CN100457041C - X-ray refractive-contrasting CT data collection method and reconstruction method - Google Patents

Abstract

The invention relates to a computer imaging technique, especially an X-ray CT data collecting method and rebuilding method, wherein the invention uses diffraction strengthen waist imaging method to use two methods that sample rotation axle is vertical to crystal rotation axle and sample rotation axle is parallel to the crystal rotation axle, to combine and convert collected four groups of CT data, to make rebuild function meet rotation constant property, and use traditional CT method to rebuild the three-dimension distribution of three refractive indexes. And said method comprises that: S1, finding the conditions of X-ray diffraction strengthen waist image; S2, collecting four groups of CT data; S3, combining and converting CT groups, to meet rotation constant property; S43, using traditional CT method to rebuild the three-dimension distribution of refractive indexes in sample.

Description

Refraction of X-ray contrasting CT data collection method and method for reconstructing

Technical field

The present invention relates to the computer tomography technical field.Be a kind of refraction of X-ray contrasting CT data collection method and method for reconstructing that is different from traditional X-ray ray CT collecting method and method for reconstructing.

Background technology

Traditional computer tomography (Computed Tomography), abbreviation CT) technology is since 20th century, developed rapidly the seventies, comparative maturity, all obtain the progress that attracts people's attention in many-sides such as data acquisition, method for reconstructing and application, and become the important tool in fields such as medical science, biology, archaeology and material science.The physical basis of traditional CT principle is the difference that material absorbs X ray, and Fundamentals of Mathematics are that thunder is when (Radon) conversion.Therefore, the traditional CT technology is that X ray absorbs contrast rotating and projection imaging technique and thunder combining when conversion.Because the biomedical sample that light element constitutes is very little to the difference that X ray absorbs, the traditional CT technology often can not provide enough contrasts for biological medical sample imaging.

The X ray phase contrast projection imaging method that development in recent years is got up utilizes X ray to pass the phase place difference of the acquisition behind the light element sample, can form than absorbing the much higher phase contrast of contrast, thereby obtain in the world developing rapidly.Diffraction enhanced imaging (Diffraction EnhancedImaging) method is one of several main X ray phase contrast projection imaging methods, and it has very high angular resolution, can obtain the figure image contrast that is directly proportional with the refraction angle.Therefore, X ray phase contrast rotating and projection imaging technique when combining, conversion is just become the problem that people study with thunder.Though in recent years diffraction enhanced imaging method and CT obtained certain progress in conjunction with research, the condition that need satisfy the reconstruction function and the traditional suitability of method for reconstructing in the diffraction enhanced CT also lack research.Diffraction enhanced imaging has multiple image-forming mechanism, and wherein the refractive-contrasting image-forming mechanism is one of main image-forming mechanism.Diffraction to be strengthened refractive-contrasting image-forming mechanism and thunder when conversion combines, just need the research refractive index gradient whether to satisfy the condition of rebuilding function.In traditional CT, rebuilding function is the absorptance of object, and it is scalar still not, and is rotational invariants.Refractive index gradient is a vector, the condition that its discontented heavy sensation in the foot is built function.Though the refractive index gradient component is a scalar, it still rotates variable, and still discontented heavy sensation in the foot is built the function condition.If there is a kind of conversion on the mathematics, can make between refraction projection imaging data and the refractive index gradient component relation that satisfies the CT condition of setting up by conversion, and make the refractive index gradient component satisfy reconstruction function condition, so just diffraction can be strengthened refractive-contrasting image-forming mechanism and thunder and successfully combine principle and the method for foundation refraction of X-ray contrast CT when conversion.

The present invention is according to the law of refraction of X ray in object, successfully on mathematics, search out a kind of conversion, make between refraction projection imaging data and the refractive index gradient component by conversion and to have set up the relation that satisfies the CT condition, and make the refractive index gradient component satisfy reconstruction function condition, thereby principle and the method for refraction of X-ray contrast CT have been founded.

Summary of the invention

The present invention proposes to utilize X-ray diffraction to strengthen waist position formation method, gather one group of low angle CT data and one group of angle of elevation CT data with the sample rotating shaft respectively perpendicular to the mode of crystal rotating shaft, gather one group of low angle CT data and one group of angle of elevation CT data with the sample shaft parallel respectively in the mode of crystal rotating shaft again, four groups of CT data are made up and conversion, make the reconstruction function satisfy rotational invariance, utilize the traditional CT method to reconstruct the distributed in three dimensions of three refractive index gradient components in the sample then.

Described CT collecting method and method for reconstructing, in order to reconstruct the distributed in three dimensions of refractive index gradient component in the sample, must strengthen under the image-forming condition of waist position at diffraction, when the sample rotating shaft is parallel to the crystal rotating shaft perpendicular to crystal rotating shaft and sample rotating shaft, gather low position, angle and the four groups of CT data in angle of elevation position respectively.

Described CT collecting method and method for reconstructing will make up and conversion with four groups of diffraction enhanced CT data of four kinds of different modes collections, constitute three covers and rebuild the CT data that function satisfies rotational invariance.

The basic light path sketch map of diffraction enhanced imaging as shown in Figure 1, imaging device mainly is made up of light source, monochromator crystal, sample platform, analyzing crystal and imaging detector.X ray is after the sample outgoing, and the pass in its refraction angle and the sample between the refractive index gradient component is

${\mathrm{\θ}}_x=\underset{\mathrm{sample}}{\∫}\frac{\∂n(x,y,z)}{\∂x}\mathrm{dz},---\left(1\right)$

${\mathrm{\θ}}_y=\underset{\mathrm{sample}}{\∫}\frac{\∂n(x,y,z)}{\∂y}\mathrm{dz},---\left(2\right)$

$0=\underset{\mathrm{sample}}{\∫}\frac{\∂n(x,y,z)}{\∂z}\mathrm{dz}.---\left(3\right)$

(3) physical significance of formula is, the starting and ending of integration all is positioned at the identical sample boundary of refractive index, and the increment of refractive index is zero.When X-axis was parallel to the crystal rotating shaft, as shown in Figure 1, according to crystal diffraction character, the position imaging of diffraction enhancing waist can only record the refraction angle information in the Y-Z plane, and can not record the refraction angle information in the X-Z plane.When Y-axis was parallel to the crystal rotating shaft, according to crystal diffraction character, the position imaging of diffraction enhancing waist can only record the refraction angle information in the X-Z plane, and can not record the refraction angle information in the Y-Z plane.Strengthen waist position imaging characteristics according to diffraction, developed two kinds of typical diffraction enhanced CT light paths, a kind of is that the sample rotating shaft is perpendicular to the crystal rotating shaft, shown in Fig. 2 (a); Another kind is that the sample shaft parallel is in the crystal rotating shaft, shown in Fig. 2 (b).In order to narrate conveniently, name two cover coordinate systems, a cover is that (x, y z), another set ofly are the coordinate system of following the sample rotation (x ', y ', z ') to fixed coordinate system.The Y-axis and the Y ' axle of two cover coordinate systems overlap, and their initial point also overlaps.In Fig. 2 (a), monochromator crystal and analyzing crystal are fixed on that (z) in the coordinate system, the crystal rotating shaft is parallel with X-axis for x, y, and the sample rotating shaft is parallel with Y-axis, and the direction of x-ray spread is consistent with the Z axle.In Fig. 2 (b), monochromator crystal and analyzing crystal are fixed on that (z) in the coordinate system, the crystal rotating shaft is all parallel with Y-axis with the sample rotating shaft for x, y, and the direction of x-ray spread is consistent with the Z axle.

When sample rotating shaft during, shown in Fig. 2 (a), can easily reconstruct perpendicular to the crystal rotating shaft

The someone proposes corresponding C T data combination and method for reconstructing.When sample shaft parallel during, shown in Fig. 2 (b),, yet there are no corresponding C T data combination and method for reconstructing and deliver though the someone utilizes this device to carry out the CT experiment in the crystal rotating shaft.Two kinds of light paths geometry at Fig. 2 (a) and (b) provide the discussion about CT data combination conversion and method for reconstructing respectively below.

In the diffraction enhanced CT light path shown in Fig. 2 (a), analyzing crystal is right

The refraction of optical beam angle that causes is insensitive,

Can not in projection image, cause corresponding contrast; And analyzing crystal is right

The refraction of optical beam angle that causes is very responsive,

In projection image, can cause significant contrast; In this diffraction enhanced CT light path, owing to the sample rotating shaft is placed along Y direction,

The sample rotation is rotational invariants, so can not cause

Contrast in projection image changes.In the diffraction enhanced CT light path shown in Fig. 2 (b), analyzing crystal is right The refraction of optical beam angle that causes is very responsive,

In projection image, can cause significant contrast; And analyzing crystal is right

The refraction of optical beam angle that causes is insensitive,

Can not in projection image, cause corresponding contrast; In this diffraction enhanced CT light path, owing to the sample rotating shaft is placed along Y direction,

The sample rotation is the rotation variable, so will cause

Contrast in projection image changes.

According to the diffraction enhanced imaging of crystal diffraction character decision and the characteristics of diffraction enhanced CT, forefathers have proposed a kind of refractive-contrasting CT data collection method and combined method: utilize shown in Fig. 2 (a), the sample rotating shaft is perpendicular to the diffraction enhanced CT light path of crystal rotating shaft, gather one group of low angle CT data and one group of angle of elevation CT data respectively, and strengthen the dioptric imaging formula according to diffraction and make up, obtain the refraction angle CT data of a cover invariable rotary, promptly

${\left({\mathrm{\θ}}_y\right)}_{\mathrm{\Θ}}=\frac{{\mathrm{\θ}}_D}{2}{\left(\frac{I_L^{\⊥}-I_H^{\⊥}}{I_K^{\⊥}+I_H^{\⊥}}\right)}_{\mathrm{\Θ}}.---\left(4\right)$

(4) in the formula, I _L ^⊥The low angle of representative CT data, I _H ^⊥Represent angle of elevation CT data, subscript ⊥ represents the sample rotating shaft perpendicular to the crystal rotating shaft, the subscript Θ representative sample anglec of rotation, (θ _y) _ΘBe the refraction angle CT data of invariable rotary, θ _DBe crystalline Darwin's width (Darwin width).With (4) formula substitution (2) formula, just obtain rebuilding function and be The refractive-contrasting CT formula:

${\left({\mathrm{\θ}}_y\right)}_{\mathrm{\Θ}}=\frac{{\mathrm{\θ}}_D}{2}{\left(\frac{I_L^{\⊥}-I_H^{\⊥}}{I_L^{\⊥}+I_H^{\⊥}}\right)}_{\mathrm{\Θ}}=\underset{\mathrm{sample}}{\∫}\frac{\∂n(x^{\′},y^{\′},z^{\′})}{{\∂y}^{\′}}\mathrm{dz}.---\left(5\right)$

(5) in the formula, the coordinate system of sample rotation is followed in (x ', y ', z ') expression.

According to the diffraction enhanced imaging of crystal diffraction character decision and the characteristics of diffraction enhanced CT, the present invention is on the basis of previous work, new refractive-contrasting CT data collection method and combined transformation method have creatively been proposed: the present invention propose to utilize shown in Fig. 2 (b), the sample shaft parallel is in the diffraction enhanced CT light path of crystal rotating shaft, gather one group of low angle CT data and one group of angle of elevation CT data respectively, and strengthen the dioptric imaging formula according to diffraction and make up, obtain the refraction angle CT data that a cover rotation becomes, promptly

${\left({\mathrm{\θ}}_x\right)}_{\mathrm{\Θ}}=\frac{{\mathrm{\θ}}_D}{2}{\left(\frac{I_L^{//}-I_H^{//}}{I_L^{//}+I_H^{//}}\right)}_{\mathrm{\Θ}},---\left(6\right)$

(6) in the formula, I _L ^∥The low angle of representative CT data, I _H ^∥Represent angle of elevation CT data, subscript ∥ represents the sample shaft parallel in the crystal rotating shaft, the subscript Θ representative sample anglec of rotation, (θ _x) _ΘBe the refraction angle CT data that rotation becomes, θ _DBe crystalline Darwin's width.Under Fig. 2 (b) situation, (x ', y ', z ') coordinate system is around the Y-axis rotation.Therefore, the deflection angle that causes of sample refraction from With The contribution of two aspects for any component wherein, all can not utilize traditional CT method to rebuild out.With this understanding, rebuild this two components, must seek the condition that satisfies invariable rotary according to the relation of each refractive index component between rotating coordinate system and fixed coordinate system.

According to Fig. 2 (b), have

$\frac{\∂n}{\∂x}=\sin \mathrm{\Θ}\frac{\∂n}{{\∂z}^{\′}}+\cos \mathrm{\Θ}\frac{\∂n}{{\∂x}^{\′}}---\left(7\right)$

$\frac{\∂n}{\∂z}=\cos \mathrm{\Θ}\frac{\∂n}{{\∂z}^{\′}}-\sin \mathrm{\Θ}\frac{\∂n}{{\∂x}^{\′}},$

In the formula, Θ is the angle of coordinate axes Z and Z ', also is the angle of rotation of sample in the CT data acquisition simultaneously.(7) formula is brought into (1) and (3) Shi Kede

$\sin \mathrm{\Θ}\∫\frac{\∂n}{{\∂z}^{\′}}\mathrm{dz}+\cos \mathrm{\Θ}\∫\frac{\∂n}{{\∂x}^{\′}}\mathrm{dz}={\mathrm{\θ}}_x---\left(8\right)$

$\cos \mathrm{\Θ}\∫\frac{\∂n}{{\∂z}^{\′}}\mathrm{dz}-\sin \mathrm{\Θ}\∫\frac{\∂n}{{\∂x}^{\′}}\mathrm{dz}=0.$

Because

$\left|\begin{array}{cc}\sin \mathrm{\Θ}& \cos \mathrm{\Θ}\\ \cos \mathrm{\Θ}& -\sin \mathrm{\Θ}\end{array}\right|=-1\≠0,---\left(9\right)$

So (8) formula can turn to

$\∫\frac{\∂n}{{\∂z}^{\′}}\mathrm{dz}={\mathrm{\θ}}_x\sin \mathrm{\Θ}---\left(10\right)$

$\∫\frac{\∂n}{{\∂x}^{\′}}\mathrm{dz}={\mathrm{\θ}}_x\cos \mathrm{\Θ}.$

With (6) formula substitution (10) formula, be about to the refraction angle CT data (θ that rotation becomes _x) _ΘMultiply by the cosine and the sine of sample corner respectively, just can obtain to rebuild function and be respectively

With

Two refractive-contrasting CT formula:

${\left({\mathrm{\θ}}_x\right)}_{\mathrm{\Θ}}\cos \mathrm{\Θ}=\frac{{\mathrm{\θ}}_D}{2}{\left(\frac{I_L^{//}-I_H^{//}}{I_L^{//}+I_H^{//}}\right)}_{\mathrm{\Θ}}\cos \mathrm{\Θ}=\underset{\mathrm{sample}}{\∫}\frac{\∂n(x^{\′},y^{\′},z^{\′})}{{\∂x}^{\′}}\mathrm{dz},---\left(11\right)$

${\left({\mathrm{\θ}}_x\right)}_{\mathrm{\Θ}}\sin \mathrm{\Θ}=\frac{{\mathrm{\θ}}_D}{2}{\left(\frac{I_L^{//}-I_H^{//}}{I_L^{//}+I_H^{//}}\right)}_{\mathrm{\Θ}}\sin \mathrm{\Θ}=\underset{\mathrm{sample}}{\∫}\frac{\∂n(x^{\′},y^{\′},z^{\′})}{{\∂z}^{\′}}\mathrm{dz}.---\left(12\right)$

In (11) formula and (12) formula, (x ', y ', z ') represent to follow the coordinate system of sample rotation, so rebuild the requirement that function satisfies invariable rotary.

(5) formula, (11) formula and (12) formula are combined, and what just constitute the present invention's proposition strengthens waist position CT data for projection according to four groups of diffraction, reconstructs the complete theoretical basis of the refraction of X-ray contrast CT of three components of refractive index gradient in sample:

${\left({\mathrm{\θ}}_y\right)}_{\mathrm{\Θ}}=\frac{{\mathrm{\θ}}_D}{2}{\left(\frac{I_L^{\⊥}-I_H^{\⊥}}{I_L^{\⊥}+I_H^{\⊥}}\right)}_{\mathrm{\Θ}}=\underset{\mathrm{sample}}{\∫}\frac{\∂n(x^{\′},y^{\′},z^{\′})}{{\∂y}^{\′}}\mathrm{dz},---\left(13\right)$

${\left({\mathrm{\θ}}_x\right)}_{\mathrm{\Θ}}\cos \mathrm{\Θ}=\frac{{\mathrm{\θ}}_D}{2}{\left(\frac{I_L^{//}-I_H^{//}}{I_L^{//}+I_H^{//}}\right)}_{\mathrm{\Θ}}\cos \mathrm{\Θ}=\underset{\mathrm{sample}}{\∫}\frac{\∂n(x^{\′},y^{\′},z^{\′})}{{\∂x}^{\′}}\mathrm{dz},---\left(14\right)$

${\left({\mathrm{\θ}}_x\right)}_{\mathrm{\Θ}}\sin \mathrm{\Θ}=\frac{{\mathrm{\θ}}_D}{2}{\left(\frac{I_L^{//}-I_H^{//}}{I_L^{//}+I_H^{//}}\right)}_{\mathrm{\Θ}}\sin \mathrm{\Θ}=\underset{\mathrm{sample}}{\∫}\frac{\∂n(x^{\′},y^{\′},z^{\′})}{{\∂z}^{\′}}\mathrm{dz}.---\left(15\right)$

Three components of refractive index gradient are made up according to Pythagorean theorem, also can obtain the distributed in three dimensions of refractive index gradient absolute value in sample, combinatorial formula is

$|\▿n(x^{\′},y^{\′},z^{\′})|={\{{\left[\frac{\∂n(x^{\′},y^{\′},z^{\′})}{{\∂x}^{\′}}\right]}^2+{\left[\frac{\∂n(x^{\′},y^{\′},z^{\′})}{{\∂y}^{\′}}\right]}^2+{\left[\frac{\∂n(x^{\′},y^{\′},z^{\′})}{{\∂z}^{\′}}\right]}^2\}}^{\frac{1}{2}}---\left(16\right)$

Description of drawings

Fig. 1 is the basic light path sketch map of diffraction enhanced imaging.

Fig. 2 is that two kinds of diffraction strengthen phase contrast CT experimental provision sketch map.

Fig. 3 is a refraction of X-ray contrast CT experimental technique flow chart of the present invention.

The specific embodiment

Basic light path according to diffraction enhanced imaging shown in Figure 1, on light path, be arranged in order monochromator crystal, sample platform, analyzing crystal and imaging detector, adjust crystalline Prague of monochromator (Bragg) angle, determine the energy of the homogeneous X-ray of irradiation sample, adjust the analyzing crystal angle, utilize ionization chamber to measure the twin crystal rocking curve, then angle between analyzing crystal and the monochromator crystal is separately fixed at a rocking curve left side half waist (low position, angle) and right half waist (angle of elevation position) of rocking curve, aims at imaging detector.

According to the diffraction enhanced CT light path shown in Fig. 2 (a), the rotating shaft of sample is placed perpendicular to the crystal rotating shaft, (the crystal rotor shaft direction is parallel to X-axis) is fixed on analyzing crystal respectively on the left and right half waist position of rocking curve, according to selected angle step sample is carried out 180 ° of rotation sweeps, and take two-dimensional projection's picture of sample in each angle position, gather low position, angle and the two groups of CT data in angle of elevation position; Keep sample motionless with respect to turntable, according to the diffraction enhanced CT light path shown in Fig. 2 (b), the sample rotating shaft is parallel to the crystal rotating shaft to be placed, respectively analyzing crystal is fixed on the left and right half waist position of rocking curve, according to selected angle step sample is carried out 180 ° of rotation sweeps, and take two-dimensional projection's picture of sample in each angle position, gather low position, angle and the two groups of CT data in angle of elevation position.

According to formula (13), (14) and (15), four groups of refractive-contrasting CT data are made up and conversion, utilize the traditional CT method to reconstruct the distributed in three dimensions of three components of refractive index gradient in sample, according to formula (16), reconstruct the distributed in three dimensions of refractive index gradient absolute value in sample then.

Fig. 3 is a refraction of X-ray contrast CT experimental technique flow chart.Its concrete steps are as follows:

Step S1, X-ray diffraction strengthens determining of waist position image-forming condition, basic light path according to diffraction enhanced imaging, on light path, be arranged in order monochromator crystal, sample platform, analyzing crystal and imaging detector, adjust the crystalline Prague of monochromator angle, determine the energy of the homogeneous X-ray of irradiation sample, adjust the analyzing crystal angle, utilize ionization chamber to measure the twin crystal rocking curve, then angle between analyzing crystal and the monochromator crystal is separately fixed at a rocking curve left side half waist (low position, angle) and right half waist (angle of elevation position) of rocking curve, aims at imaging detector;

Step S2 gathers the refractive-contrasting CT data

(1) rotating shaft of sample is placed perpendicular to the crystal rotating shaft, respectively analyzing crystal is fixed on the left and right half waist position of rocking curve, according to selected angle step sample is carried out 180 ° of rotation sweeps, and take two-dimensional projection's picture of sample in each angle position, gather low position, angle and the two groups of CT data in angle of elevation position;

(2) keep sample motionless with respect to turntable, the sample rotating shaft is parallel to the crystal rotating shaft to be placed, respectively analyzing crystal is fixed on the left and right half waist position of rocking curve, according to selected angle step sample is carried out 180 ° of rotation sweeps, and take two-dimensional projection's picture of sample in each angle position, gather low position, angle and the two groups of CT data in angle of elevation position;

Step S3, to gather four groups of CT data with four kinds of different modes makes up and conversion, the two groups of CT data in position, low angle and angle of elevation position of gathering when the sample rotating shaft is placed perpendicular to the crystal rotating shaft, strengthen the dioptric image formula according to diffraction and make up, obtain a cover and rebuild the CT data that function satisfies rotational invariance; The sample rotating shaft is parallel to the two groups of CT data in position, low angle and angle of elevation position of gathering when the crystal rotating shaft is placed, strengthen the dioptric image formula according to diffraction and make up and carry out conversion, obtain two covers and rebuild the CT data that functions satisfy rotational invariance according to (14) formula and (15);

Step S4, the reconstruction of refraction of X-ray contrast CT image, the traditional CT method is applied to three covers rebuilds the CT data that function satisfies rotational invariance, reconstruct the distributed in three dimensions of three refractive index gradient components in sample in the sample, three components of refractive index gradient are made up according to Pythagorean theorem, also can obtain the distributed in three dimensions of refractive index gradient absolute value in sample.

Claims (2)

1. refraction of X-ray contrasting CT data collection and method for reconstructing, utilize X-ray diffraction to strengthen waist position formation method, gather one group of low angle CT data and one group of angle of elevation CT data with the sample rotating shaft respectively perpendicular to the mode of crystal rotating shaft, gather one group of low angle CT data and one group of angle of elevation CT data with the sample shaft parallel respectively in the mode of crystal rotating shaft again, four groups of CT data are made up and conversion, make as the refractive index gradient component of rebuilding function and satisfy rotational invariance, utilize the traditional CT method to reconstruct the distributed in three dimensions of three refractive index gradient components in the sample then.

2. CT data acquisition as claimed in claim 1 and method for reconstructing, its concrete steps are as follows:

Step S1, X-ray diffraction strengthens determining of phase place contrast imaging condition, basic light path according to diffraction enhanced imaging, on light path, be arranged in order the monochromator crystal, the sample platform, analyzing crystal and imaging detector, adjust the crystalline Prague of monochromator angle, determine the energy of the homogeneous X-ray of irradiation sample, adjust the analyzing crystal angle, utilize ionization chamber to measure the twin crystal rocking curve, make between analyzing crystal and the monochromator crystal angle be separately fixed at a rocking curve left side half waist and right half waist of rocking curve then, with the beam alignment imaging detector of two-dimensional projection's picture of sample;

Step S2 gathers the refractive-contrasting CT data

(1) rotating shaft of sample is placed perpendicular to the crystal rotating shaft, respectively analyzing crystal is fixed on the left and right half waist position of rocking curve, according to selected angle step sample is carried out 180 ° of rotation sweeps, and take two-dimensional projection's picture of sample in each angle position, gather low position, angle and the two groups of CT data in angle of elevation position;

(2) keep sample motionless with respect to turntable, the sample rotating shaft is parallel to the crystal rotating shaft to be placed, respectively analyzing crystal is fixed on the left and right half waist position of rocking curve, according to selected angle step sample is carried out 180 ° of rotation sweeps, and take two-dimensional projection's picture of sample in each angle position, gather low position, angle and the two groups of CT data in angle of elevation position;

Step S3, to make up and conversion with four groups of CT data of four kinds of different modes collections, the two groups of CT data in position, low angle and angle of elevation position of gathering when the sample rotating shaft is placed perpendicular to the crystal rotating shaft, strengthening the dioptric image formula according to diffraction makes up, make refraction projection imaging data and refractive index gradient along setting up the relation that satisfies the CT condition between the sample rotating shaft component, obtain a cover and rebuild the CT data that function satisfies rotational invariance; The sample rotating shaft is parallel to the two groups of CT data in position, low angle and angle of elevation position of gathering when the crystal rotating shaft is placed, strengthen the dioptric image formula according to diffraction and make up and do conversion, make refraction projection imaging data and refractive index gradient perpendicular to setting up the relation that satisfies the CT condition between two components of sample rotating shaft, obtain two covers and rebuild the CT data that function satisfies rotational invariance;

Step S4, the reconstruction of refraction of X-ray contrast CT image, the traditional CT method is applied to three covers rebuilds the CT data that function satisfies rotational invariance, reconstruct the distributed in three dimensions of three refractive index gradient components in sample in the sample, three components of refractive index gradient are made up according to Pythagorean theorem, obtain the distributed in three dimensions of refractive index gradient absolute value in sample.

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