X射线局部显微CT伪全局算法及其应用研究
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摘要
特定材料的微结构是确定材料特性的关键。目前存在的材料测试方法很多，在这些方法中X射线显微CT(μCT)以其高分辨三维无损成像特点具有独特的优势。μCT被广泛的应用到材料科学中，包括材料的形变、疲劳和断裂，加工处理，腐蚀和环境相互作用等方面。而第三代同步辐射光源的投入使用进一步推动了μCT的应用。同步辐射光源的高单色性、高通量和高相干性使得基于同步辐射的μCT(SR-μ-CT)具有传统μCT难以比拟的优势。
随着材料科学的高速发展，人们对材料的微结构越来越关注，对μCT分辨率的要求也越来越高。现有技术条件下，所能制作的探测器大小有限。在探测器大小一定的情况下，更高的分辨率意味着更小的探测器视场(Field of view，FOV)。传统CT算法的全局特性意味着在μCT中样品要制作得更小。而在某些情况下，由于种种原因(例如样品易碎，制作太小可能会破坏样品内部微结构)，样品不能被制作得很小。由于FOV的限制，μCT分辨率不能很高，导致样品中某些精细结构不能在三维重构图中呈现。局部CT的出现成为解决这个问题的关键，由于算法的局部特性，在局部CT中样品不再受FOV的限制，对于大样品仍然可以得到高分辨率的三维结构。
局部CT上述优越性使得在最近几十年，涌现出各种不同的局部CT算法。这些局部算法在一定程度上缓解了人们对局部CT的需求。然而，现有局部算法或为定性的局部算法，或由于各种限制条件，不能广泛的应用到材料研究中。本文针对现有局部算法存在的问题，以实际应用为最终目的，致力于开展定量的局部CT算法研究及其应用，并将其与数据约束模型(data-constrained modeling, DCM)相结合，用于材料定量分析研究，取得了以下几方面的创新性成果：
1.提出了伪全局层析重构算法(pseudo-global tomography)。该算法利用传统滤波反投影算法(Filtered back projection, FBP)滤波函数的快速衰减特性及其丢失投影在重构区域的影响特点，设计了一有效的投影数据采集和预处理方法，很好的消除了由于投影数据截断所造成的伪影。通过对样品中已知材料的标定，该算法可以很好的进行定量局部重构。由于该算法是一种FBP算法，因此可以很好的移植到现有软件和设备上。
2.基于所提出的伪全局层析重构算法，编写了相应的局部CT重构程序。并用该程序对标准样品，煤样和兔腿骨局部投影数据进行了处理。程序用Matlab语言编写，通过该程序可以仅用局部投影数据重构出感兴趣区域(Region of interest，ROI)。
3.将伪全局层析重构算法和DCM相结合对煤样进行了局部定量实验研究，得到煤样成分的三维成分显微分布图。并与基于低倍全局CT的DCM计算结果进行了对比。分析结果表明，基于高分辨局部CT的DCM能够很好的进行样品局部区域三维成分分布的无损定量分析。相比基于低倍全局CT的DCM结果，该新的表征方法能够给出更多的样品局部区域精细结构，并能减少由于样品同一成分的CT重构值为区域分布所造成的孔隙率偏大的影响。材料组分显微结构的三维定量表征将使材料主要特性的预测成为可能，可以预见新表征方法在该领域将有广阔的应用前景。而在能源领域，对于非常规天然气储量的评估和开采等也有极大的应用潜力。
4.将伪全局层析重构算法应用到生物样品：兔腿骨。并和较低分辨率的全局重构进行了对比。结果表明，该局部算法不仅能够很好地对该生物样品的局部区域进行定量局部重构，还充分体现出了局部CT在细节成像方面的巨大优势。这为将该方法推广应用到类似生物样品上提供了研究参考，对于生物医学方面的研究具有重要意义。
The structure of specific material determines the material’s property. Currently, kinds ofmethods are used for materials’ testing. In these methods, X-ray micro-CT (μCT) as anon-destructive imaging technique providing maps of the interior structure of the sample has aunique advantage. X-ray μCT has been widely used in material science, specifically the study ofdeformation, fatigue and fracture, of processing and of the interactions between corrosion andenvironment. The third-generation synchrotron radiation (SR) further promotes the wide use ofμCT. The SR light source has the advantages of high-flux, high monochromatic and highcoherence, which makes SR-μCT has incomparable advantages compare with the traditionalμCT.
With high speed development of material science, the microstructures of material becomemore and more care about, and higher resolution been required in μCT. Under the condition ofexisting technology, the detector has a limited size. With the limited size of detector, higherresolution means smaller detector field of view (FOV). For some reasons (for example, thesample is fragile, the inner microstructure may broken when the sample is made too small), thesample can’t be made so small. In this case, the resolution of μCT can’t high enough to see somefine structures in the sample because of the limitation of FOV. The appearance of local CTbecomes the key to solve the problem. Because the local property, the sample can be bigger thanthe FOV of detector, and the resolution can be high enough to see the fine structure.
Because of this advantage, some local algorithms appeared in recent decades. Thesealgorithms alleviate the people’s demand for local CT in certain degree. But these algorithms orbelong qualitative local algorithm, or can’t be widely used in the material science for somerestricted condition. In order to solve these problems in the local CT, this paper aims at practicalapplication, dedicated to carry out the research and application of quantitative local CT. Andcombine with data-constrained modeling (DCM) to perform materials’ quantitative analysis. Themain contributions are summarized as follows:
1. A local algorithm pseudo-global tomography was proposed. The algorithm uses an effectivestrategy to collect and compensate the lost part of projections in the local CT according theFBP algorithm Filter’s quick attenuation and the affection of lost projections, which caneffectively reduce the artifacts caused by projection truncation. Using a known material tocalibrate the reconstruction, this local CT method can be used for quantitative X-ray imaging. The pseudo-global tomography is radically based on the conventional FBP algorithm, so it isconvenient to be transplanted into the extensively used programs and equipments based onFBP algorithm.
2. Developed a program for local CT reconstruction based on pseudo-global tomography. Andthe program had been used to process the local CT data of standard sample, coal sample andrabbit femur. The program compiled by matlab. The correct inner structure of the sampleamong all the region of interest (ROI) can be reconstructed using local projections by thisprogram.
3. Combined pseudo-global tomography with DCM to perform local quantitative analysis ofcoal sample, and get the3D distribution of composition in the coal sample. And comparedwith the result of low resolution global CT based DCM. It indicates that the3D distributionsof compositions in the ROI of the sample can be obtained nondestructively with localCT-based DCM. Compared with global-CT based DCM, the new approach can display finerstructures of compositions in the sample ROI. Elevated spatial resolution can reduce theover-estimation of void caused by broadened distribution of the CT reconstructed values,which is common in CT. Quantitative characterization of materials microstructures willenable quantitative prediction of their bulk properties. It can be foreseen that the newapproach has a vast application prospective in materials science. And it also has a greatpotential application in unconventional oil and gas resources evaluation and exploitation.
4. Apply pseudo-global tomography to biological sample rabbit femur for local quantitativereconstruction. And have a compare with traditional global reconstruction. The result showsthat this local CT algorithm not only performs well in quantitative local reconstruction of thesample’s local region, but also shows great advantage in resolution. This provides researchreference for applying the local algorithm to the similar sample, and has a significantmeaning for biomedical research.
随着材料科学的高速发展，人们对材料的微结构越来越关注，对μCT分辨率的要求也越来越高。现有技术条件下，所能制作的探测器大小有限。在探测器大小一定的情况下，更高的分辨率意味着更小的探测器视场(Field of view，FOV)。传统CT算法的全局特性意味着在μCT中样品要制作得更小。而在某些情况下，由于种种原因(例如样品易碎，制作太小可能会破坏样品内部微结构)，样品不能被制作得很小。由于FOV的限制，μCT分辨率不能很高，导致样品中某些精细结构不能在三维重构图中呈现。局部CT的出现成为解决这个问题的关键，由于算法的局部特性，在局部CT中样品不再受FOV的限制，对于大样品仍然可以得到高分辨率的三维结构。
局部CT上述优越性使得在最近几十年，涌现出各种不同的局部CT算法。这些局部算法在一定程度上缓解了人们对局部CT的需求。然而，现有局部算法或为定性的局部算法，或由于各种限制条件，不能广泛的应用到材料研究中。本文针对现有局部算法存在的问题，以实际应用为最终目的，致力于开展定量的局部CT算法研究及其应用，并将其与数据约束模型(data-constrained modeling, DCM)相结合，用于材料定量分析研究，取得了以下几方面的创新性成果：
1.提出了伪全局层析重构算法(pseudo-global tomography)。该算法利用传统滤波反投影算法(Filtered back projection, FBP)滤波函数的快速衰减特性及其丢失投影在重构区域的影响特点，设计了一有效的投影数据采集和预处理方法，很好的消除了由于投影数据截断所造成的伪影。通过对样品中已知材料的标定，该算法可以很好的进行定量局部重构。由于该算法是一种FBP算法，因此可以很好的移植到现有软件和设备上。
2.基于所提出的伪全局层析重构算法，编写了相应的局部CT重构程序。并用该程序对标准样品，煤样和兔腿骨局部投影数据进行了处理。程序用Matlab语言编写，通过该程序可以仅用局部投影数据重构出感兴趣区域(Region of interest，ROI)。
3.将伪全局层析重构算法和DCM相结合对煤样进行了局部定量实验研究，得到煤样成分的三维成分显微分布图。并与基于低倍全局CT的DCM计算结果进行了对比。分析结果表明，基于高分辨局部CT的DCM能够很好的进行样品局部区域三维成分分布的无损定量分析。相比基于低倍全局CT的DCM结果，该新的表征方法能够给出更多的样品局部区域精细结构，并能减少由于样品同一成分的CT重构值为区域分布所造成的孔隙率偏大的影响。材料组分显微结构的三维定量表征将使材料主要特性的预测成为可能，可以预见新表征方法在该领域将有广阔的应用前景。而在能源领域，对于非常规天然气储量的评估和开采等也有极大的应用潜力。
4.将伪全局层析重构算法应用到生物样品：兔腿骨。并和较低分辨率的全局重构进行了对比。结果表明，该局部算法不仅能够很好地对该生物样品的局部区域进行定量局部重构，还充分体现出了局部CT在细节成像方面的巨大优势。这为将该方法推广应用到类似生物样品上提供了研究参考，对于生物医学方面的研究具有重要意义。
The structure of specific material determines the material’s property. Currently, kinds ofmethods are used for materials’ testing. In these methods, X-ray micro-CT (μCT) as anon-destructive imaging technique providing maps of the interior structure of the sample has aunique advantage. X-ray μCT has been widely used in material science, specifically the study ofdeformation, fatigue and fracture, of processing and of the interactions between corrosion andenvironment. The third-generation synchrotron radiation (SR) further promotes the wide use ofμCT. The SR light source has the advantages of high-flux, high monochromatic and highcoherence, which makes SR-μCT has incomparable advantages compare with the traditionalμCT.
With high speed development of material science, the microstructures of material becomemore and more care about, and higher resolution been required in μCT. Under the condition ofexisting technology, the detector has a limited size. With the limited size of detector, higherresolution means smaller detector field of view (FOV). For some reasons (for example, thesample is fragile, the inner microstructure may broken when the sample is made too small), thesample can’t be made so small. In this case, the resolution of μCT can’t high enough to see somefine structures in the sample because of the limitation of FOV. The appearance of local CTbecomes the key to solve the problem. Because the local property, the sample can be bigger thanthe FOV of detector, and the resolution can be high enough to see the fine structure.
Because of this advantage, some local algorithms appeared in recent decades. Thesealgorithms alleviate the people’s demand for local CT in certain degree. But these algorithms orbelong qualitative local algorithm, or can’t be widely used in the material science for somerestricted condition. In order to solve these problems in the local CT, this paper aims at practicalapplication, dedicated to carry out the research and application of quantitative local CT. Andcombine with data-constrained modeling (DCM) to perform materials’ quantitative analysis. Themain contributions are summarized as follows:
1. A local algorithm pseudo-global tomography was proposed. The algorithm uses an effectivestrategy to collect and compensate the lost part of projections in the local CT according theFBP algorithm Filter’s quick attenuation and the affection of lost projections, which caneffectively reduce the artifacts caused by projection truncation. Using a known material tocalibrate the reconstruction, this local CT method can be used for quantitative X-ray imaging. The pseudo-global tomography is radically based on the conventional FBP algorithm, so it isconvenient to be transplanted into the extensively used programs and equipments based onFBP algorithm.
2. Developed a program for local CT reconstruction based on pseudo-global tomography. Andthe program had been used to process the local CT data of standard sample, coal sample andrabbit femur. The program compiled by matlab. The correct inner structure of the sampleamong all the region of interest (ROI) can be reconstructed using local projections by thisprogram.
3. Combined pseudo-global tomography with DCM to perform local quantitative analysis ofcoal sample, and get the3D distribution of composition in the coal sample. And comparedwith the result of low resolution global CT based DCM. It indicates that the3D distributionsof compositions in the ROI of the sample can be obtained nondestructively with localCT-based DCM. Compared with global-CT based DCM, the new approach can display finerstructures of compositions in the sample ROI. Elevated spatial resolution can reduce theover-estimation of void caused by broadened distribution of the CT reconstructed values,which is common in CT. Quantitative characterization of materials microstructures willenable quantitative prediction of their bulk properties. It can be foreseen that the newapproach has a vast application prospective in materials science. And it also has a greatpotential application in unconventional oil and gas resources evaluation and exploitation.
4. Apply pseudo-global tomography to biological sample rabbit femur for local quantitativereconstruction. And have a compare with traditional global reconstruction. The result showsthat this local CT algorithm not only performs well in quantitative local reconstruction of thesample’s local region, but also shows great advantage in resolution. This provides researchreference for applying the local algorithm to the similar sample, and has a significantmeaning for biomedical research.
引文
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