透射式X射线工业CT中的能谱硬化和散射修正
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摘要
工业CT能以计算机图象的形式，清晰、直观、准确地呈现被测物体断面内部的结构、密度变化以及缺陷的性质、位置及大小。它不仅有很高的空间分辨率，而且有很高的密度分辨率。目前为止，工业CT被认为是最佳无损检测技术，它已广泛应用于航空航天、兵工、造船工业、精密仪器制造、石油勘测、冶金以及机械制造等各个高科技领域。但随着各高科技领域新的发展，工业CT的各项性能指标已不能完全满足实际的需要。如何提高工业CT的性能指标，如怎样进一步提高空间分辨率、密度分辨率，减少扫描时间，增大可测工件尺寸，改善图像质量等等成为了CT界面临的重要任务。而其中射线的能谱硬化和散射问题，又是制约工业CT各项性能指标提高的重要瓶颈之一。因而关于射线的能谱硬化和散射研究工作，成为人们广泛关注的课题。
本文在分析研究国内外有关射线能谱硬化和散射修正问题的分析方法及其研究状况的基础上，从射线同物质相互作用的物理学机理出发，从理论上近似推导了X射线能谱硬化和散射修正计算公式，建立了散射修正的分析模型，并编制了相应的计算机修正程序。其主要工作和结论如下：
（1）对X射线能谱硬化问题，把Klein-Nishina微分散射方程，利用泰勒级数展开，在忽略高次项的情形下，近似地推导出了能谱硬化修正公式。修正公式表明：
（a）X射线的衰减系数μ，它不仅与被测物质的性质有关，同时还是坐标位置x的函数，并在文中给出了衰减系数μ与坐标位置x的函数表达式。
（b）利用本论文所推导出的能谱硬化修正公式，在图像重建时编制一个程序进行能谱硬化修正是切实可行的。
（2）对X光子的散射问题，从产生散射现象的物理学机理出发，结合所建立的理想散射模型，推导出了各探测器在理想的情形下所探测到的散射光子数计算公式，并编制了散射光子计算程序。通过计算表明：
（a）通过散射光子计算公式所得数据与新西兰科学家C. J. Leliveld和 J. G. Maas通过实验所得数据吻合得很好。这表明本文所推导的修正公式是合理的。
（b）本文所推导出的修正公式只适用于理想的圆柱形的工件，不适合不规则形状的非理想工件的散射修正。因而该修正公式有很大的局限性。还有待于进一步完善和补充。
ICT can clearly, directly and accurately show us the structure, density change, character of a absence, position and size of measured profile by computer image. ICT not only has very high-spatial resolution but also has very high-density resolution. So far, ICT has been broadly applicable to various high-tech fields, including aeronautics and astronautics, military industry, shipbuilding, precision instrument, oil reconnaissance, metallurgy and mechanism manufacture, and so on. ICT is considered the best Non-destructive testing technology. But with the development of the high-tech, many of ICT's capabilities can't satisfy the demand of the actual necessary. How improving the capability of ICT has become more and more an important task, for example, improving spatial resolution and density resolution, reducing scan time, enlarging the size of measure space, improving image quality, etc. Moreover the question of the energy spectrum hardening and the photon scattering is one of important bottleneck to restrict the improvement of ICT. So people have paid many attentions to the research of energy spectrum hardening and the photon scattering.
Reference to the convention means of the analysis and research for energy spectrum hardening and photon scattering in internal and external, and based on the physical mechanism of radial interacts with matter, this paper approximatively deduce a theoretical formula of correction of energy spectrum hardening and scattered radiation in Transmission Industrial X-ray Computerized Tomography from a ideal model. And presented a correction computer program. Following is our main work and important conclusions:
(1) The question of energy spectrum hardening. We used the Klein-Nishina's differential scatter formula, meanwhile utilize the Thaler progression to spread out, and neglected the high-power, and then we deduced a theoretical formula of correction of energy spectrum hardening. The formula show:
(a) The attenuation coefficient of X-ray not only connects with matter character, but also is a function with coordinate X. This paper has offered their expression yet.
(b) That designing a program to correct the energy spectrum hardening during reconstructing image is feasible.
(2) The question of photon scattering. Based on the physical mechanism of scattering phenomenal and the scattering model, we concluded the formal that can
approximatively counts the scattering photons which are detected by detectors. We design a program to calculate the scattering photons and present:
(a) After we compared our results with the conclusions which C. J. Leliveld, J. G. Maas drawn through experiments we can find that both are consistent preferably, which show us that our formal is reasonable.
(b) Although our correct formulas fit with ideal columniform models, they don't suit erose work pieces. Because of this, those correct formulas have a very big disadvantage, so we should take lots of efforts to improve them in our future work.
本文在分析研究国内外有关射线能谱硬化和散射修正问题的分析方法及其研究状况的基础上，从射线同物质相互作用的物理学机理出发，从理论上近似推导了X射线能谱硬化和散射修正计算公式，建立了散射修正的分析模型，并编制了相应的计算机修正程序。其主要工作和结论如下：
（1）对X射线能谱硬化问题，把Klein-Nishina微分散射方程，利用泰勒级数展开，在忽略高次项的情形下，近似地推导出了能谱硬化修正公式。修正公式表明：
（a）X射线的衰减系数μ，它不仅与被测物质的性质有关，同时还是坐标位置x的函数，并在文中给出了衰减系数μ与坐标位置x的函数表达式。
（b）利用本论文所推导出的能谱硬化修正公式，在图像重建时编制一个程序进行能谱硬化修正是切实可行的。
（2）对X光子的散射问题，从产生散射现象的物理学机理出发，结合所建立的理想散射模型，推导出了各探测器在理想的情形下所探测到的散射光子数计算公式，并编制了散射光子计算程序。通过计算表明：
（a）通过散射光子计算公式所得数据与新西兰科学家C. J. Leliveld和 J. G. Maas通过实验所得数据吻合得很好。这表明本文所推导的修正公式是合理的。
（b）本文所推导出的修正公式只适用于理想的圆柱形的工件，不适合不规则形状的非理想工件的散射修正。因而该修正公式有很大的局限性。还有待于进一步完善和补充。
ICT can clearly, directly and accurately show us the structure, density change, character of a absence, position and size of measured profile by computer image. ICT not only has very high-spatial resolution but also has very high-density resolution. So far, ICT has been broadly applicable to various high-tech fields, including aeronautics and astronautics, military industry, shipbuilding, precision instrument, oil reconnaissance, metallurgy and mechanism manufacture, and so on. ICT is considered the best Non-destructive testing technology. But with the development of the high-tech, many of ICT's capabilities can't satisfy the demand of the actual necessary. How improving the capability of ICT has become more and more an important task, for example, improving spatial resolution and density resolution, reducing scan time, enlarging the size of measure space, improving image quality, etc. Moreover the question of the energy spectrum hardening and the photon scattering is one of important bottleneck to restrict the improvement of ICT. So people have paid many attentions to the research of energy spectrum hardening and the photon scattering.
Reference to the convention means of the analysis and research for energy spectrum hardening and photon scattering in internal and external, and based on the physical mechanism of radial interacts with matter, this paper approximatively deduce a theoretical formula of correction of energy spectrum hardening and scattered radiation in Transmission Industrial X-ray Computerized Tomography from a ideal model. And presented a correction computer program. Following is our main work and important conclusions:
(1) The question of energy spectrum hardening. We used the Klein-Nishina's differential scatter formula, meanwhile utilize the Thaler progression to spread out, and neglected the high-power, and then we deduced a theoretical formula of correction of energy spectrum hardening. The formula show:
(a) The attenuation coefficient of X-ray not only connects with matter character, but also is a function with coordinate X. This paper has offered their expression yet.
(b) That designing a program to correct the energy spectrum hardening during reconstructing image is feasible.
(2) The question of photon scattering. Based on the physical mechanism of scattering phenomenal and the scattering model, we concluded the formal that can
approximatively counts the scattering photons which are detected by detectors. We design a program to calculate the scattering photons and present:
(a) After we compared our results with the conclusions which C. J. Leliveld, J. G. Maas drawn through experiments we can find that both are consistent preferably, which show us that our formal is reasonable.
(b) Although our correct formulas fit with ideal columniform models, they don't suit erose work pieces. Because of this, those correct formulas have a very big disadvantage, so we should take lots of efforts to improve them in our future work.
引文
[1] 复旦大学等. 原子核物理实验方法（上册）[M].北京： 原子能出版社1981.58-68。
[2] 杨学恒、苏显素、赵炬. γ射线ICT中的能谱硬化和散射修正[J].CT理论与应用研究，1995(8):35-39。
[3] 杨学恒 一类γ射线工业CT系统设计的研究，重庆大学学报，1994.(11):67-70。
[4] ASTM Designation: E 1570-93; Standard Practice for Computed Tomographic(CT) Examination， Annual Book of ASTM Standards. Vol. 0303.
[5] Beshan Chiang et at， Spatial Resolution in Industrial Tomography， IEEE Transactions on Nuclear Science， Vol. Ns-30， No2， April 1983
[6] D. J. Gentle et al， Scattering and Attenuation Correction in Emission Tomography in the Nuclear Industry， App. Radiate. Isot， Vol. 41， pp975-979， 1990.
[7] P. Duvauchelle et al， Development of High Resolution Focusing Collimators Intended for Nondestructive testing by the Compton Scattering Tomography Technique， App. Radiate. Isot， Vol. 41， No. 2， pp199-205， 1990.
[8] J. Kosanetzky， Advanced Radioscopic Imaging Techniques Using Compton Back-scattered Radiation. 1991 Industrial Computed Tomography Topical Conference. Paper Summaries， pp106-109， May 20-24，1991.
[9] Berodias G. and G. Peix， Nondestructive Measurement of Density and Effective Atomic Nuclear by Photon Scattering， Materials Evaluation， Vol. 46， pp1209， 1988.
[10] C.J.Leiveld，J.G.Maas "On the Significance of Scattered Radiation in Industrial X-ray Computerized Tomographic Imaging IEEE TRANSACTIONS ON NUCLEAR SCIENCE Vol 41. NO.1.FEBRUARY 1994.）
[11] Trebes J E， Dolan K W， Haddad W S， et al. High Resolution， Large Area， High Energy x-ray tomgraphy[J]. SPIE， 1997， 3149: 173~176.
[12] Sauerwein C， Schekira S， Wiacker H. CT of High Performance for the Inspection of Large Objects [J/OL]. 1998.
[13] 夏正宇，朱产培，舒方武，等. 高能 X 射线图像处理系统与 KCT.第一届全国加速器无损检测设备及其应用技术交流会论文集[C]. 江西庐山：国家科学技术部工业司，1998， 66~70.
[14] Sivers E.A.and Wilver M.D. Performance of X-Ray Computed Tomographic Imaging System[J].Materials Evaluation， 1990，(11): 706-713.
[15] Reimers P.et al， Recent Developments in the industrial Application of Computerized Tomography with Ionizing Radiation ，NDT international ， 1984.17(.4):197.
[16] C.J.Leliveld，J.G.Maas， On the Significance of Scattered Radiation in Industrial X-ray Computerized Tomographic Imaging[J] IEEE Transactions on Nuclear Scuence. 1994，41(1):290.
[17] 王韶舜. 核与粒子物理实验方法[M] 北京：原子能出版社（1989）.
[18] K.H.穆辛[俄] 著 沈志通等 译 实验核物理学（第一卷）[M] 北京：原子能出版社（1991）
[19] 王沫然 编著 MATLAB6.0 与科学计算[M] 北京：电子工业出版社（2001）
[20] 张晓春 小波变换在无损检测中的应用 [Ｊ].无损检测 1997,19(3):61 - 63
[21] 赵荣春等 数字图象处理导论[M] 西北工业大学出版社,（1996）.
[22] 康克军 实验工业 CT系统及其图象重建方法研究 [博士学位论文 ].北京:清华大学工程物理系 1988
[23] 秦前清 杨宗凯 实用小波分析 [Ｍ ].西安:西安电子科技大学出版社,1994.
[24] 李成林 复合材料超声检测信号的小波分解与人工神经网络识别 [Ｄ].上海 :同济大学 1997
[25] 荆仁杰 等编 计算机图像处理[M] 杭州: 浙江大学出版社 1990 P447
[26] 尉可道 CT剂量的测量及其表达[J] 中华放射医学与防护杂志 ,1997. 17(5): 347
[27] 杨秀琼 医用图像诊断装置进展[J] 世界医疗器械 1995 13(1)45～48
[28] 陈鹤声主编 医用影像设备学[M] 北京：人民卫生出版社 1995
[29] 孙凡庚 第十二届世界无损检测学术会议概况 .无损检测 1990 ,(6):1～ 5
[30] 张李明 等 康普顿背散射图象重建技术[J] 中国科学技术大学学报 1996 26(4) 510-515
[31] Reimers P.et al， Recent Developments in the industrial Application of Computerized Tomography with Ionizing Radiation ，NDT international ， 1984.17(.4):197.
[32] C.J.Leliveld，J.G.Maas， On the Significance of Scattered Radiation in Industrial X-ray Computerized Tomographic Imaging[J] IEEE Transactions on Nuclear Scuence. 1994，41(1):290.
[33] 王韶舜. 核与粒子物理实验方法[M] 北京：原子能出版社（1989）.
[34] K.H.穆辛[俄] 著 沈志通等 译 实验核物理学（第一卷）[M] 北京：原子能出版社（1991）
[35] 王沫然 编著 MATLAB6.0 与科学计算[M] 北京：电子工业出版社（2001）
[36] 张晓春 小波变换在无损检测中的应用 [Ｊ].无损检测 1997,19(3):61 - 63
[37] 赵荣春等 数字图象处理导论[M] 西北工业大学出版社,（1996）.
[38] 康克军 实验工业 CT系统及其图象重建方法研究 [博士学位论文 ].北京:清华大学工程物理系 1988
[39] 秦前清 杨宗凯 实用小波分析 [Ｍ ].西安:西安电子科技大学出版社,1994.
[40] 李成林 复合材料超声检测信号的小波分解与人工神经网络识别 [Ｄ].上海 :同济大学 1997
[41] 荆仁杰 等编 计算机图像处理[M] 杭州: 浙江大学出版社 1990 P447
[42] 尉可道 CT剂量的测量及其表达[J] 中华放射医学与防护杂志 ,1997. 17(5): 347
[43] 杨秀琼 医用图像诊断装置进展[J] 世界医疗器械 1995 13(1)45～48
[44] 陈鹤声主编 医用影像设备学[M] 北京：人民卫生出版社 1995
[45] 孙凡庚 第十二届世界无损检测学术会议概况 .无损检测 1990 ,(6):1～ 5
[46] 张李明 等 康普顿背散射图象重建技术[J] 中国科学技术大学学报 1996 26(4) 510-515
[2] 杨学恒、苏显素、赵炬. γ射线ICT中的能谱硬化和散射修正[J].CT理论与应用研究，1995(8):35-39。
[3] 杨学恒 一类γ射线工业CT系统设计的研究，重庆大学学报，1994.(11):67-70。
[4] ASTM Designation: E 1570-93; Standard Practice for Computed Tomographic(CT) Examination， Annual Book of ASTM Standards. Vol. 0303.
[5] Beshan Chiang et at， Spatial Resolution in Industrial Tomography， IEEE Transactions on Nuclear Science， Vol. Ns-30， No2， April 1983
[6] D. J. Gentle et al， Scattering and Attenuation Correction in Emission Tomography in the Nuclear Industry， App. Radiate. Isot， Vol. 41， pp975-979， 1990.
[7] P. Duvauchelle et al， Development of High Resolution Focusing Collimators Intended for Nondestructive testing by the Compton Scattering Tomography Technique， App. Radiate. Isot， Vol. 41， No. 2， pp199-205， 1990.
[8] J. Kosanetzky， Advanced Radioscopic Imaging Techniques Using Compton Back-scattered Radiation. 1991 Industrial Computed Tomography Topical Conference. Paper Summaries， pp106-109， May 20-24，1991.
[9] Berodias G. and G. Peix， Nondestructive Measurement of Density and Effective Atomic Nuclear by Photon Scattering， Materials Evaluation， Vol. 46， pp1209， 1988.
[10] C.J.Leiveld，J.G.Maas "On the Significance of Scattered Radiation in Industrial X-ray Computerized Tomographic Imaging IEEE TRANSACTIONS ON NUCLEAR SCIENCE Vol 41. NO.1.FEBRUARY 1994.）
[11] Trebes J E， Dolan K W， Haddad W S， et al. High Resolution， Large Area， High Energy x-ray tomgraphy[J]. SPIE， 1997， 3149: 173~176.
[12] Sauerwein C， Schekira S， Wiacker H. CT of High Performance for the Inspection of Large Objects [J/OL]. 1998.
[13] 夏正宇，朱产培，舒方武，等. 高能 X 射线图像处理系统与 KCT.第一届全国加速器无损检测设备及其应用技术交流会论文集[C]. 江西庐山：国家科学技术部工业司，1998， 66~70.
[14] Sivers E.A.and Wilver M.D. Performance of X-Ray Computed Tomographic Imaging System[J].Materials Evaluation， 1990，(11): 706-713.
[15] Reimers P.et al， Recent Developments in the industrial Application of Computerized Tomography with Ionizing Radiation ，NDT international ， 1984.17(.4):197.
[16] C.J.Leliveld，J.G.Maas， On the Significance of Scattered Radiation in Industrial X-ray Computerized Tomographic Imaging[J] IEEE Transactions on Nuclear Scuence. 1994，41(1):290.
[17] 王韶舜. 核与粒子物理实验方法[M] 北京：原子能出版社（1989）.
[18] K.H.穆辛[俄] 著 沈志通等 译 实验核物理学（第一卷）[M] 北京：原子能出版社（1991）
[19] 王沫然 编著 MATLAB6.0 与科学计算[M] 北京：电子工业出版社（2001）
[20] 张晓春 小波变换在无损检测中的应用 [Ｊ].无损检测 1997,19(3):61 - 63
[21] 赵荣春等 数字图象处理导论[M] 西北工业大学出版社,（1996）.
[22] 康克军 实验工业 CT系统及其图象重建方法研究 [博士学位论文 ].北京:清华大学工程物理系 1988
[23] 秦前清 杨宗凯 实用小波分析 [Ｍ ].西安:西安电子科技大学出版社,1994.
[24] 李成林 复合材料超声检测信号的小波分解与人工神经网络识别 [Ｄ].上海 :同济大学 1997
[25] 荆仁杰 等编 计算机图像处理[M] 杭州: 浙江大学出版社 1990 P447
[26] 尉可道 CT剂量的测量及其表达[J] 中华放射医学与防护杂志 ,1997. 17(5): 347
[27] 杨秀琼 医用图像诊断装置进展[J] 世界医疗器械 1995 13(1)45～48
[28] 陈鹤声主编 医用影像设备学[M] 北京：人民卫生出版社 1995
[29] 孙凡庚 第十二届世界无损检测学术会议概况 .无损检测 1990 ,(6):1～ 5
[30] 张李明 等 康普顿背散射图象重建技术[J] 中国科学技术大学学报 1996 26(4) 510-515
[31] Reimers P.et al， Recent Developments in the industrial Application of Computerized Tomography with Ionizing Radiation ，NDT international ， 1984.17(.4):197.
[32] C.J.Leliveld，J.G.Maas， On the Significance of Scattered Radiation in Industrial X-ray Computerized Tomographic Imaging[J] IEEE Transactions on Nuclear Scuence. 1994，41(1):290.
[33] 王韶舜. 核与粒子物理实验方法[M] 北京：原子能出版社（1989）.
[34] K.H.穆辛[俄] 著 沈志通等 译 实验核物理学（第一卷）[M] 北京：原子能出版社（1991）
[35] 王沫然 编著 MATLAB6.0 与科学计算[M] 北京：电子工业出版社（2001）
[36] 张晓春 小波变换在无损检测中的应用 [Ｊ].无损检测 1997,19(3):61 - 63
[37] 赵荣春等 数字图象处理导论[M] 西北工业大学出版社,（1996）.
[38] 康克军 实验工业 CT系统及其图象重建方法研究 [博士学位论文 ].北京:清华大学工程物理系 1988
[39] 秦前清 杨宗凯 实用小波分析 [Ｍ ].西安:西安电子科技大学出版社,1994.
[40] 李成林 复合材料超声检测信号的小波分解与人工神经网络识别 [Ｄ].上海 :同济大学 1997
[41] 荆仁杰 等编 计算机图像处理[M] 杭州: 浙江大学出版社 1990 P447
[42] 尉可道 CT剂量的测量及其表达[J] 中华放射医学与防护杂志 ,1997. 17(5): 347
[43] 杨秀琼 医用图像诊断装置进展[J] 世界医疗器械 1995 13(1)45～48
[44] 陈鹤声主编 医用影像设备学[M] 北京：人民卫生出版社 1995
[45] 孙凡庚 第十二届世界无损检测学术会议概况 .无损检测 1990 ,(6):1～ 5
[46] 张李明 等 康普顿背散射图象重建技术[J] 中国科学技术大学学报 1996 26(4) 510-515
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