Surface shape error self-calibration splicing detection method and system for x-ray plane mirror

Abstract

This invention discloses a self-calibration stitching detection method and system for surface shape errors of X-ray plane mirrors. The invention includes: conducting multi-factor, multi-level self-calibration stitching measurement simulations of measurement parameters based on environmental disturbance errors and other fixed settings, setting the additional error sources to zero, to obtain optimized measurement parameters and errors; conducting single-factor, multi-level self-calibration stitching measurement simulations of each additional error source based on the optimized measurement parameters to obtain the errors caused by each additional error source; calculating the required error control level for each additional error source; and conducting self-calibration stitching measurement simulations based on the optimized measurement parameters and the error control levels of each additional error source. If the measurement error obtained from the simulation meets the accuracy requirements, the simulation is terminated; otherwise, more stringent measurement parameters and additional error source control levels are selected, and iteration continues until the accuracy requirements are met. This invention aims to determine the required error control levels and main test parameters for the main error sources of X-ray plane mirrors.

Description

Technical Field

[0001] This invention relates to the field of X-ray plane mirror measurement technology, and specifically to a method and system for self-calibrating splicing detection of surface shape error of X-ray plane mirrors. Background Technology

[0002] X-ray plane mirrors play a crucial role in synchrotron radiation, free-electron lasers, and other advanced light source devices for beam transmission, beam splitting, and focusing. Typical surface pattern requirements include a slope error of less than 0.1 μrad RMS and a height error of less than 0.5 nm RMS. Typical aperture sizes are greater than 800 mm × 50 mm. To achieve this precision, advanced deterministic shaping methods, such as elastic emission processing (EEM) or ion beam shaping (IBF), are typically required. The test results for the three-dimensional (3-D) surface shape are a prerequisite for deterministic shaping. While long trace profilers (LTPs) can obtain two-dimensional profiles, they are difficult to use to guide deterministic shaping. Interferometry can obtain 3-D surface shapes. However, the aperture of the interferometer is usually smaller than the test surface. Therefore, sub-aperture stitching is often required, and self-calibrating stitching measurements are widely used for detecting surface shape errors in X-ray plane mirrors.

[0003] Interferometry is a relative measurement, and factors such as environmental interference, motion errors, alignment errors, overlap ratio, and sub-aperture size can all affect stitching accuracy. The highest accuracy of a commercial reference plane lens (TF) reference plane is typically λ / 40 (λ = 632.8 nm) PVr (robust peak-to-valley), with an RMS of approximately 1 nm. Therefore, it is necessary to compensate for reference plane errors. Unlike methods that calibrate reference plane errors before stitching, self-calibration stitching can calibrate reference plane errors simultaneously during the stitching process. However, it requires multiple measurements at different precise locations. Motion errors of the translation stage, and misalignment of the translation stage relative to the interferometer, introduce errors caused by inaccurate relative positions of the reference plane and the measured plane. Furthermore, sub-aperture size, stitching overlap ratio, and environmental errors can all affect the error propagation process of the stitching algorithm. To achieve sub-nanometer and nanoradian measurement accuracy, it is crucial to reveal the relationship between error sources, test parameters, and stitching measurement accuracy, and further determine the required control level for each error source and the key measurement parameters for specific mirrors. This is of great significance for advanced light source facilities and X-ray plane mirror manufacturers preparing to build X-ray planar interferometry systems. Some research has already been conducted in this area. For example, the Diamond Light Source, the European Synchrotron Radiation Facility (ESRF), Osaka University, Brookhaven National Laboratory, the Institute of Optics and Electronics, and Tongji University have all adopted a pre-calibration-re-stitching method. For instance, the Diamond Light Source constructed a one-dimensional stitching device based on the Zygo Verifre HDX interferometer and a commercial motion platform. By using intelligent averaging techniques (typically averaging the surface shape over 250-400 frames), an air-floating optical platform, and a sealed shield, environmental errors were controlled within 0.05 nm RMS (RMS fluctuation). The overlap of sub-apertures is typically >70%, and sometimes >90%. Cross-validation of the interferometric stitching system with a reproducibility accuracy of ~27 nrad RMS was performed by comparing it with Diamond-NOM. However, a comprehensive error analysis of how error sources and measurement parameters affect the measurement results has not been disclosed. On the other hand, synchrotron SOLEIL, the ALBA synchrotron light source, Brookhaven National Laboratory, and the National University of Defense Technology employ self-calibration stitching methods. Regarding error analysis, SOLEIL uses computer vision to ensure positioning accuracy better than 1 μm, with the deviation between the motion platform and the interferometer less than 0.01°. The ALBA synchrotron light source, through statistical simulation, concluded that under certain conditions, when the positioning error of the translation stage is better than 10% of the pixel size, the reconstruction error is approximately 1.8 nm PV (peak-valley value). Brookhaven National Laboratory found a strong correlation between the repeatability of height errors in stitching test results and the amplitude of the low-frequency term of environmental errors. The National University of Defense Technology simulated reconstruction errors under different shearing amounts and translation error conditions. In short, current research mainly focuses on obtaining the qualitative relationship between error sources and test accuracy. The error source data used in the simulations are inconsistent with the actual error sources.Furthermore, the simulation conditions (such as the diameter of the measured surface, the resolution of the measurement data, the error of the measured surface, the error of the reference surface, and the repeatability error) were not strictly simulated according to the actual situation. Therefore, it is impossible to obtain the actual required level of control over the main error sources and the appropriate measurement parameters for measuring a specific X-ray plane mirror. Consequently, existing error analysis methods cannot be used to guide the establishment of an X-ray plane mirror splicing measurement system that meets specific measurement accuracy targets.

[0004] In summary, previous studies have shown that motion errors introduce slope errors on the test surface, and that a higher overlap ratio reduces test errors. However, these error analyses are not comprehensive or quantitative enough for practical applications. For X-ray plane mirrors with specific accuracy requirements, the necessary control levels for error sources and the optimal measurement parameters remain unclear. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a method and system for self-calibration and splicing detection of surface shape errors of X-ray plane mirrors, which addresses the above-mentioned problems in the prior art. This invention aims to determine the error control level and main test parameters required to identify the main error sources for X-ray plane mirrors with specific aperture size and accuracy requirements. It can serve as a standard model for evaluating the test accuracy of X-ray plane mirrors and guiding the test process, so as to achieve the accuracy required for self-calibration and splicing of X-ray plane mirrors.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A self-calibration splicing detection method for surface shape error of X-ray plane mirrors includes:

[0008] S1. Obtain the measurement requirements for the X-ray plane mirror, including the measurement aperture and accuracy requirements; determine the fixed settings, measurement parameters, and additional error sources for the self-calibration splicing detection of surface shape errors. The fixed settings refer to parameters that may affect the test accuracy but need to be limited to fixed values ​​due to the objective constraints of the method. The measurement parameters affect the test accuracy, and their values ​​can be varied in subsequent error analysis simulations. The additional error sources refer to other error sources that can affect the test accuracy besides environmental interference, and their control levels can be varied in subsequent error analysis simulations.

[0009] S2, based on environmental disturbance error and fixed settings, with the additional error source set to zero, multi-factor, multi-level self-calibration splicing measurement simulation is carried out for the measurement parameters based on the X-ray plane mirror corresponding to the measurement aperture to obtain the optimized measurement parameters and the corresponding error;

[0010] S3. Based on the optimized measurement parameters, a single-factor, multi-level self-calibrated splicing measurement simulation is carried out on each additional error source based on the X-ray plane mirror corresponding to the measurement aperture to obtain the error caused by each additional error source. The required error control level for each additional error source is obtained by calculating the comprehensive error.

[0011] S4. Based on the selected optimized measurement parameters and the error control levels of each additional error source, perform self-calibration splicing measurement simulation to obtain the measurement error. If the measurement error meets the accuracy requirements, end and exit; otherwise, select stricter measurement parameters and additional error source control levels and jump to step S2 to continue iterating until the accuracy requirements are met.

[0012] Optionally, step S1 may include a reference surface error, or step S1 may include the measured surface error and the reference surface error; the measurement parameters in step S1 may include the sub-aperture size and the sub-aperture overlap rate; the additional error source in step S1 may refer to the error of the motion adjustment platform.

[0013] Optionally, the error of the motion adjustment platform includes the motion error and misalignment error of the motion adjustment platform.

[0014] Optionally, the motion errors include X-axis positioning error (position_error_x), X-axis flatness error (flatness_x), X-axis pitch error (pitch_error_x), Y-axis positioning error (position_error_y), Y-axis straightness error (linear_error_y), and Y-axis yaw error (yaw_error_y); the misalignment errors include X-axis initial yaw error (misalign_yaw_x0), X-axis initial pitch error (misalign_pitch_x0), Y-axis initial pitch error (misalign_pitch_y0), and Y-axis initial yaw error (misalign_yaw_y0).

[0015] Optionally, the functional expression for calculating the comprehensive error in step S3 is:

[0016]

[0017] In the above formula, σ C For the overall error, σ e σ is the RMS error caused by the optimized measurement parameters. i Let be the RMS error caused by the i-th additional error source, and n be the number of additional error sources.

[0018] Optionally, when selecting more stringent measurement parameters and additional error source control levels in step S4, this includes selecting additional error sources with smaller amplification coefficients (k) from a preset error level table. The preset error level table records the values ​​of additional error sources with different amplification coefficients corresponding to different error levels for each additional error source.

[0019] Optionally, before ending and exiting in step S4, self-consistency verification or mutual verification is also performed. If the self-consistency verification or mutual verification passes, the process ends and exits; otherwise, more stringent measurement parameters and additional error source control levels are selected, and the process jumps to step S1 to continue iterating until the accuracy requirements are met.

[0020] Furthermore, the present invention also provides a surface shape error self-calibration stitching detection system for X-ray plane mirrors, including a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the surface shape error self-calibration stitching detection method for X-ray plane mirrors.

[0021] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program or instructions that are programmed or configured to execute the self-calibration splicing detection method for surface shape error of an X-ray plane mirror via a processor.

[0022] In addition, the present invention also provides a computer program product, including a computer program or instructions, which are programmed or configured to execute the self-calibration splicing detection method for surface shape error of X-ray plane mirror by a processor.

[0023] Compared with existing technologies, the present invention has the following main advantages: The present invention includes conducting multi-factor, multi-level self-calibrating splicing simulation based on fixed settings and taking fixed values ​​for additional error sources to obtain optimized test parameters and corresponding errors; based on the optimized test parameters, conducting single-factor, multi-level self-calibrating splicing simulation on each additional error source at the current error level to obtain the errors caused by each additional error source; calculating the comprehensive error, and exiting if the comprehensive error meets the accuracy requirements; otherwise, selecting additional error sources with finer error levels and continuing iteration. The present invention can realize the error control level and main test parameters required to determine the main error sources for X-ray plane mirrors with specific aperture size and accuracy requirements. It can serve as a standard model for evaluating the test accuracy of X-ray plane mirrors and guiding the test process, so as to achieve the accuracy required for self-calibration splicing of X-ray plane mirrors. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0025] Figure 2This is a schematic diagram of the structure of the surface error self-correction splicing detection system in an embodiment of the present invention.

[0026] Figure 3 This is a schematic diagram of the motion error of the motion adjustment platform in an embodiment of the present invention.

[0027] Figure 4 This is a schematic diagram of motion error in an embodiment of the present invention, which introduces a relative positional error between the test surface and the reference surface in the motion adjustment platform. (a) represents the positioning error Δx, (b) represents the flatness error Δz, and (c) represents the pitch error φy.

[0028] Figure 5 This is a schematic diagram of the misalignment error of the motion adjustment platform in an embodiment of the present invention, where (a) is the yaw angle deviation of the x-axis translation stage relative to the interferometer, and (b) is the pitch angle deviation of the x-axis translation stage relative to the interferometer.

[0029] Figure 6 This represents the RMS value of environmental disturbance in this embodiment of the invention.

[0030] Figure 7 This is a surface shape error diagram of the measured surface in an embodiment of the present invention, wherein (a) is the height error of the measured surface, (b) is the slope error of the measured surface, (c) is the height error within the light-transmitting aperture, and (b) is the height slope error within the light-transmitting aperture.

[0031] Figure 8 This is a surface shape error diagram of the reference surface in an embodiment of the present invention, where (a) is the height error of the reference surface and (b) is the slope error of the reference surface.

[0032] Figure 9 The diagram shows the alignment test principle of the X-axis translation stage in the embodiment of the present invention, where (a) is the alignment test principle diagram of yaw and (b) is the alignment test principle diagram of pitch.

[0033] Figure 10 These are the simulated test errors of the height error map and the slope error map in the embodiments of the present invention, where (a) is the simulated test error of the height error map and (b) is the simulated test error of the slope error map.

[0034] Figure 11 These are point-to-point difference maps of the height error map and the slope error map in an embodiment of the present invention, wherein (a) is a point-to-point difference map of the height error map and (b) is a point-to-point difference map of the slope error map.

[0035] Figure 12 These are the point-to-point error diagrams, height diagrams, and slope diagrams of two measurement results with small overlap and large deviation in an embodiment of the present invention, where (a) is the point-to-point error diagram of the two measurement results and (b) is the slope diagram of the two measurement results. Detailed Implementation

[0036] The principle of the self-calibration splicing method in the surface shape error self-correction splicing detection system is as follows: Assume the splicing process requires M sub-apertures, and the position of any m-th sub-aperture is (s...). xm ,s ym ), where s xm =n xm ·ε, s ym =n ym ·ε, where (n xm ,n ym Let be the position coordinates of the m-th sub-aperture in pixel size, ε be the interferometer pixel resolution, and m = 1, 2, ..., M, where M is the number of sub-apertures. Each pair of sub-apertures with overlapping area will produce an equation:

[0037]

[0038] In the above formula, d1 is the difference between the measurement results of the two sub-apertures, g is the positional deviation coefficient between the two sub-apertures, r is the reference surface error vector, and G1 and D1 are relation matrices.

[0039] Combining all the equations obtained from all sub-aperture pairs, we get the matrix equation as follows:

[0040]

[0041] d'=[d1 d2…d o ] T ,

[0042] G' = [G1 G2…G o ] T ,

[0043] D'=[D1 D2…D o ] T ,

[0044] In the above equation, o represents the number of sub-aperture pairs with overlapping areas. The above equations are a set of linear equations. Under the condition that there are at least 5 sub-apertures and their positions satisfy the requirements of equation (1), the reference surface shape, except for the second-order term, can be reconstructed without theoretical error. After the absolute reference surface shape is reconstructed, the reconstructed reference surface error is used to compensate for the measured sub-apertures, and the corresponding geometric position parameters are adjusted using the calculated parameters. Finally, the adjusted sub-aperture dataset can be merged into a full-aperture surface shape with a certain weighting function. This invention aims to detect the self-calibration stitching method of the surface shape error self-calibration stitching detection system, so as to achieve the error control level and main test parameters required to determine the main error sources for X-ray plane mirrors with specific aperture size and accuracy requirements. It can be used as a standard model for evaluating the test accuracy of X-ray plane mirrors and guiding the test process, so as to achieve the accuracy required for self-calibration stitching of X-ray plane mirrors. The following section will take an X-ray plane mirror with a full aperture of 300mm×60mm and a light transmission aperture (CA) of 250mm×30mm as an example to further describe in detail the self-calibration splicing detection method and system for surface shape error of X-ray plane mirrors of the present invention.

[0045] like Figure 1 As shown, the self-calibration splicing detection method for surface shape error of X-ray plane mirrors in this embodiment includes:

[0046] S1. Obtain the measurement requirements for the X-ray plane mirror, including the measurement aperture and accuracy requirements; determine the fixed settings, measurement parameters, and additional error sources for the self-calibration splicing detection of surface shape errors. The fixed settings refer to parameters that may affect the test accuracy but need to be limited to fixed values ​​due to the objective constraints of the method. The measurement parameters affect the test accuracy, and their values ​​can be varied in subsequent error analysis simulations. The additional error sources refer to other error sources that can affect the test accuracy besides environmental interference, and their control levels can be varied in subsequent error analysis simulations.

[0047] S2, based on environmental disturbance error and fixed settings, with the additional error source set to zero, multi-factor, multi-level self-calibration splicing measurement simulation is carried out for the measurement parameters based on the X-ray plane mirror corresponding to the measurement aperture to obtain the optimized measurement parameters and the corresponding error;

[0048] S3. Based on the optimized measurement parameters, a single-factor, multi-level self-calibrated splicing measurement simulation is carried out on each additional error source based on the X-ray plane mirror corresponding to the measurement aperture to obtain the error caused by each additional error source. The required error control level for each additional error source is obtained by calculating the comprehensive error.

[0049] S4. Based on the selected optimized measurement parameters and the error control levels of each additional error source, perform self-calibration splicing measurement simulation to obtain the measurement error. If the measurement error meets the accuracy requirements, end and exit; otherwise, select stricter measurement parameters and additional error source control levels and jump to step S2 to continue iterating until the accuracy requirements are met.

[0050] In step S1 of this embodiment, when obtaining the measurement requirements for the X-ray plane mirror, the measurement requirements for the aperture are: aperture diameter of 300mm × 60mm and light transmission aperture (CA) of 250mm × 30mm; the accuracy requirements are: high accuracy better than 0.2nm RMS (@1mm-250mm) and slope error along the meridian direction better than 50nrad RMS (@1mm-250mm).

[0051] The surface shape error self-calibration splicing detection system of the X-ray plane mirror in this embodiment is a test system based on the Zygo Verifire interferometer. The Zygo Verifire interferometer is a standard Zygo TF with a rated accuracy of λ / 40PVr. It is located in a test chamber that has been built, with a temperature fluctuation of ±0.04℃ / 24 hours and a humidity fluctuation of ±0.3% / 24 hours. Figure 2 This is a schematic diagram of the surface error self-correction stitching detection system in this embodiment. The motion adjustment platform in this embodiment includes an x-axis translation stage and a y-axis translation stage. The x-axis and y-axis translation stages perform position transformations for different sub-apertures. The φx and φy tilt adjustment stages perform the adjustment of the zero fringes used for testing. The aperture of the interferometer's reference surface (TF) is typically smaller than the aperture of the surface under test (SUT). The error sources affecting the test results and the main stitching test parameters are explained below:

[0052] Environmental interference: Environmental disturbances such as airflow, vibration, and temperature fluctuations can affect the measurement results of each sub-aperture.

[0053] Motion error of the motion adjustment platform: The accuracy of the relative position between the test surface and the reference surface for different sub-apertures is guaranteed by the motion accuracy of the x and y translation stages. Without loss of generality, Figure 3 These represent six types of motion errors of the motion adjustment platform: positioning error Δx, straightness error Δy, flatness error Δz, pitch error φy, roll error φx, and yaw error φz. Only positioning error Δx, flatness error Δz, and pitch error φy introduce relative position errors between the test surface and the reference surface, as shown below. Figure 4As shown in (a) to (c), for the y-axis translation stage, the motion errors affecting the relative position between the measured surface and the reference surface are the positioning error Δx, the straightness error Δy, and the yaw error φz. Therefore, these six motion errors will introduce relative position errors through the two translation stages. These relative position errors will cause the surface shape of the measured surface at incorrect locations to be measured.

[0054] Misalignment error of the motion adjustment platform: Misalignment of each platform relative to the interferometer will also cause positional deviation of the sub-aperture relative to the reference plane. Without loss of generality, the alignment error of the x-axis translation stage is analyzed as follows: Figure 5 In the figure, (a) represents the yaw error φz of the x-axis translation stage relative to the interferometer. Figure 5 In (a) of the diagram, the green line represents the nominal direction of the x-axis translation stage axis, which should be parallel to the reference plane. Due to yaw angle misalignment, the actual direction of the x-axis translation stage axis (represented by the red line) is at an angle θ relative to the theoretical direction. mx_yaw For the m-th sub-aperture, the sliding length of the x-axis translation stage should be s. xm However, the actual distance traveled along the nominal direction is cos(θ). mx_yaw )·s xm This leads to s-cos(θ) mx_yaw )·s xm Positional deviation. Figure 5 (b) in the figure represents the pitch error φy of the x-axis translation stage relative to the interferometer. The pitch error φy is represented by the angular error θ between the actual direction of the x-axis translation axis (indicated by the red line) and the row direction of the CCD pixels. mx_pitch For the m-th sub-aperture, the theoretical sliding length of the x-axis translation stage is s. However, the actual travel length along the x-direction is cos(θ). mx_pitch )·s xm This introduces s xm -cos(θ mx_pitch )·s xm Positional deviation. Furthermore, θ mx_pitch An additional translation along the y-axis sin(θ) is also introduced. mx_pitch )·s xm Similarly, the pitch and yaw angle deviations of the y-axis translation stage will also introduce position deviations. All four alignment errors will jointly cause position deviations.

[0055] Measurement parameters: Overlap rate and sub-aperture size are two main splicing test parameters. The overlap rate affects the existence of the solution to equation (2). Furthermore, the overlap rate can affect the homogenization effect on measurement noise. A larger overlap rate can satisfy the requirements of equation (1) and reduce the influence of noise error. However, it will lengthen the test time and introduce long-term related errors. The smaller the sub-aperture size, the smaller the error of the reference surface. However, it will also increase the test time and introduce more long-term related errors. Therefore, under the condition that the surface shape error, noise error and measured surface error are the same, appropriate splicing measurement parameters should be carefully selected according to the simulation results.

[0056] As mentioned above, so many error sources and measurement parameters will affect the self-calibration splicing results. Therefore, in this embodiment, the above parameters are divided into three types: fixed settings, measurement parameters, and additional error sources. (1) Fixed settings refer to parameters that may affect the test accuracy, but due to the objective constraints of the method, they are restricted to fixed values. The characteristic of fixed settings is that the fixed settings are basically consistent with the actual situation. The surface shape error matrix of the measured surface and the surface shape error matrix of the reference surface can be obtained by using an interferometer for preliminary self-calibration splicing measurement. The single-aperture repeatability experiment can be performed using an interferometer, and the environmental disturbance matrix can be obtained by subtracting the adjacent measurement results point by point. Fixed settings include, but are not limited to, the surface shape error matrix of the measured surface, the surface shape error matrix of the reference surface, and the environmental disturbance matrix. (2) Measurement parameters refer to parameters whose values ​​may affect the test accuracy and whose values ​​can change in subsequent error analysis simulations. Determining the appropriate settings of these test parameters to meet the final measurement accuracy requirements is one of the motivations for carrying out this method. Fixed settings include, but are not limited to, sub-aperture size and the overlap rate of spliced ​​sub-apertures. (3) Additional error sources refer to other error sources besides environmental interference that can affect the test accuracy, and their control levels can be varied in subsequent error analysis simulations. Determining the control levels of these additional error sources to meet the final measurement accuracy requirements is one of the motivations for developing this method. Additional error sources include, but are not limited to, the motion error of the stitching motion stage and the adjustment and alignment error between the stitching motion stage and the interferometer.

[0057] Specifically, in step S1 of this embodiment, the measured surface error (SUT) and reference surface error are fixedly set; the measurement parameters in step S1 include the sub-aperture size and the sub-aperture overlap rate; the additional error source in step S1 refers to the error of the motion adjustment platform. As an optional implementation, the error of the motion adjustment platform in this embodiment includes the motion error and misalignment error of the motion adjustment platform. Further, the motion error in this embodiment includes X-axis positioning error position_error_x, X-axis flatness error flatness_x, X-axis pitch error pitch_error_x, Y-axis positioning error position_error_y, Y-axis straightness error linear_error_y, and Y-axis yaw error yaw_error_y; the misalignment error includes X-axis initial yaw error misalign_yaw_x0, X-axis initial pitch error misalign_pitch_x0, Y-axis initial pitch error misalign_pitch_y0, and Y-axis initial yaw error misalign_yaw_y0.

[0058] In this embodiment, a preliminary splicing test system was established to obtain data on fixed settings, namely the error of the surface under test (SUT) and the error of the reference surface (TF), as well as simulation environmental disturbances. The interferometer in this preliminary splicing test system is a Zygo Verifire equipped with a 1200×1200 CCD. The reference surface (TF) used is a standard Zygo TF with a nominal accuracy of λ / 40PVr. The resolution has been calibrated to 0.1308 mm / pixel. The X-axis translation stage is a high-load linear stage from PI (model: V-817.176211E0) with a travel range of 407 mm. The Y-axis translation stage is a PI UPL-120 precision Z-grade stage (model: 6635921130-0001) with a travel range of 13 mm. In addition, a two-dimensional electronically controlled tilt stage from ZYGO (model: 6500-0106-53) was used, allowing ±2° pitch and tilt adjustments with sub-microradian resolution. To obtain a fixed setting for the matrix representing environmental disturbance, repeatability tests were performed on the central sub-aperture. Under zero-fringe conditions, each measurement was averaged over 128 frames. Point-to-point subtraction of two consecutive results yielded the matrix representing the environmental disturbance (hereinafter denoted as E0). The RMS value of the repeatability matrix is ​​shown below. Figure 6 As shown by the curve marked with a circle, its average RMS height error is 0.156 nm. Figure 6 The straight curve in the middle is shown.

[0059] To obtain a fixed configuration representing the measured surface (SUT) and the reference surface (TF), a preliminary splicing experiment was conducted on the SUT. In this embodiment, it was specifically divided into 15 sub-apertures, from sub0 to sub14. The overlap ratio (area ratio) of the sub-apertures during the division was approximately 60%, and the size of the sub-apertures was [1016, 432] pixels, approximately [132.893, 56.506] mm. Using a self-calibration algorithm, the surface shape error T of the measured surface and the surface shape error R0 of the reference surface can be reconstructed, as shown below. Figure 7 and Figure 8 As shown. Figure 7 (a) and Figure 7 As shown in (b), the height error and slope error of the measured surface are 3.403 nm RMS and 0.99 μrad RMS, respectively. Figure 7 (c) and Figure 7 As shown in (d), the height and slope errors within the aperture are 0.582 nm RMS and 0.22 μrad RMS, respectively. The height error of the reference plane is 0.721 nm RMS, and the slope error is 0.25 μrad RMS, as shown in (d). Figure 8 As shown in (a) and (b) in the figure.

[0060] To obtain practical and representative motion errors, the specification data tables of the x and y translation stages used in the preliminary experiments were referenced, and the basic error levels of motion errors were defined as follows:

[0061] [position_error_x0=±3.0μm,

[0062] flatness_x0 = ±10μm,

[0063] pitch_error_x0 = ±60μrad,

[0064] position_error_y0=±0.05μm,

[0065] linear_error_y0=±3.0μm,

[0066] yaw_error_y0=±100μrad).

[0067] To obtain actual and representative misalignment errors, the alignment error of the translation stage relative to the interferometer was measured as follows. Considering that the testing principles for the initial X-axis yaw error misalign_yaw_x0 and the initial Y-axis pitch error misalign_pitch_y0 are similar, the following explanation will only use the testing of the initial X-axis yaw error misalign_yaw_x0 as an example.

[0068] like Figure 9 As shown, a picometer (attocube, IDS3010) with a sensor resolution of 1 pm is mounted on the X-axis translation stage. The distance the picometer moves on the X-axis translation stage is D. x The readings at the two positions are denoted as L1 and L2, respectively.

[0069] Therefore, the initial X-axis yaw error misalign_yaw_x0 between the motion axis of the X-axis translation stage and the reference plane is:

[0070]

[0071] To measure the initial X-axis pitch error misalign_pitch_x0, a polished plane with its front surface facing TF was mounted on the slider of the X-axis translation stage. A mark was drawn on the plane. Using image processing techniques, the pixel unit position ΔPv of the mark point on the fringe pattern before and after the movement can be obtained. Therefore, the initial X-axis pitch error misalign_pitch_x0 = ΔPv / D x ', where D x ' represents the forward and backward movement distance. Similarly, the initial yaw error on the Y-axis, misalign_yaw_y0, can be obtained.

[0072] Using the above method, the alignment error of the initially established test device was measured and set as the basic error level of the alignment error. The basic error level of misalignment was defined as: [misalign_yaw_x0=100μrad, misalign_pitch_y0=100μrad, misalign_pitch_x0=2mrad, misalign_yaw_y0=20mrad].

[0073] In this embodiment, step S5 performs single-factor and multi-level simulations based on the conditions and actual errors obtained in steps S1 and S2. The simulations are conducted using MATLAB 2022 on a workstation with an AMD Ryzen CPU (64 cores) and two NVIDIA GeForce RTX 3090 GPUs. In step S2, when initially determining the optimized measurement parameters, the overlap rate is divided into seven levels: ~30%, ~40%, ~50%, ~60%, ~70%, and ~80%. The four levels of sub-aperture size are [1016,432] pixels, [762,324] pixels, and [508,216] pixels. The reference surface error R0 and the environmental disturbance error E0 are added to the surface shape error T of the measured surface to generate sub-aperture test data. The motion error and alignment error of each platform are all set to 0. Then, the full aperture surface shape error of the measured surface is calculated using a self-calibration algorithm, and the theoretical surface shape error T0 is subtracted from the splicing result to calculate the height and slope RMS errors, as shown in Table 1 and Table 2, respectively.

[0074] Table 1: RMS values ​​of height error maps under different measurement parameters (unit: nm)

[0075]

[0076]

[0077] Table 2: RMS values ​​of slope error plots under different measurement parameters (unit: nrad)

[0078] (1016, 432) pixels (762, 324) pixels (508, 216) pixels 30% overlap 167 90 58 40% overlap 88 91 39 50% overlap 52 28 25 60% overlap 23 22 21 70% overlap 18 20 17 80% overlap 15 14 11

[0079] As shown in Tables 1 and 2, both the height error RMS and slope error RMS decrease with increasing overlap and decreasing sub-aperture size. Considering that a larger sub-aperture size consumes less testing time, a sub-aperture size of [1016, 432] pixels is preferred. Searching for RMS error values ​​with a sub-aperture size of [1016, 432] pixels reveals that RMS values ​​with overlap rates of 30%, 40%, and 50% do not meet the test targets of 0.2 nm RMS and 50 nrad. The RMS values ​​for a sub-aperture size of [1016, 432] pixels and an overlap rate of 60% are 0.055 nm and 23 nrad, respectively. The RMS and error values ​​meet the test targets and provide accuracy margins for additional error sources. Therefore, these two parameters are initially set as the measurement parameters.

[0080] In step S3 of this embodiment, based on the optimized measurement parameters, a single-factor, multi-level self-calibrated splicing measurement simulation is performed on each additional error source using the X-ray plane mirror corresponding to the measurement aperture to obtain the errors caused by each additional error source. This simulation uses variable additional error parameters, fixed settings, and the optimized test parameters obtained in step S2. The basic error level settings for motion error and misalignment error are shown in Table 3.

[0081] Table 3 Basic Error Levels for Motion Errors and Off-alignment Errors

[0082]

[0083]

[0084] In this embodiment, amplification factors k = 0.5, 1, and 2 are set and multiplied by the basic error level to obtain three error levels. Therefore, a total of 30 simulations were performed. Note that only one additional error parameter exists in all simulations. The RMS error values ​​are listed in columns 3-4 of Table 3. From Table 3, it can be concluded that the three motion error levels contribute very little to the test error compared to the test target (e.g., 14 pm and 4 nrad). This means that the motion table used in the pre-stitched test system is sufficient to meet the test target. Regarding misalignment error, the three levels of initial X-axis yaw error (misalign_yaw_x0) and initial Y-axis pitch error (misalign_pitch_y0) also have little impact on the test error, indicating that the initial X-axis yaw error (misalign_yaw_x0) and initial Y-axis pitch error (misalign_pitch_y0) of the pre-stitched test system are sufficient to meet the test target.

[0085] For the initial pitch error (misalign_pitch_x0) on the X-axis and the initial yaw error (misalign_yaw_y0) on the Y-axis, the basic error levels (i.e., the first 8 rows when k=1 and the last 2 rows when k=0.5) contribute 0.093 nm (54 nrad) and 0.056 nm (42 nrad) to the test error, respectively. This means that the initial pitch error (misalign_pitch_x0) on the X-axis and the initial yaw error (misalign_yaw_y0) on the Y-axis of the initially established stitching test system are unlikely to meet the test accuracy requirements. They must be adjusted and increased to the level of k=0.5, with error contributions of 0.042 nm (27 nrad) and 0.026 nm (20 nrad), respectively, to meet the test accuracy requirements.

[0086] In summary, the overall error (overall RMS error) can be calculated. The expression for the calculation function of the overall error in this embodiment is as follows:

[0087]

[0088] In the above formula, σ C For the overall error, σ e σ represents the RMS error caused by environmental disturbances under the optimized measurement parameters. i Let be the RMS error caused by the i-th additional error source, and n be the number of additional error sources. Based on the above formula, the combined RMS error can be calculated to be 0.0817 nm and 42 n rad, which meets the test objective.

[0089] In step S4 of this embodiment, when selecting more stringent measurement parameters and additional error source control levels, it includes selecting an additional error source with a smaller amplification factor k from a preset error level table. The preset error level table records the values ​​of additional error sources with different amplification factors corresponding to different error levels for each additional error source.

[0090] In step S4, when performing self-calibration splicing measurement simulation to obtain the measurement error based on the selected optimized measurement parameters and the error control levels of each additional error source, the preliminary optimized measurement parameters obtained in step S2 and the control levels of the additional error parameters obtained in steps S3 and S4 are used to perform simulation to obtain the splicing test error. The simulated test error in this embodiment is as follows: Figure 10 As shown, the RMS error is 0.111 nm and 44 nrad, which meets the test target.

[0091] As an optional implementation, see [link to implementation details]. Figure 1 In this embodiment, before ending and exiting in step S4, a self-consistency verification or mutual verification is performed. If the self-consistency verification or mutual verification passes, the process ends and exits; otherwise, a more stringent set of measurement parameters and additional error source control levels are selected, and the process jumps to step S2 to continue iteration until the accuracy requirements are met. Self-consistency verification means performing a test on the same mirror at the 0-degree position and at a position rotated 180 degrees. The test result at the 180-degree position is then rotated 180 degrees and compared with the test result at the 0-degree position to obtain the measurement error. If the self-consistency verification or mutual verification passes, the process ends and exits; otherwise, a more stringent set of measurement parameters and additional error source control levels are selected, and the process jumps to step S1 to continue iteration until the accuracy requirements are met. The SUT is a planar X-ray mirror with an aperture of 300 mm × 60 mm and a CA of 250 mm × 30 mm. The TF is a Zygo TF with a nominal accuracy of λ / 40PVr. All additional error values ​​are controlled. Since the error analysis model-driven approach demonstrates its ability to meet the testing objectives, the motion phase is identical to the preliminary experiment. The error is precisely adjusted and measured as follows:

[0092] [misalign_yaw_x0 = 55μrad,

[0093] misalign_pitch_y0 = 38μrad,

[0094] misalign_pitch_x0 = 1.3 mrad,

[0095] misalign_yaw_y0=10.1mrad],

[0096] These errors are all better than or approximately equal to the required additional error control level obtained in step S3. Then, 0° and 180° SUT tests are performed. After image registration, point-to-point error plots of the two test results are obtained as shown below. Figure 11 As shown, the RMS is 0.164 nm and the RMS is 48 nrad, achieving the target testing accuracy.

[0097] To verify that the method proposed in this embodiment can help determine the test parameters and additional error control levels to ensure test accuracy, experiments were conducted on other test parameters and other control error levels for additional error sources. The tested surface, reference surface, and motion stage were the same as those shown in step S3. The differences in test parameters and additional errors are listed in Table 4.

[0098] Table 4: Differences between test parameters, additional errors, and recommended values ​​of the method in this embodiment.

[0099]

[0100] Experiments conducted on other test parameters and other control error levels for additional error sources yielded point-to-point difference plots of the two test results, such as... Figure 12As shown, the RMS values ​​are 0.214 nm and 90 nrad, respectively. The test error is increased compared to the test error under the method-guided test parameters and error control levels. Without workflow guidance, the test results may be insufficiently accurate and fail to meet the required test precision. Results and validation demonstrate that the self-calibration stitching detection method for surface error of X-ray plane mirrors in this embodiment can guide researchers in selecting appropriate test parameters and the required error control level to meet the specific test precision goals of X-ray plane mirrors. Although the tested surface error map, reference surface error map, and environmental interference are set to fixed settings in the demonstrated method, and the test parameters are set to overlap rate and sub-aperture size, with motion error and alignment error as additional error sources, the demonstration of the proposed method is not intended to reveal all error sources and the influence of test parameters affecting the test error. However, the self-calibration stitching detection method for surface error of X-ray plane mirrors in this embodiment is open to other additional error sources (such as pixel calibration error, backtracking error, CCD mapping distortion, etc.). Furthermore, this embodiment also provides open methods for the self-calibration stitching detection of surface shape errors in X-ray plane mirrors, including the randomization degree of sub-aperture division and other test parameter settings for embedded interferometers. In summary, this embodiment proposes an error analysis model-driven self-calibration stitching detection method and system for surface shape errors in X-ray plane mirrors. This method can be used to reveal the error source control level and appropriate test parameters required to meet the measurement accuracy requirements of X-ray plane mirrors.

[0101] Furthermore, this embodiment also provides a surface shape error self-calibration stitching detection system for X-ray plane mirrors, including a microprocessor and a memory interconnected, wherein the microprocessor is programmed or configured to execute the surface shape error self-calibration stitching detection method for X-ray plane mirrors.

[0102] Furthermore, this embodiment also provides a computer-readable storage medium storing a computer program or instructions that are programmed or configured to execute the self-calibration splicing detection method for surface shape error of an X-ray plane mirror via a processor.

[0103] In addition, this embodiment also provides a computer program product, including a computer program or instructions, which are programmed or configured to execute the self-calibration splicing detection method for surface shape error of X-ray plane mirrors via a processor.

[0104] Those skilled in the art will understand that the technical solutions provided by the embodiments of this application may take the form of a method, system, or computer program product. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product embodied on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create an implementation for the process. Figure 1 One or more processes and / or boxes Figure 1 A means comprising one or more blocks that function within a block. These computer program instructions may also be stored in a computer-readable storage medium capable of directing a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process. Figure 1 One or more processes and / or boxes Figure 1 The instructions in one or more boxes provide functionality. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function in one or more boxes.

[0105] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A self-calibration splicing detection method for surface shape error of an X-ray plane mirror, characterized in that, include: S1. Obtain the measurement requirements for the X-ray plane mirror, including the measurement aperture and accuracy requirements; determine the fixed settings, measurement parameters, and additional error sources for the self-calibration splicing detection of surface shape errors. The fixed settings refer to parameters that may affect the test accuracy but need to be limited to fixed values ​​due to the objective constraints of the method. The measurement parameters affect the test accuracy, and their values ​​can be varied in subsequent error analysis simulations. The additional error sources refer to other error sources that can affect the test accuracy besides environmental interference, and their control levels can be varied in subsequent error analysis simulations. S2, based on environmental disturbance error and fixed settings, with the additional error source set to zero, multi-factor, multi-level self-calibration splicing measurement simulation is carried out for the measurement parameters based on the X-ray plane mirror corresponding to the measurement aperture to obtain the optimized measurement parameters and the corresponding error; S3. Based on the optimized measurement parameters, a single-factor, multi-level self-calibrated splicing measurement simulation is carried out on each additional error source based on the X-ray plane mirror corresponding to the measurement aperture to obtain the error caused by each additional error source. The required error control level for each additional error source is obtained by calculating the comprehensive error. S4. Based on the selected optimized measurement parameters and the error control levels of each additional error source, perform self-calibration splicing measurement simulation to obtain the measurement error. If the measurement error meets the accuracy requirements, end and exit; otherwise, select stricter measurement parameters and additional error source control levels and jump to step S2 to continue iterating until the accuracy requirements are met.

2. The self-calibration splicing detection method for surface shape error of an X-ray plane mirror according to claim 1, characterized in that, The fixed settings in step S1 include reference surface error, or the fixed settings in step S1 include measured surface error and reference surface error; the measurement parameters in step S1 include sub-aperture size and sub-aperture overlap rate; the additional error source in step S1 refers to the error of the motion adjustment platform.

3. The self-calibration splicing detection method for surface shape error of X-ray plane mirror according to claim 2, characterized in that, The error of the motion adjustment platform includes the motion error and misalignment error of the motion adjustment platform.

4. The self-calibration splicing detection method for surface shape error of an X-ray plane mirror according to claim 3, characterized in that, The motion errors include X-axis positioning error (position_error_x), X-axis flatness error (flatness_x), X-axis pitch error (pitch_error_x), Y-axis positioning error (position_error_y), Y-axis straightness error (linear_error_y), and Y-axis yaw error (yaw_error_y); the misalignment errors include X-axis initial yaw error (misalign_yaw_x0), X-axis initial pitch error (misalign_pitch_x0), Y-axis initial pitch error (misalign_pitch_y0), and Y-axis initial yaw error (misalign_yaw_y0).

5. The self-calibration splicing detection method for surface shape error of an X-ray plane mirror according to claim 1, characterized in that, The functional expression for calculating the comprehensive error in step S3 is: In the above formula, σ C For the overall error, σ e σ is the RMS error caused by the optimized measurement parameters. i Let be the RMS error caused by the i-th additional error source, and n be the number of additional error sources.

6. The self-calibration splicing detection method for surface shape error of an X-ray plane mirror according to claim 1, characterized in that, When selecting more stringent measurement parameters and additional error source control levels in step S4, this includes selecting additional error sources with smaller amplification coefficients (k) from a preset error level table. The preset error level table records the values ​​of additional error sources with different amplification coefficients corresponding to different error levels for each additional error source.

7. The self-calibration splicing detection method for surface shape error of an X-ray plane mirror according to claim 1, characterized in that, Before ending and exiting in step S4, self-consistency verification or mutual verification is performed. If the self-consistency verification or mutual verification passes, the process ends and exits; otherwise, more stringent measurement parameters and additional error source control levels are selected, and the process jumps to step S1 to continue iterating until the accuracy requirements are met.

8. A self-calibration splicing detection system for surface shape error of an X-ray plane mirror, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to perform the self-calibration splicing detection method for surface shape error of an X-ray plane mirror as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute, via a processor, the self-calibration splicing detection method for surface shape error of an X-ray plane mirror as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program or instructions, characterized in that, The computer program or instructions are programmed or configured to execute, via a processor, the self-calibration splicing detection method for surface shape error of an X-ray plane mirror as described in any one of claims 1 to 7.

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