CN113805216B - Substance decomposition method for one-time exposure X-ray phase propagation imaging - Google Patents

Substance decomposition method for one-time exposure X-ray phase propagation imaging Download PDF

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CN113805216B
CN113805216B CN202111091433.9A CN202111091433A CN113805216B CN 113805216 B CN113805216 B CN 113805216B CN 202111091433 A CN202111091433 A CN 202111091433A CN 113805216 B CN113805216 B CN 113805216B
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王志立
陈恒
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Hefei University of Technology
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Abstract

The invention discloses a material decomposition method for one-time exposure X-ray phase propagation imaging, which is applied to an X-ray phase propagation imaging system formed by sequentially arranging an X-ray source and a single photon counting detector along the Z axis; x-rays emitted by an X-ray source are transmitted to an imaged object after penetrating through the imaged object and are incident to a single photon counting detector after freely propagating a certain space distance; the intensity distribution of the incident X-rays is measured and recorded by a single photon counting detector; and processing the light intensity data recorded by the single photon counting detector by using a material decomposition algorithm to obtain a material decomposition result of the imaged object. The invention can solve the problems of quantitative and accurate substance decomposition of an imaged object under one exposure, and improves the experimental efficiency of X-ray phase propagation imaging; thereby avoiding pixel registration artifact and motion artifact and improving the accuracy of the substance decomposition result of the imaged object.

Description

一种一次曝光的X射线相位传播成像的物质分解方法A Material Decomposition Method for Single-Exposure X-ray Phase Propagation Imaging

技术领域technical field

本发明涉及X射线投影成像领域，具体的说是一种一次曝光的X射线相位传播成像的物质分解方法。The invention relates to the field of X-ray projection imaging, in particular to a material decomposition method for one-time exposure X-ray phase propagation imaging.

背景技术Background technique

经过二十多年来的成像理论完善和应用探索研究，X射线相位传播成像已经发展成为传统X射线成像技术的强力补充。原理上来说，被成像物体的吸收信号和相移信号对探测器直接测量的强度分布都有显著贡献。利用发展的信号提取公式，能够从探测器测量的强度数据中，提取得到被成像物体的吸收信号和相移信号。特别的，X射线相位传播成像对被成像物体内部不同材料的分界面非常敏感，能够区分、识别不同材料的空间分布。另外，X射线相位传播成像还具有高密度分辨率、高空间分辨率等优点，在临床乳腺成像、肺部病变早期诊断、公共安全检查等领域具有广阔的应用前景。After more than 20 years of imaging theory improvement and application exploration research, X-ray phase propagation imaging has developed into a powerful supplement to traditional X-ray imaging technology. In principle, both the absorption signal of the imaged object and the phase shift signal contribute significantly to the intensity distribution directly measured by the detector. Using the developed signal extraction formula, the absorption signal and phase shift signal of the imaged object can be extracted from the intensity data measured by the detector. In particular, X-ray phase propagation imaging is very sensitive to the interface of different materials inside the imaged object, and can distinguish and identify the spatial distribution of different materials. In addition, X-ray phase propagation imaging also has the advantages of high density resolution and high spatial resolution, and has broad application prospects in clinical breast imaging, early diagnosis of lung lesions, and public safety inspections.

在X射线相位传播成像中，物质分解方法能够实现对不同物质材料的识别，在医学成像、无损检测等领域具有重要的应用价值。现有物质分解方法是利用能量积分探测器，对被成像物体先后进行两次曝光来测量得到两个不同能量区间的X射线强度数据。即现有物质分解方法要求的两个不同光强数据不是同时获取的。两个不同光强数据的非同时获取会严重降低X射线相位传播成像的物质分解结果的准确性。第一，现有物质分解方法要求对被成像物体进行先后两次曝光，以测量两个不同的光强数据。这就降低了X射线相位传播成像的实验效率。第二，外部振动等因素会导致非同时获取的两个光强数据不可避免地存在像素偏移。因此，在计算物质分解结果前，现有方法要求先对两个光强数据进行像素配准。但是，像素配准的插值计算会引入光强数据误差，进而导致物质分解结果的像素配准伪影，降低物质分解结果的准确性。第三，被成像物体总是有着一定内部或外部运动的。这就导致非同时获取的被成像物体的两个光强数据存在有像素偏移。类似地，需要对两个光强数据进行基于插值运算的像素配准。这就不可避免地引入了光强数据误差，导致物质分解结果的准确性的下降。这些局限性制约了X射线相位传播成像的物质分解在临床医学诊疗、安全检查等领域的推广应用。因此，发展新的X射线相位传播成像的物质分解方法，就成为X射线相位传播成像在实际推广应用中需要解决的问题之一。In X-ray phase propagation imaging, the material decomposition method can realize the identification of different materials, and has important application value in medical imaging, non-destructive testing and other fields. The existing material decomposition method is to use an energy integrating detector to expose the object to be imaged twice successively to measure and obtain X-ray intensity data in two different energy intervals. That is, the two different light intensity data required by the existing material decomposition method are not acquired simultaneously. The non-simultaneous acquisition of two different light intensity data will seriously reduce the accuracy of the material decomposition results of X-ray phase propagation imaging. First, the existing material decomposition method requires two successive exposures of the imaged object to measure two different light intensity data. This reduces the experimental efficiency of X-ray phase propagation imaging. Second, factors such as external vibration will inevitably lead to pixel offset in the two light intensity data acquired not at the same time. Therefore, prior to calculating the material decomposition results, existing methods require pixel registration of the two light intensity data. However, the interpolation calculation of pixel registration will introduce light intensity data errors, which will lead to pixel registration artifacts in the material decomposition results and reduce the accuracy of the material decomposition results. Third, the imaged object always has some internal or external motion. This results in a pixel offset in the two light intensity data of the imaged object that are not acquired at the same time. Similarly, pixel registration based on interpolation operation needs to be performed on two light intensity data. This inevitably introduces light intensity data errors, leading to a decrease in the accuracy of the material decomposition results. These limitations restrict the popularization and application of material decomposition of X-ray phase propagation imaging in clinical medical diagnosis and treatment, safety inspection and other fields. Therefore, the development of a new material decomposition method for X-ray phase propagation imaging has become one of the problems to be solved in the practical application of X-ray phase propagation imaging.

发明内容Contents of the invention

本发明为避免现有X射线相位传播成像的物质分解方法的不足，提出一种一次曝光的X射线相位传播成像的物质分解方法，以期在对被成像物体仅进行一次曝光时，能够从单光子计数探测器测量的光强数据中定量获得被成像物体的物质分解结果，从而为实现快速、准确、高效的X射线相位传播成像的物质分解提供新途径。In order to avoid the deficiencies of the existing X-ray phase propagation imaging material decomposition method, the present invention proposes a single-exposure X-ray phase propagation imaging material decomposition method, with the hope that when the imaged object is only exposed once, it can be obtained from single photon Quantitatively obtain the material decomposition results of the imaged object from the light intensity data measured by the counting detector, thus providing a new way to realize the material decomposition of fast, accurate and efficient X-ray phase propagation imaging.

为达到上述发明目的，本发明采用如下技术方案：In order to achieve the above-mentioned purpose of the invention, the present invention adopts the following technical solutions:

本发明一种一次曝光的X射线相位传播成像的物质分解方法，是应用于由X射线源、单光子计数探测器组成的X射线相位传播成像系统中；The present invention is a material decomposition method for one-time exposure X-ray phase propagation imaging, which is applied to an X-ray phase propagation imaging system composed of an X-ray source and a single-photon counting detector;

以所述X射线源的位置点为坐标系原点O，以射线轴方向为Z轴向，垂直于射线轴、且平行于所述单光子计数探测器的水平列方向为Y轴向，以共同垂直于射线轴和所述单光子计数探测器的水平列方向为X轴向，建立直角坐标系O-XYZ；Taking the position point of the X-ray source as the origin O of the coordinate system, taking the direction of the ray axis as the Z-axis, and the direction perpendicular to the ray axis and parallel to the horizontal column direction of the single-photon counting detector as the Y-axis, with a common The horizontal column direction perpendicular to the ray axis and the single photon counting detector is the X axis, and a rectangular coordinate system O-XYZ is established;

在沿Z轴向上依次设置有所述X射线源、单光子计数探测器；设置所述X射线源与所述单光子计数探测器在沿Z轴向上的相对距离为L12；设置所述X射线源、单光子计数探测器在沿X轴向上中心对齐、在沿Y轴向上中心对齐；其特点是，所述X射线相位传播成像的物质分解方法是按如下步骤进行：The X-ray source and the single-photon counting detector are sequentially arranged along the Z-axis; the relative distance between the X-ray source and the single-photon-counting detector along the Z-axis is set to be L 12 ; the set The X-ray source and the single-photon counting detector are centered along the X-axis and centered along the Y-axis; it is characterized in that the material decomposition method of the X-ray phase propagation imaging is carried out in the following steps:

步骤1、获取背景光强数据：Step 1. Obtain background light intensity data:

步骤1.1、启动所述单光子计数探测器，设置所述单光子计数探测器的第一能量阈值为E1；设置所述单光子计数探测器的第二能量阈值为E2，且满足E1<E2；设置曝光时长为T；Step 1.1, start the single photon counting detector, set the first energy threshold of the single photon counting detector to E1; set the second energy threshold of the single photon counting detector to E2, and satisfy E1<E2; Set the exposure time to T;

步骤1.2、启动所述X射线源，设置所述X射线源的管电压为E3，且满足E2<E3；Step 1.2, start the X-ray source, set the tube voltage of the X-ray source to E3, and satisfy E2<E3;

步骤1.3、利用所述单光子计数探测器按照所述曝光时长T同时获取在能量区间[E1 E2]的X射线强度下的第一背景光强数据

Figure BDA0003267641840000021
以及在能量区间[E2E3]的X射线强度下的第二背景光强数据/>
Figure BDA0003267641840000022
Step 1.3, using the single photon counting detector to simultaneously acquire the first background light intensity data under the X-ray intensity in the energy interval [E1 E2] according to the exposure time T
Figure BDA0003267641840000021
and the second background light intensity data at the X-ray intensity in the energy interval [E2E3]/>
Figure BDA0003267641840000022

步骤1.4、关闭所述X射线源和所述单光子计数探测器；Step 1.4, closing the X-ray source and the single photon counting detector;

步骤2、获取被成像物体的光强数据：Step 2. Obtain the light intensity data of the imaged object:

步骤2.1、将被成像物体沿Z轴向放置在所述X射线源和所述单光子计数探测器的中间；并将所述X射线源与所述被成像物体在沿Z轴向上的相对距离记为L13，且满足0＜L13＜L12；设置所述被成像物体与所述单光子计数探测器在沿X轴向上中心对齐、在沿Y轴向上中心对齐；Step 2.1, placing the object to be imaged in the middle of the X-ray source and the single photon counting detector along the Z axis; The distance is denoted as L 13 , and it satisfies 0<L 13 <L 12 ; set the object to be imaged and the single photon counting detector to be center-aligned along the X-axis and center-aligned along the Y-axis;

步骤2.2、启动所述单光子计数探测器，设置所述单光子计数探测器的第一能量阈值仍为E1；设置所述单光子计数探测器的第二能量阈值仍为E2；设置曝光时长仍为T；Step 2.2, start the single photon counting detector, set the first energy threshold of the single photon counting detector to still be E1; set the second energy threshold of the single photon counting detector to still be E2; set the exposure time to still be E2; for T;

步骤2.3、启动所述X射线源，设置所述X射线源的管电压仍为E3；Step 2.3, start the X-ray source, and set the tube voltage of the X-ray source to still be E3;

步骤2.4、利用所述单光子计数探测器按照所述曝光时长T同时获取在能量区间[E1 E2]的X射线强度下所述被成像物体的第一光强数据

Figure BDA0003267641840000031
以及在能量区间[E2E3]的X射线强度下所述被成像物体的第二光强数据/>
Figure BDA0003267641840000032
Step 2.4, using the single photon counting detector to simultaneously acquire the first light intensity data of the imaged object under the X-ray intensity in the energy interval [E1 E2] according to the exposure time T
Figure BDA0003267641840000031
And the second light intensity data of the object to be imaged under the X-ray intensity in the energy interval [E2E3]
Figure BDA0003267641840000032

步骤2.5、关闭所述X射线源和所述单光子计数探测器；Step 2.5, turning off the X-ray source and the single photon counting detector;

步骤3、对所述被成像物体的第一光强数据

Figure BDA0003267641840000033
进行归一化处理，得到归一化的第一光强数据I1，且满足/>
Figure BDA0003267641840000034
Step 3, the first light intensity data of the imaged object
Figure BDA0003267641840000033
Perform normalization processing to obtain the normalized first light intensity data I 1 , and satisfy />
Figure BDA0003267641840000034

步骤4、对所述被成像物体的第二光强数据

Figure BDA0003267641840000035
进行归一化处理，得到归一化的第二光强数据I2，且满足/>
Figure BDA0003267641840000036
Step 4, the second light intensity data of the imaged object
Figure BDA0003267641840000035
Perform normalization processing to obtain normalized second light intensity data I 2 , and satisfy />
Figure BDA0003267641840000036

步骤5、对归一化的第一光强数据I1进行取对数处理，得到第一处理结果ln(I1)；Step 5. Logarithmic processing is performed on the normalized first light intensity data I 1 to obtain the first processing result ln(I 1 );

步骤6、对归一化的第二光强数据I2进行取对数处理，得到第二处理结果ln(I2)；Step 6. Perform logarithmic processing on the normalized second light intensity data I 2 to obtain the second processing result ln(I 2 );

步骤7、对第一处理结果ln(I1)作二维傅里叶变换，得到第一变换结果F1；Step 7, performing a two-dimensional Fourier transform on the first processing result ln(I 1 ) to obtain the first transform result F 1 ;

步骤8、对第二处理结果ln(I2)作二维傅里叶变换，得到第二变换结果F2；Step 8, performing two-dimensional Fourier transform on the second processing result ln(I 2 ), to obtain the second transform result F 2 ;

步骤9、利用式(1)得到所述被成像物体(3)的物质分解的第一分解结果t1：Step 9, using formula (1) to obtain the first decomposition result t 1 of the material decomposition of the imaged object (3):

Figure BDA0003267641840000037
Figure BDA0003267641840000037

式(1)中，

Figure BDA0003267641840000038
表示二维逆傅里叶变换；B1为第一分解常数，并由式(2)得到；B2为第二分解常数，并由式(3)得到；D为常数，并由式(4)得到：In formula (1),
Figure BDA0003267641840000038
Represents the two-dimensional inverse Fourier transform; B 1 is the first decomposition constant, and is obtained by formula (2); B 2 is the second decomposition constant, and is obtained by formula (3); D is a constant, and is obtained by formula (4 )get:

Figure BDA0003267641840000039
Figure BDA0003267641840000039

式(2)中，

Figure BDA00032676418400000310
是物质分解的第一基材料在能量区间[E2E3]的等效衰减系数；/>
Figure BDA00032676418400000311
是物质分解的第一基材料在能量区间[E2 E3]的等效相移系数；R是所述被成像物体与所述单光子计数探测器在沿Z轴向上的等效相对距离，且满足R＝(L12-L13)L13/L12；u是所述单光子计数探测器沿X轴向的空间频率；v是所述单光子计数探测器沿Y轴向的空间频率；In formula (2),
Figure BDA00032676418400000310
is the equivalent attenuation coefficient of the first base material for material decomposition in the energy interval [E2E3];/>
Figure BDA00032676418400000311
is the equivalent phase shift coefficient of the first base material for material decomposition in the energy interval [E2 E3]; R is the equivalent relative distance between the imaged object and the single photon counting detector along the Z axis, and Satisfying R=(L 12 -L 13 )L 13 /L 12 ; u is the spatial frequency of the single photon counting detector along the X axis; v is the spatial frequency of the single photon counting detector along the Y axis;

Figure BDA00032676418400000312
Figure BDA00032676418400000312

式(3)中，

Figure BDA00032676418400000313
是物质分解的第二基材料在能量区间[E2E3]的等效衰减系数；/>
Figure BDA00032676418400000314
是物质分解的第二基材料在能量区间[E2 E3]的等效相移系数；In formula (3),
Figure BDA00032676418400000313
is the equivalent attenuation coefficient of the second base material for material decomposition in the energy interval [E2E3];/>
Figure BDA00032676418400000314
is the equivalent phase shift coefficient of the second base material for material decomposition in the energy interval [E2 E3];

D＝A1×B2-A2×B1 (4)D＝A 1 ×B 2 -A 2 ×B 1 (4)

式(4)中，A1为第三分解常数，并由式(5)得到；A2为第四分解常数，并由式(6)得到：In formula (4), A1 is the third decomposition constant, and is obtained by formula (5); A2 is the fourth decomposition constant, and is obtained by formula (6):

Figure BDA0003267641840000041
Figure BDA0003267641840000041

式(5)中，

Figure BDA0003267641840000042
是物质分解的第一基材料在能量区间[E1E2]的等效衰减系数；/>
Figure BDA0003267641840000043
是物质分解的第一基材料在能量区间[E1 E2]的等效相移系数；In formula (5),
Figure BDA0003267641840000042
is the equivalent attenuation coefficient of the first base material for material decomposition in the energy interval [E1E2];/>
Figure BDA0003267641840000043
is the equivalent phase shift coefficient of the first base material for material decomposition in the energy interval [E1 E2];

Figure BDA0003267641840000044
Figure BDA0003267641840000044

式(6)中，

Figure BDA0003267641840000045
是物质分解的第二基材料在能量区间[E1E2]的等效衰减系数；/>
Figure BDA0003267641840000046
是物质分解的第二基材料在能量区间[E1 E2]的等效相移系数；In formula (6),
Figure BDA0003267641840000045
is the equivalent attenuation coefficient of the second base material for material decomposition in the energy interval [E1E2];/>
Figure BDA0003267641840000046
is the equivalent phase shift coefficient of the second base material for material decomposition in the energy interval [E1 E2];

步骤10、利用式(7)得到所述被成像物体的物质分解的第二分解结果t2：Step 10, using formula (7) to obtain the second decomposition result t 2 of the material decomposition of the imaged object:

Figure BDA0003267641840000047
Figure BDA0003267641840000047

以所述被成像物体的第一分解结果t1、第二分解结果t2作为所述一次曝光的X射线相位传播成像的物质分解结果。The first decomposition result t 1 and the second decomposition result t 2 of the imaged object are used as the material decomposition results of the single-exposure X-ray phase propagation imaging.

与已有技术相比，本发明的有益效果是：Compared with prior art, the beneficial effect of the present invention is:

1、本发明利用单光子计数探测器的能量分辨功能，通过设定单光子计数探测器的能量阈值，实现了仅对被成像物体一次曝光下，被成像物体的物质分解结果的定量、准确获取，解决了现有方法要求两次曝光的局限性，提高了X射线相位传播成像的实验效率；1. The present invention utilizes the energy resolution function of the single photon counting detector, and by setting the energy threshold of the single photon counting detector, realizes the quantitative and accurate acquisition of the material decomposition results of the imaged object under only one exposure , which solves the limitation that the existing method requires two exposures, and improves the experimental efficiency of X-ray phase propagation imaging;

2、本发明利用单光子计数探测器的能量阈值设定，同时获取了两个不同能量区间的光强数据，两个光强数据自动配准，避免了现有方法中像素配准导致的图像伪影，提高了物质分解结果的定量准确性；2. The present invention utilizes the energy threshold setting of the single photon counting detector to obtain light intensity data in two different energy intervals at the same time, and the two light intensity data are automatically registered, avoiding the image caused by pixel registration in the existing method Artifacts, improving the quantitative accuracy of material decomposition results;

3、本发明利用单光子计数探测器同时获取了被成像物体的两个不同能量区间的光强数据，避免了非同时获取时被成像物体的运动伪影，提高了物质分解结果的定量准确性；从而实现了快速、准确的X射线相位传播成像的物质分解；3. The present invention simultaneously acquires the light intensity data of two different energy intervals of the imaged object by using a single photon counting detector, which avoids the motion artifact of the imaged object during non-simultaneous acquisition, and improves the quantitative accuracy of the material decomposition results ; Thereby realizing fast and accurate material decomposition of X-ray phase propagation imaging;

附图说明Description of drawings

图1为本发明的X射线相位传播成像系统示意图；Fig. 1 is the schematic diagram of X-ray phase propagation imaging system of the present invention;

图2为本发明的物质分解方法的第一分解结果；Fig. 2 is the first decomposition result of the material decomposition method of the present invention;

图3为本发明的物质分解方法的第二分解结果；Fig. 3 is the second decomposition result of the material decomposition method of the present invention;

图中标号：1X射线源；2单光子计数探测器；3被成像物体。Labels in the figure: 1 X-ray source; 2 Single photon counting detector; 3 Object to be imaged.

具体实施方式Detailed ways

本实施例中，参见图1，设置由X射线源1、单光子计数探测器2构成的X射线相位传播成像系统；如图1所示，以X射线源1的位置点为坐标系原点O，以射线轴方向为Z轴向，垂直于射线轴、且平行于单光子计数探测器2的水平列方向为Y轴向，以共同垂直于射线轴和单光子计数探测器2的水平列方向为X轴向，建立直角坐标系O-XYZ；In this embodiment, referring to Fig. 1, an X-ray phase propagation imaging system composed of an X-ray source 1 and a single-photon counting detector 2 is set; as shown in Fig. , the ray axis direction is the Z axis, the Y axis is perpendicular to the ray axis and parallel to the horizontal column direction of the single photon counting detector 2, and the horizontal column direction of the single photon counting detector 2 is perpendicular to the ray axis and the single photon counting detector 2 For the X axis, establish a rectangular coordinate system O-XYZ;

在沿Z轴向上依次设置有X射线源1、单光子计数探测器2；设置X射线源1、单光子计数探测器2在沿X轴向上中心对齐，在沿Y轴向上中心对齐；设置X射线源1与单光子计数探测器2在沿Z轴向上的相对距离为L12，且满足：L12＞0；An X-ray source 1 and a single-photon counting detector 2 are sequentially arranged along the Z-axis; the X-ray source 1 and the single-photon counting detector 2 are arranged to be centered along the X-axis, and centered along the Y-axis ;Set the relative distance between the X-ray source 1 and the single photon counting detector 2 along the Z-axis as L 12 , and satisfy: L 12 >0;

本实施例中，一种一次曝光的X射线相位传播成像的物质分解方法是按如下步骤进行：In this embodiment, a material decomposition method of X-ray phase propagation imaging with one exposure is carried out as follows:

步骤1、获取背景光强数据：Step 1. Obtain background light intensity data:

步骤1.1、启动单光子计数探测器2，设置单光子计数探测器2的第一能量阈值为E1；设置单光子计数探测器2的第二能量阈值为E2，且满足E1<E2；设置曝光时长为T；Step 1.1, start the single photon counting detector 2, set the first energy threshold of the single photon counting detector 2 to E1; set the second energy threshold of the single photon counting detector 2 to E2, and satisfy E1<E2; set the exposure time for T;

步骤1.2、启动X射线源1，设置X射线源1的管电压为E3，且满足E2<E3；Step 1.2, start X-ray source 1, set the tube voltage of X-ray source 1 to E3, and satisfy E2<E3;

步骤1.3、利用单光子计数探测器2按照曝光时长T同时获取第一背景光强数据

Figure BDA0003267641840000051
第二背景光强数据/>
Figure BDA0003267641840000052
其中，第一背景光强数据/>
Figure BDA0003267641840000053
测量的是能量区间[E1 E2]的X射线强度；第二背景光强数据/>
Figure BDA0003267641840000054
测量的是能量区间[E2E3]的X射线强度；Step 1.3, using the single photon counting detector 2 to simultaneously acquire the first background light intensity data according to the exposure time T
Figure BDA0003267641840000051
Second background light intensity data/>
Figure BDA0003267641840000052
Among them, the first background light intensity data />
Figure BDA0003267641840000053
What is measured is the X-ray intensity in the energy interval [E1 E2]; the second background light intensity data />
Figure BDA0003267641840000054
What is measured is the X-ray intensity in the energy range [E2E3];

步骤1.4、关闭X射线源1和单光子计数探测器2；Step 1.4, turn off the X-ray source 1 and the single photon counting detector 2;

步骤2、获取被成像物体的光强数据：Step 2. Obtain the light intensity data of the imaged object:

步骤2.1、将被成像物体3沿Z轴向放置在X射线源1和单光子计数探测器2的中间；并将X射线源1与被成像物体3在沿Z轴向上的相对距离记为L13，且满足0＜L13＜L12；设置被成像物体3与单光子计数探测器2在沿X轴向上中心对齐，在沿Y轴向上中心对齐；Step 2.1, placing the imaged object 3 in the middle of the X-ray source 1 and the single photon counting detector 2 along the Z axis; and recording the relative distance between the X-ray source 1 and the imaged object 3 along the Z axis as L 13 , and satisfy 0<L 13 <L 12 ; set the object 3 to be imaged and the single photon counting detector 2 to be centered along the X-axis, and to be centered along the Y-axis;

步骤2.2、启动单光子计数探测器2，设置单光子计数探测器2的第一能量阈值仍为E1；设置单光子计数探测器2的第二能量阈值仍为E2，且满足E1<E2；设置曝光时长仍为T；Step 2.2, start the single photon counting detector 2, set the first energy threshold of the single photon counting detector 2 to still be E1; set the second energy threshold of the single photon counting detector 2 to still be E2, and satisfy E1<E2; set The exposure time is still T;

步骤2.3、启动X射线源1，设置X射线源1的管电压仍为E3，且满足E2<E3；Step 2.3, start X-ray source 1, set the tube voltage of X-ray source 1 to still be E3, and satisfy E2<E3;

步骤2.4、利用单光子计数探测器2按照曝光时长T同时获取被成像物体3的第一光强数据

Figure BDA0003267641840000055
第二光强数据/>
Figure BDA0003267641840000056
其中，第一光强数据/>
Figure BDA0003267641840000057
测量的是能量区间[E1 E2]的X射线强度；第二光强数据/>
Figure BDA0003267641840000058
测量的是能量区间[E2E3]的X射线强度；Step 2.4, using the single photon counting detector 2 to simultaneously acquire the first light intensity data of the imaged object 3 according to the exposure time T
Figure BDA0003267641840000055
Second light intensity data/>
Figure BDA0003267641840000056
Among them, the first light intensity data />
Figure BDA0003267641840000057
What is measured is the X-ray intensity in the energy interval [E1 E2]; the second light intensity data/>
Figure BDA0003267641840000058
What is measured is the X-ray intensity in the energy range [E2E3];

步骤2.5、关闭X射线源1和单光子计数探测器2；Step 2.5, turn off the X-ray source 1 and the single photon counting detector 2;

对曝光时长T：当X射线源1是同步辐射X射线源时，曝光时长的典型值是1毫秒到几十毫秒；当X射线源1是微焦点X射线源时，曝光时长的典型值是几十秒到几百秒；For the exposure time T: when the X-ray source 1 is a synchrotron radiation X-ray source, the typical value of the exposure time is 1 millisecond to tens of milliseconds; when the X-ray source 1 is a micro-focus X-ray source, the typical value of the exposure time is tens of seconds to hundreds of seconds;

对单光子计数探测器2的任一像素，获取的被成像物体3的第一光强数据

Figure BDA0003267641840000061
满足式(2.1)：For any pixel of the single photon counting detector 2, the first light intensity data of the imaged object 3 acquired
Figure BDA0003267641840000061
Satisfy formula (2.1):

Figure BDA0003267641840000062
Figure BDA0003267641840000062

式(2.1)中，μL是被成像物体3在能量区间[E1 E2]的等效衰减系数；δL是被成像物体3在能量区间[E1 E2]的等效相移系数；R是被成像物体3与单光子计数探测器2在沿Z轴向上的等效相对距离，且满足R＝(L12-L13)L13/L12＞0；

Figure BDA0003267641840000063
表示在垂直Z轴向的XY平面内的拉普拉斯运算。In formula (2.1), μ L is the equivalent attenuation coefficient of the imaged object 3 in the energy interval [E1 E2]; δ L is the equivalent phase shift coefficient of the imaged object 3 in the energy interval [E1 E2]; R is the equivalent The equivalent relative distance between the imaging object 3 and the single photon counting detector 2 along the Z-axis, and satisfying R=(L 12 -L 13 )L 13 /L 12 >0;
Figure BDA0003267641840000063
Indicates the Laplace operation in the XY plane perpendicular to the Z axis.

对单光子计数探测器2的任一像素，获取的被成像物体3的第二光强数据

Figure BDA0003267641840000064
满足式(2.2)：For any pixel of the single photon counting detector 2, the acquired second light intensity data of the imaged object 3
Figure BDA0003267641840000064
Satisfy formula (2.2):

Figure BDA0003267641840000065
Figure BDA0003267641840000065

式(2.2)中，μH是被成像物体3在能量区间[E2 E3]的等效衰减系数；δH是被成像物体3在能量区间[E2 E3]的等效相移系数。In formula (2.2), μ H is the equivalent attenuation coefficient of the imaged object 3 in the energy interval [E2 E3]; δ H is the equivalent phase shift coefficient of the imaged object 3 in the energy interval [E2 E3].

步骤3、对被成像物体3的第一光强数据

Figure BDA0003267641840000066
进行归一化处理，得到归一化的第一光强数据I1，且满足/>
Figure BDA0003267641840000067
Step 3, the first light intensity data of the imaged object 3
Figure BDA0003267641840000066
Perform normalization processing to obtain the normalized first light intensity data I 1 , and satisfy />
Figure BDA0003267641840000067

利用式(2.1)，对被成像物体3的第一光强数据

Figure BDA0003267641840000068
进行归一化处理，得到归一化的第一光强数据I1满足式(3.1)：Using formula (2.1), the first light intensity data of the imaged object 3
Figure BDA0003267641840000068
Carry out normalization processing, obtain the normalized first light intensity data I Satisfies formula (3.1):

Figure BDA0003267641840000069
Figure BDA0003267641840000069

步骤4、对被成像物体3的第二光强数据

Figure BDA00032676418400000610
进行归一化处理，得到归一化的第二光强数据I2，且满足/>
Figure BDA00032676418400000611
Step 4, the second light intensity data of the imaged object 3
Figure BDA00032676418400000610
Perform normalization processing to obtain normalized second light intensity data I 2 , and satisfy />
Figure BDA00032676418400000611

利用式(2.2)，对被成像物体3的第二光强数据

Figure BDA00032676418400000612
进行归一化处理，得到归一化的第二光强数据I2满足式(4.1)：Utilize formula (2.2), to the second light intensity data of imaged object 3
Figure BDA00032676418400000612
Carry out normalization processing, obtain the second light intensity data I of normalization Satisfy formula (4.1):

Figure BDA00032676418400000613
Figure BDA00032676418400000613

步骤5、对归一化的第一光强数据I1进行取对数处理，得到第一处理结果ln(I1)；Step 5. Logarithmic processing is performed on the normalized first light intensity data I 1 to obtain the first processing result ln(I 1 );

利用式(3.1)，对被成像物体3的归一化的第一光强数据I1进行取对数处理，得到的第一处理结果ln(I1)满足式(5.1)：Using formula (3.1), logarithmic processing is performed on the normalized first light intensity data I 1 of the imaged object 3, and the obtained first processing result ln(I 1 ) satisfies formula (5.1):

Figure BDA0003267641840000071
Figure BDA0003267641840000071

步骤6、对归一化的第二光强数据I2进行取对数处理，得到第二处理结果ln(I2)；Step 6. Perform logarithmic processing on the normalized second light intensity data I 2 to obtain the second processing result ln(I 2 );

利用式(4.1)，对被成像物体3的归一化的第二光强数据I2进行取对数处理，得到的第二处理结果ln(I2)满足式(6.1)：Using formula (4.1), logarithmic processing is performed on the normalized second light intensity data I 2 of the imaged object 3, and the obtained second processing result ln(I 2 ) satisfies formula (6.1):

Figure BDA0003267641840000072
Figure BDA0003267641840000072

步骤7、对第一处理结果ln(I1)作二维傅里叶变换，得到第一变换结果F1；Step 7, performing a two-dimensional Fourier transform on the first processing result ln(I 1 ) to obtain the first transform result F 1 ;

利用式(5.1)，对ln(I1)作二维傅里叶变换，得到第一变换结果F1满足式(7.1)：Using formula (5.1), perform two-dimensional Fourier transform on ln(I 1 ), and obtain the first transformation result F 1 satisfying formula (7.1):

Figure BDA0003267641840000073
Figure BDA0003267641840000073

式(5.1)中，

Figure BDA0003267641840000074
表示二维傅里叶变换操作；u是光子计数探测器2沿X轴向的空间频率；v是光子计数探测器2沿Y轴向的空间频率。In formula (5.1),
Figure BDA0003267641840000074
Indicates a two-dimensional Fourier transform operation; u is the spatial frequency of the photon counting detector 2 along the X axis; v is the spatial frequency of the photon counting detector 2 along the Y axis.

步骤8、对第二处理结果ln(I2)作二维傅里叶变换，得第二到变换结果F2；Step 8, performing two-dimensional Fourier transform on the second processing result ln(I 2 ), to obtain the second transform result F 2 ;

利用式(6.1)，对ln(I2)作二维傅里叶变换，得到第二变换结果F2满足式(8.1)：Using formula (6.1), perform two-dimensional Fourier transform on ln(I 2 ), and obtain the second transformation result F 2 satisfying formula (8.1):

Figure BDA0003267641840000075
Figure BDA0003267641840000075

步骤9、利用式(1)得到被成像物体3的物质分解的第一分解结果t1：Step 9, using formula (1) to obtain the first decomposition result t 1 of the material decomposition of the imaged object 3:

Figure BDA0003267641840000076
Figure BDA0003267641840000076

式(1)中，B1为第一分解常数，并由式(2)得到；B2为第二分解常数，并由式(3)得到；D为常数，并由式(4)得到：In formula (1), B1 is the first decomposition constant, and is obtained by formula (2); B2 is the second decomposition constant, and is obtained by formula (3); D is a constant, and is obtained by formula (4):

Figure BDA0003267641840000077
Figure BDA0003267641840000077

式(2)中，

Figure BDA0003267641840000078
是物质分解的第一基材料在能量区间[E2E3]的等效衰减系数；/>
Figure BDA0003267641840000079
是物质分解的第一基材料在能量区间[E2 E3]的等效相移系数；In formula (2),
Figure BDA0003267641840000078
is the equivalent attenuation coefficient of the first base material for material decomposition in the energy interval [E2E3];/>
Figure BDA0003267641840000079
is the equivalent phase shift coefficient of the first base material for material decomposition in the energy interval [E2 E3];

Figure BDA0003267641840000081
Figure BDA0003267641840000081

式(3)中，

Figure BDA0003267641840000082
是物质分解的第二基材料在能量区间[E2 E3]的等效衰减系数；/>
Figure BDA0003267641840000083
是物质分解的第二基材料在能量区间[E2 E3]的等效相移系数。In formula (3),
Figure BDA0003267641840000082
is the equivalent attenuation coefficient of the second base material for material decomposition in the energy interval [E2 E3];/>
Figure BDA0003267641840000083
is the equivalent phase shift coefficient of the second base material for material decomposition in the energy interval [E2 E3].

D＝A1×B2-A2×B1 (4)D＝A 1 ×B 2 -A 2 ×B 1 (4)

式(4)中，A1为第三分解常数，并由式(5)得到；A2为第四分解常数，并由式(6)得到：In formula (4), A1 is the third decomposition constant, and is obtained by formula (5); A2 is the fourth decomposition constant, and is obtained by formula (6):

Figure BDA0003267641840000084
Figure BDA0003267641840000084

式(5)中，

Figure BDA0003267641840000085
是物质分解的第一基材料在能量区间[E1E2]的等效衰减系数；/>
Figure BDA0003267641840000086
是物质分解的第一基材料在能量区间[E1 E2]的等效相移系数。In formula (5),
Figure BDA0003267641840000085
is the equivalent attenuation coefficient of the first base material for material decomposition in the energy interval [E1E2];/>
Figure BDA0003267641840000086
is the equivalent phase shift coefficient of the first base material for material decomposition in the energy interval [E1 E2].

Figure BDA0003267641840000087
Figure BDA0003267641840000087

式(6)中，

Figure BDA0003267641840000088
是物质分解的第二基材料在能量区间[E1E2]的等效衰减系数；/>
Figure BDA0003267641840000089
是物质分解的第二基材料在能量区间[E1 E2]的等效相移系数。In formula (6),
Figure BDA0003267641840000088
is the equivalent attenuation coefficient of the second base material for material decomposition in the energy interval [E1E2];/>
Figure BDA0003267641840000089
is the equivalent phase shift coefficient of the second base material for material decomposition in the energy interval [E1 E2].

步骤10、利用式(7)得到被成像物体3的物质分解的第二分解结果t2：Step 10, using formula (7) to obtain the second decomposition result t 2 of the material decomposition of the imaged object 3:

Figure BDA00032676418400000810
Figure BDA00032676418400000810

根据物质组成原理，在能量区间[E1 E2]，被成像物体3的等效衰减系数μL沿Z轴方向的积分满足式(10.1)：According to the principle of material composition, in the energy interval [E1 E2], the integral of the equivalent attenuation coefficient μ L of the imaged object 3 along the Z axis satisfies the formula (10.1):

Figure BDA00032676418400000811
Figure BDA00032676418400000811

被成像物体3的等效相移系数δL沿Z轴方向的积分满足式(10.2)：The integral of the equivalent phase shift coefficient δ L of the imaged object 3 along the Z axis satisfies the formula (10.2):

Figure BDA00032676418400000812
Figure BDA00032676418400000812

将式(10.1)、式(10.2)代入式(7.1)得到式(10.3)：Substitute formula (10.1) and formula (10.2) into formula (7.1) to get formula (10.3):

Figure BDA00032676418400000813
Figure BDA00032676418400000813

在能量区间[E2 E3]，被成像物体3的等效衰减系数μH沿Z轴方向的积分满足式(10.4)：In the energy interval [E2 E3], the integral of the equivalent attenuation coefficient μ H of the imaged object 3 along the Z axis satisfies the formula (10.4):

Figure BDA00032676418400000814
Figure BDA00032676418400000814

被成像物体3的等效相移系数δH沿Z轴方向的积分满足式(10.5)：The integral of the equivalent phase shift coefficient δ H of the imaged object 3 along the Z axis satisfies the formula (10.5):

Figure BDA00032676418400000815
Figure BDA00032676418400000815

将式(10.4)、式(10.5)代入式(8.1)得到式(10.6)：Substitute formula (10.4) and formula (10.5) into formula (8.1) to get formula (10.6):

Figure BDA0003267641840000091
Figure BDA0003267641840000091

以

Figure BDA0003267641840000092
为未知数，联立式(10.3)、式(10.6)求解，得到式(10.7)和式(10.8)：by
Figure BDA0003267641840000092
is the unknown, solve the simultaneous formula (10.3) and formula (10.6), and obtain formula (10.7) and formula (10.8):

Figure BDA0003267641840000093
Figure BDA0003267641840000093

Figure BDA0003267641840000094
Figure BDA0003267641840000094

对式(10.7)作二维逆傅里叶变换，从而得到如式(1)所示的被成像物体3的物质分解的第一分解结果t1；Perform a two-dimensional inverse Fourier transform to formula (10.7), thereby obtaining the first decomposition result t 1 of the material decomposition of the imaged object 3 as shown in formula (1);

对式(10.8)作二维逆傅里叶变换，从而得到如式(7)所示的被成像物体3的物质分解的第二分解结果t2；Perform two-dimensional inverse Fourier transform to formula (10.8), so as to obtain the second decomposition result t 2 of the material decomposition of the imaged object 3 as shown in formula (7);

图2所示为本申请的物质分解方法的第一分解结果，通常选择铝作为物质分解的第一基材料，两个不同能量区间的等效能量分别为25keV、35keV。如图2所示，利用式(1)得到的第一分解结果在实验误差范围内，与理论值符合的很好，是定量准确的。Figure 2 shows the first decomposition result of the material decomposition method of the present application. Aluminum is usually selected as the first base material for material decomposition, and the equivalent energies of two different energy ranges are 25keV and 35keV respectively. As shown in Figure 2, the first decomposition result obtained by using formula (1) is within the range of experimental error, which is in good agreement with the theoretical value and is quantitatively accurate.

图3所示为本申请的物质分解方法的第二分解结果，通常选择有机塑料作为物质分解的第二基材料。如图3所示，以理论值作为评价标准，利用式(7)得到的第二分解结果在实验误差范围内是定量准确的。Fig. 3 shows the second decomposition result of the substance decomposition method of the present application, and organic plastic is usually selected as the second base material for substance decomposition. As shown in Fig. 3, the second decomposition result obtained by using the formula (7) is quantitatively accurate within the range of experimental error, taking the theoretical value as the evaluation standard.

图2、图3所示的物质分解结果，证实了本发明提出的一次曝光的X射线相位传播成像的物质分解方法的可行性。The material decomposition results shown in Fig. 2 and Fig. 3 have confirmed the feasibility of the material decomposition method of X-ray phase propagation imaging of one exposure proposed by the present invention.

以被成像物体3的第一分解结果t1、第二分解结果t2作为一次曝光的X射线相位传播成像的物质分解结果。The first decomposition result t 1 and the second decomposition result t 2 of the imaged object 3 are used as the material decomposition results of X-ray phase propagation imaging for one exposure.

Claims (1)

1. A material decomposition method of one-shot X-ray phase propagation imaging is applied to an X-ray phase propagation imaging system consisting of an X-ray source (1) and a single photon counting detector (2);
establishing a rectangular coordinate system O-XYZ by taking a position point of the X-ray source (1) as a coordinate system origin O, taking a ray axis direction as a Z axis, taking a horizontal column direction which is perpendicular to a ray axis and parallel to the single photon counting detector (2) as a Y axis, and taking a horizontal column direction which is commonly perpendicular to the ray axis and the single photon counting detector (2) as an X axis;
the X-ray source (1) and the single photon counting detector (2) are sequentially arranged along the Z axis; setting the relative distance between the X-ray source (1) and the single photon counting detector (2) along the Z-axis to be L 12 The method comprises the steps of carrying out a first treatment on the surface of the Arranging the X-ray source (1) and the single photon counting detector (2) to be aligned in the center along the X-axis and aligned in the center along the Y-axis; the method is characterized in that the substance decomposition method of the X-ray phase propagation imaging is carried out according to the following steps:
step 1, obtaining background light intensity data:
step 1.1, starting the single photon counting detector (2), and setting a first energy threshold value of the single photon counting detector (2) as E1; setting a second energy threshold of the single photon counting detector (2) as E2, and meeting E1< E2; setting exposure time length as T;
step 1.2, starting the X-ray source (1), setting the tube voltage of the X-ray source (1) to be E3, and meeting E2< E3;
step 1.3, simultaneously acquiring energy intervals [ E1E2 ] according to the exposure time length T by using the single photon counting detector (2)]First background light intensity data at X-ray intensity of (C)
Figure FDA0003267641830000013
In the energy interval [ E2E3 ]]Second background light intensity data +.>
Figure FDA0003267641830000012
Step 1.4, switching off the X-ray source (1) and the single photon counting detector (2);
step 2, acquiring light intensity data of an imaged object:
step 2.1, placing an object (3) to be imaged in the middle of the X-ray source (1) and the single photon counting detector (2) along the Z axis; and the relative distance between the X-ray source (1) and the imaged object (3) along the Z-axis is denoted as L 13 And satisfy 0 < L 13 ＜L 12 The method comprises the steps of carrying out a first treatment on the surface of the -arranging said imaged object (3) in central alignment with said single photon counting detector (2) in the X-axis and in central alignment in the Y-axis;
step 2.2, starting the single photon counting detector (2), and setting a first energy threshold value of the single photon counting detector (2) to be E1; setting a second energy threshold of the single photon counting detector (2) to be E2; setting the exposure time length to be T;
step 2.3, starting the X-ray source (1), and setting the tube voltage of the X-ray source (1) to be E3;
step 2.4, simultaneously acquiring energy intervals [ E1E2 ] according to the exposure time length T by using the single photon counting detector (2)]First light intensity data of said imaged object (3) at an X-ray intensity of (2)
Figure FDA0003267641830000011
In the energy regionM [ E2E3]Second light intensity data of said object (3) to be imaged at X-ray intensity +.>
Figure FDA0003267641830000021
Step 2.5, switching off the X-ray source (1) and the single photon counting detector (2);
step 3, first light intensity data of the imaged object (3)
Figure FDA0003267641830000022
Normalization processing is carried out to obtain normalized first light intensity data I 1 And satisfy->
Figure FDA0003267641830000023
Step 4, second light intensity data of the imaged object (3)
Figure FDA0003267641830000024
Normalization processing is carried out to obtain normalized second light intensity data I 2 And satisfy->
Figure FDA0003267641830000025
Step 5, for normalized first light intensity data I 1 The logarithm is taken to obtain a first processing result ln (I 1 )；
Step 6, for normalized second light intensity data I 2 Performing logarithmic processing to obtain a second processing result ln (I 2 )；
Step 7, for the first processing result ln (I 1 ) Performing two-dimensional Fourier transform to obtain a first transformation result F 1 ；
Step 8, for the second processing result ln (I 2 ) Performing two-dimensional Fourier transform to obtain a second transformation result F 2 ；
Step 9, obtaining a first decomposition result t of the material decomposition of the imaged object (3) by using the formula (1) 1 ：
Figure FDA0003267641830000026
In the formula (1), the components are as follows,
Figure FDA0003267641830000027
representing a two-dimensional inverse fourier transform; b (B) 1 Is a first decomposition constant and is obtained from formula (2); b (B) 2 Is a second dissociation constant and is derived from formula (3); d is a constant and is obtained from formula (4):
Figure FDA0003267641830000028
in the formula (2), the amino acid sequence of the compound,
Figure FDA0003267641830000029
is a first base material decomposed by substances in the energy interval [ E2E3]Is a coefficient of equivalent attenuation of (a); />
Figure FDA00032676418300000210
Is a first base material decomposed by substances in the energy interval [ E2E3]Equivalent phase shift coefficient of (a); r is the equivalent relative distance of the imaged object (3) and the single photon counting detector (2) in the Z-axis direction, and satisfies R= (L) 12 -L 13 )L 13 /L 12 The method comprises the steps of carrying out a first treatment on the surface of the u is the spatial frequency of the single photon counting detector (2) along the X-axis; v is the spatial frequency of the single photon counting detector (2) along the Y-axis;
Figure FDA00032676418300000211
in the formula (3), the amino acid sequence of the compound,
Figure FDA00032676418300000212
is a second base material decomposed by substances in the energy interval [ E2E3]Equivalent attenuation coefficient of (a)；/>
Figure FDA00032676418300000213
Is a second base material decomposed by substances in the energy interval [ E2E3]Equivalent phase shift coefficient of (a);
D＝A 1 ×B 2 -A 2 ×B 1 (4)
in the formula (4), A 1 Is a third decomposition constant and is obtained from formula (5); a is that 2 Is a fourth decomposition constant and is obtained from formula (6):
Figure FDA0003267641830000031
in the formula (5), the amino acid sequence of the compound,
Figure FDA0003267641830000032
is a first base material decomposed by substances in the energy interval [ E1E2]Is a coefficient of equivalent attenuation of (a); />
Figure FDA0003267641830000033
Is a first base material decomposed by substances in the energy interval [ E1E2]Equivalent phase shift coefficient of (a);
Figure FDA0003267641830000034
in the formula (6), the amino acid sequence of the compound,
Figure FDA0003267641830000035
is a second base material decomposed by substances in the energy interval [ E1E2]Is a coefficient of equivalent attenuation of (a); />
Figure FDA0003267641830000036
Is a second base material decomposed by substances in the energy interval [ E1E2]Equivalent phase shift coefficient of (a);
step 10, obtaining a second decomposition result t of the material decomposition of the imaged object (3) by using the formula (7) 2 ：
Figure FDA0003267641830000037
With a first decomposition result t of the imaged object (3) 1 Second decomposition result t 2 As a result of the material decomposition of the one-shot X-ray phase-propagation imaging.
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