation and linked to it by the Kramers-Kronig relations, will change the pulsed Doppler sample volume shape and position.     

光谱线型函数的四种形式及其变换关系

从理论上研究了光谱线型函数的四种形式及其关系,以多普勒展宽导致的线型函数为例,分析了光子数、能量按频率及波长分布函数的最大值和半高全宽。结果表明,光子数、能量按频率的分布函数近似相等,光子数、能量按波长的分布函数也近似相等。通过对多普勒线型函数的分析,建立了根据两条光谱线的线型函数的最大值比值求得光子数比值的方法。     

Polarization analyzers operating in a wide spectral range

Different versions of practical realization of customary optical systems for full measurement of the polarization state of quasi-monochromatic partially polarized light are considered. They can be used to overcome measurement difficulties associated with the finite width of the spectral range being studied. The effect of changes in characteristics of optical and polarization elements over a spectral range on the character of polarization measurements is analyzed. Methods for elimination of chromatism or taking into account its effect on measurements are suggested. Relations for taking into account the effect of chromatism of a phase plate with constant thickness on measurement results are given. Operation of a classical four-channel scheme for studing quasi-monochromatic partially polarized light in the visible and near-IR regions is considered. For this system, expressions are derived which make possible determination of Stokes parameters taking into account the effect of a finite spectral range. A system using phase modulation of radiation by an electrooptical cell and measurement of the maximum and minimum intensities of the modulated signal is considered. Measurements are carried out by using a two-channel system. Expressions are derived which make possible determination of Stokes parameters for the system under consideration in the visible and near-IR spectral regions. A system for measuring the polarization state of radiation in the visible and near-IR regions and based on modulation of radiation by an electrooptical phase cell is described. Measurements are carried out for the fundamental modulation frequency and its harmonics using a two-channel scheme. Relations for determining Stokes parameters of the system are presented.     

Doppler spectroscopy of zero-phonon lines

Narrow profiles of purely electronic zero-phonon lines open up attractive possibilities for spectral investigation with the use of the Doppler effect (Doppler spectroscopy). It is established that, for a 10-MHz-wide zero-phonon line to shift to a new position, the velocity of motion of a receiver with respect to a source needs to be only ～10 m/s. It is shown that the narrower the line or the spectral hole (its negative image), the more efficient the Doppler spectroscopy. The possibility of measuring the shape of spectral holes with the use of Doppler spectroscopy is demonstrated, and the potentialities of supersensitive Doppler spectroscopy are considered. The specific feature revealed in the frequency modulation by Doppler spectroscopy is that it occurs without a perturbation of the internal states of the emitter and absorber. The conclusion is drawn that there is a need to study the interference of a photon with itself when the frequency of “one-half of it” changes with the use of Doppler spectroscopy.     

Volume estimation of symmetrical branching structures by resonance mode analysis

An exact resonance condition is derived for rigid symmetric second-order bifurcating structures. In the low-frequency range, the resonance condition can be reduced into forms that facilitate volume estimation of bifurcating structures. Two such volume approximation techniques are presented: (1) a fundamental frequency method, in which the lowest resonant frequency is inversely proportional to the structure volume, and (2) an equivalent-length method, in which an equivalent length of two daughter branches is calculated for all branches distal to the first bifurcation. An experimental study to determine the resonance modes of seven bifurcating glass structures was performed. The volume estimates obtained by either method were in very close agreement with the true volumes.     

Microwave Doppler spectra of sea return at small incidence angles: specular point scattering contribution

It is well known that the sea return echo contains contributions from at least two scattering mechanisms. In addition to the resonant Bragg scattering, the specular point scattering plays an important role as the incidence angle becomes smaller (≤20o). Here, in combination with the Kirchhoff integral equation of scattering field and the stationary phase approximation, analytical expressions for Doppler shift and spectral bandwidth of specular point scattering, which are insensitive to the polarization state, are derived theoretically. For comparison, the simulated results related to the two-scale method (TSM) and the method of moment (MOM) are also presented. It is found that the Doppler shift and the spectral bandwidth given by TSM are insufficient at small incidence angles. However, a comparison between the analytical results and the numerical simulations by MOM in the backscatter configuration shows that our proposed formulas are valid for the specular point scattering case. In this work, the dependences of the predicted results on incidence angle, radar frequency, and wind speed are also discussed. The obtained conclusions seem promising for a better understanding of the Doppler spectra of the specular point scattering fields from time-varying sea surfaces.     

Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams

New expressions are derived that predict the change of spectral density, the spectral degree of coherence and spectral degree of polarization in Young’s interference pattern when the pinholes are illuminated by an electromagnetic Gaussian Schell-mode beam. The spectral degree of polarization in the observation plane is found, in general, to take on values different from its values at each pinhole, and it changes with position at the same spatial frequency, as does the spectral density. When the light at the pinholes is completely coherent, there are singular points in the pattern, at which the spectral degree of polarization reaches minimum value.     

Delay and Doppler spreads in underwater acoustic particle velocity channels

Signal processing and communication in acoustic particle velocity channels using vector sensors are of interest in the underwater medium. Due to the presence of multiple propagation paths, a mobile receiver collects the signal with different delays and Doppler shifts. This introduces certain delay and Doppler spreads in particle velocity channels. In this paper, these channel spreads are characterized using the zero-crossing rates of channel responses in frequency and time domain. Useful expressions for delay and Doppler spreads are derived in terms of the key channel parameters mean angle of arrival and angle spread. These results are needed for design and performance prediction of systems that utilize underwater acoustic particle velocity and pressure channels.     

Some effects of optical alignment errors in a differential laser Doppler velocimeter

A formulation has been developed to treat the effects of alignment errors of the optical system used in a differential laser Doppler velocimeter. It is then applied to analyse the properties of output beat signals obtained by the velocimeter. The effects of optical alignment errors on the spectral width and signal-to-noise ratio of the output beat signals and on the probing volume are investigated in some detail. The spectral width is not affected very much by the deviation of the angle between two beams incident on the probing volume, but depends mainly on the number of interference fringes produced in that volume. The signal-to-noise ratio is very sensitive to the displacement of two incident beams on the probing volume and is also affected by the intensity and beam width differences of these two beams. The probing volume is evaluated in the case of two incident beams having different beam widths.