CN108680589B - Three-dimensional cone beam computer tomography method and device based on transverse dislocation grating - Google Patents

Three-dimensional cone beam computer tomography method and device based on transverse dislocation grating Download PDF

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CN108680589B
CN108680589B CN201810550520.8A CN201810550520A CN108680589B CN 108680589 B CN108680589 B CN 108680589B CN 201810550520 A CN201810550520 A CN 201810550520A CN 108680589 B CN108680589 B CN 108680589B
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傅健
胡棪君
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Abstract

The invention discloses an X-ray grating differential phase contrast three-dimensional cone beam computer tomography method and a device based on a transverse dislocation grating, wherein the method comprises the following steps: arranging a Talbot-Lau three-dimensional cone beam tomography structure by using a transverse dislocation absorption grating; acquiring a two-dimensional intensity image sequence of the X-ray after passing through the object by using the structure; separating three image sequences of X-ray absorption contrast, differential phase contrast and scattering contrast from the acquired two-dimensional intensity image by a Fourier analysis method; and respectively carrying out image reconstruction on the three contrast image sequences by using an absorption contrast, differential phase contrast and scattering contrast filtering back projection reconstruction algorithm to obtain three contrast CT slice images of the object. According to the invention, the absorption grating does not need to be stepped, and three contrast CT slice images can be obtained by using the traditional CT scanning method based on X-ray attenuation, so that the imaging time is greatly reduced, the imaging dose is reduced, and the imaging efficiency and stability of the system are improved.

Description

Three-dimensional cone beam computer tomography method and device based on transverse dislocation grating
Technical Field
The invention relates to the technical field of X-ray computer tomography, in particular to an X-ray grating differential phase contrast three-dimensional cone beam computer tomography method and device based on a transverse dislocation grating.
Background
In a Computed Tomography (CT) system, an X-ray source emits X-rays, which pass through a certain region of an object to be detected from different angles, and a detector disposed opposite to the X-ray source receives the X-rays at a corresponding angle. Then, according to the attenuation of each angle ray with different degrees, a certain reconstruction algorithm and a computer are used for calculation, and a ray attenuation coefficient distribution mapping image of the scanned region of the object is reconstructed, so that the image is reconstructed by projection, and the characteristics of the object in the region, such as medium density, composition, structural morphology and the like, are reproduced in a lossless manner.
The traditional CT technology based on the X-ray attenuation principle can only obtain an absorption contrast image of an internal structure of an object, and a high-contrast image is difficult to obtain for a structural sample of a material with a low atomic number. In recent years, phase contrast imaging techniques have been proposed to improve the imaging contrast of these low attenuation samples. For example, Yuan Qing Xian et al, CT research on synchrotron radiation hard X-ray diffraction enhanced peak imaging, Chinese Physics C, vol.29.No.10, pp 1023-; pfeiffer F et al, Phase regenerative Phase-coherent imaging with low-brilliance x-ray sources, Nature Physics, vol.2, No.4, pp.258-261,2006, propose a grating-based differential Phase-contrast method; zantete I et al, Package-based x-ray phase-contrast imaging using a mapping interferometer, Physical review viewer, vol.112, No.25,2014, propose a Speckle phase contrast imaging technique. The differential phase contrast method based on the grating can be realized by adopting a common X-ray tube, has great engineering application prospect and is widely researched.
However, most of the existing grating-based differential phase contrast methods are traditional methods based on absorption grating translation stepping, and have the disadvantages of long imaging time, large dosage, low stability and low efficiency, so that further engineering application of the method is restricted.
At present, an X-ray grating differential phase contrast three-dimensional cone beam computer tomography device based on a transverse dislocation absorption grating is not found.
Disclosure of Invention
The invention provides an X-ray grating differential phase contrast three-dimensional cone beam computer tomography method and device based on a transverse dislocation grating in order to overcome the defects of the prior art.
The technical scheme adopted by the invention is as follows: an X-ray grating differential phase contrast three-dimensional cone beam computer tomography method based on transverse dislocation grating comprises the following steps:
step 1, acquiring a two-dimensional projection image sequence of an X-ray passing through an object by using a Talbot-Lau three-dimensional tomography structure based on transverse dislocation grating; the two-dimensional projection image sequence is a two-dimensional projection obtained by periodically acquiring X-rays through an object by the detector in the process that the object rotates along the axial direction, and acquiring a two-dimensional projection image of the object in one acquisition period;
step 2, Fourier transform is carried out on the two-dimensional projection image sequence to separate three contrast images of X-ray absorption contrast, differential phase contrast and scattering contrast;
and 3, respectively carrying out image reconstruction on the three contrast two-dimensional image sequences by using an absorption contrast, differential phase contrast and scattering contrast filtering back projection reconstruction algorithm to obtain three CT slice images of the object absorption contrast, the phase contrast and the scattering contrast.
Further, the lateral dislocation absorption grating arrangement Talbot-Lau imaging structure includes:
the Talbot-Lau imaging structure optical path comprises six parts in total: an X-ray source, a source grating G0, a test object, a phase grating G1, an absorption grating G2 and a detector;
the Talbot-Lau imaging structure optical path parameters meet the following formulas (1) to (4):
Figure BDA0001681101200000021
kg1＝2g2， (2)
g0＝g2·L/d， (3)
s<g2·L/2d， (4)
where d represents the distance between the phase grating G1 and the absorption grating G2; k is (L + d)/L is the amplification ratio, and L is the direct distance between the source grating G0 and the phase grating G1; m represents the mth order fractional Talbot distance; g1The period of the phase grating G1, λ being the wavelength of the X-rays used, G2To absorb the period of the grating G2, G0The period of the source grating G0, s is the width of the source grating that allows transmission of X-rays at each period;
the transverse dislocation absorption grating is an absorption grating G2 in the light path of the Talbot-Lau imaging structure, and transverse periodic dislocation occurs at the relative position of the absorption grating G2 and a detector probe element, so that intensity signals obtained by a plurality of transverse adjacent detector probe elements can be equivalent to intensity signals obtained by one detector probe element at a plurality of different positions in the traditional imaging method;
for 4 laterally adjacent detector probe elements, respectively labeled as p1、p2、p3、p4Each probe px(x is 1,2,3,4) width w, and in the transverse dislocation absorbing grating, it corresponds to a segment of grating gp with length wxEach section of grating gpxHas a grating period of g2The gratings corresponding to adjacent detector elements have a position difference of f, e.g. adjacent detector element p1And p2Corresponding grating segment gp1With gp2There is a difference in the position of f, where f ═ g2/4，gpxThe position of the grating is equivalent to the position of the absorption grating when the absorption grating moves to x, the positions of the absorption gratings corresponding to the adjacent 4 detector detecting elements are different, the absorption gratings are staggered by a distance f, the grating is called as a transverse staggered grating, and the detector detecting elements pxThe obtained X-ray intensity signal values are the intensity values collected when the absorption grating G2 is moved to position X.
Further, step 1 further comprises:
in the Talbot-Lau imaging structure, when an object is not placed on the rotary table, the rotary table rotates 360 degrees at a constant speed along the rotation center, an imaging area is covered by a cone beam in the rotating process, and a detector acquires a two-dimensional projection image;
in the Talbot-Lau imaging structure, when an object is placed on the rotary table, the rotary table rotates 360 degrees along the rotation center at a constant speed, an imaging area is covered by a cone beam in the rotating process, and a detector acquires a two-dimensional projection image.
Further, still include:
and (3) carrying out image analysis on the two-dimensional projection image sequence according to formulas (5) to (14) to obtain three contrast two-dimensional projection image sequences:
I1(x,z,θ)＝I(x-1,z,θ), (5)
I2(x,z,θ)＝I(x,z,θ), (6)
I3(x,z,θ)＝I(x+1,z,θ), (7)
I4(x,z,θ)＝I(x+2,z,θ), (8)
Figure BDA0001681101200000031
Figure BDA0001681101200000032
Figure BDA0001681101200000033
Figure BDA0001681101200000034
phase(x,z,θ)＝φs(x,z,θ)-φr(x,z,θ), (13)
Figure BDA0001681101200000035
wherein x is the abscissa of the two-dimensional projection diagram point; z is the vertical coordinate of the two-dimensional projection image point, and theta is the projection angle of the two-dimensional projection image; i (x, z, theta) is the intensity value of the point (x, z) in the two-dimensional projection diagram at the projection angle theta; i is1(x,z,θ)、I2(x,z,θ)、I3(x,z,θ)、I4(x, z, theta) represent 4 different intensity values of the point (x, z) at the projection angle theta, respectively, simulating the intensity values of the point (x, z) in the conventional grating differential phase contrast image at the projection angle theta when the absorption grating is at 4 different step positions; m represents the number of different intensity values in one point (x, z), where M is 4; a is0(x, z, θ) is the mean of the sinusoids fitted to the point (x, z) at 4 different intensity values of the projection angle θ; a is1(x, z, theta) is the amplitude of a sine curve fitted to the point (x, z) at 4 different intensity values of the projection angle theta; phi (x, z, theta) is the phase value of a sine curve fitted to the 4 different intensity values of the point (x, z) at the projection angle theta;
Figure BDA0001681101200000036
denotes a when the test object is not placed at the projection angle theta0(x,z,Theta) the value of the one or more of,
Figure BDA0001681101200000041
denotes a when the test object is placed at a projection angle theta0(x, z, θ) values;
Figure BDA0001681101200000042
denotes a when the test object is not placed at the projection angle theta1The (x, z, theta) value,
Figure BDA0001681101200000043
denotes a when the test object is placed at a projection angle theta1(x, z, θ) values; phi is ar(x, z, theta) represents the value of phi (x, z, theta) at the projection angle theta without placing the test object, phis(x, z, θ) represents the value of φ (x, z, θ) at which the test object is placed at the projection angle θ; abs (x, z, θ) is the value of the absorption contrast at projection angle θ point (x, z); phase (x, z, θ) is the value of the differential phase contrast at projection angle θ point (x, z); dark (x, z, theta) is the value of scatter contrast imaging at projection angle theta point (x, z).
Further, using an absorption contrast, differential phase contrast and scattering contrast filtering back projection reconstruction algorithm to respectively perform image reconstruction on the three contrast two-dimensional image sequences to obtain three CT slice images of the object absorption contrast, the phase contrast and the scattering contrast, including:
and (2) carrying out image analysis on the two-dimensional projection image sequence according to formulas (15) to (17) to obtain three contrast two-dimensional projection image sequences:
Figure BDA0001681101200000044
Figure BDA0001681101200000045
Figure BDA0001681101200000046
wherein the content of the first and second substances,a (x, y, z), p (x, y, z) and d (x, y, z) are respectively reconstructed absorption contrast slice image, phase contrast slice image and scattering contrast slice image; abs (s, v, theta), phase (s, v, theta) and dark (s, v, theta) represent absorption contrast, differential phase contrast and scattering contrast two-dimensional projections, respectively, at a projection angle theta, s, v are coordinates of intersection points of a line connecting a pixel point on the detector and the radiation source and a virtual detector placed at the rotation axis, respectively; xi is the included angle between the ray and the central ray; d is the distance from the ray source to the plane of the virtual detector; y' is the distance from the pixel point of the reconstructed image to the plane of the virtual detector; h isa(s)、hp(s) and hd(s) filters for two-dimensional projection of absorption contrast, differential phase contrast and scattering contrast, respectively, defined by equations (18) - (19):
ha(s)＝|s|, (18)
Figure BDA0001681101200000047
hd(s)＝|s|, (20)
another aspect of the present invention provides an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography apparatus based on laterally dislocated grating, comprising:
the device comprises an acquisition module, a detection module and a display module, wherein the acquisition module is used for acquiring a two-dimensional projection image sequence acquired by a detector, the two-dimensional projection image sequence is a plurality of two-dimensional projection images acquired by periodically acquiring rays transmitted through an object by the detector in the process that the object rotates along the axial direction, and one sampling period corresponds to one two-dimensional projection image of the object;
the calculation module is used for carrying out Fourier transform on the two-dimensional projection image sequence to obtain an absorption contrast, a differential phase contrast and a scattering contrast two-dimensional projection sequence; and reconstructing the three-contrast two-dimensional projection sequence by using three-contrast filtering inverse reconstruction algorithms of absorption contrast, differential phase contrast and scattering contrast to obtain a three-dimensional CT slice image.
Further, the lateral dislocation absorption grating arrangement Talbot-Lau imaging structure includes:
the Talbot-Lau imaging structure optical path comprises six parts in total: an X-ray source, a source grating G0, a test object, a phase grating G1, an absorption grating G2 and a detector;
the Talbot-Lau imaging structure optical path parameters meet the following formulas (1) to (4):
Figure BDA0001681101200000051
kg1＝2g2， (2)
g0＝g2·L/d， (3)
s<g2·L/2d， (4)
where d represents the distance between the phase grating G1 and the absorption grating G2; k is (L + d)/L is the amplification ratio, and L is the direct distance between the source grating G0 and the phase grating G1; m represents the mth order fractional Talbot distance; g1The period of the phase grating G1, λ being the wavelength of the X-rays used, G2To absorb the period of the grating G2, G0The period of the source grating G0, s is the width of the source grating that allows transmission of X-rays at each period;
the transverse dislocation absorption grating is an absorption grating G2 in the light path of the Talbot-Lau imaging structure, and transverse periodic dislocation occurs at the relative position of the absorption grating G2 and a detector probe element, so that intensity signals obtained by a plurality of transverse adjacent detector probe elements can be equivalent to intensity signals obtained by one detector probe element at a plurality of different positions in the traditional imaging method;
for 4 laterally adjacent detector probe elements, respectively labeled as p1、p2、p3、p4Each probe px(x is 1,2,3,4) width w, and in the transverse dislocation absorbing grating, it corresponds to a segment of grating gp with length wxEach section of grating gpxHas a grating period of g2The gratings corresponding to adjacent detector elements have a position difference of f, e.g. adjacent detector element p1And p2Corresponding grating segment gp1With gp2There is a difference in the position of f, where f ═ g2/4，gpxThe position of the grating is equivalent to the position of the absorption grating when the absorption grating moves to x, the positions of the absorption gratings corresponding to the adjacent 4 detector detecting elements are different, the absorption gratings are staggered by a distance f, the grating is called as a transverse staggered grating, and the detector detecting elements pxThe obtained X-ray intensity signal values are the intensity values collected when the absorption grating G2 is moved to position X.
Further, the obtaining module further comprises:
in the Talbot-Lau imaging structure, when an object is not placed on the rotary table, the rotary table rotates 360 degrees at a constant speed along the rotation center, an imaging area is covered by a cone beam in the rotating process, and a detector acquires a two-dimensional projection image;
in the Talbot-Lau imaging structure, when an object is placed on the rotary table, the rotary table rotates 360 degrees along the rotation center at a constant speed, an imaging area is covered by a cone beam in the rotating process, and a detector acquires a two-dimensional projection image.
Further, the calculation module separates three images of X-ray absorption contrast, differential phase contrast and scattering contrast from the acquired two-dimensional intensity image by a fourier analysis method, including:
and (3) carrying out image analysis on the two-dimensional projection image sequence according to formulas (5) to (14) to obtain three contrast two-dimensional projection image sequences:
I1(x,z,θ)＝I(x-1,z,θ), (5)
I2(x,z,θ)＝I(x,z,θ), (6)
I3(x,z,θ)＝I(x+1,z,θ), (7)
I4(x,z,θ)＝I(x+2,z,θ), (8)
Figure BDA0001681101200000061
Figure BDA0001681101200000062
Figure BDA0001681101200000063
Figure BDA0001681101200000064
phase(x,z,θ)＝φs(x,z,θ)-φr(x,z,θ), (13)
Figure BDA0001681101200000065
wherein x is the abscissa of the two-dimensional projection diagram point; z is the vertical coordinate of the two-dimensional projection image point, and theta is the projection angle of the two-dimensional projection image; i (x, z, theta) is the intensity value of the point (x, z) in the two-dimensional projection diagram at the projection angle theta; i is1(x,z,θ)、I2(x,z,θ)、I3(x,z,θ)、I4(x, z, theta) represent 4 different intensity values of the point (x, z) at the projection angle theta, respectively, simulating the intensity values of the point (x, z) in the conventional grating differential phase contrast image at the projection angle theta when the absorption grating is at 4 different step positions; m represents the number of different intensity values in one point (x, z), where M is 4; a is0(x, z, θ) is the mean of the sinusoids fitted to the point (x, z) at 4 different intensity values of the projection angle θ; a is1(x, z, theta) is the amplitude of a sine curve fitted to the point (x, z) at 4 different intensity values of the projection angle theta; phi (x, z, theta) is the phase value of a sine curve fitted to the 4 different intensity values of the point (x, z) at the projection angle theta;
Figure BDA0001681101200000066
denotes a when the test object is not placed at the projection angle theta0The (x, z, theta) value,
Figure BDA0001681101200000067
denotes a when the test object is placed at a projection angle theta0(x, z, θ) values;
Figure BDA0001681101200000068
showing the hold-off test at projection angle thetaA when an object is present1The (x, z, theta) value,
Figure BDA0001681101200000069
denotes a when the test object is placed at a projection angle theta1(x, z, θ) values; phi is ar(x, z, theta) represents the value of phi (x, z, theta) at the projection angle theta without placing the test object, phis(x, z, θ) represents the value of φ (x, z, θ) at which the test object is placed at the projection angle θ; abs (x, z, θ) is the value of the absorption contrast at projection angle θ point (x, z); phase (x, z, θ) is the value of the differential phase contrast at projection angle θ point (x, z); dark (x, z, theta) is the value of scatter contrast imaging at projection angle theta point (x, z).
Further, the calculation module uses an absorption contrast, a differential phase contrast and a scattering contrast filtering back projection reconstruction algorithm to respectively perform image reconstruction on the three contrast two-dimensional image sequences to obtain three CT slice images of the object absorption contrast, the phase contrast and the scattering contrast, and the method comprises the following steps:
and (2) carrying out image analysis on the two-dimensional projection image sequence according to formulas (15) to (17) to obtain three contrast two-dimensional projection image sequences:
Figure BDA0001681101200000071
Figure BDA0001681101200000072
Figure BDA0001681101200000073
wherein a (x, y, z), p (x, y, z) and d (x, y, z) are respectively reconstructed absorption contrast slice image, phase contrast slice image and scattering contrast slice image; abs (s, v, theta), phase (s, v, theta) and dark (s, v, theta) represent the absorption, differential phase and scatter contrast two-dimensional projections, respectively, at a projection angle theta, s, v being the intersection locus of a line connecting a pixel point on the detector with the source and a virtual detector placed at the axis of rotation, respectivelyMarking; xi is the included angle between the ray and the central ray; d is the distance from the ray source to the plane of the virtual detector; y' is the distance from the pixel point of the reconstructed image to the plane of the virtual detector; h isa(s)、hp(s) and hd(s) filters for two-dimensional projection of absorption contrast, differential phase contrast and scattering contrast, respectively, defined by equations (18) - (19):
ha(s)＝|s|, (18)
Figure BDA0001681101200000074
hd(s)＝|s|, (20)
compared with the prior art, the invention has the advantages that: (1) the invention can solve the problem of multiple exposures under one projection angle and reduce the radiation dose; (2) in the process of projection imaging under an angle, grating stepping is avoided, and errors caused by mechanical shaking and the like are eliminated; (3) three-dimensional tomographic images of three kinds of contrast of absorption contrast, phase contrast and scattering contrast of an object can be obtained only by one exposure imaging at each angle.
Drawings
Fig. 1 is a flowchart of an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography method based on a laterally dislocated grating according to an embodiment of the present invention;
fig. 2 is a schematic diagram of an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography system based on a laterally displaced grating according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a structure of a novel lateral displacement absorption grating according to an embodiment of the present invention;
FIG. 4 is a two-dimensional projection image of an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography method based on a laterally dislocated absorption grating;
FIG. 5 is four two-dimensional projection images of a conventional X-ray grating differential phase contrast imaging method;
FIG. 6 is an absorption contrast, differential phase contrast, and scattering contrast image obtained by an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography method based on a laterally dislocated absorption grating;
FIG. 7 is an absorption contrast, differential phase contrast, and scattering contrast image obtained by a conventional X-ray grating differential phase contrast imaging method;
fig. 8 is a CT image of an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography method based on a laterally dislocated absorption grating according to an embodiment of the present invention;
fig. 9 is a CT image of a conventional X-ray grating differential phase contrast imaging method.
Fig. 10 is a structural diagram of an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography apparatus based on a laterally dislocated absorption grating according to an embodiment of the present invention.
In the figure: 20 is an X-ray source, 21 is an X-ray beam, 22 is a source grating G0, 23 is an object to be measured, 24 is a phase grating G1, 25 is a transverse dislocation absorption grating G2, 26 is a detector, 27 is a computer, 100 is an X-ray cylindrical three-dimensional cone beam computer tomography device, 101 is an acquisition module, and 102 is a calculation module.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
Fig. 1 is a flowchart of an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography method based on a laterally dislocated absorption grating according to an embodiment of the present invention; the embodiment of the invention provides an X-ray grating differential phase contrast three-dimensional cone beam computer tomography method based on a transverse dislocation absorption grating, aiming at the problems that the prior X-ray absorption contrast CT imaging and the prior X-ray grating differential phase contrast CT imaging have only one contrast or can obtain three contrasts, but the slice image needs to be exposed for multiple times under a projection angle, the radiation dose is large, the imaging time is long, the efficiency is low, the mechanical jitter error is large and the like, and the method comprises the following specific steps:
step S101, a two-dimensional projection image sequence of X-rays passing through an object is obtained by the aid of the Talbot-Lau three-dimensional tomography structure based on the transverse dislocation grating. The two-dimensional projection sequence is a two-dimensional projection obtained by periodically acquiring X-rays through an object by the detector in the process that the object rotates along the axial direction, and acquiring a two-dimensional projection image of the object in one acquisition period.
The Talbot-Lau three-dimensional tomography structure optical path parameters meet the following formulas (1) to (4):
Figure BDA0001681101200000081
kg1＝2g2， (2)
g0＝g2·L/d， (3)
s<g2·L/2d， (4)
where d represents the distance between the phase grating G1 and the absorption grating G2; k is (L + d)/L is the amplification ratio, and L is the direct distance between the source grating G0 and the phase grating G1; m represents the mth order fractional Talbot distance; g1The period of the phase grating G1, λ being the wavelength of the X-rays used, G2To absorb the period of the grating G2, G0The period of the source grating G0, s is the width of the source grating that allows transmission of X-rays at each period.
Fig. 2 is a schematic diagram of an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography system based on a laterally displaced grating according to an embodiment of the present invention; as shown in fig. 2, the X-ray grating differential phase contrast three-dimensional cone-beam computed tomography system based on the laterally dislocated grating comprises: the X-ray source 20, the X-ray beam 21, the source grating G022, the object 23 to be measured, the phase grating G124, the transverse dislocation absorption grating G225, the detector 26 and the computer 27. Wherein the detector 26 and the X-ray source 20 are connected to a computer 27, respectively. Computer 27 is used to control the intensity and time of the X-ray beam 21 generated by X-ray source 20 and to control detector 26 to acquire two-dimensional intensity images. The X-ray beam 21 generated by the X-ray source 20 transmits the object 23 to be detected after passing through the source grating G022, the imaging area of the object 23 to be detected is covered by the X-ray beam 21, and the X-ray beam 21 is acquired by the detector 26 after passing through the phase grating G124 and the transverse dislocation absorption grating G225 modulation signal. After the acquisition is completed, the computer 27 controls the detector 26 to stop sampling, controls the X-ray source 20 to stop generating X-rays, and completes one projection imaging at one projection angle by the X-ray grating differential phase contrast three-dimensional cone-beam computer tomography system based on the transverse dislocation grating. The whole tomography process is as follows: under each projection angle, in the Talbot-Lau three-dimensional tomography structure, the object 23 to be detected is not placed firstly, and the computer 27 controls the detector 26 to acquire the two-dimensional intensity image at the moment; then, placing the object 23 to be tested in the Talbot-Lau imaging optical path, ensuring that the object is completely covered by the X-ray beam 21 in the test area, and controlling a detector 26 by a computer 27 to acquire an X-ray two-dimensional intensity image attenuated by the object 23 to be tested; the projection angle covers 360 degrees, and after the acquisition is carried out at each projection angle, the acquisition of a tomography two-dimensional projection image sequence is completed.
Fig. 3 is a schematic structural diagram of a novel lateral misalignment absorption grating according to an embodiment of the present invention.
And S102, carrying out Fourier transform on the two-dimensional projection image sequence to separate three contrast image sequences of X-ray absorption contrast, differential phase contrast and scattering contrast.
The computer 27 performs fourier transform on the two-dimensional projection image sequence acquired by the detector to separate three contrast image sequences of X-ray absorption contrast, differential phase contrast and scattering contrast, including:
and (3) carrying out image analysis on the two-dimensional projection image sequence according to formulas (5) to (14) to obtain three contrast two-dimensional projection image sequences:
I1(x,z,θ)＝I(x-1,z,θ), (5)
I2(x,z,θ)＝I(x,z,θ), (6)
I3(x,z,θ)＝I(x+1,z,θ), (7)
I4(x,z,θ)＝I(x+2,z,θ), (8)
Figure BDA0001681101200000101
Figure BDA0001681101200000102
Figure BDA0001681101200000103
Figure BDA0001681101200000104
phase(x,z,θ)＝φs(x,z,θ)-φr(x,z,θ), (13)
Figure BDA0001681101200000105
wherein x is the abscissa of the two-dimensional projection diagram point; z is the vertical coordinate of the two-dimensional projection image point, and theta is the projection angle of the two-dimensional projection image; i (x, z, theta) is the intensity value of the point (x, z) in the two-dimensional projection diagram at the projection angle theta; i is1(x,z,θ)、I2(x,z,θ)、I3(x,z,θ)、I4(x, z, theta) represent 4 different intensity values of the point (x, z) at the projection angle theta, respectively, simulating the intensity values of the point (x, z) in the conventional grating differential phase contrast image at the projection angle theta when the absorption grating is at 4 different step positions; m represents the number of different intensity values in one point (x, z), where M is 4; a is0(x, z, θ) is the mean of the sinusoids fitted to the point (x, z) at 4 different intensity values of the projection angle θ; a is1(x, z, theta) is the amplitude of a sine curve fitted to the point (x, z) at 4 different intensity values of the projection angle theta; phi (x, z, theta) is the phase value of a sine curve fitted to the 4 different intensity values of the point (x, z) at the projection angle theta;
Figure BDA0001681101200000106
denotes a when the test object is not placed at the projection angle theta0The (x, z, theta) value,
Figure BDA0001681101200000107
denotes a when the test object is placed at a projection angle theta0(x, z, θ) values;
Figure BDA0001681101200000108
denotes a when the test object is not placed at the projection angle theta1The (x, z, theta) value,
Figure BDA0001681101200000109
denotes a when the test object is placed at a projection angle theta1(x, z, θ) values; phi is ar(x, z, theta) represents the value of phi (x, z, theta) at the projection angle theta without placing the test object, phis(x, z, θ) represents the value of φ (x, z, θ) at which the test object is placed at the projection angle θ; abs (x, z, θ) is the value of the absorption contrast at projection angle θ point (x, z); phase (x, z, θ) is the value of the differential phase contrast at projection angle θ point (x, z); dark (x, z, theta) is the value of scatter contrast imaging at projection angle theta point (x, z).
Step S103, using an absorption contrast, differential phase contrast and scattering contrast filtering back projection reconstruction algorithm to respectively carry out image reconstruction on the three contrast two-dimensional image sequences to obtain three CT slice images of the object absorption contrast, the phase contrast and the scattering contrast, wherein the CT slice images comprise:
and (2) carrying out image analysis on the two-dimensional projection image sequence according to formulas (15) to (17) to obtain three contrast two-dimensional projection image sequences:
Figure BDA00016811012000001010
Figure BDA00016811012000001011
Figure BDA0001681101200000111
wherein a (x, y, z), p (x, y, z) and d (x, y, z) are respectively reconstructed absorption contrast slice image, phase contrast slice image and scattering contrast slice image; abs (s, v, θ), phase (s, v, θ) and dark (s, v, θ) represent projections, respectivelyTwo-dimensional projection of absorption contrast, differential phase contrast and scattering contrast under an angle theta, wherein s and v are coordinates of intersection points of a connecting line of a pixel point on the detector and the ray source and a virtual detector placed at the position of the rotating shaft respectively; xi is the included angle between the ray and the central ray; d is the distance from the ray source to the plane of the virtual detector; y' is the distance from the pixel point of the reconstructed image to the plane of the virtual detector; h isa(s)、hp(s) and hd(s) filters for two-dimensional projection of absorption contrast, differential phase contrast and scattering contrast, respectively, defined by equations (18) - (19):
ha(s)＝|s|, (18)
Figure BDA0001681101200000112
hd(s)＝|s|, (20)
compared with the existing CT technology based on X-ray absorption contrast and X-ray grating differential phase contrast, the method can be used for imaging by only one exposure at each projection angle, and finally reconstructing the three kinds of contrast tomographic images of the absorption contrast, the phase contrast and the scattering contrast of the object.
In order to prove the effects of the above embodiments, the following experiments were carried out in the embodiments of the present invention, and the experimental procedures were as follows:
(1) the experimental conditions were set. The source grating G0, the phase grating G1, and the absorption grating G2 of the present experiment were designed under the condition that the X-ray energy was 28 keV. The period of the source grating G0 is 14 microns; the period of the phase grating G1 was 3.5 microns; the period of the absorption grating G2 was 2.0 microns. The distance between the source grating G0 and the phase grating G1 is 1400 mm, and the distance between the phase grating G1 and the absorption grating G2 is 200 mm, corresponding to the 5 th fraction Talbot distance (m 5). The size of the two-dimensional intensity image is 307 × 652.
(2) And arranging a Talbot-Lau imaging structure according to the parameter requirements of the Talbot-Lau imaging optical path.
(3) According to the set parameters, the computer controls the rotary table to rotate, the detector collects the projection data of the front and the back of the object to be measured, and a two-dimensional projection image sequence is generated according to the projection data.
(4) The computer performs separation of three image sequences of absorption contrast, differential phase contrast and scattering contrast using fourier analysis on the two-dimensional projection image sequences according to the above equations (5) to (14).
(5) And (4) respectively carrying out image reconstruction on the separated image sequences of the absorption contrast, the differential phase contrast and the scattering contrast of the object by the computer according to the formulas (15) to (20) to obtain three kinds of contrast tomographic images of the object.
FIG. 4 is a two-dimensional projection image obtained by an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography system based on a laterally displaced grating; FIG. 6 is a two-dimensional projection image of absorption contrast, differential phase contrast and scattering contrast resolved by an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography system based on a laterally dislocated grating; FIG. 8 is a CT image reconstructed by an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography system based on a laterally dislocated grating. As can be seen from fig. 4, 6 and 8, the X-ray grating differential phase contrast three-dimensional cone-beam computed tomography system based on the laterally dislocated grating can correctly separate three contrast two-dimensional projection images of the object and reconstruct three contrast tomographic images of the object.
FIG. 5 is a two-dimensional projection image obtained using a conventional X-ray grating differential phase contrast imaging method; FIG. 7 is a two-dimensional projection image of absorption contrast, differential phase contrast and scattering contrast resolved by a conventional X-ray grating differential phase contrast imaging method; fig. 9 is a CT image reconstructed by a conventional X-ray grating differential phase contrast computed tomography system. As can be obviously observed from fig. 5, the conventional X-ray grating differential phase contrast imaging method needs 4 exposures on the object, which greatly increases the imaging time and radiation dose and significantly reduces the imaging efficiency.
As can be seen from fig. 4, 5, 6, 7, 8, and 9, the embodiment of the present invention can rapidly and correctly perform three-dimensional imaging of absorption contrast, phase contrast, and scattering contrast on an object, and can implement a projection imaging process by only one exposure at each projection angle without multiple exposures of the conventional grating differential imaging method, thereby reducing imaging time, significantly reducing radiation dose, reducing errors caused by mechanical jitter, improving the efficiency of imaging with three kinds of contrast, and having a simple and easy process.
Fig. 10 is a structural diagram of an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography apparatus based on a laterally-displaced grating according to an embodiment of the present invention. The X-ray grating differential phase contrast three-dimensional cone-beam computed tomography apparatus based on the laterally dislocated grating provided in the embodiments of the present invention can execute the processing procedures provided in the three-dimensional cone-beam computed tomography method embodiments of the object, as shown in fig. 10, the X-ray grating differential phase contrast three-dimensional cone-beam computed tomography apparatus 100 based on the laterally dislocated grating includes an obtaining module 101 and a calculating module 102, where the obtaining module 101 is configured to obtain a two-dimensional projection image sequence acquired by a detector; the calculation module 102 is configured to perform fourier analysis on the two-dimensional projection image sequence to separate three contrast projection image sequences, and reconstruct three contrast tomographic images by using three contrast filtering inverse reconstruction algorithms, respectively.
Compared with the existing CT technology based on X-ray absorption contrast and X-ray grating differential phase contrast, the method can be used for imaging by only one exposure at each projection angle, and finally reconstructing the three kinds of contrast tomographic images of the absorption contrast, the phase contrast and the scattering contrast of the object.
The obtaining module 101 needs to arrange the devices according to the parameter requirements of the Talbot-Lau imaging optical path, and the detector collects a two-dimensional intensity image of the object to be measured.
The Talbot-Lau imaging structure optical path parameters meet the following formulas (1) to (4):
Figure BDA0001681101200000121
kg1＝2g2， (2)
g0＝g2·L/d， (3)
s<g2·L/2d， (4)
where d represents the distance between the phase grating G1 and the absorption grating G2; k is (L + d)/L is the amplification ratio, and L is the direct distance between the source grating G0 and the phase grating G1; m represents the mth order fractional Talbot distance; g1The period of the phase grating G1, λ being the wavelength of the X-rays used, G2To absorb the period of the grating G2, G0The period of the source grating G0, s is the width of the source grating that allows transmission of X-rays at each period.
The calculation module 102 performs image analysis on the two-dimensional projection image sequence according to formulas (5) to (14) to obtain three contrast two-dimensional projection image sequences:
I1(x,z,θ)＝I(x-1,z,θ), (5)
I2(x,z,θ)＝I(x,z,θ), (6)
I3(x,z,θ)＝I(x+1,z,θ), (7)
I4(x,z,θ)＝I(x+2,z,θ), (8)
Figure BDA0001681101200000131
Figure BDA0001681101200000132
Figure BDA0001681101200000133
Figure BDA0001681101200000134
phase(x,z,θ)＝φs(x,z,θ)-φr(x,z,θ), (13)
Figure BDA0001681101200000135
wherein x is the abscissa of the two-dimensional projection diagram point; z is the vertical coordinate of the two-dimensional projection image point, and theta is the projection angle of the two-dimensional projection image; i (x, z, theta) is the intensity value of the point (x, z) in the two-dimensional projection diagram at the projection angle theta; i is1(x,z,θ)、I2(x,z,θ)、I3(x,z,θ)、I4(x, z, theta) represent 4 different intensity values of the point (x, z) at the projection angle theta, respectively, simulating the intensity values of the point (x, z) in the conventional grating differential phase contrast image at the projection angle theta when the absorption grating is at 4 different step positions; m represents the number of different intensity values in one point (x, z), where M is 4; a is0(x, z, θ) is the mean of the sinusoids fitted to the point (x, z) at 4 different intensity values of the projection angle θ; a is1(x, z, theta) is the amplitude of a sine curve fitted to the point (x, z) at 4 different intensity values of the projection angle theta; phi (x, z, theta) is the phase value of a sine curve fitted to the 4 different intensity values of the point (x, z) at the projection angle theta;
Figure BDA0001681101200000136
denotes a when the test object is not placed at the projection angle theta0The (x, z, theta) value,
Figure BDA0001681101200000137
denotes a when the test object is placed at a projection angle theta0(x, z, θ) values;
Figure BDA0001681101200000138
denotes a when the test object is not placed at the projection angle theta1The (x, z, theta) value,
Figure BDA0001681101200000139
denotes a when the test object is placed at a projection angle theta1(x, z, θ) values; phi is ar(x, z, theta) represents the value of phi (x, z, theta) at the projection angle theta without placing the test object, phis(x, z, theta) denotes the placement at projection angle thetaPhi (x, z, theta) values when testing an object; abs (x, z, θ) is the value of the absorption contrast at projection angle θ point (x, z); phase (x, z, θ) is the value of the differential phase contrast at projection angle θ point (x, z); dark (x, z, theta) is the value of scatter contrast imaging at projection angle theta point (x, z).
The calculation module 102 performs image analysis on the two-dimensional projection image sequence according to formulas (15) - (17) to obtain three contrast two-dimensional projection image sequences:
Figure BDA0001681101200000141
Figure BDA0001681101200000142
Figure BDA0001681101200000143
wherein a (x, y, z), p (x, y, z) and d (x, y, z) are respectively reconstructed absorption contrast slice image, phase contrast slice image and scattering contrast slice image; abs (s, v, theta), phase (s, v, theta) and dark (s, v, theta) represent absorption contrast, differential phase contrast and scattering contrast two-dimensional projections, respectively, at a projection angle theta, s, v are coordinates of intersection points of a line connecting a pixel point on the detector and the radiation source and a virtual detector placed at the rotation axis, respectively; xi is the included angle between the ray and the central ray; d is the distance from the ray source to the plane of the virtual detector; y' is the distance from the pixel point of the reconstructed image to the plane of the virtual detector; h isa(s)、hp(s) and hd(s) filters for two-dimensional projection of absorption contrast, differential phase contrast and scattering contrast, respectively, defined by equations (18) - (19):
ha(s)＝|s|, (18)
Figure BDA0001681101200000144
hd(s)＝|s|, (20)
compared with the existing CT technology based on X-ray absorption contrast and X-ray grating differential phase contrast, the method can be used for imaging by only one exposure at each projection angle, and finally reconstructing the three kinds of contrast tomographic images of the absorption contrast, the phase contrast and the scattering contrast of the object.
The X-ray grating differential phase contrast three-dimensional cone-beam computed tomography apparatus based on the laterally dislocated grating provided in the embodiment of the present invention may be specifically configured to perform the method embodiment provided in fig. 1, and specific functions are not described herein again.
The embodiment of the invention can rapidly carry out two-dimensional projection imaging on the absorption contrast, the differential phase contrast and the scattering contrast of an object, reconstruct three-dimensional contrast tomography images, and separate three-dimensional contrast projection images by only one exposure at each projection angle, thereby reducing the imaging time, reducing the radiation dose, eliminating the error caused by mechanical shaking and improving the imaging efficiency.
In summary, compared with the existing CT technology, the embodiment of the present invention can perform three-dimensional tomographic imaging of three kinds of contrast, i.e., absorption contrast, phase contrast, and scattering contrast, on an object; the method has the advantages that the steps are simple, only one exposure is needed at each projection angle, and three contrast two-dimensional projection images can be obtained without stepping the absorption grating for multiple times; the two-dimensional projection imaging time is reduced; the radiation dose is reduced; the error caused by mechanical shaking is eliminated; the imaging efficiency is improved.
In the embodiments provided in the present invention, it should be understood that the disclosed apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, or in a form of hardware plus a software functional unit.
The integrated unit implemented in the form of a software functional unit may be stored in a computer readable storage medium. The software functional unit is stored in a storage medium and includes several instructions to enable a computer device (which may be a personal computer, a server, or a network device) or a processor (processor) to execute some steps of the methods according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
It is obvious to those skilled in the art that, for convenience and simplicity of description, the foregoing division of the functional modules is merely used as an example, and in practical applications, the above function distribution may be performed by different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules to perform all or part of the above described functions. For the specific working process of the device described above, reference may be made to the corresponding process in the foregoing method embodiment, which is not described herein again.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (2)

1. A three-dimensional cone beam computer tomography method of X-ray grating differential phase contrast based on transverse dislocation grating is characterized by comprising the following steps:
the method comprises the following steps that 1, a two-dimensional projection image sequence of an X-ray passing through an object is obtained through a Talbot-Lau three-dimensional tomography structure based on a transverse dislocation grating, the two-dimensional projection image sequence is a two-dimensional projection of the X-ray passing through the object periodically collected by a detector in the axial rotation process of the object, and a two-dimensional projection image of the object is obtained in one collection period;
step 2, Fourier transform is carried out on the two-dimensional projection image sequence to separate three contrast images of X-ray absorption contrast, differential phase contrast and scattering contrast;
step 3, respectively carrying out image reconstruction on the three contrast two-dimensional image sequences by using an absorption contrast, differential phase contrast and scattering contrast filtering back projection reconstruction algorithm to obtain three CT slice images of the object absorption contrast, the phase contrast and the scattering contrast;
the lateral dislocation absorption grating arranged Talbot-Lau imaging structure comprises:
the Talbot-Lau imaging structure optical path comprises six parts in total: an X-ray source, a source grating G0, a test object, a phase grating G1, an absorption grating G2 and a detector;
the Talbot-Lau imaging structure optical path parameters meet the following formulas (1) to (4):
Figure FDA0003096269280000011
kg1＝2g2， (2)
g0＝g2·L/d， (3)
s＜g2·L/2d， (4)
where d represents the distance between the phase grating G1 and the absorption grating G2; k is (L + d)/L is the amplification ratio, and L is the direct distance between the source grating G0 and the phase grating G1; m represents the mth order fractional Talbot distance; g1The period of the phase grating G1, λ being the wavelength of the X-rays used, G2To absorb the period of the grating G2, G0The period of the source grating G0, s is the width of the source grating that allows transmission of X-rays at each period;
the transverse dislocation absorption grating is an absorption grating G2 in the light path of the Talbot-Lau imaging structure, and transverse periodic dislocation occurs at the relative position of the absorption grating G2 and a detector probe element, so that intensity signals obtained by a plurality of transverse adjacent detector probe elements can be equivalent to intensity signals obtained by one detector probe element at a plurality of different positions in the traditional imaging method;
for 4 laterally adjacent detector probe elements, respectively labeled as p1、p2、p3、p4Each probe pxWidth w, x is 1,2,3,4, and the transverse displacement absorption grating corresponds to a segment of grating gp with length wxEach section of grating gpxHas a grating period of g2The gratings corresponding to adjacent detector elements have a position difference of f, e.g. adjacent detector element p1And p2Corresponding grating segment gp1With gp2There is a difference in the position of f, where f ═ g2/4，gpxThe position of the grating is equivalent to the position of the absorption grating when the absorption grating moves to the position X, the positions of the absorption gratings corresponding to the adjacent 4 detector detecting elements are different, the absorption gratings are staggered by a distance f, the absorption gratings are called as transverse dislocation gratings, and the X-ray intensity signal value obtained by the detector detecting element px is acquired when the absorption grating G2 moves to the position XA strength value;
the step 1 further comprises:
in the Talbot-Lau imaging structure, when an object is not placed on the rotary table, the rotary table rotates 360 degrees at a constant speed along the rotation center, an imaging area is covered by a cone beam in the rotating process, and a detector acquires a two-dimensional projection image;
in the Talbot-Lau imaging structure, when an object is placed on the rotary table, the rotary table rotates 360 degrees at a constant speed along the rotation center, an imaging area is covered by a cone beam in the rotating process, and a detector acquires a two-dimensional projection image;
three images of X-ray absorption contrast, differential phase contrast and scattering contrast are separated from the acquired two-dimensional intensity image by a Fourier analysis method, and the method comprises the following steps:
and (3) carrying out image analysis on the two-dimensional projection image sequence according to formulas (5) to (14) to obtain three contrast two-dimensional projection image sequences:
I1(x，z，θ)＝I(x－1，z，θ)， (5)
I2(x，z，θ)＝I(x，z，θ)， (6)
I3(x，z，θ)＝I(x+1，z，θ)， (7)
I4(x，z，θ)＝I(x+2，z，θ)， (8)
Figure FDA0003096269280000021
Figure FDA0003096269280000022
Figure FDA0003096269280000023
Figure FDA0003096269280000024
phase(x，z，θ)＝φs(x，z，θ)-φr(x，z，θ)， (13)
Figure FDA0003096269280000025
wherein x is the abscissa of the two-dimensional projection diagram point; z is the vertical coordinate of the two-dimensional projection image point, and theta is the projection angle of the two-dimensional projection image; i (x, z, theta) is the intensity value of the point (x, z) in the two-dimensional projection diagram at the projection angle theta; i is1(x，z，θ)、I2(x，z，θ)、I3(x，z，θ)、I4(x, z, theta) represent 4 different intensity values of the point (x, z) at the projection angle theta, respectively, simulating the intensity values of the point (x, z) in the conventional grating differential phase contrast image at the projection angle theta when the absorption grating is at 4 different step positions; m represents the number of different intensity values in one point (x, z), where M is 4; a is0(x, z, θ) is the mean of the sinusoids fitted to the point (x, z) at 4 different intensity values of the projection angle θ; a is1(x, z, theta) is the amplitude of a sine curve fitted to the point (x, z) at 4 different intensity values of the projection angle theta; phi (x, z, theta) is the phase value of a sine curve fitted to the 4 different intensity values of the point (x, z) at the projection angle theta;
Figure FDA0003096269280000031
denotes a when the test object is not placed at the projection angle theta0The (x, z, theta) value,
Figure FDA0003096269280000032
denotes a when the test object is placed at a projection angle theta0(x, z, θ) values;
Figure FDA0003096269280000033
denotes a when the test object is not placed at the projection angle theta1The (x, z, theta) value,
Figure FDA0003096269280000034
denotes a when the test object is placed at a projection angle theta1(x, z, θ) values; phi is ar(x, z, theta) represents the value of phi (x, z, theta) at the projection angle theta without placing the test object, phis(x, z, θ) represents the value of φ (x, z, θ) at which the test object is placed at the projection angle θ; abs (x, z, θ) is the value of the absorption contrast at projection angle θ point (x, z); phase (x, z, θ) is the value of the differential phase contrast at projection angle θ point (x, z); dark (x, z, θ) is the value of scatter contrast imaging at projection angle θ point (x, z);
respectively carrying out image reconstruction on three contrast two-dimensional image sequences by using an absorption contrast, differential phase contrast and scattering contrast filtering back projection reconstruction algorithm to obtain three CT slice images of the object absorption contrast, the phase contrast and the scattering contrast, wherein the three CT slice images comprise:
and (2) carrying out image analysis on the two-dimensional projection image sequence according to formulas (15) to (17) to obtain three contrast two-dimensional projection image sequences:
Figure FDA0003096269280000035
Figure FDA0003096269280000036
Figure FDA0003096269280000037
wherein a (x, y, z), p (x, y, z) and d (x, y, z) are respectively reconstructed absorption contrast slice image, phase contrast slice image and scattering contrast slice image; abs (s, v, theta), phase (s, v, theta) and dark (s, v, theta) represent the absorption, differential phase and scatter contrast two-dimensional projections, respectively, at a projection angle theta, and s, v are the intersection points of the line connecting a pixel point on the detector with the source and a virtual detector placed at the axis of rotation, respectivelyCoordinates; xi is the included angle between the ray and the central ray; d is the distance from the ray source to the plane of the virtual detector; y' is the distance from the pixel point of the reconstructed image to the plane of the virtual detector; h isa(s)、hp(s) and hd(s) filters for two-dimensional projection of absorption contrast, differential phase contrast and scattering contrast, respectively, defined by equations (18) - (19):
ha(s)＝|s|， (18)
Figure FDA0003096269280000038
hd(s)＝|s|， (20)。
2. an X-ray grating differential phase contrast three-dimensional cone-beam computed tomography device based on a transversely-dislocated grating, comprising:
the device comprises an acquisition module, a detection module and a display module, wherein the acquisition module is used for acquiring a two-dimensional projection image sequence acquired by a detector, the two-dimensional projection image sequence is a plurality of two-dimensional projection images acquired by periodically acquiring rays transmitted through an object by the detector in the process that the object rotates along the axial direction, and one sampling period corresponds to one two-dimensional projection image of the object;
the calculation module is used for carrying out Fourier transform on the two-dimensional projection image sequence to obtain an absorption contrast, a differential phase contrast and a scattering contrast two-dimensional projection sequence; carrying out image reconstruction on the three contrast two-dimensional projection sequences by utilizing a cone beam reconstruction algorithm to obtain a three-dimensional CT slice image corresponding to the cylindrical surface of the object;
the lateral dislocation absorption grating arranged Talbot-Lau imaging structure comprises:
the Talbot-Lau imaging structure optical path comprises six parts in total: an X-ray source, a source grating G0, a test object, a phase grating G1, an absorption grating G2 and a detector;
the Talbot-Lau imaging structure optical path parameters meet the following formulas (1) to (4):
Figure FDA0003096269280000041
kg1＝2g2， (2)
g0＝g2·L/d， (3)
s＜g2·L/2d， (4)
where d represents the distance between the phase grating G1 and the absorption grating G2; k is (L + d)/L is the amplification ratio, and L is the direct distance between the source grating G0 and the phase grating G1; m represents the mth order fractional Talbot distance; g1The period of the phase grating G1, λ being the wavelength of the X-rays used, G2To absorb the period of the grating G2, G0The period of the source grating G0, s is the width of the source grating that allows transmission of X-rays at each period;
the transverse dislocation absorption grating is an absorption grating G2 in the light path of the Talbot-Lau imaging structure, and transverse periodic dislocation occurs at the relative position of the absorption grating G2 and a detector probe element, so that intensity signals obtained by a plurality of transverse adjacent detector probe elements can be equivalent to intensity signals obtained by one detector probe element at a plurality of different positions in the traditional imaging method;
for 4 laterally adjacent detector probe elements, respectively labeled as p1、p2、p3、p4Each probe px (x ═ 1,2,3,4) has a width w, and in the transverse displacement absorption grating, a section of grating gp with a length w corresponds toxEach section of grating gpxHas a grating period of g2The gratings corresponding to adjacent detector elements have a position difference of f, e.g. adjacent detector element p1And p2Corresponding grating segment gp1With gp2There is a difference in the position of f, where f ═ g2/4，gpxThe position of the grating is equivalent to the position of the absorption grating when the absorption grating moves to x, the positions of the absorption gratings corresponding to the adjacent 4 detector detecting elements are different, the absorption gratings are staggered by a distance f, the grating is called as a transverse staggered grating, and the detector detecting elements pxObtained X-ray intensityThe signal values are the intensity values collected when the absorption grating G2 is moved to position x;
the acquisition module further comprises:
in the Talbot-Lau imaging structure, when an object is not placed on the rotary table, the rotary table rotates 360 degrees at a constant speed along the rotation center, an imaging area is covered by a cone beam in the rotating process, and a detector acquires a two-dimensional projection image;
in the Talbot-Lau imaging structure, when an object is placed on the rotary table, the rotary table rotates 360 degrees at a constant speed along the rotation center, an imaging area is covered by a cone beam in the rotating process, and a detector acquires a two-dimensional projection image;
the calculation module separates three images of X-ray absorption contrast, differential phase contrast and scattering contrast from the acquired two-dimensional intensity image by a Fourier analysis method, and the three images comprise:
and (3) carrying out image analysis on the two-dimensional projection image sequence according to formulas (5) to (14) to obtain three contrast two-dimensional projection image sequences:
I1(x，z，θ)＝I(x-1，z，θ)， (5)
I2(x，z，θ)＝I(x，z，θ)， (6)
I3(x，z，θ)＝I(x+1，z，θ)， (7)
I4(x，z，θ)＝I(x+2，z，θ)， (8)
Figure FDA0003096269280000051
Figure FDA0003096269280000052
Figure FDA0003096269280000053
Figure FDA0003096269280000054
phase(x，z，θ)＝φs(x，z，θ)-φr(x，z，θ)， (13)
Figure FDA0003096269280000055
wherein x is the abscissa of the two-dimensional projection diagram point; z is the vertical coordinate of the two-dimensional projection image point, and theta is the projection angle of the two-dimensional projection image; i (x, z, theta) is the intensity value of the point (x, z) in the two-dimensional projection diagram at the projection angle theta; i is1(x，z，θ)、I2(x，z，θ)、I3(x，z，θ)、I4(x, z, theta) represent 4 different intensity values of the point (x, z) at the projection angle theta, respectively, simulating the intensity values of the point (x, z) in the conventional grating differential phase contrast image at the projection angle theta when the absorption grating is at 4 different step positions; m represents the number of different intensity values in one point (x, z), where M is 4; a is0(x, z, θ) is the mean of the sinusoids fitted to the point (x, z) at 4 different intensity values of the projection angle θ; a is1(x, z, theta) is the amplitude of a sine curve fitted to the point (x, z) at 4 different intensity values of the projection angle theta; phi (x, z, theta) is the phase value of a sine curve fitted to the 4 different intensity values of the point (x, z) at the projection angle theta;
Figure FDA0003096269280000056
denotes a when the test object is not placed at the projection angle theta0The (x, z, theta) value,
Figure FDA0003096269280000057
denotes a when the test object is placed at a projection angle theta0(x, z, θ) values;
Figure FDA0003096269280000058
denotes a when the test object is not placed at the projection angle theta1(x，z, theta) value of the component (a),
Figure FDA0003096269280000059
denotes a when the test object is placed at a projection angle theta1(x, z, θ) values; phi is ar(x, z, theta) represents the value of phi (x, z, theta) at the projection angle theta without placing the test object, phis(x, z, θ) represents the value of φ (x, z, θ) at which the test object is placed at the projection angle θ; abs (x, z, θ) is the value of the absorption contrast at projection angle θ point (x, z); phase (x, z, θ) is the value of the differential phase contrast at projection angle θ point (x, z); dark (x, z, θ) is the value of scatter contrast imaging at projection angle θ point (x, z);
the calculation module uses an absorption contrast, differential phase contrast and scattering contrast filtering back projection reconstruction algorithm to respectively carry out image reconstruction on three kinds of contrast two-dimensional image sequences to obtain three CT slice images of the object absorption contrast, the phase contrast and the scattering contrast, and the method comprises the following steps:
and (2) carrying out image analysis on the two-dimensional projection image sequence according to formulas (15) to (17) to obtain three contrast two-dimensional projection image sequences:
Figure FDA0003096269280000061
Figure FDA0003096269280000062
Figure FDA0003096269280000063
wherein a (x, y, z), p (x, y, z) and d (x, y, z) are respectively reconstructed absorption contrast slice image, phase contrast slice image and scattering contrast slice image; abs (s, v, theta), phase (s, v, theta) and dark (s, v, theta) represent the absorption, differential phase and scattering contrast two-dimensional projections, respectively, at a projection angle theta, and s, v are the detectors, respectivelyThe coordinate of the intersection point of the connecting line of the upper pixel point and the ray source and the virtual detector placed at the rotating shaft; xi is the included angle between the ray and the central ray; d is the distance from the ray source to the plane of the virtual detector; y' is the distance from the pixel point of the reconstructed image to the plane of the virtual detector; h isa(s)、hp(s) and hd(s) filters for two-dimensional projection of absorption contrast, differential phase contrast and scattering contrast, respectively, defined by equations (18) - (19):
ha(s)＝|s|， (18)
Figure FDA0003096269280000064
hd(s)＝|s|， (20)
where s is the abscissa of the intersection of the line connecting the pixel point and the source of radiation on the detector and the virtual detector placed at the axis of rotation, and i represents the imaginary part.
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