CN113866195B - Multi-contrast signal extraction method for X-ray grating interferometer imaging - Google Patents
Multi-contrast signal extraction method for X-ray grating interferometer imaging Download PDFInfo
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Abstract
The invention discloses a multi-contrast signal extraction method for X-ray grating interferometer imaging, which is applied to an X-ray grating interferometer imaging system formed by sequentially arranging a light source, a phase grating, an analysis grating and a light intensity detector along the Z axis, wherein the X-ray grating interferometer imaging system is aligned with the center along the X axis and the Y axis; after the X-rays emitted by the light source sequentially penetrate through the phase grating, the imaged object and the analysis grating, the intensity distribution of the X-rays is measured by the light intensity detector and recorded as projection data; the projection data recorded by the light intensity detector is calculated by using the proposed multi-contrast signal extraction method, and the absorption signal, the refraction signal and the dark field signal of the imaged object can be accurately extracted. The invention can correct the artifacts of the multi-contrast signal caused by the random error of the relative displacement of the grating, and realize the absorption and refraction of the imaged object and the accurate and quantitative extraction of the dark field signal.
Description
Technical Field
The invention relates to the field of X-ray imaging methods, in particular to a multi-contrast signal extraction method for X-ray grating interferometer imaging.
Background
Since 2002, X-ray grating interferometer imaging has now evolved into a powerful complement to existing X-ray imaging techniques through theoretical method research and practical application exploration for nearly 20 years. In principle, an X-ray grating interferometer exploits the fractional taber self-imaging effect of a phase grating under coherent illumination. While differences in the spatial distribution of refractive indices inside the object can lead to local spatial distortions of the self-image. These local distortions are converted by the analyzer grating into light intensity variations that can be measured and recorded by the detector. The X-ray grating interferometer has multi-mode imaging capability and can acquire absorption signals, refraction signals and dark field signals of an object at the same time. The three different signals are mutually complementary, and multi-scale and multi-dimensional characterization of the object space structure information can be realized. In particular, an X-ray grating interferometer can effectively use a large-focus X-ray source to acquire a refraction signal and a dark field signal of an object, and is widely considered as one of X-ray multi-contrast imaging methods that have the highest potential to be popularized to clinical applications. Meanwhile, the imaging method of the X-ray grating interferometer has the advantages of high spatial resolution, high sensitivity and the like, and has wide popularization and application values in a plurality of fields such as clinical breast imaging, public safety inspection, food safety detection and the like.
Currently, the X-ray grating interferometer imaging method generally employs a phase stepping method to acquire projection data, and extract absorption signals, refraction signals, and dark field signals of an object. In acquiring projection data, the phase stepping method requires that the raster be scanned in equal steps in one raster period, and that one projection data be measured and recorded at each raster position scanned. When extracting multi-contrast signals of an object, the phase stepping method requires that the relative displacement of the grating when acquiring projection data satisfies equidistant distribution within one period. However, in an actual projection data acquisition environment, factors such as thermal drift of the grating, accuracy of the grating step-and-scan, and external random vibration are always present. This results in an unavoidable random error in the relative displacement of the grating, which cannot meet the requirement of equidistant distribution in one period. More seriously, when projection data has random errors of relative displacement, an object multi-contrast signal extracted by a phase stepping method has signal artifacts, and the quantitative and accurate application requirements are not met. Therefore, the popularization and the application of the X-ray grating interferometer imaging in the fields of clinical medical diagnosis and treatment, public safety inspection, industrial nondestructive detection and the like are limited. Therefore, the development of a new multi-contrast signal extraction method for imaging an X-ray grating interferometer overcomes the limitations that a phase stepping method requires equidistant distribution of relative displacement and cannot eliminate signal artifacts caused by random errors of the relative displacement, and becomes one of the problems to be solved in the practical popularization and application of the imaging method of the X-ray grating interferometer.
Disclosure of Invention
The invention provides a multi-contrast signal method for imaging by an X-ray grating interferometer to avoid the defects of the existing imaging method, so as to eliminate signal artifacts caused by random errors of relative displacement and accurately extract absorption, refraction and dark field signals of an object, thereby providing a new way for realizing accurate and quantitative X-ray multi-contrast imaging.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
the invention relates to a multi-contrast signal extraction method for X-ray grating interferometer imaging, which is applied to an X-ray grating interferometer consisting of a light source, a phase grating, an analysis grating and a light intensity detector;
establishing a rectangular coordinate system O-XYZ by taking a position point of the light source as a coordinate system origin O, taking a ray axis direction as a Z axis, taking a grid line structure direction which is perpendicular to the ray axis and parallel to the phase grating as a Y axis and taking a grid line structure direction which is commonly perpendicular to the ray axis and the phase grating as an X axis;
the light source, the phase grating, the analysis grating and the light intensity detector are sequentially arranged along the Z axis; the light source, the phase grating, the analysis grating and the light intensity detector are aligned in the center along the X axis and aligned in the center along the Y axis; the multi-contrast signal extraction method for the X-ray grating interferometer imaging is characterized by comprising the following steps of:
step 1, setting relevant positions of all devices, and meeting the following conditions: l (L) 14 ＞L 13 ＞L 12 > 0, where L 14 A relative distance between the light source and the light intensity detector along the Z axis; l (L) 13 A relative distance between the light source and the analytical grating in the Z-axis direction; l (L) 12 A relative distance between the light source and the phase grating along the Z axis;
step 2, obtaining background projection data:
step 2.1, defining a positive integer m as a serial number of the acquired projection data, and initializing m=1;
step 2.2, setting the relative displacement of the analysis grating and the phase grating along the X-axis to be (m multiplied by p) 2 ) M; after the light source is started, the light intensity detector is utilized to acquire the mth background projection data according to the exposure time tWherein p is 2 Is the period of the analyzer grating; m is the total number of the acquired projection data, and M is a positive integer and satisfies M is more than or equal to 3;
step 2.3, after m+1 is assigned to M, judging whether M > M is satisfied, if so, executing step 2.4; otherwise, returning to the step 2.2;
step 2.4, turning off the light source;
step 3, obtaining object projection data:
step 3.1, placing the imaged object between the phase grating and the analysis grating along the Z axial direction; and the relative distance between the light source and the imaged object along the Z axis is recorded as L 15 And satisfy L 12 ＜L 15 ＜L 13 The method comprises the steps of carrying out a first treatment on the surface of the Setting the object to be imaged and the light intensity detector to be aligned in the center along the X axis and aligned in the center along the Y axis;
step 3.2, initializing m=1;
step 3.3, setting the relative displacement of the analysis grating and the phase grating along the X-axis to be (m multiplied by p) 2 ) M; after the light source is started, the light intensity detector is utilized to acquire the mth object projection data of the imaged object according to the exposure time t
Step 3.4, after m+1 is assigned to M, judging whether M > M is met, if so, executing step 3.5; otherwise, returning to the step 3.3;
step 3.5, turning off the light source;
step 4, obtaining the relative displacement of the background:
step 4.1, defining a positive integer m as the serial number of the acquired relative displacement, and initializing m=1;
step 4.2, defining a background function X by using a formula (1):
in the formula (1), delta is an independent variable, and the value range is [ (M-0.5)/M (m+0.5)/M)]The method comprises the steps of carrying out a first treatment on the surface of the i represents an imaginary unit; a is the mean value of the background projection data, and
step 4.3, defining the background parameter F by using the formula (2) r ：
In the formula (2), sigma X Is the standard deviation of the background function X,is the mean of the background function X;
step 4.4, obtaining the mth background relative displacementSuch that the background parameter F r Obtaining a minimum value;
step 4.5, assigning m+1 to M, judging whether M > (M-1) is true, and if so, executing step 5; otherwise, returning to the step 4.2;
step 5, obtaining relative displacement of the object:
step 5.1, initializing m=1;
step 5.2, defining an object function Y by using a formula (3):
in formula (3), B is the mean value of the projection data of the object, and
step 5.3 defining the object parameter F using (4) s ：
In formula (4), σ Y Is the standard deviation of the object function Y,is the mean value of the object function Y;
step 5.4, obtaining the relative displacement of the mth objectSuch that the object parameter F s Obtaining a minimum value;
step 5.5, assigning m+1 to M, judging whether M > (M-1) is true, and if so, executing step 6; otherwise, returning to the step 5.2;
step 6, extracting an absorption signal T of the imaged object by using the formula (3):
T＝B 1 /A 1 (5)
in the formula (5), A 1 Represents a first background parameter, an
Coefficient c 11 、c 12 、c 13 Is an element of the background matrix C, and the background matrix C satisfies:
in the formula (5), B 1 Representing a first object parameter, an
The elements of the bulk matrix D, and the object matrix D satisfies:
step 7, extracting the refraction signal theta of the imaged object by using the formula (6) R ：
θ R ＝tan -1 (B 3 /B 2 )-tan -1 (A 3 /A 2 )-Δφ (6)
In the formula (6), B 2 Representing a second object parameter, an
B 3 Representing a third object parameter, an
A 2 Represents a second background parameter, an
A 3 Represents a third background parameter, an
Δφ represents a constant bias and is approximately equal to the mean of the signal for the no object region;
step 8, extracting a dark field signal D of the imaged object by using the formula (7):
by the absorption signal T and the refraction signal theta of the imaged object R The dark field signal D is the result of the multi-contrast signal extraction method.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention utilizes the first-order cosine approximation of the light intensity curve to provide a multi-contrast signal extraction method for X-ray grating interferometer imaging, overcomes the limitation that signals extracted by a phase stepping method have random error artifacts, solves the problem of accurately extracting absorption signals, refraction signals and dark field signals of an object when random errors exist in relative displacement of gratings, and realizes quantitative, accurate and artifact-free X-ray multi-contrast signal extraction;
2. compared with the existing phase stepping method, the method introduces an objective function with relative displacement as an independent variable, and obtains an accurate value of the relative displacement of the grating by calculating the minimum value of the standard deviation of the objective function, thereby thoroughly eliminating the random error of the relative displacement;
3. compared with the existing phase stepping method, the method utilizes a least square algorithm, eliminates the requirement of equidistant distribution of relative displacement, eliminates signal artifacts caused by random errors of relative displacement of gratings, and realizes quantitative and accurate extraction of absorption signals, refraction signals and dark field signals of objects.
Drawings
FIG. 1 is a schematic diagram of a prior art X-ray grating interferometer;
FIG. 2 is a graph of light intensity in the prior art;
FIG. 3 is a graph showing the result of the extraction of the absorption signal according to the present invention and the prior art;
FIG. 4 is a graph showing the result of extracting the refraction signal according to the present invention and the prior art;
FIG. 5 is a graph showing the result of extracting dark field signals according to the present invention and the prior art;
FIG. 6 is a graph showing the result of extracting dark field signals of an object to be imaged according to the present invention;
FIG. 7 is a quantitative comparison of the section lines of the present invention;
reference numerals in the drawings: 1, a light source; 2 phase grating; 3, analyzing the grating; 4, a light intensity detector; 5 imaged object.
Detailed Description
In the embodiment, an X-ray grating interferometer consisting of a light source 1, a phase grating 2, an analysis grating 3 and a light intensity detector 4 is arranged; as shown in fig. 1, a rectangular coordinate system O-XYZ is established by taking a position point of a light source 1 as an origin O of the coordinate system, taking a direction of a ray axis as a Z axis, taking a direction of a grating structure perpendicular to the ray axis and parallel to a phase grating 2 as a Y axis, and taking a direction of the grating structure which is commonly perpendicular to the ray axis and the phase grating 2 as an X axis;
a light source 1, a phase grating 2, an analysis grating 3 and a light intensity detector 4 are sequentially arranged along the Z axis; the light source 1, the phase grating 2, the analysis grating 3 and the light intensity detector 4 are aligned in the center along the X axis and aligned in the center along the Y axis;
in this embodiment, a multi-contrast signal extraction method for imaging by an X-ray grating interferometer is performed according to the following steps:
step 1, setting relevant positions of all devices, and meeting the following conditions: l (L) 14 ＞L 13 ＞L 12 > 0, where L 14 Is the relative distance between the light source 1 and the light intensity detector 4 along the Z axis; l (L) 13 The relative distance between the light source 1 and the analytical grating 3 along the Z axis; l (L) 12 The relative distance between the light source 1 and the phase grating 2 along the Z axis;
step 2, obtaining background projection data:
step 2.1, defining a positive integer m as a serial number of the acquired projection data, and initializing m=1;
step 2.2, setting the relative displacement of the analysis grating 3 and the phase grating 2 along the X-axis to be (m×p) 2 ) M; after the light source 1 is started, the light intensity detector 4 is utilized to acquire the mth background projection data according to the exposure time tWherein p is 2 Is the period of the analyzer grating 3; m is the total number of the acquired projection data, and M is a positive integer and satisfies M is more than or equal to 3;
step 2.3, after m+1 is assigned to M, judging whether M > M is satisfied, if so, executing step 2.4; otherwise, returning to the step 2.2;
step 2.4, turning off the light source 1;
exposure time period t: when the light source 1 is a synchrotron radiation light source, a typical value of the exposure time period t is 1 to 50 milliseconds; when the light source 1 is a laboratory light source, a typical value of the exposure time period t is ten to several tens of seconds, depending on the power of the light source;
with the result shown in fig. 2, the mth background projection data acquired by the light intensity detector 4Satisfy formula (2.1):
in the formula (2.1), the amino acid sequence,is the mean value of the background projection data, V r Is the visibility of the background projection data, satisfies 0 < V r ＜1；φ r Is the phase distribution of the background projection data; />Is the random error of the relative displacement of the mth background, satisfying +.>The experiment can be caused by external vibration, thermal drift and other factors.
Step 3, obtaining object projection data:
step 3.1, placing an imaged object 5 between the phase grating 2 and the analysis grating 3 along the Z axis; and the relative distance between the light source 1 and the imaging object 5 along the Z-axis is denoted as L 15 And satisfy L 12 ＜L 15 ＜L 13 The method comprises the steps of carrying out a first treatment on the surface of the Arranging the imaged object 5 and the light intensity detector 4 to be aligned with the center along the X axis and aligned with the center along the Y axis;
step 3.2, initializing m=1;
step 3.3, setting the relative displacement of the analysis grating 3 and the phase grating 2 along the X-axis to be (m×p) 2 ) M; after the light source 1 is started, the light intensity detector 4 is utilized to acquire the projection data of the mth object of the imaged object 5 according to the exposure time t
Step 3.4, after m+1 is assigned to M, judging whether M > M is met, if so, executing step 3.5; otherwise, returning to the step 3.3;
step 3.5, turning off the light source 1;
when the projection data of the object is acquired, the relative displacement of the analysis grating 3 and the phase grating 2 along the X-axis and the value of the exposure time t are kept consistent with the corresponding value when the background projection data is acquired, so that the quantitative extraction of the absorption signal and the dark field signal of the imaged object 5 is facilitated.
With the result shown in fig. 2, the light intensity detector 4 acquires object projection data of the mth imaged object 5Satisfy formula (3.1):
in the formula (3.1), T is an absorption signal of the imaged object 5, and satisfies 0 < T < 1; d is a dark field signal of the imaged object 5, and satisfies 0 < D < 1; θ R Is a refractive signal of the imaged object 5;is the random error of the relative displacement of the mth object, satisfying +.>
Step 4, obtaining the relative displacement of the background:
step 4.1, defining a positive integer m as the serial number of the acquired relative displacement, and initializing m=1;
step 4.2, defining a background objective function X by using a formula (1):
wherein, delta is an independent variable, and the value range is [ (M-0.5)/M (m+0.5)/M]The method comprises the steps of carrying out a first treatment on the surface of the i represents an imaginary unit; a is the mean value of the background projection data, and
step 4.3, calculating the standard deviation sigma of the background objective function X X Wherein the variation interval of the independent variable delta is [ (M-0.5)/M (m+0.5)/M]The method comprises the steps of carrying out a first treatment on the surface of the When the standard deviation of the background objective function X obtains the minimum value, the corresponding value of the independent variable delta is obtained, namely the mth background relative displacementIs a numerical value of (2);
step 4.4, assigning m+1 to M, judging whether M > (M-1) is true, and if so, executing step 5; otherwise, returning to the step 4.2;
ideally, the random error of the relative displacement of the grating is zero, and the acquired (M-1) background projection data acquired by the light intensity detector 4 can be equivalently expressed as:
in the formula (4.1), the background phase distributionIncluding a quasi-constant offset due to random errors in relative displacement.
Further, in a matrix form, the formula (4.1) is equivalently expressed as the formula (4.2):
step 5, obtaining relative displacement of the object:
step 5.1, initializing m=1;
step 5.2, defining an object objective function Y by using the formula (2):
in the formula (2), delta is an independent variable, and the value range is [ (M-0.5)/M (m+0.5)/M)]The method comprises the steps of carrying out a first treatment on the surface of the B is the mean value of the projection data of the object, and
step 5.3, calculating the standard deviation sigma of the object objective function Y Y Wherein the variation interval of the independent variable delta is [ (M-0.5)/M (m+0.5)/M]The method comprises the steps of carrying out a first treatment on the surface of the When the standard deviation of the object objective function Y obtains the minimum value, the corresponding value of the independent variable delta is obtained, namely the mth object relative displacementIs a numerical value of (2);
step 5.4, assigning m+1 to M, judging whether M > (M-1) is true, and if so, executing step 6; otherwise, returning to the step 5.2;
with the acquired (M-1) object relative displacements, the M object projection data acquired by the light intensity detector 4 can be equivalently expressed as:
in equation (5.1), the object phase distribution is due to the unpredictability of the random error of the relative displacementIs usually not equal to the background phase distribution +.>There is a quasi-constant difference between the two, which can be eliminated by post-correction.
Further, in a matrix form, the formula (5.1) is equivalently expressed as the formula (5.2):
step 6, extracting the absorption signal T of the imaging subject 5 by using the formula (3):
T＝B 1 /A 1 (3)
in the formula (3), A 1 Represents a first background parameter, an
Represents the mth background relative displacement; coefficient c 11 、c 12 、c 13 Is an element of the background matrix C, and the background matrix C satisfies:
in the formula (3), B 1 Representing a first object parameter, an
Representing the relative displacement of the mth object; coefficient d 11 、d 12 、d 13 Is an element of the object matrix D, and the object matrix D satisfies:
and (3) solving the formula (4.2) by using a least square method to obtain:
wherein the background matrix C satisfies:
obtained by using the formula (6.1):
similarly, the least square method is applied to solve the formula (5.2), and the result is:
wherein the object matrix D satisfies:
obtained by using the formula (6.3):
extracting the absorption signal T of the imaged object 5 using the formulas (6.2) and (6.4):
T＝B 1 /A 1 (3)
fig. 3 shows the result of extracting the absorption signal of the object 5. As shown in fig. 3, the left graph is an extraction result of the new method provided by the invention, and streak artifacts are hardly seen in the graph. The extraction result of the prior art method shown in the right graph has obvious streak artifact and is inaccurate.
Step 7, extracting the refraction signal θ of the imaging object 5 by using the formula (4) R ：
θ R ＝tan -1 (B 3 /B 2 )-tan -1 (A 3 /A 2 )-Δφ (4)
In the formula (4), B 2 Representing a second object parameter, an
B 3 Representing a third object parameter, an
A 2 Represents a second background parameter, an
A 3 Represents a third background parameter, an
Δφ represents a constant bias and is approximately equal to the mean of the signal for the no object region;
obtained by using the formula (6.1):
obtained by using the formula (7.1):
obtained by using the formula (6.3):
obtained by using the formula (7.3):
obtained by using the formula (7.2) and the formula (7.4):
equivalent(s)Extracting the refraction signal theta of the imaging object 5 by using the formula (3) R ：
θ R ＝tan -1 (B 3 /B 2 )-tan -1 (A 3 /A 2 )-Δφ (3)
In formula (3), the constant biasApproximately equal to the signal mean for the object-free region. Delta phi is approximately constant and can be eliminated by a simple background-subtracted average signal operation without affecting the accuracy of the refraction signal of the imaged object 5.
Fig. 4 shows the extraction result of the refraction signal of the object 5. As shown in fig. 4, the left graph is an extraction result of the new method proposed by the present invention, and streak artifacts are hardly seen in the graph. Whereas the extraction results of the prior art method shown in the right figure have significant streak artifacts. And the artifact strength of the refraction signal is significantly greater than the absorption signal. Further, the results of the present invention always agree well with the theoretical values, as compared with the section line shown in fig. 5, proving the quantitative accuracy of the novel method proposed by the present invention.
Step 8, extracting dark field signal D of the object 5 by using formula (5):
obtained by using the formula (7.1):
obtained by using the formula (7.3):
substitution of formula (3) and formula (8.1) into formula (8.2) yields:
obtained by using the formula (8.3):
/>
fig. 6 shows the extraction result of the dark field signal of the object 5. In fig. 6, the left graph is the extraction result of the new method provided by the invention, the streak artifact is well eliminated, and the streak artifact is basically not seen in the graph. The extraction result of the prior method shown in the right graph has obvious streak artifact, and does not meet the quantitative and accurate requirements. This is a direct result of the inability of existing phase stepping methods to eliminate random errors in relative displacement.
Further, FIG. 7 illustrates a quantitative comparison of section lines. As shown in the figure, the result of the invention keeps quantitative consistency with the theoretical value, and the result of the extraction of the dark field signal of the invention is proved to be quantitative and accurate.
The experimental results shown in fig. 3 to 7 confirm the feasibility, advancement and accuracy of the multi-contrast signal extraction method proposed by the present invention.
With absorption signal T, refraction signal theta of imaged object 5 R The dark field signal D is the result of the multi-contrast signal extraction method.
Claims (1)
1. A multi-contrast signal extraction method for X-ray grating interferometer imaging is applied to an X-ray grating interferometer composed of a light source (1), a phase grating (2), an analysis grating (3) and a light intensity detector (4);
establishing a rectangular coordinate system O-XYZ by taking a position point of the light source (1) as a coordinate system origin O, taking a ray axis direction as a Z axis, taking a grid line structure direction which is perpendicular to the ray axis and parallel to the phase grating (2) as a Y axis and taking a grid line structure direction which is commonly perpendicular to the ray axis and the phase grating (2) as an X axis;
the light source (1), the phase grating (2), the analysis grating (3) and the light intensity detector (4) are sequentially arranged along the Z axis; the light source (1), the phase grating (2), the analysis grating (3) and the light intensity detector (4) are aligned in the center along the X axis and aligned in the center along the Y axis; the multi-contrast signal extraction method for the X-ray grating interferometer imaging is characterized by comprising the following steps of:
step 1, setting relevant positions of all devices, and meeting the following conditions: l (L) 14 ＞L 13 ＞L 12 > 0, where L 14 Is the relative distance between the light source (1) and the light intensity detector (4) along the Z axis; l (L) 13 -a relative distance in the Z-axis of the light source (1) and the analyzer grating (3); l (L) 12 Is the relative distance between the light source (1) and the phase grating (2) along the Z axis;
step 2, obtaining background projection data:
step 2.1, defining a positive integer m as a serial number of the acquired projection data, and initializing m=1;
step 2.2, setting the relative displacement of the analytical grating (3) and the phase grating (2) along the X-axis to be (m multiplied by p) 2 ) M; after the light source (1) is started, the light intensity detector (4) is utilized to acquire the mth background projection data according to the exposure time tWherein p is 2 Is the period of the analyzer grating (3); m is the total number of the acquired projection data, and M is a positive integer and satisfies M is more than or equal to 3;
step 2.3, after m+1 is assigned to M, judging whether M > M is satisfied, if so, executing step 2.4; otherwise, returning to the step 2.2;
step 2.4, turning off the light source (1);
step 3, obtaining object projection data:
step 3.1, placing an imaged object (5) between the phase grating (2) and the analysis grating (3) along the Z axis; and the relative distance between the light source (1) and the imaged object (5) along the Z-axis is denoted as L 15 And satisfy L 12 ＜L 15 ＜L 13 The method comprises the steps of carrying out a first treatment on the surface of the The imaged object (5) and the light intensity detector (4) are arranged along the edgeThe centers are aligned in the X-axis direction and in the Y-axis direction;
step 3.2, initializing m=1;
step 3.3, setting the relative displacement of the analytical grating (3) and the phase grating (2) along the X-axis to be (m multiplied by p) 2 ) M; after the light source (1) is started, the light intensity detector (4) is utilized to acquire the m-th object projection data of the imaged object (5) according to the exposure time t
Step 3.4, after m+1 is assigned to M, judging whether M > M is met, if so, executing step 3.5; otherwise, returning to the step 3.3;
step 3.5, turning off the light source (1);
step 4, obtaining the relative displacement of the background:
step 4.1, defining a positive integer m as the serial number of the acquired relative displacement, and initializing m=1;
step 4.2, defining a background function X by using a formula (1):
in the formula (1), delta is an independent variable, and the value range is [ (M-0.5)/M (m+0.5)/M)]The method comprises the steps of carrying out a first treatment on the surface of the i represents an imaginary unit; a is the mean value of the background projection data, and
step 4.3, defining the background parameter F by using the formula (2) r ：
In the formula (2), sigma X Is the standard deviation of the background function X,is the mean of the background function X;
step 4.4, obtaining the mth background relative displacementSuch that the background parameter F r Obtaining a minimum value;
step 4.5, assigning m+1 to M, judging whether M > (M-1) is true, and if so, executing step 5; otherwise, returning to the step 4.2;
step 5, obtaining relative displacement of the object:
step 5.1, initializing m=1;
step 5.2, defining an object function Y by using a formula (3):
in formula (3), B is the mean value of the projection data of the object, and
step 5.3 defining the object parameter F using (4) s ：
In formula (4), σ Y Is the standard deviation of the object function Y,is the mean value of the object function Y;
step 5.4, obtaining the relative displacement of the mth objectSuch that the object parameter F s Obtaining a minimum value;
step 5.5, assigning m+1 to M, judging whether M > (M-1) is true, and if so, executing step 6; otherwise, returning to the step 5.2;
step 6, extracting the absorption signal T of the imaged object (5) by using the formula (3):
T＝B 1 /A 1 (5)
in the formula (5), A 1 Represents a first background parameter, anCoefficient c 11 、c 12 、c 13 Is an element of the background matrix C, and the background matrix C satisfies:
in the formula (5), B 1 Representing a first object parameter, anCoefficient d 11 、d 12 、d 13 Is an element of the object matrix D, and the object matrix D satisfies:
step 7, extracting the refraction signal theta of the imaged object (5) by using the formula (6) R ：
θ R ＝tan -1 (B 3 /B 2 )-tan -1 (A 3 /A 2 )-Δφ (6)
In the formula (6), B 2 Representing a second object parameter, an
B 3 Representing a third object parameter, an
A 2 Representing a second background parameterAnd (2) and
A 3 represents a third background parameter, an
Δφ represents a constant bias and is approximately equal to the mean of the signal for the no object region;
step 8, extracting a dark field signal D of the imaged object (5) by using the formula (7):
by absorption signal T and refraction signal theta of the imaged object (5) R The dark field signal D is the result of the multi-contrast signal extraction method.
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