Impact of local attenuation approximations when estimating correlation length from backscattered ultrasound echoes

Estimating the characteristic correlation length of tissue microstructure from the backscattered power spectrum could improve the diagnostic capability of medical ultrasound. Previously, size estimates were obtained after compensating for source focusing, the frequency-dependent attenuation along the propagation path (total attenuation), and the frequency-dependent attenuation in the scattering region (local attenuation). In this study, the impact of approximations of the local attenuation on the scatterer size estimate was determined using computer simulations and theoretical analysis. The simulations used Gaussian impedance distributions with an effective radius of 25 microm randomly positioned in a homogeneous half-space sonified by a spherically focused source (f/1 to f/4). The approximations of the local attenuation that were assessed neglected local attenuation (i.e., assume 0 dB/cm-MHz) neglected frequency dependence of the local attenuation, and assumed a finite frequency dependence (i.e., 0.5 dB/cm-MHz) independent of the true attenuation of the medium. Errors in the scatterer size estimate due to the local attenuation approximations increased with increasing window length, increasing true local attenuation and increasing f number. The most robust estimates were obtained when the local attenuation was approximated by a tissue-independent attenuation value that was greater than 70% of the largest attenuation expected in the tissue region of interest.     

衰减匹配的超声Barker码激励方法

为增加超声穿透高声衰减介质的能力,提出了一种衰减匹配的超声Barker码激励方法。基于换能器高斯响应与材料非频散线性衰减的假设,得到了Barker码激励的信号模型,求解旁瓣抑制滤波后脉冲压缩的信噪比表达式可知,该方法仅需要根据材料衰减特性与轴向分辨率的要求,分别调整Barker码的中心频率与时长,便可以获得更高的信噪比。取衰减系数为1.4 Np/(MHz·cm)、厚度为5 cm的橡胶为试样进行验证。当与方波激励方法的轴向分辨率相近时,衰减匹配的Barker码激励方法比传统Barker码激励方法的信噪比增益提高接近5 dB;当牺牲一定轴向分辨率时,信噪比增益提高接近11 dB。结果表明,衰减匹配的Barker码激励方法可以降低依频率衰减对脉冲压缩的影响,有效提高衰减回波的信噪比。      

Fractional precursors in random media

When a broadband pulse penetrates into a dissipative and dispersive medium, phase dispersion and frequency-dependent attenuation alter the pulse in a way that results in the appearance of a precursor field with an algebraic decay. We derive here the existence of precursors in non-dispersive, non-dissipative, but randomly heterogeneous and multiscale media. The shape of the precursor and its fractional power law decay with propagation distance depend on the random medium class. Three principal scattering precursor classes can be identified: (i) in exponentially decorrelating random media, and more generally in mixing random media, the precursor has a Gaussian shape and a peak amplitude that decays as the square root of the inverse of the propagation distance. (ii) In short-range correlation media, with rough multiscale medium fluctuations, the precursor has a skewed shape with a tail that exhibits an anomalous power law decay in time and a peak amplitude that exhibits an anomalous power law decay with propagation distance, both of which depend on the Hurst exponent that characterizes the roughness of the medium. (iii) In long-range correlation media with long-range memory, the situation mimics that of class (ii), but with modified power laws.     

窄带脉冲信号测量横波衰减系数-频率曲线的方法

提出一种测量材料超声横波衰减-频率曲线(αs-f)的方法:应用窄带脉冲驱动接触式横波探头的脉冲反射方式,采用石英晶体作为耦合块,通过测量耦合块和被测试块耦合界面的声压反射和透射系数,并在衍射修正下测量得到单频率下的超声横波衰减系数;在探头有效带宽内改变发射频率并重复测量,得到不同频率下超声横波衰减系数数值;利用非线性最...     

A numerical method to predict the effects of frequency-dependent attenuation and dispersion on speed of sound estimates in cancellous bone

Many studies have demonstrated that time-domain speed-of-sound (SOS) measurements in calcaneus are predictive of osteoporotic fracture risk. However, there is a lack of standardization for this measurement. Consequently, different investigators using different measurement systems and analysis algorithms obtain disparate quantitative values for calcaneal SOS, impairing and often precluding meaningful comparison and/or pooling of measurements. A numerical method has been developed to model the effects of frequency-dependent attenuation and dispersion on transit-time-based SOS estimates. The numerical technique is based on a previously developed linear system analytic model for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The numerical approach is somewhat more general in that it can be used to predict the effects of arbitrary pulse shapes and dispersion relationships. The numerical technique, however, utilizes several additional assumptions (compared with the analytic model) which would be required for the practical task of correcting existing clinical databases. These include a single dispersion relationship for all calcaneus samples, a simple linear model relating phase velocity to broadband ultrasonic attenuation, and a constant calcaneal thickness. Measurements on a polycarbonate plate and 30 human calcaneus samples were in good quantitative agreement with numerical predictions. In addition, the numerical approach predicts that in cancellous bone, frequency-dependent attenuation tends to be a greater contributor to variations in transit-time-based SOS estimates than dispersion. This approach may be used to adjust previously acquired individual measurements so that SOS data recorded with different devices using different algorithms may be compared in a meaningful fashion.     

Nonlinear propagation effects on broadband attenuation measurements and its implications for ultrasonic tissue characterization.

A study is presented in which the influence of the pressure amplitude of the incident pulse on the estimated frequency dependency of the attenuation coefficient is shown. First, the effect is demonstrated with a simple theoretical model for both transmission and reflection measurements. Simulations show that for both measurement techniques a high-amplitude incident pulse results in a biased estimate of the attenuation coefficient due to nonlinear interaction of the different frequency components of the incident pulse. It is shown that in transmission and reflection measurements the biases have opposite signs. The effect of bandwidth, central frequency, and phase of the incident pulse on this bias is investigated. Second, the effect is demonstrated both in vitro, using a broadband through-transmission substitution technique on a tissue mimicking gelatine phantom, and in vivo, using reflection measurements with standard clinical equipment. The experimental results agree well with the theoretical model. The relevance of this study for ultrasonic tissue characterization is shown.     

The dependence of time-domain speed-of-sound measurements on center frequency, bandwidth, and transit-time marker in human calcaneus in vitro

Time-domain speed-of-sound (SOS) measurements in calcaneus are effective predictors of osteoporotic fracture risk. High attenuation and dispersion in bone, however, produce severe distortion of transmitted pulses that leads to ambiguity of time-domain SOS measurements. An equation to predict the effects of system parameters (center frequency and bandwidth), algorithm parameters (pulse arrival-time marker), and bone properties (attenuation coefficient and thickness) on time-domain SOS estimates is derived for media with attenuation that varies linearly with frequency. The equation is validated using data from a bone-mimicking phantom and from 30 human calcaneus samples in vitro. The data suggest that the effects of dispersion are small compared with the effects of frequency-dependent attenuation. The equation can be used to retroactively compensate data. System-related variations in SOS are shown to decrease as the pulse-arrival-time marker is moved toward the pulse center. Therefore, compared with other time-domain measures of SOS, group velocity exhibits the minimum system dependence.     

Wideband high-frequency line-focus PVDF transducer for materials characterization

This paper presents the design, fabrication, operating characteristics and applications of a wideband, high-frequency, line-focus beam transducer we constructed using a 9 microm thick piezoelectric polyvinylidene fluoride (PVDF) film. This transducer possesses a focal length of 2.38 mm and an aperture angle of 84 degrees. The frequency spectrum of the signal measured at the focal point indicates that the transducer has a wide frequency response which extends from 10 MHz to over 100 MHz. When compensated for the frequency-dependent attenuation of the coupling medium, the operational frequency exceeds 150 MHz. The transducer can be operated in a time-resolved pulse mode or in a radio-frequency (rf) tone burst mode. An application of the transducer to determine the anisotropic elastic property of a silicon wafer is demonstrated. The phase velocities of surface acoustic waves (SAW) propagating along various directions on the (001) surface of cubic silicon are measured and compared to computed values.     

材料非线性衰减系数的二次谐波测量方法研究

采用有限幅值法测量材料在基波和非线性引起的二次谐波作用下的衰减系数:利用准线性下的KZK方程推导基波和二次谐波的声压分布,并提取波束修正系数;采用短纯音信号进行非线性实验,对检测得到的基波和二次谐波声压进行衍射修正处理,有效抑制衍射对衰减系数测量的不利影响,继而通过线性拟合的方法计算得到更精确的基波和二次谐波的衰减系数。以水为例进行实验,研究了实验测量所得衰减系数的频率依赖关系,结果表明在非线性条件下水的衰减系数与频率间存在较强的线性关系,而线性条件下衰减系数随频率呈现二次方增长的特性则不适用于非线性条件。该研究提出了准确测量非线性声波衰减系数的方法,为更有效地应用非线性超声检测提供理论依据。      

Ultrasonic slow waves in air-saturated cancellous bone

This paper describes preliminary observations of ultrasonic wave propagation in air-saturated defatted cancellous bone from the human vertebra. Using a broadband pulse transmission system, attenuation and phase velocity were measured over a wide frequency range (100 kHz-1 MHz). The observed behaviour was consistent with that expected for the decoupled slow wave predicted by Biot's theory. Velocity was lower than that of free air, and there was marked frequency-dependent attenuation and velocity dispersion. The tortuosity (alpha) of the trabecular microstructure was estimated from the high frequency limit of the dispersion curve, with a mean value of alpha = 1.040 +/- 0.004 obtained in five specimens. Ultrasonic measurements in air represent a valuable new approach, capable of yielding parameters that directly characterise bone structure. Furthermore, they may give useful insights into wave propagation in bone in vivo, where the trabecular framework is saturated with marrow fat rather than air.     

飞秒脉冲非对称互相关绝对测距

光学频率梳是一种重复频率与偏置频率锁定的新型光源,在频域上为频率间隔稳定的频率梳齿,在时域上为相对距离稳定的飞秒脉冲激光.光学频率梳在测距中的应用广泛,能够实现远距离高精度的测量.本实验使用飞秒激光脉冲作为光源,基于谐振腔扫描光学采样测距原理得到非对称的互相关干涉条纹,实现了远距离高精度的绝对测距.非对称互相关条纹可通过色散补偿与调节光学频率梳的重复频率得到,并通过得到的非对称的互相关干涉条纹对测距结果进行补偿.实验结果表明测距系统能够实现在50 m范围内误差为2 μm的绝对测距,测量相对误差为1.9×10^-7.     

CO2激光对熔石英表面小尺寸损伤的修复

利用10.6 μm的CO2激光对不同直径的点状损伤和不同宽度的划痕进行了修复。经过波长351 nm的紫外激光考核发现,对于直径小于80 μm的点状损伤和对于宽度小于40 μm的划痕,随着损伤点尺寸和划痕宽度的增加,修复后阈值提高程度逐渐降低。划痕的宽度在达到40 μm以后修复效果非常微弱。修复过程中,由于作用时间较短及温度分布不均产生了热应力导致样片损伤以后产生径向裂痕,后续的紫外激光会使裂痕明显扩展。当样品被置于高温退火炉内退火3 h以后,应力导致开裂的现象得到了解决。     

Spatially resolved amplitude and phase characterization of femtosecond optical pulses

Ultrabroadband pulses exhibit a frequency-dependent mode size owing to the wavelength dependence of free-space diffraction. Additionally, rather complex lateral dependence of the temporal pulse shape has been reported for Kerr-lens mode-locked lasers and broadband amplifier chains and in frequency-domain pulse shapers, for example. We demonstrate an ultrashort-pulse characterization technique that reveals lateral pulse-shape variations by spatially resolved amplitude and phase measurements by use of spectral phase interferometry for direct electric-field reconstruction (SPIDER). Unlike with autocorrelation techniques, with SPIDER we can obtain spatially resolved pulse characterization even after the nonlinear process. Thus, with this method the spectral phase of the pulse can be resolved very rapidly along one lateral beam axis in a single measurement.     

Compressor optimization with compressor-based multiphoton intrapulse interference phase scan (MIIPS)

The multiphoton intrapulse interference phase scan (MIIPS) technique is modified to optimize the compressor settings of a chirped pulse amplification (CPA) laser system. Here, we use the compressor itself to perform the phase scan inherent in MIIPS measurement . A frequency-resolved optical gating measurement shows that the pulse duration of the compressor optimized using the modified MIIPS technique is 33.8 fs with a 2.24 rad temporal phase variation above 2% intensity. The measured time-bandwidth product is 0.60, which is close to that of transform-limited Gaussian pulse (0.44).     

Mutual influence of the spectral components of perturbations on the modulation instability frequency interval in a cubic nonlinear medium

The influence of the shape of a Gaussian pulse propagating in a cubic nonlinear medium on the development of its modulation instability is analyzed, taking into account the time dispersion of the nonlinear response as well. Analytical dependences of the frequency interval of the perturbation development on the dispersion of the nonlinear response, the pulse duration, and the number of simultaneously acting perturbations, which affect each other due to the inhomogeneous pulse shape, are obtained. It is shown that, with increasing dispersion of nonlinear response, the frequency interval of the instability development initially narrows and then expands. Qualitative agreement between the analytical dependences and the results of computer simulation is demonstrated. The frequency interval of the modulation instability development in a medium without the nonlinear response dispersion that was previously determined by different authors under the assumption of “long” pulses is found to coincide with that obtained in this study for the Gaussian pulse under the assumption of the simultaneous action of a large number of perturbations.     

用于脉冲功率装置测量的混合式高压分压器

为准确测量脉冲放电电压,提出了固液混合式高压分压器的原理与结构,并进行了标定和实验测试。用简化模型分析了分压器系统的理想响应条件,讨论了两级分压的衰减特性,提出了控制误差的方法。通过负载标定,得到分压器脉冲电压频率响应大于2.9 MHz,最长脉冲宽度40 s,分压比(或衰减系数)为2.60 kV/V,测量误差小于5%。该高压分压器具有造价低、制作易,同时适于ns到s级脉冲电压的测量等优点,可以在实验室中得到应用。     

各向异性渗流条件下弹性波的传播特征

研究了弹性波在非均匀裂纹孔隙介质中的传播特性,建立了各向异性喷射流模型.当弹性波通过裂纹孔隙介质时,由于波的扰动及裂纹和孔隙几何结构的不一致,导致在裂纹内部及裂纹与周边孔隙之间同时存在着流体压力梯度.此时的弹性波波动响应中包含着裂纹内连通性特征和背景孔隙渗透率信息.流体的动态流动过程使得介质的等效弹性参数为复数(非完全弹性),并且具有频率依赖性.当弹性波为低频和高频极限时,介质为完全弹性;当处于中间频段时,波有衰减和频率依赖.裂纹孔隙介质的各向异性连通性(渗透率)对应着各向异性特征频率(当渗流长度等于非均匀尺度时的弹性波频率),波的传播受到裂纹内连通性的影响.在一定频段内,随着裂纹厚度的增加,将出现第二峰值,峰值大小同时受到裂纹厚度和半径的影响.     

光学频率梳基于光谱干涉实现绝对距离测量

详细分析了光学频率梳光谱干涉的原理, 建立了较全面的光谱干涉的数学模型, 为实现绝对距离测量提供理论分析基础. 基于光谱干涉, 指出通过光谱干涉条纹的振荡频率, 即一次傅里叶变换, 可以实现绝对距离测量, 数值模拟结果表明, 最大测量误差为1.5 nm; 提出了一种等效的多波长并行零差干涉的方法, 分析了多波长并行零差干涉法的测距原理. 数值模拟结果表明, 多波长并行零差干涉法的最大误差为8.7 nm; 通过脉冲啁啾实现绝对测距, 分析了基于脉冲啁啾实现绝对测距的原理, 数值模拟结果表明, 最大测距误差为5.3 nm.     

The fractal interpretation of the weak scattering of elastic waves

Nondestructive methods, in particular the measurement of elastic waves, have become increasingly important in determining the microstructure of many materials in recent years. One of these methods is observing the attenuation of ultrasonic waves of known amplitude and direction, e.g., in granular metals. The waves are exponentially attenuated with distance with a frequency-dependent attenuation fractor. The attenuation factor can be decomposed into two parts: absorption and scattering. Experimentally, the absorption part varies linearly with frequency, while the scattering part has a noninteger power law behavior, the exponent of which is related to the strength of the material. Theoretically, at long wavelengths the exponent is 4 (Rayleigh scattering) while for grain-sized wavelengths it is 2 (diffusive scattering). We relate the attenuation factor to the forward scattering amplitude which is related to the frequency dependence of the scatterers and their cross sections. We attribute the noninteger attenuation exponent to a fractal distribution of grain shapes and sizes.Supported by the Defense Advanced Research Projects Agency.