A simulation method for X-ray speckle wavefront detection

Abstract

The present invention provides a simulation method for X-ray speckle wavefront detection, comprising: determining the energy of the light source and the available experimental range, determining the complex amplitude distribution of the initial light wave, and providing the light wave diffraction equation for the light wave along the air propagation path; determining the relationship between the complex amplitude distribution and the transmission function after the light wave passes through a scatterer or a sample to be measured, and determining the transmission functions of the scatterer and the sample to be measured; determining the distances between the light source, the scatterer, the sample to be measured, and the detector, and combining the light wave diffraction equation, the relationship between the complex amplitude distribution and the transmission function, and the transmission functions of the scatterer and the sample to be measured to gradually calculate and determine the wavefront complex amplitude distribution on the detector plane; and obtaining the simulated diffraction pattern intensity based on the integration of the wavefront complex amplitude distribution. The method of the present invention can simulate and study the effects of different experimental parameters on the detection performance of speckle measurement technology, providing theoretical guidance and important reference for the efficient selection of appropriate experimental parameters in practical applications of this technology.

Description

Technical Field

[0001] The present invention relates to a simulation method for optical wavefront detection technology, and in particular to a simulation method for X-ray speckle wavefront detection. Background Art

[0002] Speckle is a granular pattern with random amplitude and phase distribution produced by light irradiating the rough surface of an object. When it was first discovered, it has always been a coherent "noise" that needs to be eliminated in various optical systems. With the in-depth analysis of the statistical characteristics of speckle and the development of high-performance lasers, speckle has gradually been successfully and widely used in fields such as metrology, imaging, and communications [1]. X-rays have been widely used in the medical field in the early days due to their high penetrability brought by their high energy, and the development of high-performance synchrotron radiation sources has further promoted the research and application of X-rays in many fields such as biology, medicine, materials, and chemistry [2]. In recent years, the scattering characteristics of speckle in the near-field region of the X-ray band (Fresnel diffraction region) have received much attention and research. Unlike the characteristics of far-field speckle that are closely related to the beam size and wavelength, the size of X-ray near-field speckle is independent of the propagation distance and energy of the beam, and its size and shape can remain unchanged within the near-field range [3]. Based on the scattering characteristics of X-ray near-field speckle, an X-ray speckle wavefront detection technology has been developed that uses speckle as a wavefront marker and characterizes the wavefront characteristics. It has been successfully applied in various imaging and measurement experiments [4].

[0003] Since the size and shape of near-field speckle remain constant, after introducing a scatterer (usually sandpaper or film) that can generate speckle into the optical path, the deformation of the resulting speckle is only related to the wavefront distortion of the X-ray propagating along the optical path. By obtaining two speckle intensity images with and without the sample in the optical path, the wavefront changes in the optical path can be "tracked". The wavefront distortion introduced by the sample when the front-end light wave passes through the sample can be extracted from the speckle deformation in these two images, and the characteristic information of the sample can be obtained. This is the speckle tracking measurement technology [5].

[0004] Digital image correlation (DIC) is a powerful tool for detecting material deformation[6]. In X-ray speckle wavefront detection, this method is often used to extract the deformation of the speckle caused by the sample being tested into the optical path from the speckle intensity map. Combined with different peak-finding algorithms, the DIC algorithm can obtain deformation with sub-pixel accuracy. Therefore, the detection accuracy of speckle tracking measurement technology is usually at the sub-pixel level.

[0005] In order to further improve the measurement accuracy of this method, a speckle scanning measurement technique has gained attention and development, which scans the scatterer with a fixed step size and then recovers the information of the sample to be measured from the series of speckle intensity maps obtained. [7] Unlike the two complete speckle intensity maps compared in speckle tracking, in speckle scanning measurement, the spliced ​​speckle intensity maps obtained by extracting the same pixel rows from the series of speckle intensity maps obtained by scanning are compared. Therefore, the accuracy of speckle scanning measurement technology can be further improved to the sub-scanning step size level, but it requires more data acquisition time.

[0006] Speckle wavefront detection technology can obtain different characteristic information of the sample under test in different application directions. In imaging applications, based on the differences in the interaction principles between X-rays and the sample under test, this technology can obtain absorption imaging, phase imaging, and dark field imaging containing scattering information of the sample under test. In measurement applications, based on the different positions of the scatterers, this technology can obtain the surface slope or wavefront curvature radius distribution of the optical element under test [8].

[0007] High measurement accuracy, appropriate coherence requirements, simple measurement structure, and affordability are the significant advantages of speckle wavefront measurement technology. Using only simple scatterers and detectors, a basic speckle measurement experimental platform can be established under synchrotron radiation illumination. These advantages have enabled numerous researchers to improve and expand upon near-field speckle measurement methods, such as speckle vector tracking, speckle self-scanning, and modulation pattern analysis. These researchers have demonstrated the potential of this technology in applications ranging from X-ray optical component inspection to biomedical imaging and crystal testing.

[0008] Currently, in various existing applications of speckle detection technology, selecting appropriate measurement parameters, such as sandpaper particle size, light source coherence, scanning step size, and detector effective pixel size, remains a key factor in achieving satisfactory detection results. Therefore, simulating the impact of different parameters on the measurement results of this technology is of great significance for promoting the rapid and efficient application of this speckle detection technology.

[0009] [1] JW GOODMAN. Speckle Phenomenon in Optics: Theory and Applications[M]. Science Press, 2009.

[0010] [2]Ice GE, Budai JD, Pang JW L. The race to x-ray microbeam and nanobeam science[J].Science, 2011, 334(6060): 1234-1239.

[0011] [3]Cerbino R, Peverini L, Potenza M A C, et al. X-ray-scattering information obtained from near-field speckle[J]. Nature Physics, 2008, 4(3): 238-243.

[0012] [4]Zdora M C. State of the art of X-ray speckle-based phase-contrast and dark-field imaging[J]. Journal of Imaging, 2018, 4(5): 60.

[0013] [5]S Bérujon, Ziegler E, Cerbino R, et al. Two-Dimensional X-Ray Beam Phase Sensing[J]. Physical Review Letters, 2012, 108(15): 158102.

[0014] [6]Pan B, Qian K, Xie H, et al. Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review[J]. Measurement science and technology, 2009, 20(6): 062001.

[0015] [7]Berujon S, Wang H, Sawhney K. X-ray multimodal imaging using a random-phase object[J]. Physical Review A, 2012, 86(6): 063813.

[0016] [8]Berujon S, Wang H, Alcock S, et al. At-wavelength metrology of hard X-ray mirror using near field speckle[J]. Optics express, 2014, 22(6): 6438-6446. Summary of the Invention

[0017] The purpose of this invention is to provide a simulation method for X-ray speckle wavefront detection, so as to simulate and study the influence of different experimental parameters on the detection performance of speckle measurement technology, and provide theoretical guidance and important reference for the efficient selection of appropriate experimental parameters in practical applications of this technology.

[0018] To achieve the above objectives, the present invention provides a simulation method for X-ray speckle wavefront detection, comprising:

[0019] S1, select the energy E of the light source and the two-dimensional coherence length; the wavelength λ of the light source and the available experimental range at this wavelength are determined by the energy E of the light source. The available experimental range is the range of values ​​of the distance from the scatterer to the detector;

[0020] S2, based on the optical path type, determines the complex amplitude distribution W of the initial light wave and gives the light wave diffraction equation on the air propagation path between the scatterer, the sample to be measured, and the detector;

[0021] S3, determining a relationship between a complex amplitude distribution of a light wave after passing through a scatterer or a sample to be measured and a transmission function of the scatterer or the sample to be measured according to a simulated speckle measurement method, and determining the transmission functions of the scatterer and the sample to be measured;

[0022] S4, based on the simulated speckle measurement method, the distances between the light source, the scatterer, the sample to be measured, and the detector, as well as the thickness distributions of the scatterer and the sample to be measured, are determined. Then, combining the light wave diffraction equation of the light wave in the air propagation path between the scatterer, the sample to be measured, and the detector in step S2, the relationship between the complex amplitude distribution and the transmission function of the light wave after passing through the scatterer or the sample to be measured in step S3, and the transmission function of the scatterer and the sample to be measured, the wavefront complex amplitude distribution of the initial light wave, the light wave after passing through the scatterer and the sample to be measured, is gradually calculated and determined until the wavefront complex amplitude distribution W on the detector plane is determined. CCD ;

[0023] S5, according to the wavefront complex amplitude distribution W on the detector plane CCD , and the integrated value is the simulated diffraction pattern intensity at the detector plane.

[0024] The available experimental range under the wavelength λ of the light source is the Fresnel near-field region L under the wavelength condition. f .

[0025] For a plane wave, the complex amplitude distribution W of the initial light wave emitted by the light source is:

[0026] W p (x, y) = exp(ikr),

[0027] For a spherical wave, the complex amplitude distribution W of the initial light wave emitted by the light source is:

[0028]

[0029] Where x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, i is the imaginary unit, k is the wave number, k = 2π / λ, and r is the spatial propagation distance of the light wave.

[0030] The diffraction equation of light waves on the air propagation path is:

[0031]

[0032] Wherein, W(x, y) is the complex amplitude distribution of the light wave in the current plane (x, y), W(x1, y1) is the complex amplitude distribution of the light wave in the next plane (x1, y1), x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, Δz is the distance from the starting plane (x, y) to the next plane (x1, y1) in the direction of light wave propagation, i is the imaginary unit, k is the wave number, k = 2π / λ, and λ is the wavelength of the light wave.

[0033] The step S2 further includes: determining the spatial coherence of the light wave, and correcting the light wave diffraction equation on the air propagation path between the scatterer, the sample to be tested, and the detector according to the spatial coherence;

[0034] When the light source is a completely correlated light source, the spatial coherence μ(x1, y1) of the light wave is 1; when the light source is a partially coherent correlated light source, the spatial coherence μ(x1, y1) of the light wave is:

[0035]

[0036] Where k is the wave number, l x , l y is the two-dimensional coherence length of the light source, x, y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and x1, y1 are the coordinate positions of another point in the space perpendicular to the direction of light wave propagation on the same plane.

[0037] The relationship between the complex amplitude distribution and the transmission function of the light wave after passing through the scatterer or the sample to be measured is:

[0038] W(x,y,z1)≈exp|-ik∫(δ(x,y,z)-iβ(x,y,z))dz|W(x,y,z),

[0039] Wherein, exp[-ik∫(δ(x, y, z)-iβ(x, y, z))dz] is the transmission function of the scatterer or the sample to be tested, δ and β are the refractive index and absorption coefficient in the complex refractive index n=1-δ+iβ of the scatterer or the sample to be tested, respectively, i is the imaginary unit, dz is the integration between the starting thickness z and z1 of the sample to be tested, exp is the e index, W(x, y, z) is the complex amplitude distribution of the light wave before passing through the scatterer or the sample to be tested, W(x, y, z1) is the complex amplitude distribution after passing through the scatterer or the sample to be tested, x, y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and z is the spatial coordinate position in the direction of light wave propagation.

[0040] When the scatterer is sandpaper, the transmission function T d (x, y) is:

[0041]

[0042] Where i is the imaginary unit, n is the complex refractive index, k is the wave number, m is the total number of particles on the sandpaper, j is the ordinal number of the particle, j = 1 ~ m, (x j ,y j ) is the center of the jth particle, r j is the radius of the jth particle, x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation;

[0043] The sample to be tested is an elliptical hemisphere with a long axis of a, a medium short axis of b, and a short axis of c. The transmission function T of the sample to be tested is x (x, y) is:

[0044]

[0045] Where i is the imaginary unit, n is the complex refractive index, k is the wave number, a is the major axis, b is the minor axis, c is the minor axis, x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and z is the spatial coordinate position in the direction of light wave propagation.

[0046] The steps S3 and S4 specifically include:

[0047] S110, simulating a light source, a scatterer, a sample to be measured, and a detector that are sequentially arranged, executing step S4 with a first distance d1 being the distance from the light source to the scatterer, a second distance d2 being the distance from the scatterer to the sample to be measured, and a third distance d3 being the distance from the sample to be measured to the detector, and executing step S5 accordingly, thereby integrating to obtain the simulated diffraction pattern intensity on the detector plane as a first speckle intensity map I. s ;

[0048] S120, remove the sample to be tested from the optical path and execute step S4 accordingly, and then execute step S5 accordingly, so as to integrate and obtain the simulated diffraction pattern intensity on the detector plane as the second speckle intensity map I r ;

[0049] S130, the first speckle intensity image I s and the second speckle intensity map I r Perform DIC algorithm processing to obtain a first speckle deformation amount; or, take the first distance d1 as the distance from the light source to the scatterer, the second distance d2 as the distance from the scatterer to the sample to be measured, and the sum of the third distance d3 and the moving distance Δd as the distance from the sample to be measured to the detector, perform step S4, and accordingly perform step S5, thereby integrating to obtain a third speckle intensity map I d ; Taking the first distance d1 as the distance from the light source to the scatterer, the second distance d2 as the distance from the scatterer to the sample to be measured, and the moving distance Δd as the distance from the sample to be measured to the detector, execute step S4, and accordingly execute step S5, thereby integrating to obtain a fourth speckle intensity map, and performing DIC algorithm processing on the first speckle intensity map and the third or fourth speckle intensity map to obtain a second speckle deformation variable.

[0050] S140: Obtain a local deflection angle of the light beam according to the first speckle deformation amount or the second speckle deformation amount as a wavefront slope change in an orthogonal direction.

[0051] In step S3, determining the transmission function of the scatterer includes: obtaining the initial transmission function T of the scatterer d (x, y), the transmission function T of the initial scatterer d Based on (x, y), the displacement of the scatterer in the x and y directions is introduced to update the transmission function T of multiple updated scatterers d '(x, y); The displacement of the scatterer in the x direction and the y direction includes a scanning displacement and / or a vibration displacement.

[0052] The displacement of the scatterer in the x-direction and the y-direction includes scanning displacement, and steps S3 to S5 specifically include:

[0053] S210, for the speckle contrast scanning detection method, execute step S3 to obtain an initial transmission function of the scatterer and multiple updated transmission functions of the scatterers. For each of the initial transmission function of the scatterer and the multiple updated transmission functions of the scatterers, simulate a light source, a scatterer, a sample to be tested, and a detector that are sequentially arranged. With a first distance d1 as the distance from the light source to the scatterer, a second distance d2 as the distance from the scatterer to the sample to be tested, and a third distance d3 as the distance from the sample to be tested to the detector, execute steps S4 and S5. Furthermore, execute steps S4 and S5 with the scatterer removed from the optical path, thereby obtaining two speckle intensity maps corresponding to each scanning position, one with and one without the sample to be tested, as a speckle intensity map sequence ∑I when the sample to be tested is present. s (h, v) and the speckle intensity map sequence ∑I when there is no sample to be tested r (h, v);

[0054] S220, according to the speckle intensity image sequence ∑I of the sample to be measured, s (h, v) and the speckle intensity map sequence ∑I when there is no sample to be tested r (h, v), the wavefront slope change caused by the sample under test is obtained using the DIC algorithm;

[0055] S230, for the one-dimensional speckle self-scanning detection method, based on the speckle intensity map sequence ∑I obtained in step S210 when there is a sample to be tested s (h, v), select the speckle intensity map sequence corresponding to one-dimensional scanning position as the speckle intensity map sequence ∑I in the front beam mode s (h, v); then, for each of the initial scatterer transmission function and the multiple updated scatterer transmission functions, steps S4 and S5 are performed respectively with the first distance d1 as the distance from the light source to the sample to be measured, the second distance d2 as the distance from the sample to be measured to the scatterer, and the third distance d3 as the distance from the scatterer to the detector, thereby obtaining a speckle intensity map corresponding to each scanning position when the sample to be measured is present, as a speckle intensity map sequence ∑I in the post-beam mode. s (h, v);

[0056] S240, for the speckle intensity map sequence ∑I in the front beam mode s (h, v) and the speckle intensity map sequence ∑I in the post-beam mode s (h, v), the speckle deformation caused by the sample to be tested is obtained by using the DIC algorithm;

[0057] Among them, the updated scatterer transmission function T d '(x, y) is:

[0058] T d'(x, y) = T d (x+f(x), y+g(y)),

[0059] Among them, T d () is the transmission function of the initial scatterer, T d '(x, y) is the updated transmission function of the scatterer, f(x) and g(y) are the displacements of the scatterer in the x and y directions, respectively.

[0060] Compared with the prior art, the present invention has achieved the following technical effects:

[0061] (1) The present invention is based on the Fresnel approximation of Kirchhoff's diffraction formula in scalar diffraction theory. By numerically calculating the approximate diffraction formula, the present invention simulates the entire process of light waves passing from the light source through various components in sequence and finally reaching the detector in X-ray near-field speckle wavefront detection, and obtains the final diffraction pattern (light intensity distribution on the detector plane). Through simulation, a simulation research tool is provided for all various wavefront detection technologies based on the principle of X-ray near-field speckle detection, which is convenient for providing theoretical guidance for the construction of detection equipment and the selection of parameters of various components before actual application.

[0062] (2) The simulation parameters of each component in the present invention can be freely adjusted and optimized as needed, which is conducive to exploring and studying the appropriate experimental parameters required to achieve the target detection requirements before actual application, facilitating the efficient and successful application of the technology, and saving detection time and cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is a flow chart of the simulation method of X-ray speckle wavefront detection of the present invention.

[0064] Figure 2 3 is a schematic diagram of the principle of an experimental simulator used in the simulation method for X-ray speckle wavefront detection according to the first embodiment of the present invention, which is used to simulate the speckle tracking detection method.

[0065] Figure 3-Figure 5 : is a schematic diagram of the principle of the experimental simulator used in the simulation method of X-ray speckle wavefront detection according to the second embodiment of the present invention, wherein Figure 3 Used to simulate speckle contrast scanning detection method, Figure 4 Speckle self-scanning detection method for simulating the front beam pattern, Figure 5 Speckle self-scanning detection method for simulating post-beam patterns. DETAILED DESCRIPTION

[0066] The features, functions, various parameter adjustments and specific simulation details of the present invention will be described in detail below to facilitate a better understanding and use of the present invention. In addition, unless otherwise specified, the definitions of symbols throughout the text remain the same.

[0067] like Figure 2-Figure 5 Shown are layouts of various experimental simulators used in the simulation method for X-ray speckle wavefront detection according to the present invention. The simulators comprise a light source 1 and a detector 4, arranged sequentially along the optical path, as well as a scatterer 2 and a sample 3 positioned between them. The scatterer 2 can be positioned upstream or downstream of the sample 3, and its placement can be flexibly adjusted to meet the measurement requirements of different speckle measurement techniques. The numerical parameters of the simulators, including light source energy, coherence length, sandpaper grain size, scanning step size, scatterer transmission function, sample transmission function, and detector effective pixel size, can all be modified and adjusted to meet different simulation needs.

[0068] like Figure 1 As shown, a simulation method for X-ray speckle wavefront detection of the present invention includes:

[0069] Step S1, selecting the energy E and two-dimensional coherence length of light source 1 according to actual experimental needs; determining the wavelength λ of light source 1 and the available experimental range at this wavelength based on the energy E of light source 1, where the available experimental range is the range of values ​​of the distance from the scatterer to the detector;

[0070] The relationship between energy and wavelength λ is: E=hc / λ, h is Planck's constant, c is the speed of light, and the wavelength can be determined from the energy of the light source 1 using the relationship between energy and wavelength λ.

[0071] The wave number is k = 2π / λ, and the available experimental range of the speckle measurement method at this time can be determined by the coherence length. The available experimental range under the wavelength λ of light source 1 is the Fresnel near-field area L under this wavelength condition. f , the Fresnel near-field region L under this wavelength condition f for:

[0072]

[0073] Where k is the wave number, l x，y It is the shorter dimension in the two-dimensional coherence length of the light source.

[0074] The experimental range is calculated in one dimension with a shorter two-dimensional coherence length of the light source to ensure that the speckles collected by the final simulated detector meet the X-ray near-field speckle generation conditions in the orthogonal directions.

[0075] In this embodiment, taking the light source energy E as 10 keV as an example, the wavelength λ is about 0.124 nm. x Taking 10μm as an example, the corresponding maximum simulation experimental distance L f About 5m (the distance from sandpaper to the detector).

[0076] Step S2, determining the complex amplitude distribution W of the initial light wave according to the optical path type, and providing the light wave diffraction equation on the air propagation path between the scatterer 2, the sample to be measured 3 and the detector 4.

[0077] Among them, the z-axis in the spatial rectangular coordinate system is selected as the propagation direction of the light wave. For the two types of parallel and focused optical paths in the X-ray near-field speckle measurement method, plane waves and spherical waves are used as the two-dimensional wavefront complex amplitude of the initial light wave respectively.

[0078] At the spatial propagation distance r of the light wave, the complex amplitude distribution W of the initial light wave emitted by the light source (that is, the complex amplitude distribution of the light wave when it propagates in the air starting from the light source 1) is:

[0079] For plane waves: W p (x, y) = exp(ikr), (2)

[0080] For spherical waves:

[0081] Where x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, i is the imaginary unit, k is the wave number, k = 2π / λ, and r is the spatial propagation distance of the light wave.

[0082] In this embodiment, for a plane wave, the light wave propagates along the z direction, which is the direction in which the light wave propagates.

[0083] In the focused optical path calculation, for spherical waves emitted by a point source, the divergent beam can be geometrically transformed into an equivalent parallel beam through coordinate system scaling transformation according to the Fresnel scaling principle. Coordinate scaling changes require a series of formulas, which can be found in the relevant reference [Munro P. Rigorous multi-slice wave optical simulation of x-ray propagation in inhomogeneous space [J]. Journal of the Optical Society of America A, 2019, 36(7): 1197]. Therefore, the subsequent simulations are mainly based on plane waves.

[0084] The diffraction equation for the light wave along the air path between the scatterer, the sample to be measured, and the detector is given. Specifically, based on scalar diffraction theory, the Fresnel approximation of Kirchhoff's diffraction formula is used as the diffraction equation for the light wave along the air path. This equation is derived. This simulates the propagation of X-ray light waves between the scatterer, the sample to be measured, and the detector in the near field.

[0085] Let the distance from the current plane (x, y) to the next plane (x1, y1) in the direction of light wave propagation be Δz, then the diffraction equation of the light wave on the air propagation path is:

[0086]

[0087] Wherein, W(x, y) is the complex amplitude distribution of the light wave in the current plane (x, y), W(x1, y1) is the complex amplitude distribution of the light wave in the next plane (x1, y1), x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, Δz is the distance from the starting plane (x, y) to the next plane (x1, y1) in the direction of light wave propagation, i is the imaginary unit, k is the wave number, k = 2π / λ, and λ is the wavelength of the light wave.

[0088] It should be noted that W(x, y) in formula (5) is the same as W p (x, y) and W s The definition of (x, y) is exactly the same, the difference is that W p (x, y) represents a plane wave, W s (x, y) represents a spherical wave. The subscripts of the two are only used to distinguish the applicable light wave types, and their meanings are the same. Since formula (5) is derived under more general conditions, it is applicable to both plane waves and spherical waves.

[0089] When calculating the initial light waves emitted by the light source, the above formula also takes into account the coherence of the light source. In the present invention, light source 1 is a fully correlated light source or a partially correlated light source. The present invention is not applicable to completely incoherent light sources. Therefore, the X-rays emitted by the light source are coherent.

[0090] Therefore, the step S2 further includes: determining the spatial coherence of the light wave, and correcting the light wave diffraction equation on the air propagation path between the scatterer 2, the sample to be measured 3 and the detector 4 according to the spatial coherence.

[0091] Considering a wider range of applications, the correlation of the light source can be dynamically adjusted according to the simulation needs. When light source 1 is a completely correlated light source (i.e., the coherence length is infinite), the spatial coherence μ(x1, y1) of the light wave is 1. When light source 1 is a partially coherent correlated light source, for the synchrotron radiation X-rays emitted by light source 1 with partial coherence, the spatial coherence μ(x1, y1) of the light wave can be expressed as:

[0092]

[0093] Where k is the wave number, l x , l yis the two-dimensional coherence length of the light source, x, y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and x1, y1 are the coordinate positions of another point in the space perpendicular to the direction of light wave propagation on the same plane.

[0094] Therefore, in combination with formulas (5) and (6), the diffraction equation of the light wave on the air propagation path between the scatterer 2, the sample to be measured 3 and the detector 4 can be corrected according to the spatial coherence of formula (6), and a corrected calculation formula for the complex amplitude distribution of the light wave on the air propagation path can be obtained.

[0095] Specifically, the diffraction equation of the light wave in the air propagation path between the scatterer 2, the sample to be measured 3 and the detector 4 is corrected according to the spatial coherence, specifically including: replacing the complex amplitude distribution W(x, y) of the light wave in the starting plane (x, y) in formula (5) with the product of W(x, y) and the spatial coherence μ(x1, y1) of the light wave.

[0096] Step S3, determining the relationship between the complex amplitude distribution of the light wave after passing through the scatterer or the sample to be measured and the transmission function of the scatterer or the sample to be measured according to the simulated speckle measurement method, and determining the transmission function of the scatterer 2 and the sample to be measured 3.

[0097] Among them, the complex refractive index of the sample to be tested is introduced, and the thickness of the sample to be tested is taken into account. The thickness of the sample to be tested is consistent with the direction of the optical axis in the z direction. The transmission function of the scatterer and the sample to be tested can be obtained based on the projection approximation. Therefore, the complex amplitude distribution of the light wave after passing through the scatterer or the sample to be tested can be determined by calculating the transmission function exp[-ik∫(δ(x, y, z)-iβ(x, y, z))dz] of the scatterer 2 or the sample to be tested 3.

[0098] For a scatterer or a sample to be tested with a thickness between distances z and z1, z and z1 are the starting and ending points of the thickness of the scatterer or the sample to be tested in the z direction, which can be regarded as the projection of the complex refractive index of the material along the propagation direction of the light wave (i.e., the z axis). The thickness direction of the scatterer 2 or the sample to be tested 3 is consistent with the propagation direction of the light wave (both are the z axis). Then, the relationship between the complex amplitude distribution and the transmission function of the light wave after passing through the scatterer 2 or the sample to be tested 3 can be expressed as:

[0099] W(x,y,z1)≈exp[-ik∫(δ(x,y,z)-iβ(x,y,z))dz]W(x,y,z), (7)

[0100] Wherein, exp[-ik∫(δ(x, y, z)-iβ(x, y, z))dz] is the transmission function of the scatterer 2 or the sample to be tested 3, δ and β are the refractive index and absorption coefficient in the complex refractive index n=1-δ+iβ of the scatterer 2 or the sample to be tested 3, respectively, i is the imaginary unit, dz is the integration between the starting thickness z and z1 of the sample to be tested, exp is the e index, W(x, y, z) is the complex amplitude distribution of the light wave before passing through the scatterer or the sample to be tested, W(x, y, z1) is the complex amplitude distribution after passing through the scatterer or the sample to be tested, x, y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and z is the spatial coordinate position in the direction of light wave propagation.

[0101] In the present invention, the simulated speckle measurement method includes the following principles: Figure 2 The speckle tracking detection method shown in Figure 3 The speckle contrast scanning detection method shown in FIG. Figure 4 and Figure 5 The speckle self-scanning detection methods of the front beam and rear beam modes are shown. Different speckle measurement methods may correspond to different transmission functions of the scatterer 2 and the sample 3 to be measured.

[0102] When the speckle measurement method used is the speckle tracking detection method, taking the scatterer 2 as sandpaper as an example, a transmission function of sandpaper is given. The scatterer 2 made of sandpaper is regarded as a plurality of radii r i The sample to be tested consists of hemispherical particles, and the corresponding transmission function T of the scatterer 2 d (x, y) is:

[0103]

[0104] Where i is the imaginary unit, n is the complex refractive index, k is the wave number, m is the total number of particles on the sandpaper, j is the ordinal number of the particle, j = 1 ~ m, (x j ,y j ) is the center of the jth particle, r j is the radius of the jth particle, different particles can overlap and exceed the radius r j When in the region, the component value of the jth particle is 0, the radius and center position of the hemispherical particle conform to the normal distribution, and x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation.

[0105] The radius and center position of the hemispherical particles in the normal distribution depend on the mesh size and particle size of the sandpaper or other scatterer to be simulated. The speckle intensity map generated by the sandpaper can then be calculated based on the complex refractive index of the sandpaper material.

[0106] Therefore, the transmission function of the scatterer 2 is represented by formula (8) as an example.

[0107] Take the elliptical hemisphere with the major axis a, the minor axis b, and the minor axis c as an example, the transmission function T of the sample 3 is: s (x, y) is specifically:

[0108]

[0109] Where i is the imaginary unit, n is the complex refractive index, k is the wave number, a is the major axis, b is the minor axis, c is the minor axis, x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and z is the spatial coordinate position in the direction of light wave propagation.

[0110] The materials of the scatterer and the sample to be tested (i.e., the complex refractive index n = 1-δ + iβ) are selected according to the specific experimental requirements. Taking the scatterer 2 as sandpaper and the sample to be tested 3 as an X-ray element as an example, the material of the sandpaper is usually SiC or mylar polyester material, and the material of the X-ray element is usually Si.

[0111] In step S4, the distances between the light source 1, the scatterer 2, the sample to be measured 3, and the detector 4, as well as the thickness distributions of the scatterer 2 and the sample to be measured 3, are determined based on the simulated speckle measurement method. Subsequently, the wavefront complex amplitude distributions of the initial light wave and the light wave after passing through the scatterer 2 and the sample to be measured 3 are gradually calculated and determined by combining the light wave diffraction equation in step S2 on the air propagation path between the scatterer 2, the sample to be measured 3, and the detector 4, the relationship between the complex amplitude distribution and the transmission function of the light wave in step S3 after passing through the scatterer or the sample to be measured, and the transmission function of the scatterer 2 and the sample to be measured 3, until the wavefront complex amplitude distribution W on the detector plane is determined. CCD .

[0112] Among them, the simulated speckle measurement methods include: Figure 2 The speckle tracking detection method shown in Figure 3 The speckle contrast scanning detection method shown in FIG. Figure 4 and Figure 5 The speckle self-scanning detection method for the front beam and rear beam modes is shown.

[0113] In step S4, the wavefront complex amplitude is calculated step by step, specifically including: determining the calculation accuracy and calculation scale, and then performing the calculation step by step with the calculation accuracy and calculation scale, thereby limiting the effective range of the calculation.

[0114] The calculation accuracy and scale are determined based on actual needs. First, the scope of the diffraction calculation, that is, the spatial range of the (x, y) coordinates, is determined based on the size of the sample to be measured. This range serves as the calculation scale. For example, the calculation scale is determined to be L×H based on the length, width, and H dimensions of the sample 3 to be measured. Subsequently, the calculation accuracy is determined based on the sampling accuracy of the detector. Assuming the calculation scale is 2048×2048, the calculation accuracy in the x and y directions is L / 2048 and H / 2048, respectively. This calculation accuracy is used to sample the complex amplitude distribution of the initial light wave emitted by the light source, the complex amplitude distribution after passing through the sample to be measured, the complex amplitude distribution after the scatterer, and finally the complex amplitude distribution at the detector plane. The effective calculation range is determined based on actual needs and determines the amount of data and computation required for the entire simulation. To simulate the sampling effect of the detector, the calculation resolution is usually smaller than the sampling accuracy of the simulated detector. For example, if the calculation is performed with a calculation scale of 2048×2048, the size of each unit is 0.5μm, but the sampling accuracy of the detector can be 1024×1024 or even 512×512, and the corresponding size of each unit is 1μm or 2μm.

[0115] As mentioned above, the transmission function of the scatterer 2 or the sample to be tested 3 is the exponential portion e in the middle of formula (7), exp[-ik∫(δ(x, y, z)-iβ(x, y, z))dz]. Formulas (8) and (10) provide specific calculation formulas for the exponential portion based on the actual thickness distribution of the sample to be tested or the scatterer. First, the complex refractive index n is extracted, and then the integration process is replaced by summation, and the specific calculation method of dz is given, corresponding to the summation in formulas (8) and (10). In other words, after using formulas (8) and (10) to obtain the transmission function of the sample to be tested or the scatterer, it is substituted into formula (7) as the exponential portion exp[-ik∫(δ(x, y, z)-iβ(x, y, z))dz] to calculate W(x, y, z1), which is the calculation process represented by formula (7).

[0116] Step S5: Based on the wavefront complex amplitude distribution W on the detector plane CCD , and the integrated value is the simulated diffraction pattern intensity at the detector plane.

[0117] In actual calculations, in order to improve simulation accuracy, a calculation accuracy lower than the detector pixel size p is used for calculation.

[0118] Considering the integral sampling effect of the detector, the intensity of the simulated diffraction pattern on the detector plane is obtained according to the shape and size of a single pixel of the detector and can be expressed as:

[0119]

[0120] Where p is the detector pixel size, and S is the area of ​​a single detector pixel, indicating that the integration is performed within the size of a single detector pixel.

[0121] Here, S = p×p rectangular area. Usually, the pixel unit of the detector is a square, so the light intensity of a single pixel on the simulated diffraction pattern intensity (speckle intensity map) on the detector plane is represented by integration within the area S with a side length of p.

[0122] That is, the intensity of the simulated diffraction pattern at the detector plane is calculated using formula (9).

[0123] For example, if a single detector pixel is a square with a pixel size of p = 1 μm, then the data at one pixel is simulated by integrating the data within a small 2×2 area to convert the 2048×2048 wavefront distribution into an intensity distribution, which is then integrated. The resulting speckle intensity map is 1024×1024 in size and 1 μm per pixel, and serves as the raw speckle intensity map processed by the DIC algorithm in the final speckle measurement method.

[0124] First embodiment: Simulation method for X-ray speckle wavefront detection for simulating speckle tracking detection method

[0125] According to the first embodiment of the present invention, steps S1 to S5 of the simulation method for X-ray speckle wavefront detection simulating the speckle tracking detection method are as described above.

[0126] Among them, the speckle tracking detection method has two detection modes: differential and absolute. The experimental simulator used in the speckle tracking detection method is as follows: Figure 2 As shown, X-rays start from a light source 1 , pass through a scatterer 2 , a sample to be measured 3 , and finally reach a detector plane 4 .

[0127] In step S3, the speckle measurement method used is the speckle tracking detection method. Taking the scatterer 2 as sandpaper as an example, a transmission function of sandpaper is given. The scatterer 2 made of sandpaper is regarded as a scatterer composed of many scatterers with a radius of r. i The sample to be tested consists of hemispherical particles, and the corresponding transmission function T of the scatterer 2 d (x, y) is:

[0128]

[0129] Where i is the imaginary unit, n is the complex refractive index, k is the wave number, m is the total number of particles on the sandpaper, j is the ordinal number of the particle, j = 1 ~ m, (x j ,y j ) is the center of the jth particle, r j is the radius of the jth particle, different particles can overlap and exceed the radius r jWhen in the region, the component value of the jth particle is 0, the radius and center position of the hemispherical particle conform to the normal distribution, and x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation.

[0130] The radius and center position of the hemispherical particles in the normal distribution depend on the mesh size and particle size of the sandpaper or other scatterer to be simulated. The speckle intensity map generated by the sandpaper can then be calculated based on the complex refractive index of the sandpaper material.

[0131] Therefore, the transmission function of the scatterer 2 is represented by formula (8) as an example.

[0132] Take the elliptical hemisphere with the major axis a, the minor axis b, and the minor axis c as an example, the transmission function T of the sample 3 is: s (x, y) is specifically:

[0133]

[0134] Where i is the imaginary unit, n is the complex refractive index, k is the wave number, a is the major axis, b is the minor axis, c is the minor axis, x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and z is the spatial coordinate position in the direction of light wave propagation.

[0135] The materials of the scatterer and the sample to be tested (i.e., the complex refractive index n = 1-δ + iβ) are selected according to the specific experimental requirements. Taking the scatterer 2 as sandpaper and the sample to be tested 3 as an X-ray element as an example, the material of the sandpaper is usually SiC or mylar polyester material, and the material of the X-ray element is usually Si.

[0136] In step S4, Figure 2 As shown, according to the simulated speckle tracking detection method, the first distance d1 is determined to be the distance from the light source 1 to the scatterer 2, the second distance d2 is determined to be the distance from the scatterer 2 to the sample 3 to be tested, and the third distance d3 is determined to be the distance from the sample 3 to the detector 4. Then, combined with formulas (5) and (7) (i.e., the light wave diffraction equation of the light wave in step S2 on the air propagation path between the scatterer 2, the sample 3 to be tested, and the detector 4, and the relationship between the complex amplitude distribution and the transmission function of the light wave in step S3 after passing through the scatterer or the sample to be tested), and the transmission function T of the scatterer 2 and the sample to be tested 3, the following equations are used: d , T s , calculate the wavefront complex amplitude distribution of the light wave after the light wave passes through the scatterer 2 and the sample to be measured 3, until the wavefront complex amplitude distribution on the detector plane is determined.

[0137] The steps S4 and S5 specifically include:

[0138] Step S110, simulating the sequential arrangement of a light source 1, a scatterer 2, a sample to be tested 3, and a detector 4, with the first distance d1 being the distance from the light source 1 to the scatterer 2, the second distance d2 being the distance from the scatterer 2 to the sample to be tested 3, and the third distance d3 being the distance from the sample to be tested 3 to the detector 4, and executing step S4 (that is, starting from the distance from the light source 1 to the scatterer 2, i.e., the first distance d1, the complex amplitude W of the light wave at the scatterer position is calculated). d , and then use the distance from the scatterer 2 to the sample 3 to be measured, that is, the second distance d2 and the transmission function T of the scatterer 2 d Calculate the complex amplitude distribution W of the wavefront after the light wave passes through the scatterer and propagates to the position of the sample to be tested 3 s Then calculate the distance from the re-propagating scatterer 2 to the sample 3 to be tested, that is, the wavefront complex amplitude distribution W on the detector plane after the third distance d3 reaches the detector CCD ), and step S5 is executed accordingly, thereby integrating and obtaining the simulated diffraction pattern intensity of the detector plane as the first speckle intensity map I s .

[0139] Step S120: Remove the sample 3 from the optical path and execute step S4 accordingly (that is, starting from the position of the scatterer 2, directly calculate the wavefront complex amplitude distribution W on the detector plane after the sum of the propagation distance d2 from the scatterer 2 to the sample 3 and the distance d3 from the scatterer 2 to the sample 3 arrives at the detector). CCD ), then step S5 is executed accordingly, thereby integrating and obtaining the simulated diffraction pattern intensity of the detector plane as the second speckle intensity map I r .

[0140] This is the simulation of the differential detection mode of the speckle tracking detection method. The simulation results are two speckle intensity images I s and I r The subsequent DIC calculation is a conventional technique and is not a simulation method patented by this invention.

[0141] Step S130: first speckle intensity image I s and the third speckle intensity map I d The DIC algorithm is used to process the first speckle pattern deformation. The result of DIC processing is the deformation of the speckle in the first and third speckle patterns after moving the distance Δd (the sample changes at different distances, but the speckle pattern remains unchanged, so speckle can be used as a marker to extract sample information). This deformation can be used to calculate the sample's characteristic information, namely phase and scattering information, according to the subsequent formulas (14-15).

[0142] Alternatively, the first distance d1 is used as the distance from the light source 1 to the scatterer 2, the second distance d2 is used as the distance from the scatterer 2 to the sample 3 to be tested, and the sum of the third distance d3 and the moving distance Δd is used as the distance from the sample 3 to the detector 4 to perform step S4 (that is, based on step S110, the wavefront complex amplitude distribution W on the detector plane is calculated). CCD Then propagate the wavefront complex amplitude distribution of the moving distance Δd), and execute step S5 accordingly, so as to integrate and obtain the third speckle intensity map I d ; Take the first distance d1 as the distance from the light source 1 to the scatterer 2, the second distance d2 as the distance from the scatterer 2 to the sample 3 to be tested, and the moving distance Δd as the distance from the sample 3 to be tested to the detector 4, and execute step S4 (that is, replace the distance d3 from the scatterer 2 to the sample 3 to be tested as the moving distance Δd, and recalculate the wavefront complex amplitude distribution W on the detector plane). CCD ), and correspondingly execute step S5, thereby integrating to obtain a fourth speckle intensity map, performing DIC algorithm processing on the first speckle intensity map and the third or fourth speckle intensity map to obtain a second speckle deformation amount.

[0143] Thus, relevant information about the sample to be tested is obtained. The deformation of the speckle before replacement comes from the two speckle intensity images with and without the sample to be tested. After replacing the distance d3 from scatterer 2 to the sample to be tested 3 with the moving distance Δd, in this method, the sample to be tested is always in the optical path. The deformation of the speckle comes from the two speckle intensity images at different distances, that is, the two speckle intensity images before and after the moving distance Δd. The speckle deformation is related to the moving distance Δd, so it is necessary to replace the distance d3 from scatterer 2 to the sample to be tested 3 with the moving distance Δd. The value of the moving distance Δd should also be within the near field range determined by equation (1).

[0144] This is a simulation of the absolute measurement mode of the speckle tracking detection method.

[0145] The core of the DIC algorithm is to calculate the correlation coefficient C of the pixel subset around the same pixel point in the speckle intensity image before deformation in a limited area around a single pixel point in the deformed speckle intensity image. The deformation variable of the speckle within the search range of the single-point pixel subset is obtained according to the position change of the pixel point when the maximum correlation coefficient C is the largest.

[0146] The size of the pixel subset is denoted as M. The size M of the pixel subset in the DIC algorithm is a set of detector pixels within a certain range. For example, if the detector pixel size is 1 μm and the size M of the pixel subset is 10×10 μm, then the pixel subset is a 10×10 rectangular area containing 100 pixels in total.

[0147] Therefore, the correlation coefficient C can be expressed as:

[0148]

[0149] in, and is the pixel mean of the second speckle intensity map and the first speckle intensity map within the size range of the pixel subset, and is the corresponding standard deviation.

[0150] Therefore, the DIC algorithm is used to calculate the speckle deformation variables Δx and Δy introduced by the sample 3 in the two previously simulated speckle intensity images on a pixel-by-pixel basis. Specifically, the calculation result of the correlation coefficient C obtained by formula (11) is used to calculate the speckle deformation variables Δx and Δy in the two simulated speckle intensity images on a pixel-by-pixel basis. The specific calculation process of formula (11) is to select a subset of pixels in the reference speckle intensity image and a subset of pixels of the same size at the same position in the speckle intensity image of the sample to be tested. The two formulas (11) are used to calculate a correlation coefficient C. The pixel subset is moved within the area centered on the position just calculated in the speckle intensity image of the sample to be tested and calculated using formula (11) to obtain a series of correlation coefficients C within this area. The deviation of the position with the largest correlation coefficient C in this area from the starting center position is the speckle deformation variables Δx and Δy in the x- and y-directions.

[0151] In step S140, a local beam deflection angle is obtained according to the first speckle deformation amount or the second speckle deformation amount. Then, according to the relationship between the wavefront gradient and the local beam deflection angle θ, the local beam deflection angle θ is used as the wavefront slope change in the orthogonal direction.

[0152] Among them, the wavefront slope changes in the orthogonal direction They represent the changes in wavefront slope in the x and y directions respectively.

[0153] Local beam deflection angle θ x，y The local deflection angle θ of the beam in the x direction x and the local deflection angle θ of the beam in the y direction y , calculated by formula (12):

[0154]

[0155] θ x and θ y are the local deflection angles of the beam in the x and y directions, Δx and Δy are the speckle deformation variables in the x and y directions, p is the detector pixel, and d3 is the distance from the sample to be measured to the detector.

[0156] Therefore, the local deflection angle and wavefront slope of the beam in the x-direction and y-direction are calculated respectively according to formula (12), and the equality of the two in this technology is indicated by formula (12).

[0157] The reason why the local beam deflection angle and the wavefront slope are equal is the small-angle approximation. In this technology, the local beam deflection angle is very small for X-rays. The calculation of formula (12) is valid under the X-ray small-angle approximation.

[0158] On the basis of step S140, step S150 may be further included: taking a derivative of the wavefront slope again, and calculating the change in the wavefront curvature after the light beam passes through the sample to be measured based on the second-order derivative of the wavefront.

[0159] Furthermore, depending on the different speckle modulations of the sample under test, after step S140, the following formulas (13)-(14) are used to respectively restore the two-dimensional phase distribution, absorption contrast distribution, and scattering information (dark field) of the sample under test, thereby obtaining lossless imaging information of the sample under test. Absorption contrast is the absorption image of the sample under test. The phase distribution can be used to analyze the low-absorption structure within the sample under test, and dark field imaging can be used to analyze the scattering information generated by the internal structure of the sample under test, thereby achieving multi-modal imaging of the sample under test using this method.

[0160] The absorption contrast distribution T can be expressed as: T = I r / I s , (13)

[0161] The two-dimensional phase distribution can be expressed as:

[0162] The dark field information can be expressed as:

[0163] The above steps are the most basic experimental simulator and simulation calculation method based on X-ray near-field speckle detection technology, which can be used for all simulation studies based on X-ray speckle tracking detection technology.

[0164] Second embodiment: Simulation method for X-ray speckle wavefront detection for simulating speckle scanning detection method

[0165] The present invention also provides a simulation method for X-ray speckle wavefront detection for simulating a speckle scanning detection method. The simulation method for X-ray speckle wavefront detection for simulating a speckle scanning detection method can be performed after the simulation method for X-ray speckle wavefront detection for simulating a speckle scanning detection method of the first embodiment of the present invention.

[0166] The corresponding experimental simulator of the speckle scanning detection method is as follows Figure 2 As shown and as Figure 1Similarly, X-rays originate from light source 1, pass through scatterer 2, sample 3, and ultimately reach detector plane 4. Compared to speckle tracking, the main difference between speckle scanning and detection methods is that the latter requires simulating the scanning motion of scatterer 2. Furthermore, it requires simulating the changes in the scatterer's transmission function during the scanning motion of the scatterer, while calculating a single speckle intensity image.

[0167] In a plurality of embodiments (ie, the second embodiment and the third embodiment below), in step S3, determining the transmission function of the scatterer 2 includes: obtaining the initial transmission function T of the scatterer d (x, y), the transmission function T of the initial scatterer d Based on (x, y), the displacement of scatterer 2 in the x and y directions is introduced to update the transmission functions T of multiple updated scatterers. d '(x,y).

[0168] When the simulated speckle measurement method is a speckle scanning detection method, the displacements of the introduced scatterer 2 in the x-direction and the y-direction are scan displacements according to different scanning modes to be simulated.

[0169] As described in the first embodiment, the transmission function of the initial scatterer may be the transmission function of sandpaper.

[0170] The updated transmission function T of the scatterer d '(x, y) can be expressed as:

[0171] T d '(x, y) = T d (x+f(x), y+g(y)),

[0172] Among them, T d () is the transmission function of the initial scatterer, T d '(x, y) is the updated transmission function of the scatterer, f(x) and g(y) are the displacements of the scatterer 2 in the x and y directions respectively. In this embodiment, the displacement is a scanning displacement, and its specific form can be changed according to the simulation requirements.

[0173] That is, the updated scatterer transmission function T d '(x, y) through the initial scatterer transmission function T d The two directions (x, y) are updated by adding the displacements f(x) and g(y) of the scatterer 2 in the x direction and the y direction.

[0174] In this embodiment, the displacement f(x) and g(y) are used as an example to represent the two-dimensional scanning displacement. The number of scanning steps in the horizontal direction is h, the number of scanning steps in the vertical direction is v, and the scanning step length Δs is selected to be smaller than the detection pixel size p. Then, the updated transmission function of the scatterer is T d '(x, y) = T d (x+hΔs, y+vΔs).

[0175] Taking a two-dimensional grid scan as an example, h is accumulated from its minimum to its maximum value, and v is accumulated once starting from its minimum value, repeating the cycle until v also reaches its maximum value. During this cycle, the updated scatterer transmission function corresponding to each position of h and v is obtained. Thus, by executing steps S1-S5, multiple speckle intensity maps can be obtained, thus completing the entire two-dimensional scan simulation.

[0176] The speckle scanning detection method includes a speckle contrast scanning detection method and a speckle self-scanning detection method.

[0177] The steps S3 to S5 specifically include:

[0178] In step S210, for the speckle contrast scanning detection method, step S3 is executed to obtain an initial transmission function of the scatterer and a plurality of updated transmission functions of the scatterers. For each of the initial transmission function of the scatterer and the plurality of updated transmission functions of the scatterers, a light source 1, a scatterer 2, a sample to be tested 3, and a detector 4, which are sequentially arranged, are simulated. Steps S4 and S5 are executed with a first distance d1 being the distance from the light source 1 to the scatterer 2, a second distance d2 being the distance from the scatterer 2 to the sample to be tested 3, and a third distance d3 being the distance from the sample to be tested 3 to the detector 4. Steps S4 and S5 are also executed with the scatterer 2 removed from the optical path, thereby obtaining two speckle intensity maps corresponding to each scanning position, one with and one without the sample to be tested, as a speckle intensity map sequence ∑I when the sample to be tested is present. s (h, v) and the speckle intensity map sequence ∑I when there is no sample to be tested r (h, v).

[0179] This is a 2D speckle contrast scanning simulation. Speckle contrast scanning is an improved detection method based on speckle tracking. With and without the sample to be tested, a 2D scan of the scatterer is performed using a raster path along orthogonal directions at a fixed step size, resulting in a series of speckle intensity maps at different scatterer locations.

[0180] Step S220: based on the speckle intensity image sequence ∑I of the sample to be tested s (h, v) and the speckle intensity map sequence ∑I when there is no sample to be tested r (h, v), the wavefront slope change caused by the sample to be tested is obtained using the DIC algorithm.

[0181] Among them, the two speckle intensity images compared by the DIC algorithm are obtained by stitching together the pixels at the same position in a series of speckle intensity images obtained at different scattering positions. This stitching process is performed on the two sets of speckle sequence images with and without the sample to be tested. The generated new speckle intensity images are in units of scanning step length. The scanning step length is Δs, and the wavefront slope change (i.e., the local deflection angle of the beam θ) obtained by scanning the speckle grating path is x，y )for:

[0182]

[0183] The comma in the formula indicates that the local deflection angle θ of the beam in the x direction is x The calculation uses Δx, for the local deflection angle θ of the beam in the y direction y The calculation of Δy is used.

[0184] In addition, in order to further reduce the amount of data collection and experimental time, a single-direction fixed-step scan can be performed along any axis other than the optical axis (x, y axis) in a single direction to meet the requirements of one-dimensional high-precision measurement of the sample to be measured. According to the different scanning directions, the transmission function T d '(x, y) = T d If one of the dimensions (x + hΔs, y + vΔs) is zero (i.e., h or v is zero), the scanning direction accuracy of the other dimension is the same as that of the speckle tracking method. The scanning accuracy of the other dimension is on the order of the detected pixel size. The scanning step size needs to be smaller than the effective pixel size of the detector. Only then will the speckle scanning accuracy be higher than that of the tracking method. The specific reason for this can be seen by comparing equations (12) and (16). The difference between these two equations is mainly the scanning step size Δs and the detector pixel size p.

[0185] Step S230, for the one-dimensional speckle self-scanning detection method, such as Figure 3 As shown, based on the speckle intensity map sequence ∑I obtained in step S210 when there is a sample to be tested s (h, v), select the speckle intensity map sequence corresponding to one-dimensional scanning position as the speckle intensity map sequence ∑I in the front beam mode s (h, v); Then, for each of the initial scatterer transmission function and the multiple updated scatterer transmission functions, respectively, Figure 4 As shown, the first distance d1 is taken as the distance from the light source 1 to the sample 3 to be tested, the second distance d2 is taken as the distance from the sample 3 to be tested to the scatterer 2, and the third distance d3 is taken as the distance from the scatterer 2 to the detector 4 to perform steps S4 and S5, thereby obtaining the speckle intensity map corresponding to each scanning position when there is a sample to be tested, which is used as the speckle intensity map sequence ∑I in the post-beam mode. s(h, v).

[0186] In the detection of X-ray optical elements, in order to further reduce the amount of data and time consumption of the speckle scanning method, a one-dimensional speckle self-scanning detection method can be selected. The one-dimensional speckle self-scanning detection method is similar to the one-dimensional scanning method mentioned in step S210. The speckle self-scanning method directly adds scatterers to the optical path and performs a one-dimensional scanning simulation to obtain a series of speckle intensity map sequences ∑I when the sample to be tested is present. s (h, v). Figure 4 and Figure 5 As shown, according to the different positions of the scatterers, the one-dimensional speckle self-scanning detection methods are divided into the following types: Figure 4 The front beam pattern shown and Figure 5 In the back beam mode shown, in the front beam mode, the scatterer 2 is located in front of the sample 3 to be measured, and in the back beam mode, the scatterer 2 is located behind the sample 3 to be measured.

[0187] Step S240: for the speckle intensity map sequence ∑I in the front beam mode s (h, v) and the speckle intensity map sequence ∑I in the post-beam mode s (h, v), respectively, the speckle deformation caused by the sample to be tested is obtained using the DIC algorithm.

[0188] Among them, in the obtained speckle intensity map sequences in the front beam mode and the rear beam mode, the DIC algorithm compares the two speckle intensity maps obtained by splicing the j-th and k-th row pixels from the speckle intensity maps at all positions in the speckle intensity map sequence.

[0189] This stitched speckle intensity map is unique to the speckle self-scanning mode and is not an operation performed by the DIC algorithm. The stitched speckle intensity map is generated as follows: for example, 100 scans are performed at a fixed step size, resulting in 100 speckle intensity maps of size 1024×1024. The jth row is the 10th row of the single speckle intensity map. Then, 1×1024 pixels from the 10th row of the single speckle intensity map from the first scan step are extracted. Then, 1×1024 pixels from the 10th row of the single speckle intensity map from the second scan step are extracted, and this process is repeated until the 100th step. These 100 1×1024 pixels from the 10th row are then combined to generate the jth row of the stitched speckle intensity map, which has a size of 100×1024. The interval on the 100th side is the scan step size Δs, and the interval on the 1024th side is the detector pixel size p. The same principle is used to extract the stitched speckle intensity map of the kth row, but j and k must satisfy the condition k≠j. Then, the DIC algorithm is used to calculate the two speckle intensity maps to further obtain the speckle deformation.

[0190] Since the scatterer is located in front of the sample 3 in the front beam mode, the speckle intensity map sequence ∑I s (h, v), specifically, the DIC algorithm is used to stitch the speckle intensity maps of adjacent rows (|ik|=1) (for example, if i is the 10th row, then k is the 9th or 11th row). At this time, the speckle shape variable extracted from the speckle intensity map sequence obtained by scanning the scatterer is related to the surface shape slope of the sample 3 to be measured. Therefore, the surface shape slope of the sample 3 to be measured can be obtained based on the speckle shape variable.

[0191] Using the existing iterative algorithm, the initial slope α of the surface shape of the sample 3 to be measured is:

[0192]

[0193] Among them, the subscript k is the scanning position, and the superscript is the number of iterations. and is the coordinate of the light beam on the mirror, l m is the distance from the center of the mirror to the detector, Y k Y is the effective pixel size of the corresponding scanning position on the detector after correction of the mirror inclination. k The value is given in the literature [8]. This formula can be used to simulate the speckle measurement technology and calculate the surface slope using the simulation method of this technology. However, the specific surface slope calculation method is not the focus of this technology, so the relevant calculation details will not be described in detail here.

[0194] Since the scatterer is located behind the sample 3 in the back-beam mode, the speckle intensity map sequence ∑I s Specifically, DIC calculation is performed by splicing speckle intensity maps using alternate lines (|ik| > 1). The speckle shape variable extracted from the speckle intensity map sequence obtained by scanning the scatterer is related to the wavefront curvature distortion of the detector plane introduced by the surface shape of the test sample 3. Therefore, the wavefront curvature radius R of the detector plane introduced by the test sample 3 can be obtained based on the speckle shape variable.

[0195] The distance from scatterer 2 to detector 4 is l n , taking the x-axis one-dimensional scanning as an example, according to the different focus positions of the sample 3 to be measured, the wavefront curvature radius R of the detector plane is:

[0196] The focus of the sample 3 to be measured is before the scatterer and the detector:

[0197]

[0198] The focus of the sample 3 to be measured is between the scatterer and the detector:

[0199]

[0200] The focus is behind the scatterer and the detector:

[0201]

[0202] It should be noted that formulas (18)-(20) are not applicable to the conditions of parallel light illumination.

[0203] Where R is the wavefront curvature radius of the detector plane, p is the pixel size of the detector, and l n is the distance from the scatterer to the detector, j and k are the number of extracted rows of the spliced ​​speckle intensity map, Δx is the speckle deformation, and Δs is the scanning step size.

[0204] Third embodiment: Simulation method for X-ray speckle wavefront detection using simulated vibration

[0205] In addition, the simulation method for X-ray speckle wavefront detection of the present invention may further include, before step S4, step S4' of simulating the vibration of the optical path elements and the light source 1 in the simulated speckle measurement method, respectively, wherein the optical path elements include the scatterer 2 and the sample to be measured 3.

[0206] Vibration of the light source or components in the optical path primarily manifests as positional displacement or angular variation. Since synchrotron X-rays typically enter the mirror at a small angle, positional variation can be used to uniformly represent the vibration of the light source and optical path components under the small-angle approximation. By further incorporating the specific form of vibrational displacement into the x-direction displacements f(x) and g(y) of scatterer 2 in the scatterer's transmission function during actual simulations, speckle scanning techniques with different motion characteristics, such as light source vibration, can be simulated. Alternatively, by varying the scanning step size parameters to meet specific research needs, specific characteristics of speckle scanning techniques can be studied. For example, by adding sinusoidal vibrations of varying frequencies and amplitudes to the scanning direction, the impact of vibration on the measurement performance of speckle scanning detection techniques can be studied.

[0207] The step S4' specifically includes:

[0208] In step S41 ′, the transmission functions of the scatterer and the sample to be measured are modified separately to simulate the vibration of the scatterer and the sample to be measured during scanning.

[0209] Assume that the scatterer has random vibrations and its distribution conforms to the Gaussian distribution N(ω,σ) with mean ω and variance σ. 2 ), the distribution is N(ω,σ 2) is a vibration with a single dimension, or a vibration in one dimension of the entire random vibration. Introducing the random vibration distribution function N into the displacement f(x) of the scatterer 2 in the x direction, the transmission function of the scatterer 2 obtained by the correction for simulating the sandpaper vibration is T d '(x, y) = T d (x+hΔs+N,y).

[0210] Simulate Gaussian distribution N(ω,σ 2 ) is multiple, for example, if the scanning step is 100 steps, then it is necessary to introduce the position offset caused by Gaussian distribution into the displacement f(x) of the scatterer 2 in the x direction of the transmission function of the scatterer 2 used in the calculation of the scanning step length at each step.

[0211] Other simulation steps can be selected and adjusted according to the selected method and the structure of the experimental simulator. In addition, the displacement f(x) of the scatterer 2 in the x direction can also introduce different forms of vibration, such as sinusoidal vibration, according to the needs of the simulation.

[0212] Furthermore, the displacement g(y) of the scatterer 2 in the y direction may be introduced into the other dimension of the transmission function of the scatterer 2 to simulate the two-dimensional vibration of the sandpaper.

[0213] The vibration simulation of the sample 3 is similar to that of the scatterer 2. Only the transmission function of the sample 3 needs to be corrected to change the final speckle intensity map intensity I s .

[0214] In step S41 ′, the transmission functions of the scatterer and the sample to be measured are synchronously corrected to simulate the vibration of the scatterer and the sample to be measured during scanning.

[0215] Based on the vibration simulation of the scatterer and the sample to be tested, the scatterer T d and the sample to be tested T s The distribution of can also be used to simulate the vibration of the light source. Taking sinusoidal vibration as an example, let light source 1 have a sinusoidal vibration with amplitude A and frequency ω, and its change with time t is: Then the transmission functions of the scatterer 2 and the sample to be measured 3 change synchronously as follows:

[0216]

[0217] By calculating the speckle intensity map generated by the transmission function of the scatterer and the sample under test at different times and frequencies, the vibration of the light source can be simulated.

[0218] Because vibration simulation involves time variables, the impact of the detector sampling time must be considered in addition to the detector integration effect. For example, assuming the detector sampling time is fixed at 1Hz, by varying the vibration frequency, individual speckle intensity images can be simulated for vibrations of different frequencies. The following examples illustrate this using high, medium, and low sinusoidal vibrations.

[0219] 1) If the vibration frequency ω l The sampling frequency is lower than 1Hz of the detector. For example, 0.1Hz. At this time, within the sampling time of the detector, the simulated single speckle intensity map can be the transmission function of the scatterer and the sample to be measured at the corresponding amplitude position at a certain moment in a single vibration cycle. The low-frequency vibration period is 10s, which is longer than the sampling time of the detector of 1s. The entire vibration cycle is subdivided with the detection sampling time as the calculation interval, and the transmission function and corresponding speckle intensity map corresponding to different moments are calculated until the simulation within the entire scanning time is completed. The obtained speckle intensity map sequence is

[0220] 2) If the vibration frequency ω m Equal to the detector sampling frequency, there is a single cycle of vibration within the detector acquisition time period. The actual detector sampling is time-dependent, and its sampling process can be considered an integration process. Therefore, under the condition that the sampling frequency limit is met (for example, the Nyquist sampling theorem), by subdividing the sampling period and calculating accordingly, multiple speckle intensity maps within the sampling period are obtained, and then superimposed to obtain the speckle intensity map of a single sampling. This process is repeated until the simulation of the entire scanning time is completed.

[0221] For example, for a sampling period of 1s, the vibration amplitude corresponding to 10 moments in a single period can be calculated by subdividing the time into 0.1s, and then superimposed on the transmission function and the corresponding speckle intensity map is calculated. Specifically, for a sampling period of 1s, subdivided into 0.1s, the displacement introduces the vibration displacement corresponding to 10 moments, that is, 10 amplitude values, and each amplitude is superimposed on the transmission function T s and T d In the corresponding displacement, each amplitude obtains a corresponding speckle intensity map, and 10 amplitudes correspond to 10 speckle intensity maps. The sum of these 10 speckle intensity maps is used as a speckle intensity map recorded within this 1s. The 10 calculated speckle intensity maps are accumulated as an approximation of the detector integration within the 1s period. The single speckle intensity map obtained by the simulated detector sampling is

[0222] 3) If the vibration frequency of the sinusoidal vibration ω hGreater than the sampling frequency of the detector. Taking 10Hz as an example, there are 10 cycles of vibration at this frequency within a 1s detector acquisition period, and the vibration period is 0.1s. Therefore, it is necessary to further subdivide the sampling period under the condition that the sampling theorem is satisfied. For example, using 0.02s as the subdivision unit, calculate multiple speckle intensity images within the entire sampling period and superimpose them to obtain a single speckle intensity image. This process is then repeated until the simulation calculation within the entire scan time is completed.

[0223] The above simulation simulates light source vibration, and the resulting speckle intensity map ∑I(x(t), y) significantly includes the displacement caused by light source vibration. Therefore, according to the principle of the DIC algorithm in formula (11), the displacement caused by light source vibration will significantly affect the search for the maximum correlation coefficient, thus reflecting the relationship between light source vibration and the calculation accuracy of the speckle scanning algorithm. By varying parameters such as vibration form and frequency amplitude, it is also possible to simulate and study the impact of other types of vibration on speckle scanning technology.

[0224] In addition to the simulation of the typical X-ray near-field speckle detection technology described above, the experimental simulator and method of the present invention can also be used to simulate other various deformation forms based on existing optical path structures.

[0225] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of the present invention. Various modifications are possible. Any simple, equivalent changes and modifications made in accordance with the claims and description of the present invention are within the scope of protection of the patent claims. Anything not fully described in this invention is conventional technology.

Claims

1. A simulation method for X-ray speckle wavefront detection, characterized in that: include: Step S1, selecting the energy E of the light source and the two-dimensional coherence length; determining the wavelength λ of the light source and the available experimental range at the wavelength based on the energy E of the light source, where the available experimental range is the range of values ​​of the distance from the scatterer to the detector; Step S2, determining the complex amplitude distribution W of the initial light wave according to the optical path type, and providing the light wave diffraction equation on the air propagation path between the scatterer, the sample to be measured, and the detector; Step S3, determining a relationship between the complex amplitude distribution of the light wave after it passes through the scatterer or the sample to be measured and the transmission function of the scatterer or the sample to be measured according to the simulated speckle measurement method, and determining the transmission function of the scatterer and the sample to be measured; In step S4, the distances between the light source, the scatterer, the sample to be measured, and the detector, as well as the thickness distributions of the scatterer and the sample to be measured are determined based on the simulated speckle measurement method. Subsequently, the wavefront complex amplitude distributions of the initial light wave, the light wave after passing through the scatterer and the sample to be measured, and the transmission functions of the scatterer and the sample to be measured are gradually calculated and determined, by combining the light wave diffraction equation in step S2 on the air propagation path between the scatterer, the sample to be measured, and the detector, and the relationship between the complex amplitude distribution and the transmission function of the light wave in step S3 after passing through the scatterer or the sample to be measured, and the transmission functions of the scatterer and the sample to be measured, until the wavefront complex amplitude distribution W on the detector plane is determined. CCD ; Step S5: Based on the wavefront complex amplitude distribution W on the detector plane CCD , and the integrated value is the simulated diffraction pattern intensity at the detector plane.

2. The simulation method for X-ray speckle wavefront detection according to claim 1, characterized in that: The available experimental range under the wavelength λ of the light source is the Fresnel near-field region L under the wavelength condition. f .

3. The simulation method for X-ray speckle wavefront detection according to claim 1, characterized in that: For a plane wave, the complex amplitude distribution W of the initial light wave emitted by the light source is: W p (x,y)=exp(ikr), For a spherical wave, the complex amplitude distribution W of the initial light wave emitted by the light source is: Where x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, i is the imaginary unit, k is the wave number, k = 2π / λ, and r is the spatial propagation distance of the light wave.

4. The simulation method for X-ray speckle wavefront detection according to claim 1, characterized in that: The diffraction equation of light waves on the air propagation path is: Where W(x, y) is the complex amplitude distribution of the light wave in the current plane (x, y), W(x1, y1) is the complex amplitude distribution of the light wave in the next plane (x1, y1), x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, Δz is the distance from the starting plane (x, y) to the next plane (x1, y1) in the direction of light wave propagation, i is the imaginary unit, k is the wave number, k×2π / λ, and λ is the wavelength of the light wave.

5. The simulation method for X-ray speckle wavefront detection according to claim 4, characterized in that: The step S2 further includes: determining the spatial coherence of the light wave, and correcting the light wave diffraction equation on the air propagation path between the scatterer, the sample to be tested, and the detector according to the spatial coherence; When the light source is a completely correlated light source, the spatial coherence μ(x1, y1) of the light wave is 1; when the light source is a partially coherent correlated light source, the spatial coherence μ(x1, y1) of the light wave is: Where k is the wave number, l x , l y is the two-dimensional coherence length of the light source, x, y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and x1, y1 are the coordinate positions of another point in the space perpendicular to the direction of light wave propagation on the same plane.

6. The simulation method for X-ray speckle wavefront detection according to claim 1, characterized in that: The relationship between the complex amplitude distribution and the transmission function of the light wave after passing through the scatterer or the sample to be measured is: W(x,y,z1)≈exp[-ik∫(δ(x,y,z)-iβ(x,y,z))dz]W(x,y,z), Wherein, exp[-ik∫(δ(x, y, z)-iβ(x, y, z))dz] is the transmission function of the scatterer or the sample to be tested, δ and β are the refractive index and absorption coefficient in the complex refractive index n=1-δ+iβ of the scatterer or the sample to be tested, respectively, i is the imaginary unit, dz is the integration between the starting thickness z and z1 of the sample to be tested, exp is the e index, W(x, y, z) is the complex amplitude distribution of the light wave before passing through the scatterer or the sample to be tested, W(x, y, z1) is the complex amplitude distribution after passing through the scatterer or the sample to be tested, x, y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and z is the spatial coordinate position in the direction of light wave propagation.

7. The simulation method for X-ray speckle wavefront detection according to claim 1, characterized in that: When the scatterer is sandpaper, the transmission function T d (x, y) is: Where i is the imaginary unit, n is the complex refractive index, k is the wave number, m is the total number of particles on the sandpaper, j is the ordinal number of the particle, j = 1 ~ m, (x j ,y j ) is the center of the jth particle, r j is the radius of the jth particle, x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation; The sample to be tested is an elliptical hemisphere with a long axis of a, a medium short axis of b, and a short axis of c. The transmission function T of the sample to be tested is s (x, y) is: Where i is the imaginary unit, n is the complex refractive index, k is the wave number, a is the major axis, b is the minor axis, c is the minor axis, x and y are the spatial coordinate positions perpendicular to the direction of light wave propagation, and z is the spatial coordinate position in the direction of light wave propagation.

8. The simulation method for X-ray speckle wavefront detection according to claim 1, characterized in that: The steps S3 and S4 specifically include: Step S110, simulating a light source, a scatterer, a sample to be measured, and a detector that are sequentially arranged, with the first distance d1 being the distance from the light source to the scatterer, the second distance d2 being the distance from the scatterer to the sample to be measured, and the third distance d3 being the distance from the sample to be measured to the detector, and executing step S4, and executing step S5 accordingly, thereby integrating to obtain the simulated diffraction pattern intensity on the detector plane as the first speckle intensity map I. s ; Step S120: remove the sample to be tested from the optical path and execute step S4 accordingly, and then execute step S5 accordingly, thereby integrating and obtaining the simulated diffraction pattern intensity on the detector plane as the second speckle intensity map I. r ; Step S130: first speckle intensity image I s and the second speckle intensity map I r Perform DIC algorithm processing to obtain a first speckle deformation amount; or, take the first distance d1 as the distance from the light source to the scatterer, the second distance d2 as the distance from the scatterer to the sample to be measured, and the sum of the third distance d3 and the moving distance Δd as the distance from the sample to be measured to the detector, perform step S4, and accordingly perform step S5, thereby integrating to obtain a third speckle intensity map I d Taking the first distance d1 as the distance from the light source to the scatterer, the second distance d2 as the distance from the scatterer to the sample to be measured, and the moving distance Δd as the distance from the sample to be measured to the detector, executing step S4, and correspondingly executing step S5, thereby integrating to obtain a fourth speckle intensity map, performing DIC algorithm processing on the first speckle intensity map and the third or fourth speckle intensity map to obtain a second speckle deformation amount; Step S140: obtaining a local deflection angle of the light beam according to the first speckle deformation amount or the second speckle deformation amount as a wavefront slope change in an orthogonal direction.

9. The simulation method for X-ray speckle wavefront detection according to claim 1, characterized in that: In step S3, determining the transmission function of the scatterer includes: obtaining the initial transmission function T of the scatterer d (x, y), the transmission function T of the initial scatterer d Based on (x, y), the displacement of the scatterer in the x and y directions is introduced to update the transmission function T of multiple updated scatterers d '(x, y); The displacement of the scatterer in the x direction and the y direction includes a scanning displacement and / or a vibration displacement.

10. The simulation method for X-ray speckle wavefront detection according to claim 9, characterized in that: The displacement of the scatterer in the x-direction and the y-direction includes scanning displacement, and steps S3 to S5 specifically include: In step S210, for the speckle contrast scanning detection method, step S3 is executed to obtain an initial transmission function of the scatterer and a plurality of updated transmission functions of the scatterers. For each of the initial transmission function of the scatterer and the plurality of updated transmission functions of the scatterers, a light source, a scatterer, a sample to be tested, and a detector arranged in sequence are simulated. Steps S4 and S5 are executed with a first distance d1 as the distance from the light source to the scatterer, a second distance d2 as the distance from the scatterer to the sample to be tested, and a third distance d3 as the distance from the sample to be tested to the detector. Steps S4 and S5 are also executed with the scatterer removed from the optical path, thereby obtaining two speckle intensity maps corresponding to each scanning position, one with and one without the sample to be tested, as a speckle intensity map sequence ∑I when the sample to be tested is present. s (h, v) and the speckle intensity map sequence ∑I when there is no sample to be tested r (h, v); Step S220: based on the speckle intensity image sequence ∑I of the sample to be tested s (h, v) and the speckle intensity map sequence ∑I when there is no sample to be tested r (h, v), the wavefront slope change caused by the sample under test is obtained using the DIC algorithm; Step S230: for the one-dimensional speckle self-scanning detection method, based on the speckle intensity map sequence ∑I obtained in step S210 when there is a sample to be tested s (h, v), select the speckle intensity map sequence corresponding to one-dimensional scanning position as the speckle intensity map sequence ∑I in the front beam mode s (h, v); then, for each of the initial scatterer transmission function and the multiple updated scatterer transmission functions, steps S4 and S5 are performed respectively with the first distance d1 as the distance from the light source to the sample to be measured, the second distance d2 as the distance from the sample to be measured to the scatterer, and the third distance d3 as the distance from the scatterer to the detector, thereby obtaining a speckle intensity map corresponding to each scanning position when the sample to be measured is present, as a speckle intensity map sequence ∑I in the post-beam mode. s (h, v); Step S240: for the speckle intensity map sequence ∑I in the front beam mode s (h, v) and the speckle intensity map sequence ∑I in the post-beam mode s (h, v), the speckle deformation caused by the sample to be tested is obtained by using the DIC algorithm; Among them, the updated scatterer transmission function T d '(x, y) is: T d ’(x,y)=T d (x+f(x),y+g(y)), Among them, T d () is the transmission function of the initial scatterer, T d '(x, y) is the updated transmission function of the scatterer, f(x) and g(y) are the displacements of the scatterer in the x and y directions, respectively.

Images