Errors in ultrasonic scatterer size estimates due to phase and amplitude aberration

Current ultrasonic scatterer size estimation methods assume that acoustic propagation is free of distortion due to large-scale variations in medium attenuation and sound speed. However, it has been demonstrated that under certain conditions in medical applications, medium inhomogeneities can cause significant field aberrations that lead to B-mode image artifacts. These same aberrations may be responsible for errors in size estimates and parametric images of scatterer size. This work derives theoretical expressions for the error in backscatter coefficient and size estimates as a function of statistical parameters that quantify phase and amplitude aberration, assuming a Gaussian spatial autocorrelation function. Results exhibit agreement with simulations for the limited region of parameter space considered. For large values of aberration decorrelation lengths relative to aberration standard deviations, phase aberration errors appear to be minimal, while amplitude aberration errors remain significant. Implications of the results for accurate backscatter and size estimation are discussed. In particular, backscatter filters are suggested as a method for error correction. Limitations of the theory are also addressed. The approach, approximations, and assumptions used in the derivation are most appropriate when the aberrating structures are relatively large, and the region containing the inhomogeneities is offset from the insonifying transducer.     

聚焦部分相干涡旋光束的传输和相干特性

根据部分相干光的传输理论,研究了部分相干高斯 贝塞尔涡旋光束通过光阑透镜聚焦后的传输和空间相关性质.数值计算结果表明,涡旋暗核的大小和焦平面上的光谱相干度都取决于入射光的拓扑电荷n、截断参量δ、相对相干长度σg和参量α.当选择适当的参量,在几何焦点附近会出现局域空心光束.研究还发现在焦面上光谱相干度会产生一个或多个的相位奇点（相干涡旋）,而且拓扑电荷和相对相干长度会对相干涡旋的位置和个数产生影响.在相干极限下,相干涡旋可逐渐演变为光学涡旋.     

Reciprocity relations for scattering from quasi-homogeneous anisotropic media

Valid within the accuracy of the first-order Born approximation, we obtain the analytical expressions of the three-dimensional spatial Fourier transforms, which show the reciprocity relations for the scattering of a polychromatic plane wave incident upon a Gaussian-correlated, quasi-homogeneous, anisotropic scatterer. We find that the spectral degree of coherence of the scattered field is only related with the effective radius of the scatterer and the normalized spectral density of the scattered field is only related with the correlation length of the scatterer.     

Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams

By expanding the Debye theory into the tight focusing of partially coherent field, the intensity and spatial correlation properties of partially coherent radially polarized vortex beams are studied. Expressions are derived for the intensity distribution and the spectral degree of coherence in the focal region. It is found that the intensity and the transverse and longitudinal coherence degrees in the focal region change with the variation of the topological charge and coherence length of the vortex beam. In addition, the degree of coherence is shown to exhibit phase singularities.     

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.     

Experimental demonstration of an intensity minimum at the focus of a laser beam created by spatial coherence: application to the optical trapping of dielectric particles

In trying to manipulate the intensity distribution of a focused field, one typically uses amplitude or phase masks. Here we explore an approach, namely, varying the state of spatial coherence of the incident field. We experimentally demonstrate that the focusing of a Bessel-correlated beam produces an intensity minimum at the geometric focus rather than a maximum. By varying the spatial coherence width of the field, which can be achieved by merely changing the size of an iris, it is possible to change this minimum into a maximum in a continuous manner. This method can be used, for example, in novel optical trapping schemes, to selectively manipulate particles with either a low or high index of refraction.     

Fourier-domain low-coherence interferometry for light-scattering spectroscopy

We present a novel method for obtaining depth-resolved spectra for determining scatterer size through elastic-scattering properties. Depth resolution is achieved with a white-light source in a Michelson interferometer with the mixed signal and reference fields dispersed by a spectrograph. The spectrum is Fourier transformed to yield the axial spatial cross correlation between the signal and reference fields with near 1-microm depth resolution. Spectral information is obtained by windowing to yield the scattering amplitude as a function of wave number. The technique is demonstrated by determination of the size of polystyrene microspheres in a subsurface layer with subwavelength accuracy. Application of the technique to probing the size of cell nuclei in living epithelial tissues is discussed.     

大气湍流对部分相干厄米-高斯光束空间相干性的影响

基于广义惠更斯-菲涅耳原理,并采用Rytov相位结构函数二次近似,推导出了部分相干厄米-高斯(H-G)光束通过大气湍流传输的光谱相干度公式,研究了湍流对光束的空间相干特性的影响.研究表明,部分相干H-G光束通过大气湍流传输其光谱相干度会出现振荡和相位奇异现象,但随着湍流的增强,振荡减弱,直至振荡和相位奇异现象消失,这一特性与高斯-谢尔模型光束的差异很大.光束的相干参数越小,光束空间相干性受湍流的影响也越小.此外,还研究了光谱相干度二阶矩宽度与光谱强度二阶矩宽度间的关系,得到一些有意义的结果,并给出了合理的 关键词： 部分相干厄米-高斯光束 大气湍流 光谱相干度 二阶矩宽度     

部分相干涡旋光束在大气湍流中的远场传输特性

运用广义惠更斯-菲涅耳原理,详细研究了部分相干涡旋光束在湍流介质中的远场传输规律.研究表明,部分相干涡旋光束的光谱相干度及光强分布与光束的拓扑电荷数、空间相对相干长度及湍流介质的折射率结构常数等因素有关.在湍流介质中,光谱相干度存在相位奇点,并且随着空间相对相干长度的增大,相干涡旋逐渐演化为强度涡旋,而湍流介质的强弱对部分相干涡旋光束的影响则相反,随着湍流介质的折射率常数的增大,强度涡旋逐渐演化为相干涡旋.     

Correlation between amplitude and phase noise in a mode-locked Cr:LiSAF laser

The coherence function between the amplitude and phase fluctuations of a mode-locked Cr:LiSAF laser has been measured with a time-domain demodulation technique. A relatively large correlation has been found for the noise components that originate in the pump-power fluctuation. Through an examination of the modulation-induced change in the noise power spectral densities, the influences of pump-power and cavity-length variations on these fluctuations have been investigated.     

Spatial correlation properties of apertured partially coherent beams propagating through atmospheric turbulence

The spatial correlation properties of apertured partially coherent beams propagating through atmospheric turbulence are studied in detail. By using the quadratic approximation of the Rytov’s phase structure function and the finite complex Gaussian expansion of the aperture function, the closed-form expression for the spectral degree of coherence of apertured partially coherent beams in turbulence is derived. It is shown that the larger the aperture width h is, and the smaller the spatial correlation length σ₀ of the source is, the less the spatial correlation is affected by turbulence. Specially, the influence of turbulence on the spatial correlation for unapertured partially coherent beams is less than that for apertured ones. The spectral degree of coherence is shown to possess phase singularities for apertured partially coherent beams, but the phase singularities behavior disappears when the turbulence is strong enough, which is very different from the behavior of unapertured partially coherent beams. In addition, a comparison between the width of the spectral degree of coherence and that of the spectral intensity of apertured partially coherent beams in turbulence is also given, and some interesting results are obtained. The results are interpreted physically. PACS  42.68.Bz; 42.79.Ag; 42.25.Fx     

Statistics of ultrasonic scatterer size estimation with a reference phantom

A theoretical expression for the variance of scatterer size estimates is derived for a modified least squares size estimator used in conjunction with a reference phantom method for backscatter coefficient measurement. A Gaussian spatial autocorrelation function is assumed. Simulations and phantom experiments were performed to verify the results for backscatter and size variances. The dependence of size estimate errors upon free experimental parameters is explored. Implications of the findings for the optimization of scatterer size estimation are discussed. The utility of scatterer size parametric imaging is examined through the signal to noise ratio comparison with standard ultrasonic B-mode imaging.     

Focusing of Partially Coherent Vortex Beams by an Aperture Lens

The focusing properties of partially coherent vortex wave fields are studied. Expressions are derived for the intensity distribution and the degree of coherence near the geometrical focus. It is found that the size of coherence vortex dark core in the focal region depends on the topological charges and normalized coherence lengths. It is found that the desired vortex dark core near the geometrical focus can be generated by choosing appropriate values of parameters. The degree of coherence possesses a pair of phase singularities regions in the geometrical focus neighbourhood.     

Spatial statistics of a partially coherent wave in a randomly inhomogeneous cubic medium

The spatial statistics of a partially coherent light wave in a randomly inhomogeneous medium is considered on the basis of perturbation theory. The equations for the spatial coherence function of the light wave in a nonlinear irregular medium were solved. The variation in the fluctuation field dispersion, in its amplitude and phase, as well as the behavior of the radius of spatial correlation for various perturbations of the incident radiation, were investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 27, No. 1, pp. 56–64, January, 1984.     

Scatterer size estimation in pulse-echo ultrasound using focused sources: calibration measurements and phantom experiments

In a companion paper [T. A. Bigelow and W. D. O'Brien Jr., J. Acoust. Soc. Am. 116, 578 (2004)], theory, supported by simulations, showed that accurate scatterer size estimates could be obtained using highly focused sources provided that the derived generalized attenuation-compensation function was used and the velocity potential field near the focus could be approximated as a three-dimensional Gaussian. Herein, the theory is further evaluated via experimental studies. A calibration technique is developed to find the necessary equivalent Gaussian dimensions for a focused source using reflections obtained from a rigid plane scanned through the focus. Then, the theoretical analysis of focused sources is validated experimentally using three spherically focused ultrasound transducers to estimate the radius of glass beads imbedded in tissue mimicking phantoms. Both the impact of focusing (f/1, f/2, and f/4) and the effect of scatterer type (comparing glass bead results to simulation results that used scatterers with Gaussian impedance distributions) were tested. The simulated differences agree with the measured differences to within 2.5% provided that the comparison is made between the same scatterer type and sources with the same equivalent Gaussian dimensions. The improvement provided by the generalized attenuation-compensation function is greatly influenced by the type of scatterer whose size is being estimated and decreases as the wavelength dependence of the Gaussian depth of focus is reduced.     

Optimizing two-photon fluorescence of Coumarin dye by combined temporal–spatial pulse shaping

Two-photon fluorescence (TPF) process is an important research subject and can be optimized by pulse shaping techniques. In addition to temporal femtosecond pulse shaping by spectral phase modulation, we take into account of spatial configuration in the shaping process. The TPF of Coumarin 500 increases 40% with this additional modulation step. This spatial modulation results in not only transverse spatial profile variation but also effect of temporal redistribution at focus. We show that this spatial modulation is an important dimension for pulse shaping and optimization for TPF.     

Spatial correlation properties and phase singularity annihilation of Gaussian Schell-model beams in the focal region

By using the generalized Debye diffraction integral, this paper studies the spatial correlation properties and phase singularity annihilation of apertured Gaussian Schell-model （GSM） beams in the focal region. It is shown that the width of the spectral degree of coherence can be larger, less than or equal to the corresponding width of spectral density, which depends not only on the scalar coherence length of the beams, but also on the truncation parameter. With a gradual increase of the truncation parameter, a pair of phase singularities of the spectral degree of coherence in the focal plane approaches each other, resulting in subwavelength structures. Finally, the annihilation of pairs of phase singularities takes place at a certain value of the truncation parameter. With increasing scalar coherence length, the annihilation occurs at the larger truncation parameter. However, the creation process of phase singularities outside the focal plane is not found for GSM beams.     

The time-frequency characteristics of violin vibrato: modal distribution analysis and synthesis

A high-resolution time-frequency distribution, the modal distribution, is applied to the study of violin vibrato. The analysis indicates that the frequency modulation induced by the motion of the stopped finger on the string is accompanied by a significant amplitude variation in each partial of that note. Amplitude and frequency estimates for each partial are extracted from the modal distribution of ten pitches that span the range of the violin instrument. The frequency modulation is well-represented by a single sinusoid with a mean rate of 5.9 Hz and a mean excursion of +/- 15.2 cents. A spectral decomposition of the amplitude envelopes of the partials shows that the peaks lie primarily at integer multiples of the vibrato rate. These amplitude and frequency estimates are used in an additive synthesis model to generate synthetic replicates of violin vibrato. Simple approximations to these estimates are created, and synthesized sounds using these are evaluated perceptually by seven subjects using discrimination, nonmetric multidimensional scaling (MDS), and sound quality scoring tasks. It is found that the absence of frequency modulation has little effect on the perceptual response to violin vibrato, while the absence of amplitude modulation causes marked changes in both sound quality and MDS results. Low-order spectral decompositions of the amplitude and frequency estimates also occupy the same perceptual space as the original recording for a subset of the pitches studied.     

Role of spatial coherence in polarization tomography

We analyze an experimental setup in which a quasi-monochromatic spatially coherent beam of light is used to probe a paraxial optical scatterer. We discuss the effect of the spatial coherence of the probe beam on the Mueller matrix representing the scatterer. We show that, according to the degree of spatial coherence of the beam, the same scattering medium can be represented by different Mueller matrices. This result should serve as a warning for experimentalists.     

Significance and measurability of the phase of a spatially coherent optical field

In usual measurements of the phase of an optical field it is generally assumed that the field is monochromatic. In reality this assumption is never justified. The distinction between monochromaticity and complete spatial coherence is first discussed, and it is then shown that with every spatially coherent field (e.g., a laser mode) one can associate a monochromatic wave that, in a well-defined sense, represents the average behavior of the field. Its phase can be measured by standard interferometric techniques and also by techniques developed in recent years for the measurement of the spectral degree of coherence of fields of arbitrary states of coherence.