Three-dimensional reconstruction of biological objects' internal structure heterogeneity from the set of ultrasonic tomograms

The paper presents the method of the three-dimensional reconstruction of biological objects' internal structure heterogeneity based on the ultrasonic examination of a woman's breast biopsy phantom. The phantom is made of quasi-homogeneous dense gel in which drops of lesions, characterized by fixed sizes and two different acoustic impedances, were dipped at random. For the purpose of this research a special measurement setup was elaborated, enabling a non-invasive in vitro imaging of biological objects' internal structure in cross-sections for fixed levels, by means of ultrasound transmission tomography (UTT) using the parallel-ray projection geometry of scanning. The two-dimensional images of the local values of ultrasonic wave's propagation velocity in the phantom's internal structure (ultrasonic tomograms) were reconstructed for fixed levels (by using the convolution and back-projection algorithm) from the measurements of average values of ultrasonic signals' runtime propagated from many directions around the object dipped in water. Analyzing the values of particular pixels and using an appropriate image processing technique, in effect the three-dimensional image of heterogeneity boundaries in the examined phantom's internal structure was computer-reconstructed. The obtained results are compatible with the specification provided by the phantom's producer in terms of sizes and acoustic parameters of lesions, which can simulate pathological changes and of the gel imitating the healthy tissue. It means that the method presented, after an appropriate modification and development of the measurement setup with an aim to accelerate the object scanning process and thus provide an opportunity for non-invasive in vivo examinations, could be applied for detecting and diagnosing tumors in women's breasts.     

The ultrasonic probe for the investigating of internal object structure by ultrasound transmission tomography

The main component of every device used for investigating internal object structure by Ultrasound Transmission Tomography (UTT) is a special ultrasonic probe. This paper presents the structure of model multielement ring probe for examining objects using this method in divergent ray projection geometry. The probe is made up of 1024 rectangular separate piezoelectric transducers working at frequency f=1.7 MHz, placed inside a ring with diameter D=30 cm and height h=9 cm. Each element of the probe is equipped with a quarter-wave matching layer. All the transducers function as transmitters and receivers, and can be joined in groups both during transmitting and during receiving. Some examples of admittance characteristics of a single piezoelectric transducer and examples of shapes of pulses generated and received by particular transducers were presented. Important factors affecting the measurement resolution are the sizes of the active surface of the transducers.     

凹面相控阵聚焦声场在液固界面上的反射和折射

开展了凹面线性相控阵列辐射声场在液固界面上的反射和折射特性研究,利用射线近似方法,得到了凹面相控阵聚焦声场在液固界面上反射和折射后的声场渐近解析表达式,对声波在液固曲面上的反射和折射声场进行了分析和讨论. 利用这个解析表达式,对凹面线性聚焦声场在液固平界面和液固圆柱界面情况下固体中折射纵波和折射横波的相控阵声场进行了分析和讨论,发现凹面线阵声场在液固圆柱界面下比液固平界面具有更好的聚焦效果. 关键词： 凹面阵列 超声相控阵 反射与折射     

Horizontal refraction of propagating sound due to seafloor scours over a range-dependent layered bottom on the New Jersey shelf

Three-dimensional propagation effects of low frequency sound from 100 to 400 Hz caused by seafloor topography and range-dependent bottom structure over a 20 km range along the New Jersey shelf are investigated using a hybrid modeling approach. Normal modes are used in the vertical dimension, and a parabolic-equation approximate model is applied to solve the horizontal refraction equation. Examination of modal amplitudes demonstrates the effect of environmental range dependence on modes trapped in the water column, modes interacting with the bottom, and modes trapped in the bottom. Using normal mode ray tracing, topographic features responsible for three-dimensional effects of horizontal refraction and focusing are identified. These effects are observed in the measurements from the Shallow Water 2006 experiment. Specifically, signals from a pair of fixed sources recorded on a horizontal line array sitting on the seafloor show an intensification caused by horizontal focusing due to the seabed topography of 4 dB along the array.     

Recognition of external object features in gas media using ultrasound transmission tomography

The paper presents and analyzes a new way of recognizing external object features (shape, size, location) in gas media using ultrasound transmission tomography (UTT) with parallel-ray-projection scanning geometry. The concept of UTT in a gas medium is close to classical tomography, however because of the nature of the measurement environment, visualizing the internal structure of solid objects is difficult; whereas it is possible to image their external features: their shape, size and spatial location. The paper presents the results of examining the shape, size and location of different objects in the air in the form of tomographic images, obtained in parallel-ray-projection geometry, using a specially elaborated research setup for UTT. Applying parallel-ray-projection geometry enabled us to investigate the influence of scanning resolution on image quality. In order to test the operation of the elaborated algorithm of tomographic image reconstruction on the basis of correct measurement data, special software was written for simulating the binary matrix of the measurements for a set of a dozen or so solid objects of different shapes and a few simulations were performed.     

多层介质中超声相控阵声场仿真*

由于良好的声束偏转与聚焦特性,超声相控阵已经广泛应用于多层固体介质的缺陷检测。当超声束经过多层介质时,由于反射、透射以及模式转换的存在,多种声束存在于这种结构中,使得声场分析变得复杂。为了提高多层介质检测的准确性,有必要对超声声场的分布规律进行深入地了解。该文结合高斯声束等效点源模型以及射线追踪法,给出了相控阵声源在多层固体介质中激发声场的仿真方法,并且模拟计算了一维线型相控阵在楔块-铝-黄铜-钢四层固体介质中的辐射声场。通过对不同延时法则的计算,实现了声波在这种复杂介质中的偏转与聚焦,进而研究了不同焦点处聚焦声场的分布。结果表明:相控阵方法能使聚焦点处的声场幅值增大,能量集中,提高了检测分辨率;不同聚焦点处声场聚焦效果不同,实际检测时应根据检测区域结构及位置特点,合理放置相控阵换能器。与瑞利积分法的比较表明,该文的仿真方法适用于多层介质相控阵声场的计算。     

Analysis of Internal Conical Refraction Using Ray Tracing Formulas for the Biaxial Crystal

Internal or external conical refractions are strange optical phenomena appearing in biaxial crystal. In this paper the analysis of internal conical refraction is derived using the ray tracing formulas for the biaxial crystals, after explaining the theory of the ray tracing for the biaxial or uniaxial crystals. The double rings of conical refraction are also investigated; these are affected by the polarization state or angular intensity distributions of the incident light beam causing conical refraction.     

Thermally tempered glass surface stress measurement by critical ray

A critical ray was excited along the glass surface by laser beam incidence. Part of the critical ray was refracted during propagation. The angle of refraction depended on the refractive index of the glass sirface. When the glass surface was birefringent due to the photoelastic effect, the angles of refraction differed from each other between two linearly polarized beams. This difference allows surface stress determination.     

非寻常光的折射规律

在单轴晶体的光轴与入射面平行的情形下用费马原理计算非寻常光光线的折射角，然后就怎样定义非寻常光作些讨论，最后在单轴晶体的光轴任意取向的普遍情形下给出计算非寻常光光线折射方向的公式。     

Synchrotron radiation refraction topography for characterization of lightweight materials

The employment of synchrotron radiation for refraction topography of materials has considerable advantages over standard x‐ray sources. The much higher beam intensity and the parallel and monochromatic radiation provide faster measurements and better angular and spatial resolution. X‐ray refraction techniques image the inner surface and interface concentration of micro‐structured materials. This effect of x‐ray optics is additional to small‐angle scattering by diffraction, when the scattering objects reach micrometre dimensions. We have developed x‐ray refraction techniques within the last decade in order to meet the growing demands for improved non‐destructive characterization of high‐performance composites, ceramics and other low‐density materials. Sub‐micron particle dimensions, the pore size of ceramics, the crack density distribution and single fibre debonding within damaged composites can be measured and visualized by computer‐generated interface topographs. For this purpose investigations are now being performed at the new hard x‐ray beamline of the Federal Institute for Materials Research and Testing (BAM) at BESSY, Berlin. This BAMline provides monochromatic radiation of photon energies from 5 to 60 keV from a double multilayer and/or a double‐crystal monochromator. A separate instrument is dedicated to the further development and application of synchrotron radiation refraction (SRR) topography. Different from conventional small‐angle scattering cameras with collimating slits and pinholes, scattering angles down to a few seconds of arc are selected by a single‐crystal analyser, similar to a Bonse–Hart diffractometer. A 20 µm spatial resolution of the scattering micro‐structures is achieved by a CCD camera with a fluorescent converter. First SRR topographs of aircraft composites [carbon fibre‐reinforced plastics (CFRP), carbon fibre‐reinforced ceramics (C/C), metal matrix ceramics (MMC)] will be reported. Copyright © 2004 John Wiley & Sons, Ltd.     

A novel ray refraction matrix for curved interface

A problem in fundamental 2 × 2 ray matrix for refraction at curved interface proposed by A. E. Siegman was found out and a novel one was derived in this paper. An experiment is introduced in detail to verify the reasonability of the novel ray matrix. Using the novel 2 × 2 ray matrix, augmented 5 × 5 ray matrix of refraction at misaligned curved interface between media of different refractive indices was deduced. With the refraction matrix, it is easy to characterize the effect of an astigmatic thick lens. The augmented ray matrix approach was applied to model and estimate the performance of an optical alignment system. Utilizing these matrices, one can readily design and evaluate optical systems, where contain astigmatic elements such as tilted spherical or cylindrical lenses, mirrors and so on. These results are also useful for cavity design, alignment, ray tracing and beam position control in 3D optical systems.     

内外锥折射锥顶角的研究

利用光波面和光波法线面的曲线方程,得出了光波面上光轴角和光线轴角的表达式。以此为基础,借助内锥折射和外锥折射的性质及对应光波面上的位置关系,推导了内锥折射锥顶角和外锥折射锥顶角的表达式。并以堇青石和黄玉为例给出了具体的锥顶角数值大小,分析了锥顶角很小的原因。     

衍射增强成像信息分离方法研究

衍射增强成像（DEI）是一种功能强大的相位衬度成像技术,对于软组织,它能获得比基于吸收的传统X射线成像技术更高的衬度.研究了一种基于DEI的信息分离方法,它能同时获得三种参数图像,即吸收像、折射像和小角散射像.信息分离利用解析方程求解,获得的参数图像质量取决于在三个不同的分析晶体角度处获得的DEI图像.利用矩阵条件数对方程求解的稳定性进行了讨论,推导出理论上的折射角和小角散射宽度的最大值.最后,利用豚鼠耳蜗DEI图像对研究结果进行了验证. 关键词： 信息分离 衍射增强成像 矩阵条件数 豚鼠耳蜗     

A critical analysis of ultrasonic therapy.

The authors have examined the effect of ultrasonic irradiation on myopy. Fourty-two eyes of 24 patients were treated. In more than 76% of the cases, there was an average decrease of 1.04 D in refraction. When myopy was accompanied by astigmatism, this also decreased or even disappeared.     

Exhaustive study of reflection and refraction at spherical surfaces on the basis of the newly discovered generalized vectorial laws of reflection and refraction

This paper deals with the application of the newly discovered generalized vectorial laws of reflection and refraction for making an extensive analysis of reflection and refraction at spherical surfaces. Various cases of image formation have been considered. It has been observed that, direct application of the generalized vectorial laws of reflection and refraction leads to the appropriate formula of ray optics for each of the cases considered. The analysis of the results are ultimately summed up to give birth to the generalized mirror formula as well as the generalized formula for refraction at spherical surfaces. Also by using the results obtained for refraction at spherical surfaces, the Lens makers’ formulae have been finally offered.     

The coefficients of reflection and refraction on interface of the crystals in the Savart polariscope

According to the boundary conditions of the electromagnetic field, the coefficients of reflection and refraction on the interface of crystal in the Savart polariscope are obtained for ordinary ray (o-ray) and extraordinary ray (e-ray).The coefficients of reflection and refraction are different from an isotropic medium and have more complicated forms than isotropic medium.     

单轴晶体光轴任意取向时非寻常光的折射规律

在单轴晶体光轴任意取向的情形下 ,应用惠更斯原理导出了非寻常光折射方向的普遍计算公式 ,并给出了确定非寻常光线折射面和折射角的具体解。结合几种熟知的特殊情形进行了简要讨论 ,揭示了文中所得到的折射规律较之斯涅尔定律更具有普遍性 ,从而为光学系统中各类单轴晶体光学元件的应用提供了一个理论依据     

Measurements of Coster–Kronig enhancement factors of some elements in the atomic number range 66 ≤ Z ≤ 72

The Lι, Lα, Lβ and Lγ x‐ray production cross‐sections in four elements with Z ranging from 66 to 72 at seven different energies in the interval 8.265–11.730 keV were measured. Experimental measurements were carried out on a few elemental samples to examine the effect of Coster–Kronig transitions on fluorescence cross‐sections for the L x‐ray line using an Si(Li) detector system with an energy resolution of 160 eV at 5.96 keV x‐ray energy. Absolute values of L x‐ray cross‐sections were calculated with incorporation of the enhancement due to the Coster–Kronig effect for these elements. The measured enhancement factors are smaller than predicted by theory. Copyright © 2003 John Wiley & Sons, Ltd.     

Tomography in Optically Axisymmetric Media

A generalization of the Cormac algorithm for the inversion of the Radon transformation in an optical medium with an axisymmetric index of refraction has been proposed. The distribution of rays is such that only one ray passes through any two points in the circle. A “parallel scanning scheme” of tomography has been considered: a cylindrical object is illuminated by a parallel beam of light, the rays of which are deflected into the cylinder. There is no refraction on the surface of the cylinder. The algorithm assumes the possibility of attenuation on a ray, which also has an axisymmetric character. Such a type of ray deflection occurs in problematic issues of the tomography of GRADANs, light guides, and plasma.

     

基于声光折射的聚焦超声焦点声压检测

提出了一种基于声光折射对聚焦超声焦点声压进行非侵入式检测的方法。当一束直径小于声波长的平行光束入射穿过聚焦超声的焦点时,通过研究焦点声压与光线偏转的具体关系,建立了光线最大偏转距离与焦点声压变化的关系模型,从而计算出焦点峰值声压。为了对理论模型进行验证,采用凹球面型聚焦换能器进行实验研究。通过与采用光纤水听器测量的结果进行对比,证明理论模型的可行性。结果表明实验得到的光斑图像与理论分析的结果一致,且用该方法测得的焦点峰值声压与光纤水听器测量的结果相比,相对误差小于15%,证明该方法具有可行性,能够定量检测焦点峰值声压。模型的提出也为将声光折射效应用于整个聚焦声场的定量检测提供了实验依据和理论依据。