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

Abstract

The invention discloses a surface shape error self-calibration splicing detection method and system for an X-ray plane mirror, and the method comprises the steps: enabling the value of an additional error source to be zero based on an environment disturbance error and other fixed settings, and carrying out the multi-factor and multi-level self-calibration splicing measurement simulation of measurement parameters, so as to obtain optimized measurement parameters and errors; carrying out single-factor multi-level self-calibration splicing measurement simulation on each additional error source based on the optimized measurement parameters to obtain errors caused by each additional error source; calculating an error control level required by each additional error source; carrying out self-calibration splicing measurement simulation according to the optimized measurement parameters and the error control level of each additional error source, and exiting if the measurement error obtained by simulation meets the precision requirement; otherwise, more strict measurement parameters and additional error source control levels are selected, and iteration is continued until the precision meets the requirement. The invention aims to determine the error control level and the main test parameters required by the main error source of the X-ray plane mirror.

Description

Technical Field

[0001] The present invention relates to the technical field of measuring X-ray plane mirrors, and in particular to a surface error self-calibration splicing detection method and system for X-ray plane mirrors. Background Art

[0002] X-ray mirrors play a vital role in synchrotron radiation, free electron lasers and other advanced light source devices for beam transmission, beam splitting and focusing. Typical surface graphics requirements are slope errors less than 0.1μrad RMS (root mean square) and height errors less than 0.5nm RMS. Typical aperture sizes are greater than 800mm×50mm. In order to achieve this accuracy, advanced deterministic shaping methods such as elastic emission machining (EEM) or ion beam shaping (IBF) are usually required. The test results of the three-dimensional (3-D) surface shape are the premise of deterministic shaping. The long trace profiler (LTP) can obtain a two-dimensional profile, but it is difficult to use it to guide deterministic shaping. Interferometry can obtain 3-D surface shape. However, the aperture of the interferometer is usually smaller than the test surface. Therefore, sub-aperture stitching is usually required, and self-calibration stitching measurement is widely used in the detection of surface shape errors of X-ray mirrors.

[0003] Interferometry is a relative measurement, and factors such as environmental interference, motion error, alignment error, overlap ratio, and sub-aperture size can affect the stitching accuracy. The highest accuracy of the reference surface of a commercial reference plane lens (TF) is usually λ / 40 (λ=632.8nm) PVr (robust peak-to-valley), and the RMS is about 1nm. Therefore, it is necessary to compensate for the reference surface error. Unlike the method of calibrating the reference surface error before stitching, the self-calibration stitching method can calibrate the reference surface error simultaneously during the stitching process. However, it requires multiple measurements at different precise positions. The motion error of the translation stage and the misalignment of the translation stage relative to the interferometer will introduce errors caused by the inaccurate relative position of the reference surface and the measured surface. In addition, the sub-aperture size, stitching overlap ratio, and environmental errors may affect the error propagation process of the stitching algorithm. In order to achieve sub-nanometer and nanoradian measurement accuracy, it is important to reveal the relationship between the error source, test parameters, and stitching measurement accuracy, and further determine the control level required for each error source and the key measurement parameters of a specific mirror. This is of great significance to advanced light source facilities and X-ray plane mirror manufacturers who are preparing to build X-ray plane interferometry systems. In this regard, some research has been carried out. For example, Diamond Light Source, European Synchrotron Radiation Source (ESRF), Osaka University, Brookhaven National Laboratory, Institute of Optoelectronics, Tongji University, etc. have adopted the pre-calibration-re-stitching method. For example, Diamond Light Source built a one-dimensional stitching device based on Zygo Verifre HDX interferometer and commercial motion platform. By using intelligent averaging technology (usually 250-400 frames of average surface shape), air-floating optical platform and closed shielding cover, the environmental error is controlled within 0.05nm RMS (RMS value fluctuation). The overlap rate of sub-apertures is usually >70%, and sometimes >90% is required. By comparing with Diamond-NOM, the reproducibility accuracy of the interferometric stitching system was cross-verified to be ~27nrad RMS. However, a comprehensive error analysis of how error sources and measurement parameters affect the measurement results has not been disclosed. On the other hand, the synchrotron SOLEIL, ALBA synchrotron light source, Brookhaven National Laboratory, National University of Defense Technology, etc. adopt the self-calibration stitching method. In terms of error analysis, the synchrotron SOLEIL uses computer vision methods to ensure that the positioning accuracy is better than 1μm, and the deviation between the motion platform and the interferometer is less than 0.01°. The ALBA synchrotron light source draws the following conclusions through statistical simulation: under certain conditions, when the positioning error of the translation stage is better than 10% of the pixel size, the reconstruction error is about 1.8nm PV (peak-to-valley value). Brookhaven National Laboratory found that the high error repeatability of the stitching test results is strongly correlated with the amplitude of the low-frequency term of the environmental error. The National University of Defense Technology simulated the reconstruction error under different shear and translation error conditions. In short, the current research is mainly to obtain the qualitative relationship between the error source and the test accuracy. The error source data used in the simulation is inconsistent with the actual error source.Furthermore, the simulation conditions (such as the diameter of the measured surface, the resolution of the measurement data, the measured surface error, the reference surface error, the repeatability error, etc.) were not simulated strictly in accordance with the actual situation. Therefore, it is impossible to obtain the actual required control level of the main error sources and the appropriate measurement parameters for measuring a specific X-ray plane mirror. Therefore, the existing error analysis method 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 can introduce slope errors on the test surface and that higher overlap ratios can reduce the test error. However, these error analyses are not comprehensive or quantitative enough for practical applications. For X-ray mirrors with specific accuracy requirements, the necessary level of control of error sources and the optimal measurement parameters remain unclear. Summary of the invention

[0005] Technical problem to be solved by the present invention: In view of the above-mentioned problems in the prior art, a method and system for self-calibration and splicing detection of surface errors of X-ray plane mirrors are provided. The present invention aims 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 sizes 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 and splicing of X-ray plane mirrors.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A surface error self-calibration splicing detection method for an X-ray plane mirror, comprising:

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

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

[0010] S3, based on the optimized measurement parameters, a single-factor multi-level self-calibration splicing measurement simulation is performed 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, and the error control level required for each additional error source is obtained by calculating the comprehensive error;

[0011] S4, carry out self-calibration stitching measurement simulation according to the selected optimized measurement parameters and the error control level of each additional error source to obtain the measurement error. If the measurement error meets the accuracy requirement, end and exit; otherwise, select stricter measurement parameters and additional error source control level and jump to step S2 to continue iterating until the accuracy meets the requirement.

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

[0013] Optionally, the error of the motion adjustment platform includes a motion error and an offset error of the motion adjustment platform.

[0014] Optionally, the motion error 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.

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

[0016]

[0017] In the above formula, σ C is the comprehensive error, σ e is the RMS error caused by the optimized measurement parameters, σ i is the RMS error caused by the ith additional error source, and n is the number of additional error sources.

[0018] Optionally, when selecting stricter measurement parameters and additional error source control levels in step S4, it includes selecting, for the additional error source, an additional error source with a smaller amplification factor k in a preset error level table, wherein the preset error level table records, for each additional error source, the values ​​of the additional error sources with different amplification factors corresponding to the error levels.

[0019] Optionally, before ending and exiting in step S4, self-consistency verification or mutual check verification is also included. If the self-consistency verification or mutual check 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 meets the requirements.

[0020] In addition, the present invention also provides a surface error self-calibration and stitching detection system for an X-ray plane mirror, comprising a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to execute the surface error self-calibration and stitching detection method for an X-ray plane mirror.

[0021] In addition, the present invention also provides a computer-readable storage medium, which stores a computer program or instruction, and the computer program or instruction is programmed or configured to execute the surface error self-calibration splicing detection method for X-ray plane mirrors through 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 surface error self-calibration splicing detection method for X-ray plane mirrors through a processor.

[0023] Compared with the prior art, the present invention mainly has the following advantages: the present invention includes, based on fixed settings, taking additional error sources as fixed values, carrying out multi-factor and multi-level self-correction stitching simulation to obtain optimized test parameters and corresponding errors; on the basis of the optimized test parameters, carrying out single-factor and multi-level self-correction stitching simulation for various additional error sources at the current error level to obtain the errors caused by various additional error sources; calculating the comprehensive error, and exiting if the comprehensive error meets the accuracy requirement; otherwise, selecting additional error sources with finer error levels and continuing to iterate. The present invention can achieve the error control level and main test parameters required to determine the main error sources for X-ray plane mirrors with specific aperture sizes and accuracy requirements, and 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 Schematic diagram of the basic flow of the method of the embodiment of the present invention.

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

[0026] Figure 3 Schematic diagram of motion error of the motion adjustment platform in an embodiment of the present invention.

[0027] Figure 4 Schematic diagram of motion error of relative position error between the test surface and the reference surface introduced by the motion adjustment platform in an embodiment of the present invention, where (a) is the positioning error Δx, (b) is the flatness error Δz, and (c) is the pitch error φy.

[0028] Figure 5 Schematic diagram of the misalignment error of the motion adjustment platform in an embodiment of the present invention, wherein (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 is the RMS value of the environmental disturbance in the embodiment of the present invention.

[0030] Figure 7 : is the surface error diagram of the measured surface in the 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 clear aperture, and (b) is the height slope error within the clear aperture.

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

[0032] Fig. 9 Schematic diagrams of alignment tests for yaw and pitch of an X-axis translation stage in an embodiment of the present invention, wherein (a) is a schematic diagram of alignment tests for yaw, and (b) is a schematic diagram of alignment tests for pitch.

[0033] Fig.10 1 and 2 are simulated test errors of the height error graph and the slope error graph in the embodiment of the present invention, wherein (a) is the simulated test error of the height error graph, and (b) is the simulated test error of the slope error graph.

[0034] Fig.11 1 is a point-to-point difference diagram of a height error diagram and a slope error diagram in an embodiment of the present invention, wherein (a) is a point-to-point difference diagram of a height error diagram, and (b) is a point-to-point difference diagram of a slope error diagram.

[0035] Fig.12 1 and 2 are point-to-point error graphs, height graphs and slope graphs of two measurement results with relatively small overlap and large deviation in an embodiment of the present invention, wherein (a) is a point-to-point error graph of the two measurement results, and (b) is a slope graph of the two measurement results. DETAILED DESCRIPTION

[0036] The principle of the self-calibration stitching method of the surface error self-correction stitching detection system is as follows: Assume that the stitching 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 ) is the position coordinate of the mth subaperture expressed in pixel size, ε is the interferometer pixel resolution, m = 1, 2, ..., M, M is the number of subapertures. Each pair of subapertures with overlapping area will generate an equation:

[0037]

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

[0039] Combining all equations obtained for all subaperture pairs, the matrix equation is:

[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 formula, o is 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 meet the requirements of equation (1), the reference surface shape except the second-order term can be reconstructed without theoretical error. After the absolute reference surface shape is reconstructed. The measured sub-aperture is compensated with the reconstructed reference surface error, and adjusted with the calculated corresponding geometric position parameters. Finally, the adjusted sub-aperture data set can be merged into a full-aperture surface shape with a certain weight function. The present invention aims to detect the self-calibration splicing method of the surface shape error self-correction splicing detection system to achieve the error control level and main test parameters required to determine the main error source for an X-ray plane mirror with a specific aperture size and accuracy requirement. It can be used as a standard model for evaluating the test accuracy of an X-ray plane mirror and guiding the test process to achieve the accuracy required for the self-calibration splicing of an X-ray plane mirror. The following will take an X-ray plane mirror with a full aperture of 300mm×60mm and a clear aperture (CA) of 250mm×30mm as an example to further explain in detail the surface error self-calibration splicing detection method and system for the X-ray plane mirror of the present invention.

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

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

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

[0048] S3, based on the optimized measurement parameters, a single-factor multi-level self-calibration splicing measurement simulation is performed 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, and the error control level required for each additional error source is obtained by calculating the comprehensive error;

[0049] S4, carry out self-calibration stitching measurement simulation according to the selected optimized measurement parameters and the error control level of each additional error source to obtain the measurement error. If the measurement error meets the accuracy requirement, end and exit; otherwise, select stricter measurement parameters and additional error source control level and jump to step S2 to continue iterating until the accuracy meets the requirement.

[0050] When obtaining the measurement requirements of the X-ray plane mirror in step S1 of this embodiment, the measurement requirements of the measurement aperture are: the aperture is 300mm×60mm, and the clear aperture (CA) is 250mm×30mm; the accuracy requirements are that the height accuracy is better than 0.2nm RMS (@1mm-250mm), and the slope error along the meridian direction is better than 50nrad RMS (@1mm-250mm).

[0051] The surface error self-calibration splicing detection system of the X-ray plane mirror in this embodiment is a test system based on the ZygoVerifire interferometer. The Zygo Verifire interferometer is a standard Zygo TF with a rated accuracy of λ / 40PVr. In an already built test room, the temperature fluctuation is ±0.04°C / 24 hours and the humidity fluctuation is ±0.3% / 24 hours. Figure 2 This is a structural diagram of the surface error self-correction splicing detection system in this embodiment. In this embodiment, the motion adjustment platform includes an x-axis translation stage and a y-axis translation stage. The x-axis translation stage and the y-axis translation stage perform position transformations of different sub-apertures. The φx and φy tilt adjustment stages perform the adjustment of the zero stripes for testing. The aperture of the reference plane (TF) of the interferometer is usually smaller than the aperture of the surface under test (SUT). The error sources and main splicing test parameters that affect the test results are described as follows:

[0052] Environmental disturbances: Environmental disturbances introduced by airflow, vibration, temperature fluctuations, etc. will affect the measurement results of each sub-aperture.

[0053] Motion error of motion adjustment platform: The relative position accuracy between the test surface and the reference surface of different sub-apertures is guaranteed by the motion accuracy of the x and y translation stages. Without loss of generality, Figure 3 They respectively express the six kinds 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 the positioning error Δx, flatness error Δz and pitch error φy will introduce the relative position error between the test surface and the reference surface, as shown in Figure 4As shown in (a) to (c) in the figure. For the y-axis translation stage, the motion errors that affect 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, the six motion errors will introduce relative position errors through the two translation stages. The relative position error will cause the surface shape of the measured surface to be measured at the wrong position.

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

[0055] Measurement parameters: Overlap ratio and sub-aperture size are two main stitching test parameters. Overlap ratio affects the existence of the solution of equation (2). Furthermore, overlap ratio can affect the averaging effect on the measurement noise. A larger overlap ratio can meet the requirements of equation (1) and reduce the impact of noise errors. 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 reference surface shape error, noise error and measured surface error are the same, the appropriate stitching measurement parameters should be carefully selected according to the simulation situation.

[0056] As mentioned above, so many error sources and measurement parameters will affect the self-calibration stitching 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 target constraints of the method, they are limited to fixed values. The characteristic of fixed settings is that the fixed settings are basically consistent with the actual situation. An interferometer can be used to perform preliminary self-calibration stitching measurements to obtain the surface error matrix of the measured surface and the surface error matrix of the reference surface. An interferometer is used to perform a single-aperture repeatability experiment, and the adjacent measurement results are point-to-point subtraction to obtain the environmental disturbance matrix. Fixed settings include but are not limited to the surface error matrix of the measured surface, the surface 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 be changed 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 overlap rate of spliced ​​sub-apertures. (3) Additional error sources refer to other error sources that can affect the test accuracy in addition to environmental interference, and their control level can be changed in subsequent error analysis simulations. Determining the control level 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 splicing motion stage and the adjustment alignment error of the splicing motion stage and the interferometer.

[0057] Specifically, in step S1 of this embodiment, the fixed settings are the measured surface error (SUT) and the reference surface (TF) error; the measurement parameters in step S1 include the sub-aperture size and the overlap rate of the sub-aperture; 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 errors in this embodiment 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 linearity 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 fixed settings, namely the data of the error of the surface under test (SUT), the error of the reference surface (TF), and the simulated environmental disturbance. The interferometer in the preliminary splicing test system is a Zygo Verifire equipped with a 1200×1200CCD. The reference surface (TF) used is a standard Zygo TF with a nominal accuracy of λ / 40PVr. The resolution has been calibrated to 0.1308mm / pixel. The X-axis translation stage is a high-load linear stage from PI (model: V-817.176211E0) with a travel range of 407mm. The y-axis translation stage is PI's UPL-120 precision Z-stage (model: 6635921130-0001), which has a travel range of 13 mm. In addition, a two-dimensional electronically controlled tilt stage from ZYGO (model: 6500-0106-53) is used, allowing ±2° pitch and tilt adjustment with sub-micro-radian resolution. In order to obtain a fixed setting of the matrix representing the environmental disturbance, the central subaperture was tested for repeatability. Under zero fringe conditions, 128 frames were averaged for each measurement. The matrix representing the environmental disturbance (hereinafter referred to as E0) was obtained by point-to-point subtraction of two consecutive results. The RMS value of the repeatability matrix is ​​as follows: Figure 6 As shown in the circled curve, the average RMS height error is 0.156nm. Figure 6 The straight curve in the middle.

[0059] In order to obtain a fixed setting representing the surface under test (SUT) and the reference surface (TF), a preliminary splicing test was conducted on the surface under test (SUT). In this embodiment, it is specifically divided into 15 sub-apertures from sub0 to sub14. The sub-aperture overlap ratio (area ratio) during division is about 60%, and the size of the sub-aperture is [1016,432] pixels, which is about [132.893,56.506] mm. Using the self-calibration algorithm, the surface shape error T of the surface under test and the surface shape error R0 of the reference surface can be reconstructed as follows: Figure 7 and Figure 8 As shown. Figure 7 (a) and Figure 7 As shown in (b) of Figure 1, the height error and slope error of the measured surface are 3.403nm RMS and 0.99μradRMS respectively. Figure 7 (c) and Figure 7 As shown in (d) in the figure, the height and slope errors within the clear aperture are 0.582nm RMS and 0.22μrad RMS, respectively. The height error of the reference surface is 0.721nm RMS, and the slope error is 0.25μrad RMS, respectively. Figure 8 As shown in (a) and (b) in .

[0060] In order to obtain a practical and representative motion error, the specification data sheet of the x, y translation stage used in the preliminary experiment was referred to, and the basic error level of motion error was defined as:

[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] In order to obtain the actual and representative misalignment error, the alignment error of the translation stage relative to the interferometer is measured as follows. Considering that the test principles of the initial yaw error misalign_yaw_x0 of the X-axis and the initial pitch error misalign_pitch_y0 of the Y-axis are similar, the following only takes the test of the initial yaw error misalign_yaw_x0 of the X-axis as an example for explanation.

[0068] like Fig. 9 As shown in the figure, a picometer interferometer (attocube, IDS3010) with a sensor resolution of 1pm is installed on the X-axis translation stage. The distance that the picometer interferometer moves on the X-axis translation stage is D x The readings at the two positions are recorded 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 surface is:

[0070]

[0071] In order to measure the initial pitch error misalign_pitch_x0 of the X axis, a polished plane with its front surface facing the TF is installed on the slider of the X translation stage. Draw a mark on the plane. Using image processing technology, the pixel unit position ΔPv on the fringe diagram before and after the movement of the mark point can be obtained. Therefore, the initial pitch error misalign_pitch_x0 of the X axis = ΔPv / D x ', where D x ' is the forward and backward movement distance. Similarly, the initial yaw error misalign_yaw_y0 of the Y axis can be obtained.

[0072] Using the above method, the alignment error of the preliminarily established test device is measured and set as the basic error level of the alignment error. The basic error level of misalignment is defined as: [misalign_yaw_x0 = 100 μrad, misalign_pitch_y0 = 100 μrad, misalignt_pitch_x0 = 2 mrad, misalign_yaw_y0 = 20 mrad].

[0073] In step S5 of this embodiment, single-factor and multi-level simulations are performed based on the conditions and actual errors obtained in steps S1 and S2. The simulation is performed using MATLAB 2022 on a workstation using an AMD Ryzen CPU (64 cores) and two NVIDIA GeForce RTX3090 GPUs. When the optimized measurement parameters are preliminarily determined in step S2, 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, and the motion errors and alignment errors of each platform are set to 0. Then, the full-aperture surface error of the measured surface is calculated using the self-calibration algorithm, and the theoretical surface error T0 is subtracted from the stitching result to calculate the height and slope RMS errors, as shown in Table 1 and Table 2, respectively.

[0074] Table 1: RMS value of height error diagram under different measurement parameters (unit: nm)

[0075]

[0076]

[0077] Table 2: RMS value of slope error graph 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] It can be seen from Tables 1 and 2 that with the increase of overlap ratio and the decrease of subaperture size, both the height error RMS and the slope error RMS decrease. Considering that the larger the subaperture size, the less test time is consumed, the subaperture size of [1016,432] pixels is given priority. By searching for the RMS error value when the subaperture size is [1016,432] pixels, it can be seen that the RMS values ​​with overlap ratios of 30%, 40%, and 50% do not meet the 0.2nm RMS and 50nrad test targets. The RMS values ​​when the subaperture size is [1016,432] pixels and the overlap ratio is 60% are 0.055nm and 23nrad, respectively. The RMS and error values ​​meet the test objectives and provide accuracy margin for additional error sources. Therefore, this pair of parameters is initially set as the measurement parameters.

[0080] In step S3 of this embodiment, on the basis of the optimized measurement parameters, when a single-factor multi-level self-calibration splicing measurement simulation is carried out for each additional error source based on the X-ray plane mirror corresponding to the measurement aperture to obtain the errors caused by each additional error source, a single-factor multi-level simulation is performed using the 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 misalignment errors

[0082]

[0083]

[0084] In this embodiment, the amplification coefficients k=0.5, 1, and 2 are set to multiply the basic error level to obtain three levels of error values. Therefore, a total of 30 simulations were performed. Please note that only one additional error parameter exists in all simulations. The RMS error values ​​are listed in columns 3-4 of Table 3. It can be concluded from Table 3 that the contribution of the three motion error levels to the test error is very small compared to the test target (for example, 14pm and 4nrad). This means that the motion stage used in the pre-splicing test system is sufficient to meet the test target. In terms of misalignment error, the three levels of X-axis initial yaw error misalign_yaw_x0 and Y-axis initial pitch error misalign_pitch_y0 also have little effect on the test error, indicating that the X-axis initial yaw error misalign_yaw_x0 and Y-axis initial pitch error misalign_pitch_y0 of the pre-splicing test system are sufficient to meet the test target.

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

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

[0087]

[0088] In the above formula, σ C is the comprehensive error, σ e is the RMS error caused by environmental disturbance under the optimized measurement parameters, σ i is the RMS error caused by the ith additional error source, and n is the number of additional error sources. Based on the above formula, the comprehensive RMS error can be calculated to be 0.0817nm and 42nrad, which meets the test objectives.

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

[0090] When the self-calibration splicing measurement simulation is carried out in step S4 according to the selected optimized measurement parameters and the error control level of each additional error source to obtain the measurement error, the splicing test error is obtained by simulation using the optimized measurement parameters preliminarily determined in step S2 and the control level of the additional error parameters obtained in steps S3 and S4. The simulation test error in this embodiment is as follows: Fig.10 As shown, the RMS error is 0.111nm and 44nrad, which meets the test objectives.

[0091] As an optional implementation, see Figure 1 , before the end and exit in step S4 in this embodiment, it also includes self-consistency verification or mutual inspection verification. If the self-consistency verification or mutual inspection verification passes, it ends and exits; otherwise, more stringent measurement parameters and additional error source control levels are selected and the step S2 is jumped to continue iteration until the accuracy meets the requirements. Among them, self-consistency verification means that the same measured mirror is tested once at the 0 degree position and the position where the measured mirror is rotated 180 degrees, and the detection result at the 180 degree position is rotated 180 degrees and compared with the detection result at the 0 degree position to obtain the measurement error. If the self-consistency verification or mutual inspection verification passes, it ends and exits; otherwise, more stringent measurement parameters and additional error source control levels are selected and the step S1 is jumped to continue iteration until the accuracy meets the requirements. The SUT is a plane x-ray reflector 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 showed that it could meet the test objectives, the motion phase was the same as the preliminary experiments. The error was precisely adjusted and measured as:

[0092] [misalign_yaw_x0=55μrad,

[0093] misalign_pitch_y0=38μrad,

[0094] misalign_pitch_x0=1.3mrad,

[0095] misalign_yaw_y0=10.1mrad],

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

[0097] In order to verify that the method proposed in this embodiment can help determine the test parameters and additional error control levels that ensure test accuracy, experiments were conducted on other test parameters and other control error levels of additional error sources. The measured surface, reference surface, and motion stage are 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 with other test parameters and other controlled error levels for additional error sources yield point-to-point difference plots of the two test results, e.g. Fig.12As shown, the RMS are 0.214nm and 90nrad respectively. Compared with the test error under the test parameters and error control level guided by the method, the test error has increased. Without the guidance of the workflow, the test results may be at risk of insufficient accuracy and fail to meet the test accuracy. The results and verification show that the self-calibration stitching detection method for surface shape errors of X-ray plane mirrors in this embodiment can guide researchers to select appropriate test parameters and the required error control level to meet the specific test accuracy goals of X-ray plane mirrors. Although the error map of the measured surface, the error map of the reference surface and the environmental interference are set as fixed settings in the demonstrated method, the test parameters are set to the overlap rate and the sub-aperture size, and the motion error and alignment error are set as additional error sources. However, the demonstration of the proposed method is not intended to reveal the influence of all error sources and test parameters that affect the test error. However, the self-calibration stitching detection method for surface shape errors of X-ray plane mirrors in this embodiment is open to other additional error sources (such as pixel calibration error, tracing error, CCD mapping distortion, etc.). In addition, the present embodiment is also open to other test parameters such as the randomization degree of sub-aperture division and other test parameter settings of the embedded interferometer. In summary, the present embodiment method proposes a method and system for self-calibration and splicing detection of surface errors of X-ray plane mirrors driven by an error analysis model. The present embodiment 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 reflectors.

[0101] In addition, this embodiment also provides a surface error self-calibration and stitching detection system for an X-ray plane mirror, comprising a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to execute the surface error self-calibration and stitching detection method for an X-ray plane mirror.

[0102] In addition, this embodiment also provides a computer-readable storage medium, which stores a computer program or instruction, and the computer program or instruction is programmed or configured to execute the surface error self-calibration splicing detection method for the X-ray plane mirror through 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 surface error self-calibration splicing detection method for an X-ray plane mirror through a processor.

[0104] Those skilled in the art will appreciate that the technical solutions provided by the embodiments of the present application may be in the form of methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 Steps to define functions in one box or multiple boxes.

[0105] The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A self-calibration and splicing detection method for surface error of an X-ray plane mirror, characterized in that: include: S1. Obtain the measurement requirements of 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 stitching detection of surface errors. The fixed settings refer to parameters that may affect the test accuracy but need to be limited to fixed values ​​due to the target constraints of the method. The measurement parameters affect the test accuracy and their values ​​can be changed in subsequent error analysis simulations. The additional error sources refer to error sources other than environmental interference that can affect the test accuracy, and their control levels can be changed in subsequent error analysis simulations. S2, based on the environmental disturbance error and the fixed setting, setting the additional error source to zero, performing a multi-factor and multi-level self-calibration stitching measurement simulation on the measurement parameters based on the X-ray plane mirror corresponding to the measurement aperture to obtain optimized measurement parameters and corresponding errors; S3, based on the optimized measurement parameters, performing a single-factor multi-level self-calibration stitching measurement simulation on each additional error source based on the X-ray plane mirror corresponding to the measurement aperture to obtain the errors caused by each additional error source, and obtaining the error control level required for each additional error source by calculating the comprehensive error; S4, based on the selected optimized measurement parameters and the error control level of each additional error source, a self-calibration stitching measurement simulation is performed to obtain the measurement error. If the measurement error meets the accuracy requirements, the process ends and exits; otherwise, more stringent measurement parameters and additional error source control levels are selected and the process jumps to step S2 to continue iterating until the accuracy meets the requirements.

2. The surface error self-calibration and splicing detection method for an X-ray plane mirror according to claim 1, characterized in that: The fixed setting in step S1 includes the reference surface error, or the fixed setting in step S1 is the measured surface error and the reference surface error; 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.

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

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

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

7. The surface error self-calibration and splicing detection method for 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 also included. 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 meets the requirements.

8. A self-calibration and splicing detection system for surface error of an X-ray plane mirror, comprising a microprocessor and a memory connected to each other, characterized in that: The microprocessor is programmed or configured to execute the surface error self-calibration and stitching detection method for an X-ray plane mirror as claimed in any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program or instruction stored therein, characterized in that: The computer program or instruction is programmed or configured to execute the surface error self-calibration and splicing detection method for an X-ray plane mirror as claimed in any one of claims 1 to 7 through a processor.

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

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