CN113805216B - Substance decomposition method for one-time exposure X-ray phase propagation imaging - Google Patents
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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
Technical Field
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.
Background
Through the imaging theory improvement and application research and study for over twenty years, the X-ray phase propagation imaging has been developed as a powerful complement to the traditional X-ray imaging technology. In principle, both the absorption signal and the phase-shifted signal of the imaged object contribute significantly to the intensity distribution measured directly by the detector. By using the developed signal extraction formula, the absorption signal and the 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 interfaces of different materials inside the imaged object, and can distinguish and identify the spatial distribution of the different materials. In addition, the X-ray phase propagation imaging has the advantages of high density resolution, high spatial resolution and the like, and has wide application prospect in the fields of clinical breast imaging, early diagnosis of lung lesions, public safety inspection and the like.
In the X-ray phase propagation imaging, the substance decomposition method can realize the identification of different substance materials, and has important application value in the fields of medical imaging, nondestructive detection and the like. The existing substance decomposition method is to measure and obtain X-ray intensity data of two different energy intervals by using an energy integral detector to sequentially expose an imaged object twice. I.e. the two different light intensity data required by the existing material decomposition methods are not acquired simultaneously. Non-simultaneous acquisition of two different intensity data can severely degrade the accuracy of the material decomposition results of the X-ray phase-propagation imaging. First, existing material decomposition methods require two subsequent exposures of the imaged object to measure two different light intensity data. This reduces the experimental efficiency of X-ray phase propagation imaging. Second, external vibration or the like causes unavoidable pixel shift of two light intensity data acquired at non-same time. Thus, prior methods require pixel registration of two intensity data prior to calculation of the material decomposition result. However, interpolation computation of pixel registration may introduce errors in light intensity data, thereby causing pixel registration artifacts of the material decomposition result, and reducing accuracy of the material decomposition result. Third, the object to be imaged always has some internal or external motion. This results in a pixel shift in the two intensity data of the imaged object acquired non-simultaneously. Similarly, pixel registration based on interpolation operations is required for both intensity data. This inevitably introduces errors in the light intensity data, resulting in a decrease in the accuracy of the decomposition result of the substance. These limitations restrict the popularization and application of the material decomposition of X-ray phase propagation imaging in the fields of clinical medical diagnosis and treatment, safety inspection and the like. Therefore, developing a new substance decomposition method for X-ray phase propagation imaging becomes one of the problems that needs to be solved in practical popularization and application of X-ray phase propagation imaging.
Disclosure of Invention
In order to avoid the defects of the existing substance decomposition method of X-ray phase propagation imaging, the invention provides a substance decomposition method of X-ray phase propagation imaging of one exposure, so that when an imaged object is only subjected to one exposure, the substance decomposition result of the imaged object can be quantitatively obtained from the light intensity data measured by a single photon counting detector, thereby providing a new way for realizing the rapid, accurate and efficient substance decomposition of X-ray phase propagation imaging.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the invention relates to a material decomposition method of one-shot X-ray phase propagation imaging, which is applied to an X-ray phase propagation imaging system consisting of an X-ray source and a single photon counting detector;
establishing a rectangular coordinate system O-XYZ by taking a position point of the X-ray source as a coordinate system origin O, taking a ray axis direction as a Z axis, taking a horizontal column direction which is perpendicular to the ray axis and parallel to the single photon counting detector as a Y axis, and taking a horizontal column direction which is commonly perpendicular to the ray axis and the single photon counting detector as an X axis;
the X-ray source and the single photon counting detector are sequentially arranged along the Z axis; setting the relative distance between the X-ray source and the single photon counting detector along the Z-axis to be L 12 The method comprises the steps of carrying out a first treatment on the surface of the Setting the X-ray source, the single photon counting detector to be aligned with the center along the X-axis and 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, and setting a first energy threshold value of the single photon counting detector as E1; setting a second energy threshold of the single photon counting detector as E2, and meeting E1< E2; setting exposure time length as T;
step 1.2, starting the X-ray source, setting the tube voltage of the X-ray source as 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]First background light intensity data at X-ray intensity of (C)
In the energy interval [ E2E3 ]]Second background light intensity data +.>
Step 1.4, turning off the X-ray source and the single photon counting detector;
step 2.1, placing an object to be imaged in the middle of the X-ray source and the single photon counting detector along the Z axis; and the relative distance between the X-ray source and the imaged object along the Z-axis is recorded 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 Setting the imaged object to be aligned with the single photon counting detector in the center along the X axis and in the center along the Y axis;
step 2.2, starting the single photon counting detector, and setting a first energy threshold of the single photon counting detector to be E1; setting a second energy threshold of the single photon counting detector to be E2; setting the exposure time length to be T;
step 2.3, starting the X-ray source, and setting the tube voltage of the X-ray source 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]First light intensity data of said imaged object at X-ray intensity of (c)
In the energy interval [ E2E3 ]]Second light intensity data of said object to be imaged at X-ray intensity +.>
Step 2.5, turning off the X-ray source and the single photon counting detector;
step 3, first light intensity data of the imaged object
Normalization processing is carried out to obtain normalized first light intensity data I 1 And satisfy->
Step 7, for the first processing result ln (I 1 ) Performing two-dimensional Fourier transform to obtain a first transformation result F 1 ；
Step 9, obtaining a first decomposition result t of the material decomposition of the imaged object (3) by using the formula (1) 1 ：
In the formula (1), the components are as follows,
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):
in the formula (2), the amino acid sequence of the compound,
is a first base material decomposed by substances in the energy interval [ E2E3]Is a coefficient of equivalent attenuation of (a); />
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 and the single photon counting detector 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 along the X axis; v is the spatial frequency of the single photon counting detector along the Y-axis;
in the formula (3), the amino acid sequence of the compound,
is a second base material decomposed by substances in the energy interval [ E2E3]Is a coefficient of equivalent attenuation of (a); />
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):
in the formula (5), the amino acid sequence of the compound,
is a first base material decomposed by substances in the energy interval [ E1E2]Equivalent of (a)An attenuation coefficient; />
Is a first base material decomposed by substances in the energy interval [ E1E2]Equivalent phase shift coefficient of (a);
in the formula (6), the amino acid sequence of the compound,
is a second base material decomposed by substances in the energy interval [ E1E2]Is a coefficient of equivalent attenuation of (a); />
Is a second base material decomposed by substances in the energy interval [ E1E2]Equivalent phase shift coefficient of (a);
With the first decomposition result t of the imaged object 1 Second decomposition result t 2 As a result of the material decomposition of the one-shot X-ray phase-propagation imaging.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention utilizes the energy resolution function of the single photon counting detector, and by setting the energy threshold of the single photon counting detector, the quantitative and accurate acquisition of the substance decomposition result of the imaged object under the condition of exposing the imaged object only once is realized, the limitation that the prior method requires two exposures is solved, and the experimental efficiency of X-ray phase propagation imaging is improved;
2. according to the invention, the energy threshold value of the single photon counting detector is utilized to set, and meanwhile, the light intensity data of two different energy intervals are obtained, and the two light intensity data are automatically registered, so that image artifacts caused by pixel registration in the existing method are avoided, and the quantitative accuracy of a substance decomposition result is improved;
3. according to the invention, the single photon counting detector is utilized to simultaneously acquire light intensity data of two different energy intervals of the imaged object, so that motion artifact of the imaged object during non-simultaneous acquisition is avoided, and the quantitative accuracy of a substance decomposition result is improved; thereby realizing rapid and accurate material decomposition of X-ray phase propagation imaging;
drawings
FIG. 1 is a schematic diagram of an X-ray phase propagation imaging system of the present invention;
FIG. 2 shows the first decomposition result of the material decomposition method of the present invention;
FIG. 3 is a second decomposition result of the material decomposition method of the present invention;
reference numerals in the drawings: a 1X-ray source; 2 a single photon counting detector; 3 imaged object.
Detailed Description
In the present embodiment, referring to fig. 1, an X-ray phase propagation imaging system constituted by an X-ray source 1, a single photon counting detector 2 is provided; as shown in fig. 1, a rectangular coordinate system O-XYZ is established with the position point of the X-ray source 1 as the origin O of the coordinate system, the direction of the ray axis as the Z axis, the direction of the horizontal row perpendicular to the ray axis and parallel to the single photon counting detector 2 as the Y axis, and the direction of the horizontal row commonly perpendicular to the ray axis and the single photon counting detector 2 as the X axis;
an X-ray source 1 and a single photon counting detector 2 are sequentially arranged along the Z axis; arranging an X-ray source 1 and a single photon counting detector 2 to be aligned with the center along the X-axis and aligned with the center along the Y-axis; the relative distance between the X-ray source 1 and the single photon counting detector 2 along the Z-axis is set to be L 12 And satisfies: l (L) 12 ＞0；
In this embodiment, a method for decomposing a substance for one-shot X-ray phase propagation imaging is performed as follows:
step 1, obtaining background light intensity data:
step 1.1, starting a 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 as E3, and meeting E2< E3;
step 1.3, simultaneously acquiring first background light intensity data according to the exposure time T by using the single photon counting detector 2
Second background light intensity data->
Wherein the first background light intensity data +.>
The energy interval [ E1E2 ] is measured]X-ray intensity of (2); second background light intensity data->
The energy interval [ E2E3 ] is measured]X-ray intensity of (2);
step 1.4, turning off the X-ray source 1 and the single photon counting detector 2;
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 the imaged object 3 to be aligned with the single photon counting detector 2 in the center in the X-axis direction and aligned with the center in the Y-axis direction;
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 the second energy threshold of the single photon counting detector 2 to be E2, and meeting E1< E2; setting the exposure time length to be T;
step 2.3, starting the X-ray source 1, setting the tube voltage of the X-ray source 1 to be E3, and meeting E2< E3;
step 2.4, simultaneously acquiring first light intensity data of the imaged object 3 according to the exposure time period T by using the single photon counting detector 2
Second light intensity data->
Wherein the first light intensity data->
The energy interval [ E1E2 ] is measured]X-ray intensity of (2); second light intensity data->
The energy interval [ E2E3 ] is measured]X-ray intensity of (2);
step 2.5, turning off the X-ray source 1 and the single photon counting detector 2;
for an exposure time period T: when the X-ray source 1 is a synchrotron radiation X-ray source, a typical value of the exposure time period is 1 millisecond to several tens of milliseconds; when the X-ray source 1 is a micro-focus X-ray source, a typical value of the exposure time period is several tens of seconds to several hundreds of seconds;
for any pixel of the single photon counting detector 2, first light intensity data of the imaged object 3 are acquired
Satisfy formula (2.1):
in the formula (2.1), μ L Is that the imaged object 3 is in the energy interval [ E1E2 ]]Is a coefficient of equivalent attenuation of (a); delta L Is that the imaged object 3 is in the energy interval [ E1E2 ]]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 ＞0；
Shows the Laplace operation in the XY plane perpendicular to the Z axis.
For any pixel of the single photon counting detector 2, second light intensity data of the imaged object 3 are acquired
Satisfy formula (2.2):
in the formula (2.2), μ H Is that the imaged object 3 is in the energy interval [ E2E3 ]]Is a coefficient of equivalent attenuation of (a); delta H Is that the imaged object 3 is in the energy interval [ E2E3 ]]Is a phase shift coefficient equivalent to the above.
Step 3, first light intensity data of the imaged object 3
Normalization processing is carried out to obtain normalized first light intensity data I 1 And satisfy->
First light intensity data for the imaged object 3 using equation (2.1)
Normalization processing is carried out to obtain normalized first light intensity data I 1 Satisfy formula (3.1):
Second light intensity data for the imaged object 3 using equation (2.2)
Normalization processing is carried out to obtain normalized second light intensity data I 2 Satisfy formula (4.1):
Normalized first light intensity data I for the imaged object 3 using formula (3.1) 1 The log-taking process is performed to obtain a first processing result ln (I 1 ) Satisfy formula (5.1):
Normalized second light intensity data I for the imaged object 3 using equation (4.1) 2 The log-taking process is performed to obtain a second processing result ln (I 2 ) Satisfy formula (6.1):
step 7, for the first processing result ln (I 1 ) Performing two-dimensional Fourier transform to obtain a first transformation result F 1 ；
For ln (I) using formula (5.1) 1 ) Performing two-dimensional Fourier transform to obtain a first transformation result F 1 Satisfy formula (7.1):
in the formula (5.1), the amino acid sequence,
representing 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 in the Y-axis direction.
For ln (I) using formula (6.1) 2 ) Performing two-dimensional Fourier transform to obtain a second transformation result F 2 Satisfy formula (8.1):
step 9, obtaining a first decomposition result t of the material decomposition of the imaged object 3 by using the formula (1) 1 ：
In the formula (1), 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):
in the formula (2), the amino acid sequence of the compound,
is decomposed by substancesThe first base material is in the energy interval [ E2E3 ]]Is a coefficient of equivalent attenuation of (a); />
Is a first base material decomposed by substances in the energy interval [ E2E3]Equivalent phase shift coefficient of (a);
in the formula (3), the amino acid sequence of the compound,
is a second base material decomposed by substances in the energy interval [ E2E3]Is a coefficient of equivalent attenuation of (a); />
Is a second base material decomposed by substances in the energy interval [ E2E3]Is a phase shift coefficient equivalent to the above.
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):
in the formula (5), the amino acid sequence of the compound,
is a first base material decomposed by substances in the energy interval [ E1E2]Is a coefficient of equivalent attenuation of (a); />
Is a first base material decomposed by substances in the energy interval [ E1E2]Is a phase shift coefficient equivalent to the above.
In the formula (6), the amino acid sequence of the compound,
is a second base material decomposed by substances in the energy interval [ E1E2]Is a coefficient of equivalent attenuation of (a); />
Is a second base material decomposed by substances in the energy interval [ E1E2]Is a phase shift coefficient equivalent to the above.
In the energy interval [ E1E2 ] according to the principle of composition of matter]Equivalent attenuation coefficient mu of imaged object 3 L The integral along the Z-axis satisfies the formula (10.1):
equivalent phase shift coefficient delta of imaged object 3 L The integral along the Z-axis satisfies the formula (10.2):
substituting formula (10.1) and formula (10.2) into formula (7.1) to obtain formula (10.3):
in the energy interval [ E2E3]Equivalent attenuation coefficient mu of imaged object 3 H The integral along the Z-axis satisfies the formula (10.4):
equivalent phase shift coefficient delta of imaged object 3 H The integral along the Z-axis satisfies the formula (10.5):
substituting formula (10.4) and formula (10.5) into formula (8.1) to obtain formula (10.6):
to be used for
Solving for unknowns, the simultaneous formula (10.3), formula (10.6), and obtaining formula (10.7) and formula (10.8):
performing a two-dimensional inverse Fourier transform on the formula (10.7) to obtain a first decomposition result t of the material decomposition of the imaged object 3 as shown in the formula (1) 1 ；
Performing a two-dimensional inverse Fourier transform on the formula (10.8) to obtain a second decomposition result t of the material decomposition of the imaged object 3 as shown in the formula (7) 2 ；
Fig. 2 shows the first decomposition result of the material decomposition method of the present application, in which aluminum is generally selected as the first base material for material decomposition, and the equivalent energies of two different energy intervals are 25keV and 35keV, respectively. As shown in fig. 2, the first decomposition result obtained by the formula (1) is well matched with the theoretical value within the experimental error range, and is quantitatively accurate.
Fig. 3 shows the second decomposition result of the material decomposition method of the present application, and organic plastics are generally selected as the second base material for material decomposition. As shown in fig. 3, the second decomposition result obtained by the formula (7) was quantitatively accurate within the experimental error range, using the theoretical value as an evaluation criterion.
The material decomposition results shown in fig. 2 and 3 prove the feasibility of the material decomposition method of the one-exposure X-ray phase propagation imaging.
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.
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)
In the energy interval [ E2E3 ]]Second background light intensity data +.>
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)
In the energy regionM [ E2E3]Second light intensity data of said object (3) to be imaged at X-ray intensity +.>
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)
Normalization processing is carried out to obtain normalized first light intensity data I 1 And satisfy->
Step 4, second light intensity data of the imaged object (3)
Normalization processing is carried out to obtain normalized second light intensity data I 2 And satisfy->
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 ：
In the formula (1), the components are as follows,
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):
in the formula (2), the amino acid sequence of the compound,
is a first base material decomposed by substances in the energy interval [ E2E3]Is a coefficient of equivalent attenuation of (a); />
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;
in the formula (3), the amino acid sequence of the compound,
is a second base material decomposed by substances in the energy interval [ E2E3]Equivalent attenuation coefficient of (a)；/>
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):
in the formula (5), the amino acid sequence of the compound,
is a first base material decomposed by substances in the energy interval [ E1E2]Is a coefficient of equivalent attenuation of (a); />
Is a first base material decomposed by substances in the energy interval [ E1E2]Equivalent phase shift coefficient of (a);
in the formula (6), the amino acid sequence of the compound,
is a second base material decomposed by substances in the energy interval [ E1E2]Is a coefficient of equivalent attenuation of (a); />
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 ：
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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