Imaging mechanism and image acquisition and reconstruction method for X-ray nanometer resolution microscope

Abstract

The invention discloses an imaging mechanism and an image acquisition and reconstruction method for an X-ray nanometer resolution microscope, and belongs to the field of X-ray microscope imaging. According to the invention, the property that the image displacement of an area light source is in direct proportion to the refraction angle of a sample is utilized to regulate and control the imaging light intensity of the sample, and an X-ray differential phase contrast microscope imaging mechanism based on sample refraction is established by utilizing the illumination of an asymmetric semi-area light source and a filtering hole. A method for acquiring nine Radon transformations of eight physical quantities related to the refractive index by using an X-ray differential phase contrast microscope is provided, the eight physical quantities related to the refractive index are reconstructed according to nine inverse Radon transformations, and a simple method for acquiring six Radon transformations by acquiring rotation projection data of two sets of samples is provided. And a foundation is laid for simple, convenient, rapid, low-dose and multi-contrast-mechanism X-ray differential phase contrast nano CT (Computed Tomography).

Description

Technical Field

[0001] The present invention relates to the field of X-ray microscope imaging, and in particular to an imaging mechanism and an image acquisition and reconstruction method for an X-ray nano-resolution microscope. Background Art

[0002] Nano-CT with X-ray nano-resolution microscopy as its core is another crystallization of the development of human science and technology after optical microscopy and electron microscopy. It is opening a new window for people to observe the microscopic world and becoming a new growth point for the development of human science. Like visible light, X-rays have diverse imaging mechanisms and rich contrast sources. Information such as absorption, phase shift, refraction, scattering, and fluorescence can be used to observe and analyze a variety of physical changes, chemical reactions, and nanostructures. Although nano-CT with X-ray nano-resolution microscopy as its core has played a strong role in promoting the development of multiple disciplines, it still cannot meet the growing and urgent needs of scientific research, industrial testing, medical and health care, etc.

[0003] For example, the absorption coefficient of "water window" soft X-rays for biological samples such as proteins is one order of magnitude higher than that of water, which can provide a natural contrast enhancement mechanism for imaging of water-containing biological samples. However, nano-CT based on "water window" soft X-ray nano-resolution microscope is limited in two aspects. On the one hand, the penetration of "water window" soft X-rays is weak. When imaging cells with a diameter greater than 10μm, the transmitted light intensity is less than 5% of the incident light intensity. On the other hand, the "water window" soft X-ray nano-resolution microscope does not have enough depth of field. When the resolution is 60nm, the "water window" soft X-ray nano-resolution microscope has a depth of field of about 5μm, while when the resolution is 50nm, the depth of field is shortened to 3.4μm, and when the resolution is 30nm, the depth of field is further shortened to 1.3μm. It can be seen from this that nano-CT with the "water window" soft X-ray nano-resolution microscope as its core is not suitable for nano-resolution three-dimensional imaging of intact cells with a diameter of more than 5μm. The diameter of most mammalian cells is about 10μm, the size of tumor cells is usually larger than 10μm, and the diameter of liver cells can even reach 20-30μm.

[0004] For example, hard X-rays have strong penetrating power, and hard X-ray nano-resolution microscopes have sufficient depth of field. However, hard X-ray nano-resolution microscopes have not solved the problem of phase contrast quantification, which makes it difficult for nano-CT with hard X-ray nano-resolution microscopes as the core to make a difference in the three-dimensional imaging of light element materials and biological samples. When imaging thick samples in three dimensions, phase contrast quantification encounters difficulties. First, phase contrast is a periodic function of sample thickness. Quantitatively solving the phase from the periodic oscillation phase contrast is only one aspect of the difficulty; second, there is not only phase contrast in imaging, but also absorption contrast. How to quantitatively separate absorption contrast and phase contrast from imaging contrast is even more difficult. Some people in the world have proposed the research idea of ​​using differential contrast to achieve quantification. In 2002, B. Kaulich et al. proposed to use staggered double-wave zone plate lens imaging to obtain differential contrast. In 2003, E. Fabrizio and 2011, T. Nakamura et al. proposed to use specially designed dual-focus diffraction optical elements to obtain differential contrast. However, the diffraction efficiency of dual-zone plates and dual-focus zone plates is too low. In 2009, Momose et al. introduced gratings into X-ray nano-resolution microscopy and obtained twin phase images of light element samples using Talbot grating interferometer. However, this method has two disadvantages. First, the grating inserted into the X-ray nano-resolution microscope will greatly reduce the diffraction efficiency of the overall imaging optical path; second, the twin phase images are misaligned and overlapped, making it difficult to separate the phase image that is not interfered by the twin image.

[0005] It can be seen that nano-CT with X-ray nano-resolution microscopy as the core urgently needs to solve bottleneck problems such as high-contrast imaging mechanism, quantitative separation of absorption contrast and phase contrast, and simple and fast acquisition of projection data. Summary of the invention

[0006] The present invention proposes an imaging mechanism and an image acquisition and reconstruction method for an X-ray nano-resolution microscope, wherein a nano-CT in one of the embodiments is a nano-CT based on an X-ray differential phase contrast microscope, and the imaging mechanism and image acquisition method described in the invention are suitable for an X-ray differential phase contrast microscope.

[0007] The specific contents of the present invention are as follows: One of the objectives of the present invention is to utilize the property that the displacement of the surface light source image is proportional to the refraction angle of the sample to control the imaging light intensity of the sample and establish an X-ray differential phase contrast microscope imaging mechanism based on sample refraction.

[0008] The second object of the present invention is to use an X-ray differential phase contrast microscope to collect nine Radon transforms of eight physical quantities related to the refractive index of the sample, and to reconstruct the eight physical quantities using nine corresponding inverse Radon transforms. The eight physical quantities are: absorption coefficient, scattering coefficient, three-dimensional gradient of the real part of the refractive index, two-dimensional gradient perpendicular to the sample rotation axis, three gradient components and reduction of the real part of the refractive index.

[0009] The third purpose of the present invention is to propose a simple method for acquiring six Radon transforms by collecting two sets of sample rotation projection data using the symmetry of positive and negative images, thereby laying the foundation for a simple, fast, low-dose, multi-contrast mechanism X-ray differential phase contrast nano-CT.

[0010] The theoretical logic of the present invention is as follows: first, a proportional relationship between the displacement of the surface light source image and the refraction angle of the sample is derived, and a differential phase contrast microscope imaging mechanism in which the sample refraction modulates the imaging light intensity of the sample is established; second, based on the relationship that the refraction angle of the imaging light is the vector sum of each small refraction angle on the path, a mathematical relationship of the Radon transform of the real part of the refractive index gradient is established, and based on the relationship between the imaging light intensity and the refraction angle, a method for collecting the Radon transform of the real part of the refractive index gradient is proposed; third, based on the Radon transform of the real part of the refractive index gradient, a reconstruction algorithm for the real part of the refractive index gradient and the real part of the refractive index reduction is proposed; fourth, based on the relationship between the imaging light intensity and the variance of the scattering angle, a method for collecting the Radon transform of the scattering coefficient is proposed.

[0011] The present invention intends to use the property that the image displacement of the surface light source is proportional to the refraction angle of the sample to regulate the imaging light intensity of the sample and establish an X-ray differential phase contrast microscope imaging mechanism based on sample refraction. The present invention first derives the proportional relationship between the image displacement of the surface light source and the refraction angle of the sample, then proves that the refraction of the sample does not affect the imaging of the sample itself, and then establishes a differential phase contrast microscope imaging mechanism in which the sample refraction modulates the imaging light intensity of the sample.

[0012] The present invention proposes an X-ray differential phase contrast nano CT based on an X-ray differential phase contrast microscope and the symmetric properties of positive and negative images, namely an X-ray nano resolution microscope, a method for collecting nine Radon transforms of eight physical quantities related to the refractive index, and a method for reconstructing the eight physical quantities related to the refractive index according to the nine inverse Radon transforms, wherein the eight physical quantities are: an absorption coefficient, a scattering coefficient, a three-dimensional gradient of the real part of the refractive index, a two-dimensional gradient perpendicular to the rotation axis of the sample, three gradient components and a reduction amount of the real part of the refractive index; and on this basis, by utilizing the symmetric properties of positive and negative images, a simple method for obtaining six of the Radon transforms by collecting two sets of sample rotation projection data is proposed; the X-ray differential phase contrast microscope comprises an X-ray surface light source, and an aperture, a sample turntable, a wave zone plate, a filter hole and an imaging detector arranged in sequence along the optical axis.

[0013] According to some exemplary embodiments, the X-ray differential phase contrast microscope is formed by adding two optical elements to an X-ray nano-resolution microscope using a zone plate as an objective lens: One of the optical elements feeds into a filter hole on the imaging surface of the symmetrical surface light source, the shape and size of the filter hole are exactly the same as the image of the symmetrical surface light source, and the filter hole and the image of the surface light source are precisely aligned; The second optical element feeds an aperture into the light outlet of the surface light source to block half of the surface light source, thereby forming an asymmetric half-surface light source illumination.

[0014] According to some exemplary embodiments, the surface light source of the X-ray differential phase contrast microscope is a symmetrical surface light source or an asymmetrical surface light source; when the surface light source is a symmetrical surface light source, the symmetrical surface light source is symmetrical in both the x-axis direction and the y-axis direction; when the surface light source is an asymmetrical surface light source, the symmetrical surface light source is divided into two along the symmetry axis to form two surface light sources of equal shape, and one of them is blocked by an aperture at the outlet of the surface light source to obtain the required asymmetrical surface light source; the asymmetrical surface light source can be a semi-circular surface light source, a rectangular surface light source, a trapezoidal surface light source, or a circular surface light source deviating from the optical axis; for the asymmetrical surface light source, the shape of the filter hole must be exactly the same as the shape of the symmetrical surface light source image, and when dimming, the filter hole must be precisely aligned with the symmetrical surface light source image.

[0015] According to some exemplary embodiments, the surface light source of the X-ray differential phase contrast microscope is an annular surface light source or a semi-annular surface light source; when the surface light source is an annular surface light source, the annular surface light source is generated by a point light source through a condenser or is generated by an annular array target embedded in diamond; when the annular surface light source is generated by an annular array target embedded in diamond, the X-rays generated by the annular array target are directly used to illuminate the sample without using a condenser; when the surface light source is a semi-annular surface light source, the semi-annular surface light source is first generated by a point light source through a condenser to generate an annular surface light source, and then is blocked by an aperture at the outlet of the surface light source, or is generated by a semi-annular array target embedded in diamond; when the semi-annular surface light source is generated by a semi-annular array target embedded in diamond, the X-rays generated by the semi-annular array target are directly used to illuminate the sample without using an aperture at the outlet of the surface light source.

[0016] According to some exemplary embodiments, the physical process of the X-ray differential phase contrast microscope imaging mechanism based on sample refraction is as follows: Refracted, passing through the sample point Each light ray changes direction, causing the sample point The relevant surface light source image is displaced, and the filter hole blocks the displaced surface light source image, forming an imaging mechanism in which the displacement distance, the blocked area, and the decrease in imaging light intensity at the sample point are proportional to the refraction angle of the sample point, that is, an X-ray differential phase contrast microscope imaging mechanism based on sample refraction is formed.

[0017] According to some exemplary embodiments, the X-ray differential phase contrast microscope, based on the differential phase contrast imaging mechanism of sample refraction, collects two-dimensional absorption contrast images, two-dimensional scattering contrast images and two-dimensional refraction contrast images of each sample angle on the image plane, and obtains them by the following method: The X-ray differential phase contrast microscope comprises an X-ray surface light source, and an aperture, a sample turntable, a zone plate, a filter hole and an imaging detector arranged in sequence along the optical axis; the zone plate is an element with a lens imaging function, which not only magnifies the sample to be measured but also reduces the surface light source to form an image; the aperture is close to the surface light source and is used to block the surface light source to make it an asymmetric semi-surface light source; the sample turntable is used to load the sample to be measured, the plane where the sample is located is called the sample object plane, and the imaging detector is located on the image plane of the sample; the filter hole is located on the imaging plane of the surface light source, and its shape and size are exactly the same as the surface light source image, and the filter hole and the surface light source image are precisely aligned; the zone plate, the surface light source and its image plane, the sample object plane and the image plane, the aperture, the filter hole and the imaging detector surface are all perpendicular to the optical axis; S1, turning on and adjusting the surface light source: making the center of the surface light source coincide with the optical axis, and the surface light source is perpendicular to the optical axis; S2, adjusting the sample turntable: aligning the focus of the hollow cone light beam emitted by the surface light source to the sample-carrying position on the sample turntable, and aligning the hollow cone light beam passing through the sample position to the downstream zone plate; S3, adjusting the zone plate: making the surface light source form a surface light source image near the rear focal plane of the zone plate, and making the hollow cone light beam passing through the sample position be focused by the zone plate and aligned with the imaging detector located on the sample image plane, so that the imaging detector presents a bright field state; S4, adjusting the object distance and the image distance: placing a resolution test card on the sample turntable, and precisely adjusting the distances between the sample turntable, the zone plate and the imaging detector so that the resolution test card can achieve a clear imaging state; S5, adjusting the filter hole: making the filter hole and the surface light source image accurately aligned; S6, feed aperture: blocks half of the surface light source to form an asymmetric half-surface light source illumination; S7, measuring the angle signal response curve: perpendicular to the optical axis, gradually moving the filter hole along the asymmetric direction of the half-surface light source, and using the imaging detector to measure the angle signal response curve of the light intensity changing with the displacement of the filter hole on the sample image plane; S8, adjusting the asymmetric direction of the half-surface light source: rotating the aperture around the optical axis, and using the aperture to adjust the asymmetric direction of the half-surface light source to the direction of the refraction angle component to be collected; S9, collecting data of a refraction angle component in one direction: placing a sample to be tested, and the imaging detector collects a two-dimensional magnified image of the sample when it is rotated from 0 degree to 180 degrees, or collects a two-dimensional magnified image of the sample when it is rotated from 0 degree to 360 degrees; S10, collecting refraction angle component data in another direction: because there may be more than one refraction angle component to be collected, steps S8 and S9 need to be repeated until sufficient refraction angle component data are collected; S11, collecting scattering contrast projection data: removing the aperture, using a symmetrical surface light source for illumination, canceling the response mechanism of the imaging light intensity drop depending on a specific refraction angle component, and the imaging detector captures a two-dimensional magnified image of the sample rotated from 0 degrees to 180 degrees on the sample image plane; S12, collecting absorption contrast projection data: removing the aperture, using a symmetrical surface light source for illumination, removing the filter hole, canceling the response mechanism of the imaging light intensity drop depending on the scattering angle variance, and the imaging detector captures a two-dimensional magnified image of the sample rotated from 0 degrees to 180 degrees on the sample image plane.

[0018] According to some exemplary embodiments, the X-ray differential phase contrast nano-CT based on the X-ray differential phase contrast microscope and the positive and negative image symmetry property, under the conditions of an annular surface light source illuminating the sample and a semi-annular surface light source illuminating the sample, proposes nine Radon transforms of eight physical quantities related to the refractive index of the sample: ① Collect Radon transform of absorption coefficient μ: (49).

[0019] ② Radon transform of the collected scattering coefficient α: (85); Where m s is the magnification of the light source imaging, R f is the outer radius of the annular surface light source image, ΔI scat is the decrease in light intensity caused by scattering, It uses an annular surface light source to illuminate the sample, and an X-ray nano-resolution microscope optical path without a filter hole, and collects the imaging light intensity of the sample when it rotates from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by the left semi-ring light source, collecting the imaging light intensity of the sample from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by a right half-ring light source, collecting imaging light intensity when the sample rotates from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by the lower semi-ring light source, collecting the imaging light intensity of the sample from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by the upper semi-ring light source, collecting the imaging light intensity of the sample from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by an oblique upper semi-ring light source, collecting imaging light intensity when the sample rotates from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by an oblique lower semi-ring light source, collecting imaging light intensity when the sample is rotated from 0 degrees to 180 degrees.

[0020] ③ Collect the real part of the refractive index along x o 'Axis derivative The Radon transform is: (86), Where q is the ratio of the inner radius to the outer radius of the annular surface light source image, It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0021] ④ Collect the real part of the refractive index along z o'Axis derivative The Radon transform is: (87), in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0022] ⑤ Collect the real part of the refractive index along y o 'Axis derivative The Radon transform is: (88), in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0023] ⑥ Collect the real part of the refractive index two-dimensional gradient The Radon transform is: (89), in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours. is the two-dimensional gradient on the rotation plane perpendicular to the rotation axis.

[0024] ⑦ Collect the real part of the refractive index three-dimensional gradient The Radon transform is: (78), Where ω is the angle between the refraction angle component and the X-axis, θ x is the refraction angle In the measurement coordinate system x o Axis component, θ y is the refraction angle In the measurement coordinate system y o Axis component, and They are x o Axis and y o The unit vector on the axis, For samples with small refraction angles that require accurate reconstruction, ,have: , For samples with large refraction angles that require improved contrast and highlighted contours, ,have: , in It is an X-ray differential phase contrast microscope optical path illuminated by an oblique upper semi-ring light source, collecting imaging light intensity of the sample from 180 degrees to 360 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by an oblique lower semi-ring light source, collecting imaging light intensity of the sample from 180 degrees to 360 degrees.

[0025] ⑧ Collect the real part of the refractive index three-dimensional gradient The Radon transform of can be converted into the Radon transform of the reduction of the real part of the refractive index δ: (90), Where Φ is the phase function and ρ is the o Axis spatial frequency, F x and F x -1 Along x o The Fourier transform and inverse transform of the axis, ν is the Fourier transform along the y axis. o Axis spatial frequency, F y and F y -1 Along y o The Fourier transform and inverse transform of the axis, is the two-dimensional gradient parallel to the object plane, For samples with small refraction angles that require accurate reconstruction, ,have: , , For samples with large refraction angles that require improved contrast and highlighted contours, ,have: , .

[0026] ⑨ The Radon transform of the reduction in the real part of the refractive index δ on a rotation plane of the sample can be simplified to: (91), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is aimed at samples with large refraction angles that require improved contrast and highlighted contours. Each imaging light intensity is the imaging light intensity collected by the detector when the sample is rotated from 0 degrees to 180 degrees.

[0027] According to some exemplary embodiments, the X-ray differential phase contrast nano-CT based on X-ray differential phase contrast microscopy and positive and negative image symmetry properties, under the conditions of annular surface light source illuminating the sample and semi-annular surface light source illuminating the sample, proposes nine inverse Radon transforms for reconstructing eight physical quantities related to the refractive index: ① The inverse Radon transform of the reconstructed absorption coefficient μ is: (51).

[0028] ② The inverse Radon transform of the reconstructed scattering coefficient α is: (92).

[0029] ③ Reconstruct the real part of the refractive index along x o 'Axis derivative The inverse Radon transform of is: (93), in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0030] ④Reconstruct the real part of the refractive index along z o 'Axis derivative The inverse Radon transform of is: (94), in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0031] ⑤ Reconstruct the real part of the refractive index along y o 'Axis derivative The inverse Radon transform of is: (95), in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0032] ⑥ Reconstruct the two-dimensional gradient of the real part of the refractive index of the sample rotation surface The inverse Radon transform of is: (96), in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0033] ⑦Reconstruct the three-dimensional gradient of the real part of the refractive index The inverse Radon transform of is: (97), For samples with small refraction angles that require accurate reconstruction, ,have: , For samples with large refraction angles that require improved contrast and highlighted contours, ,have: .

[0034] ⑧ The inverse Radon transform of the reconstructed real part of the refractive index reduction δ is: (98), For samples with small refraction angles that require accurate reconstruction, ,have: , , For samples with large refraction angles that require improved contrast and highlighted contours, ,have: , .

[0035] ⑨Reconstruct the reduction of the real part of the refractive index in the sample rotation plane δ, and convert the sample phase function Φ and the refraction angle x o Axis component θ x The y in o Variables are considered as constants, and we have: (99), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0036] According to some exemplary embodiments, based on X-ray differential phase contrast microscopy and X-ray differential phase contrast nano-CT with positive and negative image symmetry, a simple image acquisition and reconstruction method is proposed: (1) Collect two sets of projection data: First, use the left half-ring light source to illuminate the sample and the X-ray differential phase contrast microscope light path with a filter hole to collect the imaging light intensity of the sample when it rotates from 0 degrees to 360 degrees, where is the imaging light intensity from 0 degrees to 180 degrees, The imaging light intensity is from 180 degrees to 360 degrees, and then the sample is illuminated by a ring-shaped surface light source and an imaging light path without a filter hole is used to collect the imaging light intensity of the sample from 0 degrees to 180 degrees. ; (2) Arrange and process the collected projection data: sort out the six Radon transforms of physical quantities related to the refractive index: ① The Radon transform of the absorption coefficient μ is: (49).

[0037] ②The Radon transform of the scattering coefficient α is (100).

[0038] ③The real part of the refractive index along x o 'Axis derivative The Radon transform is: (101), For samples with small refraction angles that require accurate reconstruction, : (68), For samples with large refraction angles that require improved contrast and highlighted contours, : (70).

[0039] ④The real part of the refractive index along z o 'Axis derivative The Radon transform is: (102), For samples with small refraction angles that require accurate reconstruction, : (68), For samples with large refraction angles that require improved contrast and highlighted contours, : (70).

[0040] ⑤ Two-dimensional gradient of the real part of the refractive index on the sample rotation surface The Radon transform is: (103), For samples with small refraction angles that require accurate reconstruction, : (68), For samples with large refraction angles that require improved contrast and highlighted contours, : (70).

[0041] ⑥ The phase function Φ and refraction angle x of the sample o Axis component θ x The y in o The variable is regarded as a constant, and the real part of the refractive index is a two-dimensional function in the sample rotation plane. The Radon transform is (104), For samples with small refraction angles that require accurate reconstruction, : (68), For samples with large refraction angles that require improved contrast and highlighted contours, : (70).

[0042] (3) Six inverse Radon transforms to reconstruct physical quantities related to the refractive index: ① The inverse Radon transform of the reconstructed absorption coefficient μ is: (51).

[0043] ② The inverse Radon transform of the reconstructed scattering coefficient α is: (105).

[0044] ③ Reconstruct the real part of the refractive index along x o 'Axis derivative The inverse Radon transform of is: (106), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0045] ④ Reconstruct the real part of the refractive index along z o 'Axis derivative The inverse Radon transform of is: (107), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0046] ⑤ Reconstruct the two-dimensional gradient of the real part of the refractive index on the sample rotation surface The inverse Radon transform of is: (108), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0047] ⑥ The inverse Radon transform of the reduction of the real part of the refractive index in the sample rotation plane is: (109), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

[0048] ⑦ In order to obtain the three-dimensional distribution of the reduction of the real part of the refractive index δ, o Axis area, according to the required resolution, select a series of constants arranged in ascending order, with y o =y 1 ,y 2 ,y 3 ,···,y j ,···,y J， Substitute into θ x , we get: θ x (x o ,C, )=(x o ,y j , ), reconstruct a series of reductions in the real part of the refractive index δ, namely: (110); Then put these According to y 1 ,y 2 ,y 3 ,···,y j ,···,y J Sequentially along y o By arranging the axes in sequence, the three-dimensional distribution of the reduction amount δ of the real part of the refractive index can be obtained.

[0049] According to some exemplary embodiments, γ is the slope coefficient of an approximate linear function. If the surface light source is an annular surface light source, its value varies with the ratio of the inner radius to the outer radius of the annular surface light source image, that is, γ varies with q.

[0050] The benefits of the present invention are: The patent of this invention breaks through the three bottlenecks that restrict the development of nano-CT with X-ray nano-resolution microscope as the core, establishes the differential phase contrast microscope imaging mechanism based on sample refraction, proposes a method for quantitatively separating absorption contrast, scattering contrast and phase contrast, and proposes a method for simply and quickly collecting multiple imaging contrast projection data. It lays the foundation for X-ray differential phase contrast nano-CT with simple, fast, low-dose and multiple contrast imaging mechanisms. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram showing that sample refraction plays no role in lens imaging.

[0052] Figure 2 Light path diagram of an X-ray nanoresolution microscope illuminating a sample with a ring-shaped surface light source.

[0053] Figure 3 Light path diagram of X-ray nanoresolution microscope when a ring-shaped surface light source is used to illuminate the sample with a filter hole.

[0054] Figure 4 Light path diagram of X-ray differential phase contrast microscope with the left half ring light source illuminating the sample.

[0055] Figure 5 Light path diagram of X-ray differential phase contrast microscope with the right half ring light source illuminating the sample.

[0056] Figure 6 Light path diagram of X-ray differential phase contrast microscope with lower semi-ring light source illuminating the sample.

[0057] Figure 7 Light path diagram of X-ray differential phase contrast microscope with upper semi-ring light source illuminating the sample.

[0058] Figure 8 Light path diagram of X-ray differential phase contrast microscope with oblique lower semi-ring light source illuminating the sample.

[0059] Fig. 9 Light path diagram of an X-ray differential phase contrast microscope with an oblique upper semi-ring light source illuminating the sample.

[0060] Fig.10 The right semi-annular light source produces the left semi-annular image (represented by the horizontal bar) and the left semi-annular light source produces the right semi-annular image (represented by the vertical bar).

[0061] Fig.11is the curve of imaging light intensity function changing with the refraction angle signal.

[0062] Fig.12 Schematic diagram of the direction of the oblique component of the refraction angle.

[0063] Fig.13 Two sets of coordinate systems used for Radon transformation.

[0064] Fig.14 The refraction angle is the vector sum of a series of small refraction angles along the light path. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments and the accompanying drawings. Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0066] It should also be noted that, in order to avoid obscuring the present invention due to unnecessary details, only structures and / or processing steps closely related to the solutions according to the present invention are shown in the accompanying drawings, while other details that are not closely related to the present invention are omitted.

[0067] As used herein, the term "image" refers broadly to both a viewable image and data representing the viewable image.

[0068] One of the objectives of the present invention is to utilize the property that the displacement of the surface light source image is proportional to the refraction angle of the sample to control the imaging light intensity of the sample and establish an X-ray differential phase contrast microscope imaging mechanism based on sample refraction.

[0069] The second object of the present invention is to use an X-ray differential phase contrast microscope to collect nine Radon transforms of eight physical quantities related to the refractive index of the sample, and to reconstruct the eight physical quantities using nine corresponding inverse Radon transforms. The eight physical quantities are: absorption coefficient, scattering coefficient, three-dimensional gradient of the real part of the refractive index, two-dimensional gradient perpendicular to the sample rotation axis, three gradient components and reduction of the real part of the refractive index.

[0070] The third purpose of the present invention is to propose a simple method for acquiring six Radon transforms by collecting two sets of sample rotation projection data using the symmetry of positive and negative images, thereby laying the foundation for a simple, fast, low-dose, multi-contrast mechanism X-ray differential phase contrast nano-CT.

[0071] The theoretical logic of the present invention is as follows: first, a proportional relationship between the displacement of the surface light source image and the refraction angle of the sample is derived, and a differential phase contrast microscope imaging mechanism in which the sample refraction modulates the imaging light intensity of the sample is established; second, based on the relationship that the refraction angle of the imaging light is the vector sum of each small refraction angle on the path, a mathematical relationship of the Radon transform of the real part of the refractive index gradient is established, and based on the relationship between the imaging light intensity and the refraction angle, a method for collecting the Radon transform of the real part of the refractive index gradient is proposed; third, based on the Radon transform of the real part of the refractive index gradient, a reconstruction algorithm for the real part of the refractive index gradient and the real part of the refractive index reduction is proposed; fourth, based on the relationship between the imaging light intensity and the variance of the scattering angle, a method for collecting the Radon transform of the scattering coefficient is proposed.

[0072] In lens imaging, although sample refraction will change the direction of Fresnel diffraction, it will not change the spatial position of the sample imaging light intensity. Figure 1 It is vividly demonstrated that the refraction of the inclined sample has no effect on the lens imaging result of the sample itself. The dotted light cone in the figure is the Fresnel diffraction without considering the refraction of the sample, and the solid light cone is the Fresnel diffraction taking into account the refraction of the sample. Although there are differences in the directions of the two Fresnel diffractions, it does not affect the focusing of the two Fresnel diffractions on the same image point.

[0073] In microscope imaging, if the illumination surface light source is included, the objective lens has two parallel imaging processes. One is the magnified imaging of the sample, and the other is the reduced imaging of the surface light source. Although sample refraction has no effect on the imaging of the sample itself, it will change the position of the surface light source imaging.

[0074] The present invention intends to use the property that the image displacement of the surface light source is proportional to the refraction angle of the sample to regulate the imaging light intensity of the sample and establish an X-ray differential phase contrast microscope imaging mechanism based on sample refraction. The present invention first derives the proportional relationship between the image displacement of the surface light source and the refraction angle of the sample, then proves that the refraction of the sample does not affect the imaging of the sample itself, and then establishes a differential phase contrast microscope imaging mechanism in which the sample refraction modulates the imaging light intensity of the sample.

[0075] Embodiment 1: Figure 2 is the imaging optical path of an X-ray nano-resolution microscope with a zone plate as the objective lens. The z-axis is the optical axis of the lens imaging system. The surface light source is composed of many incoherent point light sources. The two-dimensional coordinate system is , and its light intensity distribution is , the two-dimensional coordinate system where the sample is located is , the two-dimensional coordinate system where the objective lens is located is , the two-dimensional coordinate system where the surface light source image is located is , the two-dimensional coordinate system where the sample image is located is The distance between the surface light source and the object surface is z 1 , the distance between the object plane and the objective lens is z 2 , the distance between the objective lens and the surface light source image is z 3 , the distance between the surface light source image and the sample image is z 4 .

[0076] The physical function describing the sample action is: (1) Where M is the absorption function and Φ is the phase function. Because this application is for weak absorption and weak phase samples, and the absorption and phase satisfy the relationship of M<<Φ<<1, when calculating the optical path of the imaging light, the weak absorption of the sample is ignored and the sample phase is retained, and the pure phase sample approximation is adopted, that is: (2);

[0077] The phase function of the objective lens is: (3);

[0078] Where k=2π / λ, and F is the focal length of the objective lens.

[0079] Before placing the sample, the complex amplitude of the spherical wave emitted by a point light source in the surface light source propagating to the front surface of the objective lens is: (4); Formula (4) can be transformed into: (5); Where S is from Spread to , and then spread to The optical path function is: (6);

[0080] According to Fermat's principle, To satisfy the condition that S is a minimum value, we have: (7); in , and x 0 Axis and y 0 The unit vector of the axis; is the two-dimensional gradient parallel to the object plane, is the two-dimensional gradient on the rotation plane perpendicular to the rotation axis.

[0081] According to equations (5) and (3), the Fresnel diffraction complex amplitude propagating from the objective lens to the image plane of the surface light source is: (8);

[0082] Since the phase factor before the integral sign and the three secondary phase factors after the integral sign do not affect the light intensity distribution on the image plane and can be discarded, equation (8) can be simplified to: (9); in represents the Dirac function, m s is the magnification of the light source imaging, and its expression is: (10);

[0083] According to formula (9), before placing the sample, the light intensity of the surface light source image is: (11);

[0084] After placing the sample, assuming that the propagation direction of the light emitted from the sample remains unchanged, the refraction of the sample changes the direction of the incident light, and the starting point of the light changes from Move to have to: (12); Because M<<Φ<<1, the weak absorption of the sample has almost no effect on the phase of the sample imaging light, so when calculating the optical path, the physical function in equation (12) can be In the equation (12), we ignore the weak absorption effect of the sample and retain the phase effect of the sample. We substitute equation (2) into equation (12) to obtain: (13); in: (14); is the optical path function.

[0085] According to Fermat's principle, To satisfy The conditions for the minimum value are: (15).

[0086] According to formula (15) and formula (7), we can get: (16); in For point The refraction angle.

[0087] In order to study the effect of sample refraction on the imaging of the surface light source, along the reverse extension line of the refracted light, it can be equivalent to consider that the sample refraction changes the starting point of the incident light from Move to , as if the light does not come from the point It is not emitted, but from the point Issued, must (17); Substituting formula (17) into formula (5), we get: (18);

[0088] According to equation (18) and equation (3), the Fresnel diffraction complex amplitude propagating from the objective lens to the image plane of the point light source is: (19);

[0089] Because in formula (19), the phase factor before the integral sign and the three secondary phase factors after the integral sign do not affect the light intensity distribution on the image plane and can be discarded, formula (19) can be simplified as: (20);

[0090] According to formula (20), after placing the sample, the light intensity of the surface light source image is: (twenty one);

[0091] Comparing equation (21) with equation (11), we can see that the refraction of the sample causes the spatial displacement of the surface light source image. Since each luminous point on the surface light source has light passing through point , these passing points The light must be near the rear focal plane of the objective lens, forming a displacement and point Considering that there are many points on the sample surface , and the refraction angle size and direction of each point are different, so how many points does the sample have? , there are many displaced surface light source images near the rear focal plane of the objective lens. In short, the imaging of the surface light source by the sample is like inserting a piece of sandpaper in the imaging light path. Each grain of sand will refract and produce a displaced surface light source image. These displaced surface light source images are superimposed together, resulting in blurred surface light source imaging.

[0092] Although equation (16) deduces that the refracted light of the sample produces a displacement on the surface of the objective lens, which then causes a spatial displacement of the surface light source image, this displacement will not affect the imaging result of the sample. Figure 1 This physical image has been drawn, and the following is a theoretical proof of this point. Combining equation (12) and equation (3), and substituting into equation (1), the Fresnel diffraction complex amplitude propagating from the objective lens to the sample image plane is: (twenty two);

[0093] Since the phase factor before the integral sign and the three quadratic phase factors after the integral sign do not affect the light intensity distribution on the image plane and can be discarded, equation (22) can be simplified to: (twenty three); Where m o is the magnification of the objective lens imaging the sample, and its expression is: (twenty four);

[0094] According to formula (23), the light intensity distribution of sample imaging is: (25);

[0095] Formula (25) only considers the contribution of a point light source with a unit area in the surface light source. We further consider the contribution of all the light-emitting points on the surface light source. Assume that the area of ​​the surface light source is A and the light intensity is evenly distributed. , then the result of integrating the surface light source in equation (25) is: (26);

[0096] Equation (26) proves that the refraction of the sample does not affect the imaging result of the sample. In other words, even if the sample is a piece of sandpaper, the refraction direction of each point is different, and the chaotic refraction will not affect the clear imaging of the sample's absorption contrast.

[0097] Although the refraction of the sample does not leave any trace in the sample imaging light intensity, see equation (26), it causes the surface light source imaging light intensity to shift, see equation (21). The present invention intends to use the surface light source image displacement proportional to the sample refraction angle to regulate the sample imaging light intensity and establish a differential phase contrast microscopy imaging mechanism based on sample refraction.

[0098] The surface light source image near the rear focal plane of the objective lens is actually the smallest light opening of the sample imaging beam near the rear focal plane of the objective lens, that is, the thinnest waist of the entire imaging beam. Refraction angle and phase gradient The relationship is: (27);

[0099] It can be equivalently considered that the displacement of the surface light source caused by sample refraction is: (28);

[0100] The displacement of the surface light source image is: (29);

[0101] Because each light point on the surface light source has light passing through the point , so these rays are displaced near the rear focus of the objective lens See also Figure 3, the surface light source is a ring. If a filter hole with the same diameter as the outer diameter of the ring image is inserted at the ring image, the filter hole will block the displaced ring image and reduce the sample point The imaging light intensity is . Therefore, the physical process of the X-ray differential phase contrast microscope imaging mechanism is: Refracted, passing through the sample point Each light ray changes direction, causing the sample point The relevant surface light source image is displaced, and the filter hole blocks the displaced surface light source image, forming the displacement distance, blocking area, and sample point The imaging light intensity decreases, and each point is related to the sample. The imaging mechanism is proportional to the refraction angle, forming a sample point Imaging light intensity drop and sample point An angular signal response mechanism that is proportional to the refraction angle.

[0102] Under the conditions of annular surface light source illuminating the sample and small refraction angle, the imaging mechanism of the imaging light intensity decrease in response to the refraction angle signal can be expressed by the following formula: (30);

[0103] Where ΔI ref is the decrease in light intensity caused by refraction, R f and r f are the outer radius and inner and outer diameters of the surface light source image, respectively, and q is the ratio of the inner radius to the outer radius of the annular surface light source image, that is, Formula (30) reveals the basic principle of the decrease in imaging light intensity caused by the refraction angle. However, since the direction of the refraction angle cannot be determined, a quantitative refraction angle signal response imaging mechanism cannot be formed.

[0104] In order to establish a quantitative refraction angle signal response imaging mechanism, an asymmetrically distributed surface light source must be used in a given direction. It is possible to use a semi-surface light source that is symmetrically distributed in the x-axis direction and asymmetrically distributed in the y-axis direction; it is possible to use a semi-surface light source that is symmetrically distributed in the y-axis direction and asymmetrically distributed in the x-axis direction; it is also possible to use a semi-surface light source that is symmetrically distributed in any given direction and asymmetrically distributed in the perpendicular direction. Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Fig. 9 The optical paths of the X-ray differential phase contrast microscope illuminated by the left semi-ring surface light source, the right semi-ring surface light source, the lower semi-ring surface light source, the upper semi-ring surface light source, the oblique lower semi-ring surface light source, and the oblique upper semi-ring surface light source are respectively. Figure 4 and Figure 5 The light path shown is the same as the one shown in the figure. The other light paths are studied similarly.

[0105] exist Figure 4 In the optical path shown, the refraction angle component is limited to x o Axis direction. Sample point The imaging light intensity depends on the passing rate of the semi-ring surface light source image in the filter hole. The left semi-ring surface light source produces the right semi-ring image (indicated by the vertical bar), see Fig.10 When the sample point When the refraction angle is zero, the right half ring image produced by the left half ring light source passes through the filter hole completely, see Fig.10 In the middle figure, the vertical bar area is all within the filter hole, and the sample point The imaging light intensity is the maximum. The refraction angle along x o As the positive axis increases, the displacement of the right half ring image produced by the left half ring light source increases, and its passing area in the filter hole decreases accordingly. Fig.10 In the right figure, the vertical bar area in the filter hole is decreasing, and the sample point The imaging light intensity also decreases. The refraction angle along x o As the axis increases in the negative direction, the displacement of the right half ring image produced by the left half ring light source increases accordingly, but see Fig.10 In the left figure, the passing area in the filter hole does not decrease, that is, the vertical bar area in the filter hole remains unchanged. The imaging light intensity remains unchanged. The relationship between the imaging light intensity and the refraction angle can be described by a curve, see Fig.11 I L This curve is Figure 4 The response curve of the imaging light intensity of the optical path to the refraction angle signal is referred to as the angle signal response curve.

[0106] exist Figure 5 In the optical path shown, the refraction angle component is limited to x o Axis direction. Sample point The imaging light intensity depends on the passing rate of the semi-ring surface light source image in the filter hole. The right semi-ring surface light source produces the left semi-ring image (indicated by the horizontal bar), see Fig.10 When the sample point When the refraction angle is zero, the left half ring image produced by the right half ring light source passes through the filter hole completely, see Fig.10 In the middle figure, the horizontal bar area is all within the filter hole, and the sample point The imaging light intensity is the maximum. The refraction angle along x o As the negative direction of the axis increases, the displacement of the left half ring image produced by the right half ring light source increases, and its passing area in the filter hole decreases accordingly. Fig.10 In the left figure, the area of ​​the horizontal strip in the filter hole is decreasing, and the sample point The imaging light intensity also decreases. The refraction angle along x o As the positive axis increases, the displacement of the left half ring image produced by the right half ring light source increases accordingly, but see Fig.10 In the right figure, the passing area in the filter hole does not decrease, that is, the horizontal area in the filter hole remains unchanged. The imaging light intensity remains unchanged. The relationship between the imaging light intensity and the refraction angle can be described by a curve, see Fig.11 I R This curve is Figure 5 Response curve of the angle signal of the optical path.

[0107] Under small refraction angle conditions, Figure 4 In the optical path shown, the imaging light intensity of the left half ring light source is determined by the following formula: (31);

[0108] exist Figure 5 In the optical path shown, the imaging light intensity of the right half annular light source is determined by the following formula: (32), where θ x For along x o The component of the refraction angle in the direction of the axis.

[0109] Subtracting formula (31) from formula (32) yields: (33); Formula (33) is the theoretical basis for establishing a quantitative refraction angle signal response imaging mechanism.

[0110] Adding formula (32) to formula (31), we get: (34).

[0111] Dividing formula (33) by formula (34), we get: (35).

[0112] Under the condition of semi-circular surface light source illuminating the sample, in order to examine the above-mentioned various imaging light intensity functions not only in the small refraction angle range but also in the large refraction angle range, Fig.11 Describe I L ,I R ,I R -I L ,I R +I L and The curves of the five imaging light intensity functions changing with the refraction angle signal. Fig.11 It is known that in The range of I R -I L is the refraction angle component θ x A linear function of range, although It is not a strict linear function, but it can be used as an approximate linear function: (36), Where γ is the slope coefficient of the approximate linear function, and its value varies with the ratio of the inner radius to the outer radius of the annular surface light source image, that is, γ varies with q.

[0113] The derivation of equations (33), (34) and (35) is based on the sample point The refraction angle is limited to x o The above three equations are based on the assumption that the refraction angles in other directions affect the above three equations. The main factor is the effect of the refraction angles in other directions on the difference between the two imaging light intensities and the sum of the two imaging light intensities. First, the difference between the two imaging light intensities is not affected by the refraction angles in other directions. The reason is that no matter the sample point The refraction angle can be decomposed into x in any direction. o Axis component and y o For the left and right half-ring light sources, x o The axial component effect is additive in the difference between the two imaging light intensities, while the y o The axial component effect is a subtraction relationship in the difference between the two imaging light intensities. Secondly, the sum of the two imaging light intensities will be affected by the refraction angle in any direction. The reason is that the sum of the two imaging light intensities is actually the same as Figure 3 The images taken on the imaging optical path are equivalent. Figure 3 and Figure 2 , it can be found Figure 3 There is a filter hole in the imaging light path, and the sample point The refraction angle will reduce the sample point The imaging light intensity is Figure 2 There is no filter hole in the imaging light path, and the sample point The refraction angle will not reduce the sample point Therefore, Figure 3 The image captured by the imaging optical path is better than Figure 2 The image contrast taken by the imaging optical path is high.

[0114] Because the sum of the two imaging light intensities is not only affected by A component of Other components affect, so equation (34) should be corrected as follows: (37).

[0115] Although the approximation degree of equation (37) is higher than that of equation (34), the direction of the refraction angle in equation (37) is unknown and cannot be used for quantitative calculation. x and The difference caused is a small amount in the sum of the two imaging light intensities and has limited impact on the sum of the two imaging light intensities. When the sum of the two imaging light intensities appears in the denominator of equation (35), the impact of this difference will be even smaller.

[0116] In summary, for samples with small refraction angles and requiring accurate reconstruction, the quantitative information of the refraction angle can be obtained according to equation (38) derived from equation (33): (38), Where I is Figure 2 For samples with large refraction angles and the desire to improve the contrast and highlight the contour, the approximate quantitative information of the refraction angle can be obtained using equation (39) derived from equation (36): (39).

[0117] In order to Figure 2 In order to avoid the decrease of imaging light intensity caused by refraction as described in equation (30), the numerical aperture of the condenser should be slightly smaller than that of the objective lens in the optical path.

[0118] Similarly, for the o The refraction angle component θ in the axial direction y , with similar results. Figure 6 and Figure 7 The optical path shown in the figure is used to obtain quantitative information of the refraction angle for samples with small refraction angles and accurate reconstruction is required according to equation (40): (40), For samples with large refraction angles and in order to improve the contrast and highlight the contours, the approximate quantitative information of the refraction angle can be obtained according to formula (41): (41), Among them I T and I B They are the imaging light intensities of the upper and lower semi-ring surface light sources respectively.

[0119] Similarly, for the refraction angle component θ along the oblique direction ω , there are similar results. Figure 8 and Fig. 9 The optical path shown in the figure is used to obtain quantitative information of the refraction angle for samples with small refraction angles and accurate reconstruction is required according to equation (42): (42), For samples with large refraction angles and in order to improve the contrast and highlight the contours, the approximate quantitative information of the refraction angle can be obtained according to formula (43): (43), Among them I 斜上 and I 斜下 are the imaging light intensities illuminated by the upper oblique semi-annular surface light source and the lower oblique semi-annular surface light source respectively.

[0120] Regardless of whether the refraction angle is small or large, the following formula is valid: (44), Where ω is the angle between the oblique direction and the x-axis, , , x o Unit vectors in the axis, yo axis, and oblique directions, see Fig.12 .

[0121] X-ray nano-resolution microscope imaging has a depth of field. Within the depth of field, the propagation of X-rays in the sample can be regarded as a straight line propagation parallel to the optical axis. According to the principle of reversibility of the optical path, the depth of field of the objective lens imaging is actually the focal depth of the objective lens, and its calculation formula is: (45), in is the minimum resolution interval, also known as imaging resolution. It can be seen that the depth of field is inversely proportional to the wavelength and decreases as the square of the resolution interval decreases. When the sample diameter is less than or equal to the depth of field, the light intensity and angle carried by the X-ray emitted from the sample can be regarded as the projection data of the sample. This is the physical basis for collecting nano-CT projection data using an X-ray nano-resolution microscope.

[0122] The expression for the sample refractive index is: (46), Where δ and β are the reduction in the real part and imaginary part of the refractive index respectively. The relationship between the imaginary part β and the absorption coefficient μ is: (47).

[0123] Absorption contrast CT first collects the Radon transform of the imaginary part of the refractive index, and then uses the inverse Radon transform to reconstruct the imaginary part of the refractive index. Similarly, phase contrast CT first collects the Radon transform of the reduction in the real part of the refractive index, and then uses the inverse Radon transform to reconstruct the reduction in the real part of the refractive index. Absorption contrast comes from the sample absorbing X-ray energy, while phase contrast is caused by the sample phase shift changing the X-ray energy distribution. It is precisely because phase contrast is caused by energy transfer rather than energy loss that phase contrast CT has much richer content than absorption contrast CT.

[0124] According to formula (1), the sample information carried by the outgoing X-ray, that is, the material function, is expressed as: (48).

[0125] When the sample placed in the X-ray nanoresolution microscope is rotated, according to equation (26), the absorption contrast imaging light intensity I collected by the detector can be written as the absorption function M, that is, the Radon transform of the absorption coefficient μ, which is mathematically expressed as: (49).

[0126] Where R represents the Radon transform operator, I 0 is the light intensity before placing the sample, R represents the Radon transform operator, (x o ,y o ,z o ) is a fixed measurement coordinate system, (x o ',y o ',z o ') is the coordinate system that rotates with the sample, is the angle between the two coordinate systems. The relationship between the two coordinate systems can be found in Fig.13 And the following formula: (50), After collecting the Radon transform of μ, the three-dimensional spatial structure of μ can be reconstructed based on the inverse Radon transform. The formula for reconstructing μ using the inverse Radon transform is: (51).

[0127] According to this logic, if the phase function Φ of the sample can be collected, that is, the Radon transform of the reduction in the real part of the refractive index δ, its mathematical expression is: (52), Then, according to the inverse Radon transform, the three-dimensional spatial distribution of δ can be reconstructed. The formula for reconstructing δ by inverse Radon transform is: (53).

[0128] Unfortunately, however, there is no method to directly collect the Radon transform of δ in X-ray nano-resolution microscopy so far. Although a two-dimensional phase contrast image of the sample can be taken by inserting a phase shift ring near the rear focal plane of the objective lens, there are halo artifacts, making it difficult to obtain quantitative projection data of the phase. The patent of this invention proposes a theory and method for collecting the three-dimensional gradient Radon transform of the real part of the refractive index using an X-ray differential phase contrast microscope. Mathematically, the three-dimensional gradient of the real part of the refractive index is equivalent to the reduction in the real part of the refractive index.

[0129] Generally speaking, the density in the sample is not uniform, and unevenness will cause refraction. Although the propagation path of X-rays in the sample cannot be an absolute straight line, it is still an approximate straight line around the forward direction, like a snake moving forward. Fig.14 It can be seen that the refraction angle of the outgoing X-ray is the vector sum of the small refraction angles on the path. According to geometric optics, the refraction angle is equivalent to the phase gradient. When the sample rotates, the phase gradient , which is the refraction angle of the outgoing X-ray , which can be expressed as the three-dimensional gradient of the real part of the refractive index The Radon transform is: (54), where θ x and θ y Refraction angle In the measurement coordinate system x o Axis component and y o Axis component, θ x According to equations (38) and (39), θ y According to formula (40) and formula (41), is a two-dimensional gradient operator, is a three-dimensional gradient operator, and They are the measurement coordinate system x o Axis and y o The unit vector on the axis, 、 、 The sample coordinate system x is o 'axis, y o 'axis, z o 'Unit vector on the axis.

[0130] Equation (54) has three mutually perpendicular components, two of which are in the rotation plane perpendicular to the axis of rotation, and one is parallel to the axis of rotation.

[0131] use Multiplying formula (54) yields x o 'The component formula in the axial direction is also The Radon transform is: (55), where θ x’ is the refraction angle x in the sample coordinate system o 'Axis component.

[0132] Use points Multiplying (54), we get z o The component formula in the axial direction is also The Radon transform is: (56), where θ z' is the refraction angle z in the sample coordinate system o 'Axis component.

[0133] use Multiplying formula (54), we get y o 'The component formula in the axial direction is also The Radon transform is: (57), where θ y’ is the refraction angle y in the sample coordinate system o 'Axis component.

[0134] Performing vector sum operations on equations (55) and (56), we can derive is the two-dimensional gradient of the real part of the refractive index in the sample rotation plane The Radon transform is: (58), in is the two-dimensional gradient operator within the sample rotation plane, (59), (60),

[0135] In addition, you can also use Figure 8 and Fig. 9 The optical path shown in the figure collects the refraction angle component θ in any given direction ω According to equations (44), (55), (56) and (57), θ ω It can be expressed as a combination of Radon transforms: (61), When ω=0, we have (62), When ω=π / 2, we have (63).

[0136] To collect the Radon transform of μ, the detector only needs to collect the projection data of the sample rotating from 0 degrees to 180 degrees. , , , and To perform Radon transform, the projection data of the sample rotated from 0 degree to 180 degree must be collected on at least two to five optical paths.

[0137] In order to simplify the cumbersome data collection process, the present invention proposes to simplify the collection process by using the symmetry of the positive and negative images. , , , and The Radon transform method.

[0138] The symmetry properties of the positive and negative images are related to the rotation axis of the sample. When the sample is rotated 180 degrees, the positive image becomes the negative image. This rotation operation does not change the scalar and the vector components parallel to the rotation axis, but it changes the vector components perpendicular to the rotation axis. In other words, the scalar and the vector components parallel to the rotation axis are rotationally symmetric, while for a rotation of 180 degrees, the vector components perpendicular to the rotation axis are rotationally antisymmetric. These properties of the positive and negative images can be expressed by the following three formulas: (64), (65), (66).

[0139] For samples with small refraction angles, the sample is rotated 180 degrees, and equations (64) and (65) are substituted into equation (31), yielding: (67).

[0140] Substituting equation (67) into equation (38), we get: (68), Formula (68) shows that for a sample with a small refraction angle that requires accurate reconstruction, by using the symmetry of the positive and negative images, only Figure 2 and Figure 4 The refraction angle x can be collected by two optical paths o Axis component θ x .

[0141] For samples with large refraction angles that require improved contrast and highlighted contours, Fig.11 Middle I L Curve and I R The symmetric relationship between the curves gives: (69).

[0142] Substituting equation (69) into equation (39), we get: (70), Formula (70) shows that for samples with large refraction angles that require improved contrast and prominent contours, the symmetry of the positive and negative images only requires Figure 4 One optical path can collect the refraction angle x o Axis component θ x .

[0143] Substituting equation (68) and equation (70) into equation (55), The Radon transform of can be obtained according to the following formula: (71),

[0144] Substituting equation (68) and equation (70) into equation (56), The Radon transform of can be obtained according to the following formula: (72),

[0145] Substituting equation (68) and equation (70) into equation (58), The Radon transform of can be obtained according to the following formula: (73), For samples with small refraction angles that require accurate reconstruction, , only need Figure 2 The optical path collects the imaging light intensity of the sample when it rotates from 0 degrees to 180 degrees. Figure 4 The optical path collects the imaging light intensity of the sample from 0 degrees to 360 degrees. For samples with large refraction angles that require improved contrast and prominent contours, , only need Figure 4 The optical path collects the imaging light intensity of the sample when it rotates from 0 degree to 360 degrees.

[0146] According to formula (44), we have: (74), The sample is rotated 180 degrees and substituted into equations (65) and (66), we have: (75).

[0147] Subtracting (74) from (75) yields: (76), Adding formula (74) to formula (75), we get: (77).

[0148] Substituting equation (76) and equation (77) into equation (54), and then into equation (42) and equation (43), we get: (78), For samples with small refraction angles that require accurate reconstruction, ,use Figure 2 The optical path collects the imaging light intensity of the sample when it rotates from 0 degree to 180 degrees, and uses Figure 8 and Fig. 9 The optical paths of the samples are used to collect the imaging light intensity from 0 degree to 360 degree rotation. , It is the projection data rotated from 0 degrees to 180 degrees. and is the projection data rotated from 180 degrees to 360 degrees. Substituting it into formula (42), we have: , For samples with large refraction angles that require improved contrast and highlighted contours, , Figure 8 and Fig. 9 The two optical paths respectively collect the imaging light intensity of the sample from 0 degrees to 360 degrees. , It is the projection data rotated from 0 degrees to 180 degrees. and is the projection data rotated from 180 degrees to 360 degrees. Substituting it into formula (43), we have: .

[0149] Sample a little In addition to the refraction angle signal, there is also a scattering angle signal. The inside of the resolution unit is filled with discontinuous particles. The particles have various possibilities such as spherical, cylindrical, conical, flake, and strip shapes. There are also many possibilities for the relative positions and directions between different particles. Generally speaking, the micro-refraction of these particles forms a high-dimensional scattering tensor. The patent of this invention does not delve into the scattering tensor, but only studies two types of symmetrical scattering. One is the scattering of spherical particles, and the other is the scattering of a variety of particles distributed in a disorderly manner. The former is an ideal situation. Whether it is the scattering of a single particle or the scattering of a group of particles, it is symmetrical; the latter is closer to the actual situation. Although the scattering of a single particle is not symmetrical, when the particles inside the resolution unit are sufficient and disordered enough, the scattering of the group of particles tends to be symmetrical. Both situations cause the high-dimensional scattering tensor to degenerate into an isotropic zero-dimensional tensor, that is, the scattering angle variance scalar. According to the additivity of the scattering angle variance, the linear scattering coefficient that produces the scattering angle variance per unit length can be defined. Therefore, when the sample rotates, a point on the sample The scattering angle variance is the Radon transform of the linear scattering coefficient, that is: (79), where σ 2 is the scattering angle variance of the X-ray emitted by the sample, and α is the linear scattering coefficient.

[0150] The point diffusion caused by the sample scattering on the surface light source can be equivalently considered as: (80), The point spread generated by the surface light source image is: (81), Each light point on the surface light source has light passing through the point When each ray reaches the image point near the rear focal plane of the objective lens, it will have a scattering radius of m s z 1 σ point spread. Therefore, due to the sample point The surface light source image is diffused by the point, and the area increment is: (82), The area increment of the surface light source image is Figure 3 The imaging light path will inevitably be blocked by the filter hole, thus causing the sample point The decrease of imaging light intensity. Since the ratio of light intensity decrease to light intensity is equal to the ratio of area increment to area, we have: (83), Where ΔI scat The decrease in light intensity caused by scattering is also Figure 2 The imaging light intensity and Figure 3 The difference in imaging light intensity.

[0151] Substituting equation (83) into equation (79), the Radon transform of the scattering angle variance can be derived as: (84), The sum of the two imaging light intensities I R +I L ,I B +IT、I 斜上 +I 斜下 and Figure 3 The imaging light intensity is equivalent to , and substituting it into formula (84), we can get: (85).

[0152] Embodiment 2: The X-ray differential phase contrast microscope uses a symmetrical surface light source to illuminate the sample in order to collect the absorption information of the sample and realize absorption contrast imaging. Figure 2 The optical path of an X-ray nanometer resolution microscope with an annular surface light source illuminating the sample; in order to collect the scattering information of the sample and realize scattering contrast imaging, an X-ray nanometer resolution microscope optical path with a symmetrical surface light source illuminating the sample and a filter hole is used. Figure 3 An X-ray nano-resolution microscope optical path with a filter hole for illuminating a sample with an annular surface light source; in order to establish a quantitative refraction angle signal response imaging mechanism, a symmetrical surface light source distribution is used in a given direction, while an asymmetrical surface light source distribution is used in a perpendicular direction. For example, a symmetrical surface light source distribution can be used in the x-axis direction, while an asymmetrical surface light source distribution can be used in the y-axis direction. For another example, a symmetrical surface light source distribution can be used in the y-axis direction, while an asymmetrical surface light source distribution can be used in the x-axis direction. For another example, a symmetrical surface light source distribution can be used in any given direction, while an asymmetrical surface light source distribution can be used in a perpendicular direction. Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Fig. 9 The optical paths of the X-ray differential phase contrast microscope are respectively the left semi-ring surface light source plus a filter hole, the right semi-ring surface light source plus a filter hole, the lower semi-ring surface light source plus a filter hole, the upper semi-ring surface light source plus a filter hole, the oblique lower semi-ring surface light source plus a filter hole, and the oblique upper semi-ring surface light source plus a filter hole.

[0153] The X-ray differential phase contrast microscope described above, based on the differential phase contrast imaging mechanism of sample refraction, collects two-dimensional absorption contrast images, two-dimensional scattering contrast images and two-dimensional refraction contrast images of each sample angle on the image plane, and obtains them by the following method: The X-ray differential phase contrast microscope comprises an X-ray surface light source, and an aperture, a sample turntable, a zone plate, a filter hole and an imaging detector arranged in sequence along the optical axis; the zone plate is an element with a lens imaging function, which not only magnifies the sample to be measured but also reduces the surface light source to form an image; the aperture is close to the surface light source and is used to block the surface light source to make it an asymmetric semi-surface light source; the sample turntable is used to load the sample to be measured, the plane where the sample is located is called the sample object plane, and the imaging detector is located on the image plane of the sample; the filter hole is located on the imaging plane of the surface light source, and its shape and size are exactly the same as the surface light source image, and the filter hole and the surface light source image are precisely aligned; the zone plate, the surface light source and its image plane, the sample object plane and the image plane, the aperture, the filter hole and the imaging detector surface are all perpendicular to the optical axis; S1, turning on and adjusting the surface light source: making the center of the surface light source coincide with the optical axis, and the surface light source is perpendicular to the optical axis; S2, adjusting the sample turntable: aligning the focus of the hollow cone light beam emitted by the surface light source to the sample-carrying position on the sample turntable, and aligning the hollow cone light beam passing through the sample position to the downstream zone plate; S3, adjusting the zone plate: making the surface light source form a surface light source image near the rear focal plane of the zone plate, and making the hollow cone light beam passing through the sample position be focused by the zone plate and aligned with the imaging detector located on the sample image plane, so that the imaging detector presents a bright field state; S4, adjusting the object distance and the image distance: placing a resolution test card on the sample turntable, and precisely adjusting the distances between the sample turntable, the zone plate and the imaging detector so that the resolution test card can achieve a clear imaging state; S5, adjusting the filter hole: making the filter hole and the surface light source image accurately aligned; S6, feed aperture: blocks half of the surface light source to form an asymmetric half-surface light source illumination; S7, measuring the angle signal response curve: perpendicular to the optical axis, gradually moving the filter hole along the asymmetric direction of the half-surface light source, and using the imaging detector to measure the angle signal response curve of the light intensity changing with the displacement of the filter hole on the sample image plane; S8, adjusting the asymmetric direction of the half-surface light source: rotating the aperture around the optical axis, and using the aperture to adjust the asymmetric direction of the half-surface light source to the direction of the refraction angle component to be collected; S9, collecting data of a refraction angle component in one direction: placing a sample to be tested, and the imaging detector collects a two-dimensional magnified image of the sample when it is rotated from 0 degree to 180 degrees, or collects a two-dimensional magnified image of the sample when it is rotated from 0 degree to 360 degrees; S10, collecting refraction angle component data in another direction: because there may be more than one refraction angle component to be collected, steps S8 and S9 need to be repeated until sufficient refraction angle component data are collected; S11, collecting scattering contrast projection data: removing the aperture, using a symmetrical surface light source for illumination, canceling the response mechanism of the imaging light intensity drop depending on a specific refraction angle component, and the imaging detector captures a two-dimensional magnified image of the sample rotated from 0 degrees to 180 degrees on the sample image plane; S12, collecting absorption contrast projection data: removing the aperture, using a symmetrical surface light source for illumination, removing the filter hole, canceling the response mechanism of the imaging light intensity drop depending on the scattering angle variance, and the imaging detector captures a two-dimensional magnified image of the sample rotated from 0 degrees to 180 degrees on the sample image plane.

[0154] Embodiment three: There are nine Radon transforms collected by X-ray differential phase contrast microscopy: ① Use Figure 2 The optical path is used to collect the imaging light intensity of the sample from 0 degrees to 180 degrees. The collected absorption contrast imaging light intensity I can be written as the Radon transform of the absorption coefficient μ: (49); ② Use Figure 2 , Figure 4 and Figure 5 The optical paths are used to collect imaging light intensities I and I L and I R , or use Figure 2 , Figure 6 and Figure 7 The optical paths are used to collect imaging light intensities I and I B and I T , or use Figure 2 , Figure 8 and Fig. 9 The optical paths are used to collect imaging light intensities I and I 斜下 and I 斜上 , or use Figure 2 and Figure 3 The difference in imaging light intensity ΔI is collected by the optical path scat , each imaging light intensity is the imaging light intensity collected by the detector when the sample rotates from 0 degrees to 180 degrees. The square of the difference between the collected imaging light intensities can be written as the Radon transform of the scattering coefficient α: (85); ③ For samples with small refraction angles that require accurate reconstruction, that is, ,use Figure 2 , Figure 4 and Figure 5 The three optical paths collect imaging light intensities I, I L and IR , for samples with large refraction angles that require improved contrast and highlighted contours, that is ,use Figure 4 and Figure 5 The two optical paths collect imaging light intensity I respectively L and I R Each imaging light intensity is the imaging light intensity collected by the detector when the sample rotates from 0 degrees to 180 degrees. The refraction angle x o Axis component θ x and the cosine of the angle The product of the real part of the refractive index along x o 'Axis derivative The Radon transform is: (86); ④ For samples with small refraction angles that require accurate reconstruction, that is, ,use Figure 2 , Figure 4 and Figure 5 The three optical paths collect imaging light intensities I, I L and I R , for samples with large refraction angles that require improved contrast and highlighted contours, that is ,use Figure 4 and Figure 5 The two optical paths collect imaging light intensity I respectively L and I R Each imaging light intensity is the imaging light intensity collected by the detector when the sample rotates from 0 degrees to 180 degrees. The refraction angle x o Axis component θ x and the angle cosine sin The product of the real part of the refractive index along z o 'Axis derivative The Radon transform is: (87); ⑤ For samples with small refraction angles that require accurate reconstruction, that is, ,use Figure 2 , Figure 6 and Figure 7 The optical paths are respectively collected I and I B and I T , for samples with large refraction angles that require improved contrast and highlighted contours, that is ,use Figure 6 and Figure 7 The two optical paths collect I B and I T Each imaging light intensity is the imaging light intensity collected by the detector when the sample rotates from 0 degrees to 180 degrees, and the refraction angle is along y o The axis component θ y is the real part of the refractive index along yo 'Axis derivative The Radon transform is: (88); ⑥ For samples with small refraction angles that require accurate reconstruction, that is, ,use Figure 2 , Figure 4 and Figure 5 The three optical paths collect imaging light intensities I, I L and I R , for samples with large refraction angles that require improved contrast and highlighted contours, that is ,use Figure 4 and Figure 5 The two optical paths collect imaging light intensity I respectively L and I R Each imaging light intensity is the imaging light intensity collected by the detector when the sample rotates from 0 degrees to 180 degrees. The refraction angle x o Axis vector is the two-dimensional gradient of the real part of the refractive index in the sample rotation plane The Radon transform is: (89); ⑦ Refraction angle , that is, x o Axis vector and o Axis vector The vector sum is the three-dimensional gradient of the real part of the refractive index The Radon transform is: (78); For samples with small refraction angles that require accurate reconstruction, ,use Figure 2 The optical path collects the imaging light intensity of the sample when it rotates from 0 degree to 180 degrees, and uses Figure 8 and Fig. 9 The optical paths collect the imaging light intensity of the sample from 0 degrees to 360 degrees, respectively: , For samples with large refraction angles that require improved contrast and highlighted contours, ,use Figure 8 and Fig. 9 The two optical paths respectively collect the imaging light intensity of the sample rotating from 0 degrees to 360 degrees, which are: ; in , It is the projection data rotated from 0 degrees to 180 degrees. and It is the projection data rotated from 180 degrees to 360 degrees; ⑧ Although the X-ray differential phase contrast microscope cannot directly collect the Radon transform of the real part of the refractive index decrease δ, it can use Fourier transform and inverse transform to obtain the three-dimensional gradient of the real part of the refractive index. The Radon transform of is converted into the Radon transform of the real part of the refractive index reduction δ. According to the phase Φ and the phase gradient and the refraction angle The relationship is: (90), where ρ is the value along x o Axis spatial frequency, F x and F x -1 Along x o The Fourier transform and inverse transform of the axis, ν is the Fourier transform along the y axis. o Axis spatial frequency, F y and F y -1 Along y o The Fourier transform and inverse transform of the axis are used for samples with small refraction angles that require accurate reconstruction, that is, ,use Figure 2 The optical path collects the imaging light intensity of the sample when it rotates from 0 degree to 180 degrees, and uses Figure 8 and Fig. 9 The optical paths collect the imaging light intensity of the sample from 0 degrees to 360 degrees, respectively: , , For samples with large refraction angles that require improved contrast and highlighted contours, ,use Figure 8 and Fig. 9 The two optical paths respectively collect the imaging light intensity of the sample rotating from 0 degrees to 360 degrees, which are: , ; in , It is the projection data rotated from 0 degrees to 180 degrees. and It is the projection data rotated from 180 degrees to 360 degrees; ⑨ If we only care about one rotation plane of the sample, we can replace y in equation (90) with o If the variable is regarded as a constant, the Radon transform of the reduction of the real part of the refractive index δ on a rotation plane of the sample can be simplified to: (91), in , For samples with small refraction angles that require accurate reconstruction, ,use Figure 2 , Figure 4 and Figure 5 The three optical paths collect imaging light intensities I, I L and I R , for samples with large refraction angles that require improved contrast and highlighted contours, that is ,use Figure 4 and Figure 5 The two optical paths collect imaging light intensity I respectively L and I R , each imaging light intensity is the imaging light intensity collected by the detector when the sample is rotated from 0 degrees to 180 degrees.

[0155] Embodiment 4: Nine inverse Radon transforms are proposed for the nine Radon transforms collected by X-ray differential phase contrast microscopy: ① The inverse Radon transform of the reconstructed absorption coefficient μ is: (51); ② The inverse Radon transform of the reconstructed scattering coefficient α is: (92); ③ Reconstruct the real part of the refractive index along x o 'Axis derivative The inverse Radon transform of is: (93); ④Reconstruct the real part of the refractive index along z o 'Axis derivative The inverse Radon transform of is: (94); ⑤ Reconstruct the real part of the refractive index along y o 'Axis derivative The inverse Radon transform of is: (95); ⑥ Reconstruct the two-dimensional gradient of the real part of the refractive index of the sample rotation surface The inverse Radon transform of is: (96); ⑦Reconstruct the three-dimensional gradient of the real part of the refractive index The inverse Radon transform of is: (97), For samples with small refraction angles that require accurate reconstruction, ,have: , For samples with large refraction angles that require improved contrast and highlighted contours, ,have: ; ⑧ The inverse Radon transform of the reconstructed real part of the refractive index reduction δ is: (98), For samples with small refraction angles that require accurate reconstruction, ,have: , , For samples with large refraction angles that require improved contrast and highlighted contours, ,have: , ; ⑨ If only the decrease in the real part of the refractive index δ in the sample rotation plane is reconstructed, equation (98) can be simplified. In equation (98), the phase function Φ of the sample and the refraction angle x are o Axis component θ x The y in o Variables are considered as constants, and we have: (99), in .

[0156] Embodiment 4: If there is a method that can obtain enough sample information to meet basic needs at less than half the cost, then at least half of the people will consider using this method. This half cost may be time, energy, investment in experimental equipment, or radiation dose received by the sample. When doing scientific and technological research, sometimes you need to consider subtraction. The simple method proposed by the patent of this invention using the symmetry of positive and negative images is as follows: (1) Collect two sets of projection data: first use Figure 4 The optical path is used to collect the imaging light intensity of the sample from 0 degree to 360 degree, where is the imaging light intensity from 0 degrees to 180 degrees, For imaging light intensity from 180 degrees to 360 degrees, Figure 2 The optical path collects the imaging light intensity of the sample from 0 degree to 180 degree .

[0157] (2) Arrange and process the collected projection data: sort out the six Radon transforms of physical quantities related to the refractive index: ① The Radon transform of the absorption coefficient μ is: (49), ②The Radon transform of the scattering coefficient α is (100), ③The real part of the refractive index along x o 'Axis derivative The Radon transform is: (101), For samples with small refraction angles that require accurate reconstruction, : (68), For samples with large refraction angles that require improved contrast and highlighted contours, : (70), ④The real part of the refractive index along z o 'Axis derivative The Radon transform is: (102), For samples with small refraction angles that require accurate reconstruction, : (68), For samples with large refraction angles that require improved contrast and highlighted contours, : (70), ⑤ Two-dimensional gradient of the real part of the refractive index on the sample rotation surface The Radon transform is: (103), For samples with small refraction angles that require accurate reconstruction, : (68), For samples with large refraction angles that require improved contrast and highlighted contours, : (70), ⑥ The phase function Φ and refraction angle x of the sample o Axis component θ x The y in o The variable is regarded as a constant, and the real part of the refractive index is a two-dimensional function in the sample rotation plane. The Radon transform is (104), For samples with small refraction angles that require accurate reconstruction, : (68), For samples with large refraction angles that require improved contrast and highlighted contours, : (70).

[0158] (3) Six inverse Radon transforms to reconstruct physical quantities related to the refractive index: ① The inverse Radon transform of the reconstructed absorption coefficient μ is: (51), ② The inverse Radon transform of the reconstructed scattering coefficient α is: (105), ③ Reconstruct the real part of the refractive index along x o 'Axis derivative The inverse Radon transform of is: (106), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours. ④Reconstruct the real part of the refractive index along z o 'Axis derivative The inverse Radon transform of is: (107), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours. ⑤ Reconstruct the two-dimensional gradient of the real part of the refractive index on the sample rotation surface The inverse Radon transform of is: (108), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours. ⑥ The inverse Radon transform of the reduction of the real part of the refractive index in the sample rotation plane is: (109), in , in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours. ⑦ In order to obtain the three-dimensional distribution of the reduction of the real part of the refractive index δ, o Axis area, according to the required resolution, select a series of constants arranged in ascending order, with y o =y 1 ,y 2 ,y 3 ,···,y j ,···,y J， Substitute into θ x , we get: θ x (x o ,C, )=(x o ,y j , ), reconstruct a series of reductions in the real part of the refractive index δ, namely: (110); Then put these According to y 1 ,y 2 ,y 3 ,···,y j ,···,y J Sequentially along y o By arranging the axes in sequence, the three-dimensional distribution of the reduction amount δ of the real part of the refractive index can be obtained.

[0159] It should be understood by those skilled in the art that the exemplary imaging mechanisms, image acquisition and reconstruction methods and applications described in conjunction with the embodiments or examples disclosed herein can be implemented in hardware, software or a combination of the two. Whether it is performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention. When implemented in hardware, it can be, for example, an electronic circuit, an application-specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc. When implemented in software, the elements of the present invention are programs or code segments used to perform the required tasks. The program or code segment can be stored in a machine-readable medium or transmitted on a transmission medium or a communication link via a data signal carried in a carrier. "Machine-readable medium" may include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROMs, flash memory, erasable ROMs (EROMs), floppy disks, CD-ROMs, optical disks, hard disks, optical fiber media, radio frequency (RF) links, and the like. The code segment can be downloaded via a computer network such as the Internet, an intranet, or the like.

[0160] It should also be noted that the exemplary embodiments mentioned in the present invention are based on a series of steps or applications corresponding to the CT describing some methods and the application of the methods. However, the present invention is not limited to the order of the above steps, that is, the steps can be performed in the order mentioned in the embodiment, or in a different order from the embodiment, or several steps can be performed simultaneously.

[0161] In the present invention, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with features of other embodiments or replace features of other embodiments.

[0162] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the embodiments of the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An imaging mechanism and an image acquisition and reconstruction method for an X-ray nano-resolution microscope, characterized in that: A method for collecting nine Radon transforms of eight physical quantities related to the refractive index based on an X-ray differential phase contrast microscope and the symmetry of positive and negative images, namely an X-ray nano-resolution microscope, is proposed, and the eight physical quantities related to the refractive index are reconstructed according to the nine inverse Radon transforms. The eight physical quantities are: absorption coefficient, scattering coefficient, three-dimensional gradient of the real part of the refractive index, two-dimensional gradient perpendicular to the rotation axis of the sample, three gradient components and the reduction of the real part of the refractive index; and on this basis, a simple method for obtaining six of the Radon transforms by collecting two sets of sample rotation projection data using the symmetry of positive and negative images is proposed; the X-ray differential phase contrast microscope comprises an X-ray surface light source, and an aperture, a sample turntable, a zone plate, a filter hole and an imaging detector arranged in sequence along the optical axis; The X-ray differential phase contrast nano-CT based on X-ray differential phase contrast microscopy and the symmetric properties of positive and negative images proposes nine Radon transforms of eight physical quantities related to the refractive index of the sample under the conditions of annular surface light source and semi-annular surface light source illuminating the sample: ① Collect Radon transform of absorption coefficient μ: (49)； Where M is the absorption function, μ is the absorption coefficient, R represents the Radon transform operator, I0 is the light intensity before placing the sample, R represents the Radon transform operator, (x o ,y o ,z o ) is a fixed measurement coordinate system, (x o ',y o ',z o ') is the coordinate system that rotates with the sample, is the angle between the two sets of coordinate systems, δ is the decrease in the real part of the refractive index; ② Radon transform of the collected scattering coefficient α: (85)； Where m s is the magnification of the light source imaging, R f is the outer radius of the annular surface light source image, ΔI scat is the decrease in light intensity caused by scattering, It uses an annular surface light source to illuminate the sample, and an X-ray microscope optical path without a filter hole, collects the imaging light intensity of the sample from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by the left half ring light source, collecting the imaging light intensity of the sample from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by a right half-ring light source, collecting imaging light intensity when the sample rotates from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by the lower semi-ring light source, collecting the imaging light intensity of the sample from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by the upper semi-ring light source, collecting the imaging light intensity of the sample from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by an oblique upper semi-ring light source, collecting imaging light intensity when the sample rotates from 0 degrees to 180 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by an oblique lower semi-ring light source, collecting imaging light intensity when the sample is rotated from 0 to 180 degrees; ③ Collect the real part of the refractive index along x o 'Axis derivative The Radon transform is: (86)， Where q is the ratio of the inner radius to the outer radius of the annular surface light source image, It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ④ Collect the real part of the refractive index along z o 'Axis derivative The Radon transform is: (87)， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ⑤ Collect the real part of the refractive index along y o 'Axis derivative The Radon transform is: (88)， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ⑥ Collect the real part of the refractive index two-dimensional gradient The Radon transform is: (89)， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours. is the two-dimensional gradient on the rotation plane perpendicular to the rotation axis; ⑦ Collect the real part of the refractive index three-dimensional gradient The Radon transform is: (78)， Where ω is the angle between the refraction angle component and the X-axis, θ x is the refraction angle In the measurement coordinate system x o Axis component, θ y is the refraction angle In the measurement coordinate system y o Axis component, and They are x o Axis and y o The unit vector on the axis, For samples with small refraction angles that require accurate reconstruction, ,have: ， For samples with large refraction angles that require improved contrast and highlighted contours, ,have: ， in It is an X-ray differential phase contrast microscope optical path illuminated by an oblique upper semi-ring light source, collecting imaging light intensity of the sample from 180 degrees to 360 degrees. It is an X-ray differential phase contrast microscope optical path illuminated by an oblique lower semi-ring light source, collecting imaging light intensity of the sample from 180 degrees to 360 degrees; ⑧ Collect the real part of the refractive index three-dimensional gradient The Radon transform of can be converted into the Radon transform of the reduction of the real part of the refractive index δ: (90)， Where Φ is the phase function and ρ is the o Axis spatial frequency, F x and F x -1 Along x o The Fourier transform and inverse transform of the axis, ν is the Fourier transform along the y axis. o Axis spatial frequency, F y and F y -1 Along y o The Fourier transform and inverse transform of the axis, is the two-dimensional gradient parallel to the object plane; For samples with small refraction angles that require accurate reconstruction, ,have: ， ， For samples with large refraction angles that require improved contrast and highlighted contours, ,have: ， ； ⑨ The Radon transform of the reduction in the real part of the refractive index δ on a rotation plane of the sample can be simplified to: (91)， in ， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is aimed at samples with large refraction angles that require improved contrast and prominent contours. Each imaging light intensity is the imaging light intensity collected by the detector when the sample rotates from 0 degrees to 180 degrees. The X-ray differential phase contrast nano-CT based on X-ray differential phase contrast microscopy and the symmetric properties of positive and negative images, under the conditions of annular surface light source illuminating the sample and semi-annular surface light source illuminating the sample, proposes nine inverse Radon transforms for reconstructing eight physical quantities related to the refractive index: ① The inverse Radon transform of the reconstructed absorption coefficient μ is: (51)； ② The inverse Radon transform of the reconstructed scattering coefficient α is: (92)； ③ Reconstruct the real part of the refractive index along x o 'Axis derivative The inverse Radon transform of is: (93)， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ④ Reconstruct the real part of the refractive index along z o 'Axis derivative The inverse Radon transform of is: (94)， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ⑤ Reconstruct the real part of the refractive index along y o 'Axis derivative The inverse Radon transform of is: (95)， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ⑥ Reconstruct the two-dimensional gradient of the real part of the refractive index of the sample rotation surface The inverse Radon transform of is: (96)， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ⑦ Reconstruction of the three-dimensional gradient of the real part of the refractive index The inverse Radon transform of is: (97)， For samples with small refraction angles that require accurate reconstruction, ,have: ， For samples with large refraction angles that require improved contrast and highlighted contours, ,have: ； ⑧ The inverse Radon transform of the reconstructed real part of the refractive index reduction δ is: (98)， For samples with small refraction angles that require accurate reconstruction, ,have: ， ， For samples with large refraction angles that require improved contrast and highlighted contours, ,have: ， ； ⑨ Reconstruct the reduction of the real part of the refractive index in the sample rotation plane δ, and convert the sample phase function Φ and the refraction angle x o Axis component θ x The y in o Variables are considered as constants, and we have: (99)， in ， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is designed for samples with large refraction angles that require improved contrast and highlighted contours.

2. The imaging mechanism and image acquisition and reconstruction method for X-ray nano-resolution microscopy according to claim 1, characterized in that: The X-ray differential phase contrast microscope is formed by adding two optical elements to an X-ray microscope with a zone plate as an objective lens: One of the optical elements feeds into a filter hole on the imaging surface of the symmetrical surface light source, the shape and size of the filter hole are exactly the same as the image of the symmetrical surface light source, and the filter hole and the image of the surface light source are precisely aligned; The second optical element feeds an aperture into the light outlet of the surface light source to block half of the surface light source, thereby forming an asymmetric half-surface light source illumination.

3. The imaging mechanism and image acquisition and reconstruction method for X-ray nano-resolution microscopy according to claim 1 or 2, characterized in that: The X-ray differential phase contrast microscope has a surface light source that is a symmetrical surface light source or an asymmetrical surface light source. When the surface light source is a symmetrical surface light source, the symmetrical surface light source is symmetrical in both the x-axis direction and the y-axis direction. When the surface light source is an asymmetrical surface light source, the symmetrical surface light source is divided into two along the symmetry axis to form two surface light sources of equal shape, and one of the two surface light sources is blocked by an aperture at the exit of the surface light source to obtain the required asymmetrical surface light source. The asymmetrical surface light source can be a semi-circular surface light source, a rectangular surface light source, a trapezoidal surface light source, or a circular surface light source deviating from the optical axis. For the asymmetrical surface light source, the shape of the filter hole must be exactly the same as the shape of the symmetrical surface light source image, and when dimming, the filter hole must be precisely aligned with the symmetrical surface light source image.

4. The imaging mechanism and image acquisition and reconstruction method for X-ray nano-resolution microscopy according to claim 1 or 2, characterized in that: The X-ray differential phase contrast microscope has a surface light source that is an annular surface light source or a semi-annular surface light source. When the surface light source is an annular surface light source, the annular surface light source is generated by a point light source through a condenser or by an annular array target embedded in diamond. When the annular surface light source is generated by an annular array target embedded in diamond, the X-rays generated by the annular array target are directly used to illuminate the sample without using a condenser. When the surface light source is a semi-annular surface light source, the semi-annular surface light source is first generated by a point light source through a condenser to generate an annular surface light source, and then blocked by an aperture at the outlet of the surface light source, or generated by a semi-annular array target embedded in diamond. When the semi-annular surface light source is generated by a semi-annular array target embedded in diamond, the X-rays generated by the semi-annular array target are directly used to illuminate the sample without using an aperture at the outlet of the surface light source.

5. The imaging mechanism and image acquisition and reconstruction method for X-ray nano-resolution microscopy according to claim 1, characterized in that: The physical process of the X-ray differential phase contrast microscope imaging mechanism based on sample refraction is as follows: Refracted, passing through the sample point Each light ray changes direction, causing the sample point The relevant surface light source image is displaced, and the filter hole blocks the displaced surface light source image, forming an imaging mechanism in which the displacement distance, the blocked area, and the decrease in imaging light intensity at the sample point are proportional to the refraction angle of the sample point, that is, an X-ray differential phase contrast microscope imaging mechanism based on sample refraction is formed.

6. The imaging mechanism and image acquisition and reconstruction method for X-ray nano-resolution microscopy according to claim 1, characterized in that: The X-ray differential phase contrast microscope, based on the differential phase contrast imaging mechanism of sample refraction, collects two-dimensional absorption contrast images, two-dimensional scattering contrast images and two-dimensional refraction contrast images of each corner of the sample on the image plane, and obtains them by the following method: The X-ray differential phase contrast microscope comprises an X-ray surface light source, and an aperture, a sample turntable, a zone plate, a filter hole and an imaging detector arranged in sequence along the optical axis; the zone plate is a component with a lens imaging function, which not only magnifies the sample to be measured but also reduces the surface light source to form an image; the aperture is close to the surface light source and is used to block the surface light source to make it an asymmetric half-surface light source; the sample turntable is used to load the sample to be measured, the plane where the sample is located is called the sample object plane, and the imaging detector is located on the image plane of the sample; The filter hole is located on the imaging surface of the surface light source, and its shape and size are exactly the same as the surface light source image, and the filter hole and the surface light source image are precisely aligned; the zone plate, the surface light source and its image surface, the sample object surface and the image surface, the aperture, the filter hole and the imaging detector surface are all perpendicular to the optical axis; S1, turning on and adjusting the surface light source: making the center of the surface light source coincide with the optical axis, and the surface light source is perpendicular to the optical axis; S2, adjusting the sample turntable: aligning the focus of the hollow cone light beam emitted by the surface light source to the sample-carrying position on the sample turntable, and aligning the hollow cone light beam passing through the sample position to the downstream zone plate; S3, adjusting the zone plate: making the surface light source form a surface light source image near the rear focal plane of the zone plate, and making the hollow cone light beam passing through the sample position be focused by the zone plate and aligned with the imaging detector located on the sample image plane, so that the imaging detector presents a bright field state; S4, adjusting the object distance and the image distance: placing a resolution test card on the sample turntable, and precisely adjusting the distances between the sample turntable, the zone plate and the imaging detector so that the resolution test card can achieve a clear imaging state; S5, adjusting the filter hole: making the filter hole and the surface light source image accurately aligned; S6, feed aperture: blocks half of the surface light source to form an asymmetric half-surface light source illumination; S7, measuring the angle signal response curve: perpendicular to the optical axis, gradually moving the filter hole along the asymmetric direction of the half-surface light source, and using the imaging detector to measure the angle signal response curve of the light intensity changing with the displacement of the filter hole on the sample image plane; S8, adjusting the asymmetric direction of the half-surface light source: rotating the aperture around the optical axis, and using the aperture to adjust the asymmetric direction of the half-surface light source to the direction of the refraction angle component to be collected; S9, collecting data of a refraction angle component in one direction: placing a sample to be tested, and the imaging detector collects a two-dimensional magnified image of the sample when it is rotated from 0 degree to 180 degrees, or collects a two-dimensional magnified image of the sample when it is rotated from 0 degree to 360 degrees; S10, collecting refraction angle component data in another direction: because there may be more than one refraction angle component to be collected, steps S8 and S9 need to be repeated until sufficient refraction angle component data are collected; S11, collecting scattering contrast projection data: removing the aperture, using a symmetrical surface light source for illumination, canceling the response mechanism of the imaging light intensity drop depending on a specific refraction angle component, and the imaging detector captures a two-dimensional magnified image of the sample rotated from 0 degrees to 180 degrees on the sample image plane; S12, collecting absorption contrast projection data: removing the aperture, using a symmetrical surface light source for illumination, removing the filter hole, canceling the response mechanism of the imaging light intensity drop depending on the scattering angle variance, and the imaging detector captures a two-dimensional magnified image of the sample rotated from 0 degrees to 180 degrees on the sample image plane.

7. The imaging mechanism and image acquisition and reconstruction method for X-ray nano-resolution microscopy according to claim 1, characterized in that: Based on X-ray differential phase contrast microscopy and the symmetric properties of positive and negative images in X-ray differential phase contrast nano-CT, a simple image acquisition and reconstruction method is proposed: (1) Collect two sets of projection data: First, use the left half-ring light source to illuminate the sample and the X-ray differential phase contrast microscope light path with a filter hole to collect the imaging light intensity of the sample when it rotates from 0 degrees to 360 degrees, where is the imaging light intensity from 0 degrees to 180 degrees, The imaging light intensity is from 180 degrees to 360 degrees, and then the sample is illuminated by a ring-shaped surface light source and an imaging light path without a filter hole is used to collect the imaging light intensity of the sample from 0 degrees to 180 degrees. ; (2) Arrange and process the collected projection data: sort out the six Radon transforms of physical quantities related to the refractive index: ① The Radon transform of the absorption coefficient μ is: (49)； ② The Radon transform of the scattering coefficient α is (100)； ③ The real part of the refractive index along x o 'Axis derivative The Radon transform is: (101)， For samples with small refraction angles that require accurate reconstruction, : (68)， For samples with large refraction angles that require improved contrast and highlighted contours, : (70)； ④ The real part of the refractive index along z o 'Axis derivative The Radon transform is: (102)， For samples with small refraction angles that require accurate reconstruction, : (68)， For samples with large refraction angles that require improved contrast and highlighted contours, : (70)； ⑤ Two-dimensional gradient of the real part of the refractive index on the sample rotation surface The Radon transform is: (103)， For samples with small refraction angles that require accurate reconstruction, : (68)， For samples with large refraction angles that require improved contrast and highlighted contours, : (70)； ⑥ The phase function Φ and refraction angle x of the sample o Axis component θ x The y in o The variable is regarded as a constant, and the real part of the refractive index is a two-dimensional function in the sample rotation plane. The Radon transform is (104)， For samples with small refraction angles that require accurate reconstruction, : (68)， For samples with large refraction angles that require improved contrast and highlighted contours, : (70)； (3) Six inverse Radon transforms to reconstruct physical quantities related to the refractive index: ① The inverse Radon transform of the reconstructed absorption coefficient μ is: (51)； ② The inverse Radon transform of the reconstructed scattering coefficient α is: (105)； ③ Reconstruct the real part of the refractive index along x o 'Axis derivative The inverse Radon transform of is: (106)， in ， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ④ Reconstruct the real part of the refractive index along z o 'Axis derivative The inverse Radon transform of is: (107)， in ， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ⑤ Reconstruct the two-dimensional gradient of the real part of the refractive index on the sample rotation surface The inverse Radon transform of is: (108)， in ， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ⑥ The inverse Radon transform of the reduction of the real part of the refractive index in the sample rotation plane is: (109)， in ， in It is aimed at samples with small refraction angles that require accurate reconstruction. It is for samples with large refraction angles that require improved contrast and highlighted contours; ⑦ In order to obtain the three-dimensional distribution of the reduction of the real part of the refractive index δ, o Axis area, according to the required resolution, select a series of constants arranged in ascending order, with y o =y1,y2,y3,···,y j ,···,y J， Substitute into θ x , we get: θ x (x o ,C, )=(x o ,y j , ), reconstruct a series of reductions in the real part of the refractive index δ, namely: （110）； Then put these According to y1,y2,y3,···,y j ,···,y J Sequentially along y o By arranging the axes in sequence, a three-dimensional distribution of the reduction amount δ of the real part of the refractive index can be obtained.

8. An imaging mechanism and an image acquisition and reconstruction method for an X-ray nano-resolution microscope according to any one of claims 1 and 7, characterized in that: The γ is the slope coefficient of the approximate linear function. If the surface light source is an annular surface light source, its value varies with the ratio of the inner radius to the outer radius of the annular surface light source image, that is, γ varies with q.

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