A weighted probe-based method for correcting the position of stacked diffraction

Abstract

This invention provides a weighted probe-based method for correcting the position of stacked diffraction, belonging to the field of coherent diffraction imaging. The method involves: acquiring diffraction light field intensity information, simultaneously initializing the information functions of the illumination probe and the sample under test, as well as the probe position; obtaining the exit wave and importing it into a propagation model to obtain a simulated diffraction light field, replacing the diffraction light field intensity information to obtain an updated diffraction light field; importing the updated diffraction light field into a reverse propagation model to obtain the diffraction exit wave, thereby updating the information functions of the sample under test and the illumination probe at each scanning position; forming a probe matrix around the probe position, calculating the correlation, and updating the probe position; repeating the above steps iteratively until a preset number of iterations is completed or a preset condition is met. This invention avoids crosstalk between local non-converged regions and global scanning position correction, greatly improving the convergence stability and convergence accuracy of the stacked diffraction position correction method.

Description

Technical Field

[0001] This invention belongs to the field of coherent diffraction imaging, and more specifically, relates to a method for correcting the position of stacked diffraction based on a weighted probe. Background Technology

[0002] Coherent diffraction (CDI) is a technique for high-resolution imaging that uses coherent light to perform diffraction experiments, reconstructing the physical structure of a sample by measuring the wavefront information scattered from its surface. Phase problems are a common issue in CDI because cameras can only record light intensity information and cannot directly measure phase information. However, phase information is crucial for reconstructing images of objects and is a key factor in determining their shape and structure. Generally, CDI can be divided into two parts based on the number of diffraction fields recorded: single-intensity and multi-intensity. Ptychography is the most commonly used method in multi-intensity algorithms.

[0003] Ptychography divides the scanned area into multiple overlapping regions and collects a series of diffraction images by moving the probe relative to the sample. These diffraction fields can be used to reconstruct the sample's structure and phase information using the ePIE algorithm (see Ultramicroscopy 109(2009)338–343). In a ptychography acquisition system, inaccurate parameters, such as lateral positional errors in probe movement or axial positional errors in the camera, can significantly reduce the reconstruction quality of the sample. Therefore, probe position correction is particularly important in ptychography studies.

[0004] Among existing technologies, the simulated annealing position correction method (see Ultramicroscopy 120 (2012) 64-72) is a relatively classic approach. The annealing position correction method is based on an experiment-selection strategy, testing many experimental positions for each probe location. This method is consistent with the principle of genetic algorithms (see J. Appl. Phys. 109, 124510 (2011)) and machine learning methods based on structural similarity indices (J. Instrum. 13 (6), C06002 (2018)), but the cost is a large computational load, which is a significant disadvantage when dealing with a large amount of experimental data. Based on efficient subpixel image registration algorithms (see Opt. Lett. 33(2), 156–158 (2008)), a position cross-correlation algorithm is proposed (see Opt. Express 21(11), 13592–13606 (2013)). This algorithm searches for the position update direction and magnitude by cross-correlation of the test samples before and after the update through Fourier domain upsampling. This method has high computational accuracy, which improves with the accuracy of upsampling, but the position correction speed is relatively slow. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a weighted probe-based method for position correction in stacked diffraction, which addresses the problems of sample contrast degradation caused by position errors in existing Ptychography, slow convergence speed of position correction methods, and the problem that position correction methods may get stuck in local optima or fail to converge altogether when the error is large.

[0006] To achieve the above objectives, the present invention provides a method for correcting the position of stacked diffraction based on a weighted probe, the method comprising the following steps:

[0007] S1 collects the diffraction light field intensity information at each scanning position of the sample under test, and simultaneously initializes the information functions of the illumination probe and the sample under test, as well as the probe position.

[0008] S2 multiplies the information parameters of the sample under test and the illumination probe at each scanning position to obtain the exit wave;

[0009] S3 imports the exit wave obtained in step S2 into the propagation model to obtain a simulated diffraction field, and replaces the intensity information in the simulated diffraction field with the intensity information of the diffraction field obtained in step S1, thereby obtaining an updated diffraction field.

[0010] S4 imports the updated diffraction field into the reverse propagation model and obtains the diffraction exit wave;

[0011] S5 is a function that updates the information of the sample and illumination probe at each scanning position based on the exit wave obtained in step S1 and the diffraction exit wave obtained in step S4.

[0012] S6 forms a probe matrix around the probe position and calculates the correlation with the updated information function of the sample to be tested and the illumination probe, and then updates the probe position accordingly.

[0013] S7 repeats steps S2 to S6 to iterate based on the updated information functions of the illumination probe and the sample under test, as well as the probe position, until a preset number of iterations are completed or a preset condition is met. Then, the information functions of the illumination probe and the sample under test, as well as the probe position, are output to complete the stacked diffraction position correction.

[0014] As a further preferred embodiment, in step S1, the illumination probe maintains the same dimension as the sample to be tested.

[0015] As a further preferred embodiment, in step S3, the propagation mode of the propagation model includes Fresnel propagation, Fraunhofer propagation, and angular spectrum propagation.

[0016] As a further preferred embodiment, step S5 specifically comprises:

[0017]

[0018]

[0019] In the formula, α and β are the search step sizes for updating the sample and illumination probe, respectively, and O m (r),O m ′(r) are the information functions of the sample before and after updating at the m-th scan position, respectively, and P m (r,λ),P m ′(r,λ) are the information functions of the illumination probe before and after updating at the m-th scan position, respectively. Let r be the exit wave and the diffraction exit wave at the m-th scanning position, respectively, r be the real space coordinates, λ be the illumination probe wavelength, and * be the conjugate operation of the complex matrix.

[0020] As a further preferred embodiment, step S6 is specifically performed as follows:

[0021] S61 moves up, down, left, and right around the illumination probe to form a probe matrix.

[0022] r′ m (i)=r m (i)+l i

[0023] In the formula, r′ m (i) represents the real-space coordinates of the i-th illumination probe in the m-th scan position probe matrix, r m (i) represents the center coordinates of the i-th illumination probe in the m-th scan position probe matrix, l i This represents the offset distance of the i-th illumination probe in the probe matrix relative to the center;

[0024] S62 calculates the correlation between the probe matrix obtained in step S61 and the updated information functions of the sample to be tested and the illumination probe.

[0025]

[0026] In the formula, CC m (i) is the correlation numerical matrix in the probe matrix, O m ′(r) is the information function of the sample to be tested after updating at the m-th scan position, P m ′(r,λ) is the information function of the illumination probe after updating at the m-th scan position, P m (r′ m (i),λ) is the information function of the i-th illumination probe in the probe matrix before updating the m-th scan position, O m (r) is the information function of the sample to be tested before the m-th scan position is updated;

[0027] S63 updates the probe position based on the correlation obtained in step S62.

[0028]

[0029] In the formula, β is the search step size of the illumination probe update iteration, γ is the proportion of the update that retains the previous update step size, and D j and D j-1 These are the probe positions for the j-th and (j-1)-th iterations, respectively.

[0030] As a further preferred embodiment, in step S7, the preset number of iterations is 100 or more.

[0031] As a further preferred embodiment, in step S7, the preset condition is that the position error meets the convergence condition, and the formula for calculating the position error is:

[0032]

[0033] In the formula, E M The position error is M, the number of diffraction fields is M, and r′ is r′. m r represents the actual position coordinates of the probe. m These are the coordinates of the correct probe position.

[0034] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0035] 1. This invention expands the probe search range by forming a probe matrix around the actual probe, updates the search position by weighting the probe matrix, and uses the cross-correlation gradient of the virtual array probes before and after the update to update the position of the central probe. Compared with heuristic position correction methods, it can achieve sub-pixel position correction accuracy. When the position error converges to the correct position, the central axis symmetrical array probes constrain each other, avoiding crosstalk between local non-converged regions and global scanning position correction, which greatly improves the convergence stability and convergence accuracy of the stacked diffraction position correction method.

[0036] 2. In particular, this invention proposes to use a weighting function to optimize the position correction of the stacked diffraction, and to perform the position calibration update search based on the cross-correlation gradient of the weighting function. This can greatly avoid the reconstruction algorithm from getting trapped in local optima. Compared with mean weight and traditional single probe cross-correlation position error correction methods, this method greatly improves the convergence speed and convergence robustness of the algorithm without sacrificing computational efficiency. Attached Figure Description

[0037] Figure 1 This is a flowchart of the stacked diffraction position correction method based on weighted probe provided in an embodiment of the present invention;

[0038] Figure 2 This is a schematic diagram of the optical path of the stacked diffraction imaging system provided in an embodiment of the present invention;

[0039] Figure 3 These are the amplitude and phase patterns of the sample under test used in the simulation process of this embodiment of the invention, wherein (a) is the amplitude pattern and (b) is the phase pattern;

[0040] Figure 4 This is a two-dimensional motion plane trajectory of the sample under test in the stacked diffraction imaging system provided in the embodiments of the present invention, wherein (a) is a grid motion trajectory and (b) is a concentric circle motion trajectory;

[0041] Figure 5 These are diffraction field intensity distribution maps collected by the illumination probe of the stacked diffraction imaging system provided in this embodiment of the invention, wherein (a) is a sample amplitude and phase reconstruction map without position correction, and (b) is a probe amplitude and phase reconstruction map without position correction.

[0042] Figure 6 These are diffraction field intensity distribution maps collected after correction by the weighted probe-based stacked diffraction position correction method provided in this embodiment of the invention, wherein (a) is a sample amplitude and phase reconstruction map after position correction, and (b) is a probe amplitude and phase reconstruction map after position correction.

[0043] Figure 7 These are distribution diagrams of the illumination probe positions before and after correction in the stacked diffraction imaging system provided in this embodiment of the invention, wherein (a) is the illumination probe position diagram before correction and (b) is the illumination probe position diagram after correction.

[0044] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0045] 1-Laser, 2-Beam expander, 3-Adjustable aperture, 4-Focusing lens / mirror, 5-Sample to be tested, 6-Camera. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0047] like Figure 1 As shown, this invention provides a method for correcting the position of stacked diffraction based on a weighted probe, which is applicable to, for example... Figure 1The stacked diffraction imaging system shown employs either a reflection imaging system or a transmission imaging system. It includes a laser 1, a beam expander 2, an adjustable aperture, a focusing lens / mirror 4, a sample to be tested 5, and a camera 6, arranged sequentially along the light propagation direction. The method specifically includes the following steps:

[0048] S1 uses camera 6 to acquire diffraction light field intensity information at various scanning positions of the sample under test. m (q), m is the scanning position during the motion process, q is the frequency domain coordinate, and the complex amplitude function P(r,λ) of the illumination probe and the complex amplitude function O(r) of the sample to be tested are initialized at the same time, as well as the probe position r, λ is the wavelength of the illumination probe, to ensure that the dimensions of the illumination probe and the sample to be tested are the same, and the real-time position coordinates of the probe must correspond one-to-one.

[0049] S2 multiplies the complex amplitude function P(r,λ) of the sample under test at each scanning position with the complex amplitude function P(r,λ) of the illumination probe to obtain the exit wave.

[0050]

[0051] In the formula, For export wave;

[0052] S3 will obtain the exit wave from step S2. The light is imported into the propagation model and propagated to the reciprocal space, thus obtaining the simulated diffraction light field at different positions on the detection plane of camera 6.

[0053]

[0054] In the formula, Φ m (q,λ) represents the simulated diffraction field of the illumination probe in reciprocal space at the m-th scanning position, and prop represents the propagation mode of the light field (including but not limited to Fresnel propagation, Fraunhofer propagation, angular spectrum propagation, etc.).

[0055] Then, the intensity information in the diffracted light field is replaced with the diffracted light field intensity information I obtained in step S1. m (q), i.e., the amplitude constraint of the reciprocal space, is used to obtain the updated diffraction field.

[0056]

[0057] In the formula, Φ ′ m (q,λ) represents the updated diffraction field obtained by the illumination probe after amplitude constraint at the m-th scanning position;

[0058] S4 will update the diffraction field and import it into the reverse propagation model of step S3 to obtain the diffraction exit wave.

[0059]

[0060] In the formula, For the diffracted exit wave, iprop is the inverse propagation model of the light field;

[0061] S5 updates the information functions of the sample under test and the illumination probe at each scanning position based on the exit wave obtained in step S1 and the diffraction exit wave obtained in step S4.

[0062]

[0063]

[0064] In the formula, α and β are the search step sizes for updating the sample and illumination probe, respectively, and their values ​​are between [0,1]. m (r),O m ′ (r) represents the information function of the sample before and after updating at the m-th scan position, respectively, P m (r,λ),P m ′ (r, λ) are the information functions of the illumination probe before and after updating at the m-th scan position, respectively. Let r be the exit wave and the diffraction exit wave at the m-th scanning position, respectively; r is the real space coordinate; λ is the wavelength of the illumination probe; and * is the conjugate operation of the complex matrix.

[0065] S6 forms a probe matrix around the unupdated illumination probe, calculates the correlation with the updated illumination probe, and then updates the probe position based on it.

[0066] S7 repeats steps S2 to S6 to iterate based on the updated information functions of the illumination probe and the sample under test, as well as the probe position, until a preset number of iterations are completed or a preset condition is met. Then, the information functions of the illumination probe and the sample under test, as well as the probe position, are output to complete the stacked diffraction position correction.

[0067] Furthermore, the specific method for step S6 is as follows:

[0068] S61 moves around the original illumination probe in all directions to form a probe matrix.

[0069] r′ m (i)=r m (i)+l i (7)

[0070] In the formula, r′ m (i) represents the real-space coordinates of the i-th illumination probe in the m-th scan position probe matrix, r m (i) represents the center coordinates of the i-th illumination probe in the m-th scan position probe matrix, l iThis represents the offset distance of the i-th illumination probe in the probe matrix relative to the center;

[0071] S62 calculates the correlation between the probe matrix obtained in step S61 and the updated information functions of the sample to be tested and the illumination probe.

[0072] CC m (i)=∑O m ′ (r)·P m ′ (r,λ)·P m (r′ m (i),λ)·O m (r) (8)

[0073] In the formula, CC m (i) is the correlation numerical matrix in the probe matrix, P m (r′ m (i),λ) is the information function of the i-th illumination probe in the probe matrix before updating the m-th scan position;

[0074] S63 updates the probe position based on the correlation obtained in step S62.

[0075] g=∑CC m (i)*r′ m (i) (9)

[0076] D j =βg+γD j-1 (10)

[0077] In the formula, g x g y The gradient for the weighted probe update is γ, which takes values ​​between [0,1]. γ is the proportion of the update that maintains the previous update step size, also taking values ​​between [0,1]. j Let be the probe position in the j-th iteration.

[0078] Furthermore, in step S7, the preset number of iterations is 100 or more; the preset condition is that the position error meets the convergence condition, and the formula for calculating the position error is:

[0079]

[0080] In the formula, E M The position error is M, the number of diffraction fields is M, and r′ is r′. m r represents the actual position coordinates of the probe. m The coordinates are the correct position coordinates of the probe. The convergence condition is that the position error no longer changes drastically. The specific values ​​are set as needed in practical applications.

[0081] The technical solution provided by the present invention will be further described below with reference to specific embodiments.

[0082] The experimental optical system was set up with laser 1 operating at a wavelength of 632.8 nm and an output beam diameter (1 / e²) of 0.54 mm. The beam was expanded 10 times by beam expander 2, and the spot diameter was adjusted to 2 mm using adjustable aperture 3. The collimated parallel beam then passed through a focusing lens / mirror 4 with an effective focal length of 10 cm and illuminated the sample 5 located approximately 1.5 mm from the back focal plane of the focusing mirror. A precision motion platform propelled the sample 5 along a specific curve in a two-dimensional plane (including but not limited to grating curves, Fermat curves, concentric circle curves, etc.), ensuring that the overlap area between adjacent probe spots was not less than 60%, serving as an overlap constraint between probes. The aforementioned weighted probe-based stacked diffraction position correction method was used for calibration. Figure 3 These are the amplitude and phase patterns of the sample under test used in the simulation process, where the amplitude information is as follows: Figure 3 As shown in (a), the phase information is as follows Figure 3 As shown in (b), the illumination probe wavelength is 632.8 nm, the sample size is 512 × 512 pixels, and the beam diameter is 256 × 256 pixels. Figure 4 These are the two-dimensional planar trajectories of the sample under test in a stacked diffraction imaging system, where (a) is the grid motion trajectory and (b) is the concentric circle motion trajectory. The precision motion stage drives the sample under test 5 to perform two-dimensional planar motion, such as... Figure 4 As shown, the motion step size in the XY direction is 16 pixels, and the sample under test is scanned in a 21×21 region. Therefore, the CMOS camera collected a total of 441 coherent diffraction fields. The position error is ±15 pixels. Before using the position correction method, the mPIE operation was iterated 200 times, and then the position correction method was iterated 200 times. Figure 5 These are the intensity distribution maps of the diffraction field collected by the illumination probe of the stacked diffraction imaging system. (a) is the sample amplitude and phase reconstruction map without position correction, and (b) is the probe amplitude and phase reconstruction map without position correction. Figure 6 The images show the intensity distribution of the diffraction field after correction using a weighted probe-based stacked diffraction position correction method. (a) is the sample amplitude and phase reconstruction image after position correction, and (b) is the probe amplitude and phase reconstruction image after position correction. Figure 7 These are distribution diagrams of the illumination probe positions before and after correction in a stacked diffraction imaging system, where (a) is the illumination probe position diagram before correction and (b) is the illumination probe position diagram after correction. It can be seen that the weighted probe-based stacked diffraction position correction method provided by this invention can achieve efficient sub-pixel probe position calibration.

[0083] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for correcting the position of stacked diffraction based on a weighted probe, characterized in that, The method includes the following steps: S1 collects the diffraction light field intensity information at each scanning position of the sample under test, and simultaneously initializes the information functions of the illumination probe and the sample under test, as well as the probe position. S2 multiplies the information parameters of the sample under test and the illumination probe at each scanning position to obtain the exit wave; S3 imports the exit wave obtained in step S2 into the propagation model to obtain a simulated diffraction field, and replaces the intensity information in the simulated diffraction field with the intensity information of the diffraction field obtained in step S1, thereby obtaining an updated diffraction field. S4 imports the updated diffraction field into the reverse propagation model and obtains the diffraction exit wave; S5 is a function that updates the information of the sample and illumination probe at each scanning position based on the exit wave obtained in step S1 and the diffraction exit wave obtained in step S4. S6 forms a probe matrix around the probe position and calculates the correlation with the updated information function of the sample to be tested and the illumination probe, and then updates the probe position accordingly. S7 repeats steps S2 to S6 to iterate based on the updated information functions of the illumination probe and the sample under test, as well as the probe position, until the preset number of iterations is completed or the preset conditions are met. Then, the information functions of the illumination probe and the sample under test, as well as the probe position, are output to complete the stacked diffraction position correction.

2. The method for correcting the position of stacked diffraction based on a weighted probe as described in claim 1, characterized in that, In step S1, the illumination probe maintains the same dimension as the sample to be tested.

3. The method for correcting the position of stacked diffraction based on a weighted probe as described in claim 1, characterized in that, In step S3, the propagation modes of the propagation model include Fresnel propagation, Fraunhofer propagation, and angular spectrum propagation.

4. The method for correcting the position of stacked diffraction based on a weighted probe as described in claim 1, characterized in that, Step S5 is as follows: In the formula, α and β are the search step sizes for updating the sample and illumination probe, respectively, and O m (r),O m ′(r) are the information functions of the sample before and after updating at the m-th scan position, respectively, and P m (r,λ),P m ′(r,λ) are the information functions of the illumination probe before and after updating at the m-th scan position, respectively. Let r be the exit wave and the diffraction exit wave at the m-th scanning position, respectively, r be the real space coordinates, λ be the illumination probe wavelength, and * be the conjugate operation of the complex matrix.

5. The method for correcting the position of stacked diffraction based on a weighted probe as described in claim 1, characterized in that, The specific method for step S6 is as follows: S61 moves up, down, left, and right around the illumination probe to form a probe matrix. r′ m (i)=r m (i)+l i In the formula, r′ m (i) represents the real-space coordinates of the i-th illumination probe in the m-th scan position probe matrix, r m (i) represents the center coordinates of the i-th illumination probe in the m-th scan position probe matrix, l i This represents the offset distance of the i-th illumination probe in the probe matrix relative to the center; S62 calculates the correlation between the probe matrix obtained in step S61 and the updated information functions of the sample to be tested and the illumination probe. CC m (i)=∑O m ′(r)·P m ′(r,λ)·P m (r′ m (i),λ)·O m (r) In the formula, CC m (i) is the correlation numerical matrix in the probe matrix, O m ′(r) is the information function of the sample to be tested after updating at the m-th scan position, P m ′(r,λ) is the information function of the illumination probe after updating at the m-th scan position, P m (r′ m (i),λ) is the information function of the i-th illumination probe in the probe matrix before updating the m-th scan position, O m (r) is the information function of the sample to be tested before the m-th scan position is updated; S63 updates the probe position based on the correlation obtained in step S62. D j =β[∑CC m (i)*r′ m (i)]+γD j-1 In the formula, β is the search step size of the illumination probe update iteration, γ is the proportion of the update that retains the previous update step size, and D j and D j-1 These are the probe positions for the j-th and (j-1)-th iterations, respectively.

6. The method for correcting the position of stacked diffraction based on a weighted probe as described in any one of claims 1 to 5, characterized in that, In step S7, the preset number of iterations is 100 or more.

7. The method for correcting the position of stacked diffraction based on a weighted probe as described in any one of claims 1 to 5, characterized in that, In step S7, the preset condition is that the position error meets the convergence condition, and the formula for calculating the position error is: In the formula, E M The position error is M, the number of diffraction fields is M, and r′ is r′. m r represents the actual position coordinates of the probe. m These are the coordinates of the correct probe position.

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