时域有限差分算法在超声非衍射波声场仿真中的应用
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摘要
对于生物医学超声成像而言,声场的计算机仿真是其重要的研究手段,也一直受到研究人员广泛的关注。使用声场仿真来研究超声成像,具有重复性好、精度较高、灵活性大、使用方便、成本较低等优点,这些优点在实际使用中表现的非常明显。
本文对时域有限差分算法在平面直角坐标系和柱坐标系下的超声场中的应用以及超声非衍射波的声场仿真进行了比较深入的研究。取得了如下几个方面的研究成果：
1.研究了平面直角坐标系和柱坐标系下超声场中的时域有限差分算法,给出了具体的空间离散方式、理论推导过程和递推公式。
2.对平面直角坐标系和柱坐标系下的仿真区域边界处做了二阶Mur吸收边界处理,对特殊位置上的角点也做了专门的处理,并最终将时域有限差分算法成功运用在超声非衍射波的声场仿真中,扶得令人满意的效果。
3.提出了一种基于非衍射波轴对称特性的简化生成方法,该方法利用一组同心环形超声换能器对非衍射波声源进行近似。该简化生成方法具有结构简单的优点。
In bio medical ultrasound imaging, acoustic field computer simulation is an important research means, mam researchers pay close attention to it.The useage of sound field simulation to study the ultrasound imaging has good repeatability, high precision, flexibility, efficiency and with low cost, these advantages are obvious in practical use.
This thesis concentrates on the finite difference time domain algorithm in plane rectangular coordinates and cylindrical coordinates of the ultrasonic field and the application of ultrasonic non diffraction wave field simulation. We got the following several aspects of research results:
1. This thesis studies the finite difference time domain algorithm in plane rectangular coordinates and cylindrical coordinates in ultrasonic field; it gives a specific spatial diseretization method, theoretical derivation and recursive formula.
2.In this thesis, the boundaries of ultrasound field in plane rectangular coordinates and cylindrical coordinates are calculated with second order Mur absorbing boundary condition, some individual points of the ultrasound field are calculated in a special way, and finally the FDTD algorithm is successfully used in ultrasonic non diffraction wave sound field simulation, the results are satisfactory.
3.This thesis proposed one simplified method which is based on the axis symmetry properties of non diffraction wave to make a nondiffraction field, the method uses a set of concentric annular ultrasonic transducers to obtain an approximation of non diffraction wave source.The simplified generation method has the advantage of simple structure.
This research is sponsored by "Research of Imaging Method with Bone Mineral Density Measurement BUA Parameter Based on Non-diffraction Beam"(No.60871087) of NSFC (National Science Foundation of China).
本文对时域有限差分算法在平面直角坐标系和柱坐标系下的超声场中的应用以及超声非衍射波的声场仿真进行了比较深入的研究。取得了如下几个方面的研究成果：
1.研究了平面直角坐标系和柱坐标系下超声场中的时域有限差分算法,给出了具体的空间离散方式、理论推导过程和递推公式。
2.对平面直角坐标系和柱坐标系下的仿真区域边界处做了二阶Mur吸收边界处理,对特殊位置上的角点也做了专门的处理,并最终将时域有限差分算法成功运用在超声非衍射波的声场仿真中,扶得令人满意的效果。
3.提出了一种基于非衍射波轴对称特性的简化生成方法,该方法利用一组同心环形超声换能器对非衍射波声源进行近似。该简化生成方法具有结构简单的优点。
In bio medical ultrasound imaging, acoustic field computer simulation is an important research means, mam researchers pay close attention to it.The useage of sound field simulation to study the ultrasound imaging has good repeatability, high precision, flexibility, efficiency and with low cost, these advantages are obvious in practical use.
This thesis concentrates on the finite difference time domain algorithm in plane rectangular coordinates and cylindrical coordinates of the ultrasonic field and the application of ultrasonic non diffraction wave field simulation. We got the following several aspects of research results:
1. This thesis studies the finite difference time domain algorithm in plane rectangular coordinates and cylindrical coordinates in ultrasonic field; it gives a specific spatial diseretization method, theoretical derivation and recursive formula.
2.In this thesis, the boundaries of ultrasound field in plane rectangular coordinates and cylindrical coordinates are calculated with second order Mur absorbing boundary condition, some individual points of the ultrasound field are calculated in a special way, and finally the FDTD algorithm is successfully used in ultrasonic non diffraction wave sound field simulation, the results are satisfactory.
3.This thesis proposed one simplified method which is based on the axis symmetry properties of non diffraction wave to make a nondiffraction field, the method uses a set of concentric annular ultrasonic transducers to obtain an approximation of non diffraction wave source.The simplified generation method has the advantage of simple structure.
This research is sponsored by "Research of Imaging Method with Bone Mineral Density Measurement BUA Parameter Based on Non-diffraction Beam"(No.60871087) of NSFC (National Science Foundation of China).
引文
曹晖.2001.时域有限差分法在光纤光场中的应用[D].华中师范大学.
曹培杰.马东.1999.有限衍射声束的特性及应用[J].生物医学工程学杂志.16(001)：112-115
杜功焕,朱哲民,龚秀芬.2001.声学基础[M].南京大学出版社.
杜宏伟.2007.生物医学超声中若干非线性问题的研究[D],合肥：中国科学技术大学.
杜宏伟,彭虎,江朝晖,et al.2007.基于Fourier-Bessel级数的Bessel型超声场二次谐波近场特性研究[J].物理学报,56(1)：6496r6502.
冯若.1993.超声诊断设备原理与设计[M].中国医药科技出版社.
冯若.1993.超声诊断设备原理与设计[M].中国医药科技出版社.
冯若.1999.超声手册[M].南京大学出版社.
冯若.2003.超声空化与超声治疗[J].自然杂志,25(6)：311-314.
冯若.2004.超声空化与超声医学[J].中华超声影像学杂志,13(001)：63-65.
冯若,王智彪.2002.实用超声治疗学[M].科学技术文献出版社
冯若,朱辉,邹建中.2006.高强度聚焦超声(HIFU)技术迅速发展的五年[J].声学技术.25(4)：387-392.
高本庆.1995.时域有限差分法[M].国防工业出版社.
高上凯.2002.对超声诊断仪器中若干新技术的点评[J].中国医疗器械信息,8(002)：5-6.
葛德彪,闫玉波.2005.电磁波时域有限差分方法[M].西安电子科技大学出版社
葛均波.2000.血管内超声波多普勒学[M].人民卫生出版社.
胡来平,刘占军.2003FDTD方法中的吸收边界条件[J].现代电子技术.26(9)：30-32.
黄丽芳.2001.FDTD法在光纤中的研究与应用[D].燕山大学.
黄文武.2005.弹性波和声波的时域仿真方法研究[J].天津大学学报,31.
李太宝.2005.计算声学：声场的方程和计算方法[M].科学出版社.
李晓东,张庆红.叶瑾琳.1999.气候学研究的若干理论问题[J],北京大学学报：自然科学版,35(1)：101-106.
林书玉.2004.超声换能器的原理及设计[M].科学出版社.
刘吉斌.2004.现代介入性超声诊断与治疗[M].科学技术文献出版社
马大猷.2004.现代声学理论基础[M].科学出版社
马万明.2008FDTD方法及其在电磁兼容问题中的应用[D].西安电子科技大学.
彭虎.2008.超声成像算法导论[M].中国科学技术大学出版社.
彭旗宇.2003.数字化医学超声成像方法的研究[D][D].清华犬学
舒贞权.2002.医学超声影像新技术综述[J].中国医疗器械信息.8(002)：9-14.
王长清,祝西里.1994.电磁场计算中的时域有限差分法[M].北京大学出版社.
王鸿樟.19991.声学及医学超声应用--生物医学学声学[M],上海交通大学出版社.
王威琪.汪源源.余建国.2002.诊断用医学超声学的现状[J].声学技术.(002).
徐瑶.彭虎.冯焕清.2011.基于吸收边界条件的平面直角坐标系下点声源声场的仿真[J].中国科学技术大学学报.41(11)：10)1 6-1021.
喻志远.1998.时域有限差分法计算中源的研究[J].电子科技大学学报.270(001)：43-46.
张关泉,魏素花.1998.声波方程吸收边界条件的稳定性分析[J][J].计算数学,20(1)：103-103.
张了俊,高木庆.1995.柱坐标系下FDTD算法的吸收边界条件[J].微波学报,11(003)：170-175.
周永吕,郭万学.2002.超声医学[M].
Berenger J P. 1994. A perfectly matched layer for the absorption of electromagnetic waves[J]. Journal of computational physics. 114(2): 185-200.
Brittingham J N. 1983. Focus waves modes in homogeneous Maxwell's equations: Transverse electric mode[J]. Journal of Applied Physics, 54(3): 1179-1189.
Calliada F, Campani R, Bottinelli O, et al. 1998. Ultrasound contrast agents: basic principles[J]. European journal of radiology, 27: S157-S160.
Caplan P, 2011. Cataloging Internet Resources[J]. Public Access-Computer Systems Review, 4(2): 61-66.
Cheng J, Lu J. Fourier based imaging method with steered plane waves and limited-diffraction array beams[C]//Fourier based imaging method with steered plane waves and limited-diffraction array beams. 1976-1979.
Cheng J, Lu J. 2006. Extended high-frame rate imaging method with limited-diffraction beams[J]. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, 53(5): 880-899.
Choi D H, Hoefer W J R. 1986. The finite-difference-time-domain method and its application to eigenvalue problems[J]. Microwave Theory and Techniques, IEEE Transactions on, 34(12): 1464-1470.
Christensen D A. 1988. Ultrasonic bioinstrumentation[M]. Wiley New York.
Curie J, Curie P. 1880. Development by pressure of polar electricity in hemihedral crystals with inclined faces[J]. Development by Pressure of Polar Electricity in Mem ihedraI Crystals with Inclined Faces.
Durnin J. 1987. Exact solutions for nondiffracting beams. I. The scalar theory[J]. J. Opt. Soc. Am. A. 4(4): 651-654.
Durnin J, Miceli Jr J, Eberly J. 1987. Diffraction-free beams[J]. Physical Review Letters, 58(15): 1499-1501.
Engquist B,Majda A. 1977. Absorbing boundary conditions for numerical simulation of waves[J]. Proceedings of the National Academy of Sciences. 74(5): 1765.
Evans D H. 1989. Doppler ultrasound: Physics, instrumentation, and clinical applications[M]. John Wilev & Sons.
Firestone F A. 1946. Supersonic inspection device[M]. Google Patents.
Fox P D, Holm S. 2002. Modeling of CW annular arrays using limited diffraction Bessel beams[J]. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on. 49(1): 85-93.
Germain L, Cheeke J. 1988. Generation and detection of high - order harmonics in liquids using a scanning acoustic microscope[J]. The Journal of the Acoustical Society of America, 83: 942.
Goldberg B B. 1988. Medical diagnostic ultrasound: a retrospective on its 40th anniversary[M]. Kodak Health Sciences.
Goldberg B B. 2001. Ultrasound Contrast Agents: Basic Principles And Clinical Applications Author: Barry B. Goldberg, Joel S Raichlen, Flemming[J].
Halliwell M. 2000. Doppler ultrasound: physics, instrumentation and signal processing[J]. Physiological Measurement, 21:425.
Holland R. 1983. THREDS: A finite-difference time-domain EMP code in 3D spherical coordinates[J]. Nuclear Science, IEEE Transactions on, 30(6): 4592-4595.
Hsu D. Margetan F, Thompson D. 1989. Bessel beam ultrasonic transducer: fabrication method and experimental results[J]. Applied physics letters, 55(20): 2066-2068.
Jensen J A. 1996. Estimation of blood velocities using ultrasound: A signal processing approach[M]. Cambridge Univ Pr.
Rasher J. Yee K. 1987. A numerical example of a 2-D scattering problem using a subgrid[J]. Applied Computational Electromagnetics Society Journal and Newsletter. 2(2): 75-102.
Kunz K S, Luebbers R J. 1993. The finite difference time domain method for electromagnetics[M]. CRC.
Leighton T. 1994. The acoustic bubble[M]. Academic Pr.
Lu J. 1995. Bowtie limited diffraction beams for low-sidelobe and large depth of field imaging[J]. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on. 42(6): 1050-1063.
Lu J. Improving accuracy of transverse velocity measurement with a new limited diffraction beam[C]//Improving accuracy of transverse velocity measurement with a new limited diffraction beam. IEEE,2: 1255-1260 vol. 1252.
Lu J. 1997. 2D and 3D high frame rate imaging with limited diffraction beams[J]. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, 44(4): 839-856.
Lu J. 1997. Limited diffraction array beams[J]. International journal of imaging systems and technology. 8(1):126-136.
Lu J. 1998. Experimental study of high frame rate imaging with limited diffraction beams[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on. 45(1):84-97.
Lu J. Cheng J. Wang J. 2006. High frame rate imaging system for limited diffraction array beam imaging with square-wave aperture weightings high frame rate imaging system for limited diffraction array beam imaging with square-wave aperture weightings[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on, 53(10):1796-1812.
Lu J. Greenleaf J. 1991. Pulse-echo imaging using a nondiffracting beam transducer[J]. Ultrasound in medicine & biology, 17(3): 265-281.
Lu J. Greenleaf J F. Evaluation of a nondiffracting transducer for tissue characterization[C]//Evaluation of a nondiffracting transducer for tissue characterization. IEEE: 795-798 vol. 792.
Lu J. Greenleaf J F. Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization[C]//Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization. 1733: 92-119.
Lu J. Song T K. Kinnick R R. et al. 1993. In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams[J]. Medical Imaging, IEEE Transactions on, 12(4): 819-829.
Lu J. Xu X L. Zou H. et al. 1995. Application of Bessel beam for Doppler velocity estimation[J]. Ultrasonics. Ferroelectrics and Frequency Control, IEEE Transactions on,42(4): 649-662.
Lu J.Zou H. Greenleaf J F. 1994. Biomedical ultrasound beam forming[J]. Ultrasound in medicine & biology. 20(5): 403-428.
Lu J. Zou H. Greenleaf J. F. 1995.Anew approach to obtain limited diffraction beams[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on, 42(5): 850-853.
Lu J Y. Greenleaf J. 1993. Sidelobe reduction for limited diffraction pulse-echo systems[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on, 40(6): 735-746.
Lu J Y. Greenleaf J F. 1990. Ultrasonic nondiffracting transducer for medical imaging[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on. 37(5): 438-447.
Lu J Y. Greenleaf J F. 1992. Nondiffracting X waves-exact solutions to free-space scalar wave equation and their Unite aperture realizations[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on. 39(1): 19-31.
Maloney J G. Smith G S. Scott Jr W R. 1990. Accurate computation of the radiation from simple antennas using the finite-difference time-domain method[J]. Antennas and Propagation. IEEE Transactions on. 38(7): 1059-1068.
Maxwell J C. 1873. A treatise on electricity and magnelism[M]. Clarendon Press.
Merewether D E. 1971. Transient currents induced on a metallic body of revolution by an electromagnetic pulse|Jj. Electromagnetic Compatibility, IEEE Transactions on. (2): 41-44.
Moore T G Biaschak .J G Taflove A. et al. 1988. Theory and application of radiation boundary operators[J]. Antennas and Propagation. IEEE. Transactions on. 36(12): 1797-1812.
Morse P M C. Ingard K U. 1986. Theoretical acoustics[M]. Princeton Univ Pr.
Mur G. 1981. Absorbing boundary conditions for the Unite-difference approximation of the time-domain electromagnetic-field equations[J]. Electromagnetic Compatibility, IEEE Transactions on, (4): 377-382.
Peng H, Lu J. High frame rate 2D and 3D imaging with a curved or cylindrical array[C]//High frame rate 2Dand 3D imaging with acurved or cylindrical array. IEEE,2: 1725-1728 vol. 1722.
Shung K K. 2006. Diagnostic ultrasound: Imaging and blood flow measurements[M]. CRC.
Sullivan D. 1990. Three-dimensional computer simulation in deep regional hyperthermia using the finite-difference time-domain method[J]. Microwave Theory and Techniques, IEEE Transactions on, 38(2): 204-211.
Szabo T L. 2004. Diagnostic ultrasound imaging: inside out[M]. Academic Press.
Szabo T E. 2004. Diagnostic ultrasound imaging: inside out[M]. Academic Press.
Taflove A. 1988. Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures[J]. Wave Motion. 10(6): 547-582.
Taflove A. Brodwin M E. 1975. Computation of the electromagnetic fields and induced temperatures within a model of the microwave-irradiated human eye[J]. Microwave Theory and Techniques, IEEE Transactions on, 23(11): 888-896.
Taflove A, Brodwin M E. 1975. Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations[J]. Microwave Theory and Techniques, IEEE Transactions on, 23(8): 623-630.
Taflove A, Hagness S C. 1995. Computational electrodynamics[M]. Artech house Boston.
Taflove A, Umashankar K R, Beker B, et al. 1988. Detailed FD-TD analysis of electromagnetic fields penetrating narrow slots and lapped joints in thick conducting screens[J]. Antennas and Propagation, IEEE Transactions on. 36(2): 247-257.
Umashankar K, Taflove A, 1982. A novel method to analyze electromagnetic scattering of complex objects[J]. Electromagnetic Compatibility, IEEE Transactions on. (4): 397-405.
Umashankar K, Taflove A, Beker B, 1987. Calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavily[J]. Antennas and Propagation, IEEE Transactions on. 35(11): 1248-1257.
Wells P N T. 1977. Biomedical ultrasonics|M]. Academic Press London.
Wells P N T. 1999. Ultrasonic imaging of the human body[J]. Reports on Progress in Physics. 62: 671.
Wells P N T. 2006. Ultrasound imaging[J]. Physics in medicine and bio logs. 51: R83.
Xiao lei Z. Mei K K. 1988. Time-domain finite difference approach to the calculation of the frequency-dependent characteristics of microstrip discontinuities[J]. Microwave Theory and Techniques. IEEE Transactions on, 36(12):1775-1787.
Yao X, Hu P. A Simplified Method for Simulating Zero-Order Bessel Beams Field[C]//A Simplified Method for Simulating Zero-Order Bessel Beams field. IEEE: 1-4.
Yee K. 1966. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media[J]. Antennas and Propagation. IEEE Transactions on, 14(3): 302-307.
Ying L. 2006. Numerical methods for exterior problems[M]. World Scientific Pub Co Inc.
Ziolkowski R W. 1985. Exact solutions of the wave equation with complex source locations[J]. Journal of Mathematical Physics, 26: 861.
曹培杰.马东.1999.有限衍射声束的特性及应用[J].生物医学工程学杂志.16(001)：112-115
杜功焕,朱哲民,龚秀芬.2001.声学基础[M].南京大学出版社.
杜宏伟.2007.生物医学超声中若干非线性问题的研究[D],合肥：中国科学技术大学.
杜宏伟,彭虎,江朝晖,et al.2007.基于Fourier-Bessel级数的Bessel型超声场二次谐波近场特性研究[J].物理学报,56(1)：6496r6502.
冯若.1993.超声诊断设备原理与设计[M].中国医药科技出版社.
冯若.1993.超声诊断设备原理与设计[M].中国医药科技出版社.
冯若.1999.超声手册[M].南京大学出版社.
冯若.2003.超声空化与超声治疗[J].自然杂志,25(6)：311-314.
冯若.2004.超声空化与超声医学[J].中华超声影像学杂志,13(001)：63-65.
冯若,王智彪.2002.实用超声治疗学[M].科学技术文献出版社
冯若,朱辉,邹建中.2006.高强度聚焦超声(HIFU)技术迅速发展的五年[J].声学技术.25(4)：387-392.
高本庆.1995.时域有限差分法[M].国防工业出版社.
高上凯.2002.对超声诊断仪器中若干新技术的点评[J].中国医疗器械信息,8(002)：5-6.
葛德彪,闫玉波.2005.电磁波时域有限差分方法[M].西安电子科技大学出版社
葛均波.2000.血管内超声波多普勒学[M].人民卫生出版社.
胡来平,刘占军.2003FDTD方法中的吸收边界条件[J].现代电子技术.26(9)：30-32.
黄丽芳.2001.FDTD法在光纤中的研究与应用[D].燕山大学.
黄文武.2005.弹性波和声波的时域仿真方法研究[J].天津大学学报,31.
李太宝.2005.计算声学：声场的方程和计算方法[M].科学出版社.
李晓东,张庆红.叶瑾琳.1999.气候学研究的若干理论问题[J],北京大学学报：自然科学版,35(1)：101-106.
林书玉.2004.超声换能器的原理及设计[M].科学出版社.
刘吉斌.2004.现代介入性超声诊断与治疗[M].科学技术文献出版社
马大猷.2004.现代声学理论基础[M].科学出版社
马万明.2008FDTD方法及其在电磁兼容问题中的应用[D].西安电子科技大学.
彭虎.2008.超声成像算法导论[M].中国科学技术大学出版社.
彭旗宇.2003.数字化医学超声成像方法的研究[D][D].清华犬学
舒贞权.2002.医学超声影像新技术综述[J].中国医疗器械信息.8(002)：9-14.
王长清,祝西里.1994.电磁场计算中的时域有限差分法[M].北京大学出版社.
王鸿樟.19991.声学及医学超声应用--生物医学学声学[M],上海交通大学出版社.
王威琪.汪源源.余建国.2002.诊断用医学超声学的现状[J].声学技术.(002).
徐瑶.彭虎.冯焕清.2011.基于吸收边界条件的平面直角坐标系下点声源声场的仿真[J].中国科学技术大学学报.41(11)：10)1 6-1021.
喻志远.1998.时域有限差分法计算中源的研究[J].电子科技大学学报.270(001)：43-46.
张关泉,魏素花.1998.声波方程吸收边界条件的稳定性分析[J][J].计算数学,20(1)：103-103.
张了俊,高木庆.1995.柱坐标系下FDTD算法的吸收边界条件[J].微波学报,11(003)：170-175.
周永吕,郭万学.2002.超声医学[M].
Berenger J P. 1994. A perfectly matched layer for the absorption of electromagnetic waves[J]. Journal of computational physics. 114(2): 185-200.
Brittingham J N. 1983. Focus waves modes in homogeneous Maxwell's equations: Transverse electric mode[J]. Journal of Applied Physics, 54(3): 1179-1189.
Calliada F, Campani R, Bottinelli O, et al. 1998. Ultrasound contrast agents: basic principles[J]. European journal of radiology, 27: S157-S160.
Caplan P, 2011. Cataloging Internet Resources[J]. Public Access-Computer Systems Review, 4(2): 61-66.
Cheng J, Lu J. Fourier based imaging method with steered plane waves and limited-diffraction array beams[C]//Fourier based imaging method with steered plane waves and limited-diffraction array beams. 1976-1979.
Cheng J, Lu J. 2006. Extended high-frame rate imaging method with limited-diffraction beams[J]. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, 53(5): 880-899.
Choi D H, Hoefer W J R. 1986. The finite-difference-time-domain method and its application to eigenvalue problems[J]. Microwave Theory and Techniques, IEEE Transactions on, 34(12): 1464-1470.
Christensen D A. 1988. Ultrasonic bioinstrumentation[M]. Wiley New York.
Curie J, Curie P. 1880. Development by pressure of polar electricity in hemihedral crystals with inclined faces[J]. Development by Pressure of Polar Electricity in Mem ihedraI Crystals with Inclined Faces.
Durnin J. 1987. Exact solutions for nondiffracting beams. I. The scalar theory[J]. J. Opt. Soc. Am. A. 4(4): 651-654.
Durnin J, Miceli Jr J, Eberly J. 1987. Diffraction-free beams[J]. Physical Review Letters, 58(15): 1499-1501.
Engquist B,Majda A. 1977. Absorbing boundary conditions for numerical simulation of waves[J]. Proceedings of the National Academy of Sciences. 74(5): 1765.
Evans D H. 1989. Doppler ultrasound: Physics, instrumentation, and clinical applications[M]. John Wilev & Sons.
Firestone F A. 1946. Supersonic inspection device[M]. Google Patents.
Fox P D, Holm S. 2002. Modeling of CW annular arrays using limited diffraction Bessel beams[J]. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on. 49(1): 85-93.
Germain L, Cheeke J. 1988. Generation and detection of high - order harmonics in liquids using a scanning acoustic microscope[J]. The Journal of the Acoustical Society of America, 83: 942.
Goldberg B B. 1988. Medical diagnostic ultrasound: a retrospective on its 40th anniversary[M]. Kodak Health Sciences.
Goldberg B B. 2001. Ultrasound Contrast Agents: Basic Principles And Clinical Applications Author: Barry B. Goldberg, Joel S Raichlen, Flemming[J].
Halliwell M. 2000. Doppler ultrasound: physics, instrumentation and signal processing[J]. Physiological Measurement, 21:425.
Holland R. 1983. THREDS: A finite-difference time-domain EMP code in 3D spherical coordinates[J]. Nuclear Science, IEEE Transactions on, 30(6): 4592-4595.
Hsu D. Margetan F, Thompson D. 1989. Bessel beam ultrasonic transducer: fabrication method and experimental results[J]. Applied physics letters, 55(20): 2066-2068.
Jensen J A. 1996. Estimation of blood velocities using ultrasound: A signal processing approach[M]. Cambridge Univ Pr.
Rasher J. Yee K. 1987. A numerical example of a 2-D scattering problem using a subgrid[J]. Applied Computational Electromagnetics Society Journal and Newsletter. 2(2): 75-102.
Kunz K S, Luebbers R J. 1993. The finite difference time domain method for electromagnetics[M]. CRC.
Leighton T. 1994. The acoustic bubble[M]. Academic Pr.
Lu J. 1995. Bowtie limited diffraction beams for low-sidelobe and large depth of field imaging[J]. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on. 42(6): 1050-1063.
Lu J. Improving accuracy of transverse velocity measurement with a new limited diffraction beam[C]//Improving accuracy of transverse velocity measurement with a new limited diffraction beam. IEEE,2: 1255-1260 vol. 1252.
Lu J. 1997. 2D and 3D high frame rate imaging with limited diffraction beams[J]. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, 44(4): 839-856.
Lu J. 1997. Limited diffraction array beams[J]. International journal of imaging systems and technology. 8(1):126-136.
Lu J. 1998. Experimental study of high frame rate imaging with limited diffraction beams[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on. 45(1):84-97.
Lu J. Cheng J. Wang J. 2006. High frame rate imaging system for limited diffraction array beam imaging with square-wave aperture weightings high frame rate imaging system for limited diffraction array beam imaging with square-wave aperture weightings[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on, 53(10):1796-1812.
Lu J. Greenleaf J. 1991. Pulse-echo imaging using a nondiffracting beam transducer[J]. Ultrasound in medicine & biology, 17(3): 265-281.
Lu J. Greenleaf J F. Evaluation of a nondiffracting transducer for tissue characterization[C]//Evaluation of a nondiffracting transducer for tissue characterization. IEEE: 795-798 vol. 792.
Lu J. Greenleaf J F. Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization[C]//Diffraction-limited beams and their applications for ultrasonic imaging and tissue characterization. 1733: 92-119.
Lu J. Song T K. Kinnick R R. et al. 1993. In vitro and in vivo real-time imaging with ultrasonic limited diffraction beams[J]. Medical Imaging, IEEE Transactions on, 12(4): 819-829.
Lu J. Xu X L. Zou H. et al. 1995. Application of Bessel beam for Doppler velocity estimation[J]. Ultrasonics. Ferroelectrics and Frequency Control, IEEE Transactions on,42(4): 649-662.
Lu J.Zou H. Greenleaf J F. 1994. Biomedical ultrasound beam forming[J]. Ultrasound in medicine & biology. 20(5): 403-428.
Lu J. Zou H. Greenleaf J. F. 1995.Anew approach to obtain limited diffraction beams[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on, 42(5): 850-853.
Lu J Y. Greenleaf J. 1993. Sidelobe reduction for limited diffraction pulse-echo systems[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on, 40(6): 735-746.
Lu J Y. Greenleaf J F. 1990. Ultrasonic nondiffracting transducer for medical imaging[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on. 37(5): 438-447.
Lu J Y. Greenleaf J F. 1992. Nondiffracting X waves-exact solutions to free-space scalar wave equation and their Unite aperture realizations[J]. Ultrasonics. Ferroelectrics and Frequency Control. IEEE Transactions on. 39(1): 19-31.
Maloney J G. Smith G S. Scott Jr W R. 1990. Accurate computation of the radiation from simple antennas using the finite-difference time-domain method[J]. Antennas and Propagation. IEEE Transactions on. 38(7): 1059-1068.
Maxwell J C. 1873. A treatise on electricity and magnelism[M]. Clarendon Press.
Merewether D E. 1971. Transient currents induced on a metallic body of revolution by an electromagnetic pulse|Jj. Electromagnetic Compatibility, IEEE Transactions on. (2): 41-44.
Moore T G Biaschak .J G Taflove A. et al. 1988. Theory and application of radiation boundary operators[J]. Antennas and Propagation. IEEE. Transactions on. 36(12): 1797-1812.
Morse P M C. Ingard K U. 1986. Theoretical acoustics[M]. Princeton Univ Pr.
Mur G. 1981. Absorbing boundary conditions for the Unite-difference approximation of the time-domain electromagnetic-field equations[J]. Electromagnetic Compatibility, IEEE Transactions on, (4): 377-382.
Peng H, Lu J. High frame rate 2D and 3D imaging with a curved or cylindrical array[C]//High frame rate 2Dand 3D imaging with acurved or cylindrical array. IEEE,2: 1725-1728 vol. 1722.
Shung K K. 2006. Diagnostic ultrasound: Imaging and blood flow measurements[M]. CRC.
Sullivan D. 1990. Three-dimensional computer simulation in deep regional hyperthermia using the finite-difference time-domain method[J]. Microwave Theory and Techniques, IEEE Transactions on, 38(2): 204-211.
Szabo T L. 2004. Diagnostic ultrasound imaging: inside out[M]. Academic Press.
Szabo T E. 2004. Diagnostic ultrasound imaging: inside out[M]. Academic Press.
Taflove A. 1988. Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures[J]. Wave Motion. 10(6): 547-582.
Taflove A. Brodwin M E. 1975. Computation of the electromagnetic fields and induced temperatures within a model of the microwave-irradiated human eye[J]. Microwave Theory and Techniques, IEEE Transactions on, 23(11): 888-896.
Taflove A, Brodwin M E. 1975. Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations[J]. Microwave Theory and Techniques, IEEE Transactions on, 23(8): 623-630.
Taflove A, Hagness S C. 1995. Computational electrodynamics[M]. Artech house Boston.
Taflove A, Umashankar K R, Beker B, et al. 1988. Detailed FD-TD analysis of electromagnetic fields penetrating narrow slots and lapped joints in thick conducting screens[J]. Antennas and Propagation, IEEE Transactions on. 36(2): 247-257.
Umashankar K, Taflove A, 1982. A novel method to analyze electromagnetic scattering of complex objects[J]. Electromagnetic Compatibility, IEEE Transactions on. (4): 397-405.
Umashankar K, Taflove A, Beker B, 1987. Calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavily[J]. Antennas and Propagation, IEEE Transactions on. 35(11): 1248-1257.
Wells P N T. 1977. Biomedical ultrasonics|M]. Academic Press London.
Wells P N T. 1999. Ultrasonic imaging of the human body[J]. Reports on Progress in Physics. 62: 671.
Wells P N T. 2006. Ultrasound imaging[J]. Physics in medicine and bio logs. 51: R83.
Xiao lei Z. Mei K K. 1988. Time-domain finite difference approach to the calculation of the frequency-dependent characteristics of microstrip discontinuities[J]. Microwave Theory and Techniques. IEEE Transactions on, 36(12):1775-1787.
Yao X, Hu P. A Simplified Method for Simulating Zero-Order Bessel Beams Field[C]//A Simplified Method for Simulating Zero-Order Bessel Beams field. IEEE: 1-4.
Yee K. 1966. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media[J]. Antennas and Propagation. IEEE Transactions on, 14(3): 302-307.
Ying L. 2006. Numerical methods for exterior problems[M]. World Scientific Pub Co Inc.
Ziolkowski R W. 1985. Exact solutions of the wave equation with complex source locations[J]. Journal of Mathematical Physics, 26: 861.
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