A high-precision measuring device and method for relative angular vibration of an X-ray double mirror system

Abstract

The application discloses a kind of high-precision measurement device and method of relative angle vibration of X-ray double mirror system.The device includes laser, focusing unit, light splitting unit, reflector, position detection sensor and data processing unit;The light beam output by laser is incident to the double mirror system to be measured through light splitting unit, and reaches reflector by being reflected to first measured mirror and second measured mirror of double mirror system in turn;Reflector is used to reflect incident light beam to double mirror system, and is reflected into light splitting unit by second measured mirror and first measured mirror in turn;The light beam reflected into focusing unit by first measured mirror is incident to focusing unit by light splitting unit, forms parallel light and is incident to position sensitive detector;Position detection sensor is used to generate monitoring image according to received incident light beam and send to data processing unit;Data processing unit is used to obtain the angle vibration result of double mirror system according to monitoring image, parameter and focal length of double mirror system.The application greatly improves the precision of relative angle vibration.

Description

Technical Field

[0001] This invention belongs to the field of optical system technology and relates to a high-precision measurement device and method for relative angular vibration of an X-ray dual-mirror system. Background Technology

[0002] Precision measurement, exemplified by angle measurements, is a crucial component of precision manufacturing and assembly, playing a vital role in the manufacturing and assembly of large optical mirrors. For instance, in the manufacturing and assembly of large optical mirrors, the reflecting mirror of a giant-aperture solar telescope is composed of multiple mirrors assembled together; by detecting displacement and tilt angles, the mirror's position and orientation can be corrected. Angle measurement is widely used in the manufacturing and assembly of mirrors in synchrotron radiation facilities. Synchrotron beamlines contain a large number of optical components. For example, the ID16B beamline of the European Synchrotron Radiation Facility (ESRF) includes a double white beam mirror (DWM) for adjusting the optical path position, a double crystal monochromator (DCM) for converting the light source into the desired monochromatic light, and a Krikpatrick-Baez mirror for focusing. To obtain high-purity spectra, the Shanghai Synchrotron Radiation Facility (SSN) XAFS beamline includes high-harmonic suppression mirrors. For beamlines that can be tens of meters long, even a tiny angular difference can cause a huge shift in the direction of the emitted light or a drastic deviation in the beam effect. Therefore, high-precision angle measurement is of great significance for the assembly and adjustment of optical instruments at synchrotron radiation beamlines.

[0003] Existing commercially available optical angle measurement instruments, such as autocollimators and laser interferometers, are widely used in angle measurement of optical components. For example, the high-precision photoelectric autocollimator ELCOMAT HR produced by MOLLER WEDEL in Germany has a resolution of 0.005 arcseconds and a measurement accuracy of ±0.01 arcseconds within 10 arcseconds. The domestically produced Otmel high-precision photoelectric autocollimator has a resolution of 0.01 arcseconds and a measurement accuracy of 0.1 arcseconds within ±100 arcseconds. Renishaw's XL-80 laser interferometer and Keysight's 5530 laser calibration system, when used with angle-measuring optical components, can also achieve high-precision angle measurements. These instruments are widely used in the assembly and adjustment of beamline optical instruments. For instance, the soft X-ray spectroscopy beamline at the Shanghai Synchrotron Radiation Facility uses an autocollimator to measure the repeatability of the plane mirror and grating rotation angles in an angular plane grating monochromator; the PETRA III third-generation synchrotron radiation source in Germany also uses a laser interferometer to measure the angular vibrations of a single crystal. The principle of autocollimator angle measurement is as follows: Figure 1As shown in (a), after passing through the aperture, beam splitter, and objective lens, light is collimated and projected to infinity. After being reflected by the plane mirror and focused by the objective lens, the image point falls on the plane of the photodetector. By measuring the displacement Δy of the image point on the photodetector, the rotation angle of the reflecting mirror can be calculated. Liu Kai et al. proposed to install the reflecting mirror on the upper mirror to be measured for measurement (refer to Liu Kai, Xue Song, Lu Qipeng et al. Mechanical accuracy analysis and testing of variable-inclusion-angle plane grating monochromator [J]. Nuclear Technology. 2009, 32(12), 881-884). The angle measurement principle of the laser interferometer is as follows: Figure 1 As shown in (b), the light emitted by the laser is split into parallel polarized light (p-ray, corresponding to the thin black line in the figure) and perpendicular polarized light (s-ray, corresponding to the dashed line in the figure) after passing through a polarizing beam splitter. After being reflected twice by a quarter-wave plate and the mirror under test, the polarization state of the light changes, and the light is reflected by a corner prism. After being reflected by the corner prism, the light passes through a quarter-wave plate and the mirror under test again, and the outgoing light is received by a photodetector. Based on the distance between the mirror and the polarizing beam splitter in the angle interferometer, and the change in the position signal received by the signal receiver, the rotation angle of the mirror under test can be calculated. There are also reports in the literature that the mirror under test is mounted on a monochromator for use (see P. Kristiansen, J. Horbach, R. Dohrmannb, et al. Vibration measurements of high-heat-load monochromators for DESY PETRA III extension[J]. J. Synchrotron Rad, 2015, 22, 879-885).

[0004] In synchrotron radiation sources, the aforementioned measurement methods effectively solve the angle measurement problem of a single optical instrument, but they cannot meet the measurement requirements of relative angular vibrations in dual-mirror systems with extremely small relative positional intervals. Paired optical elements are common in synchrotron X-ray source beamlines. For example, paired harmonic suppression mirrors can suppress higher harmonics in monochromatic light generated based on the grating equation and Bragg's formula while ensuring that the propagation direction of the outgoing light is parallel to the incident light; dual-crystal monochromators are also dual-mirror optical devices, and the wavelength of the output light source can be changed by adjusting the orientation of the two crystals; in addition, paired white light mirrors can achieve horizontal or vertical translation of the outgoing light. Furthermore, many dual-mirror structures in X-ray sources are designed very compactly; for example, the maximum adjustable interval between the two mirrors in the harmonic mirror optomechanical design of the High Energy Synchrotron Radiation Source (HEPS) X-ray absorption spectroscopy beamline is only 8 mm. For dual-mirror systems, ensuring that the two optical mirrors are relatively parallel during initial assembly and measuring the relative angular vibrations of the mirrors is essential. Therefore, methods for measuring the relative angular vibrations of dual-mirror systems have attracted widespread attention. Figure 2(a) A dual-mirror system for measuring angular vibration was designed, consisting of a double slit and a CCD camera. A slit was added in front of the autocollimator beam, and two parallel slits were added behind the slit. This caused the outgoing light to become two parallel beams after passing through the collimating objective. One parallel beam did not pass through the mirror under test and was directly received by the CCD camera through the eyepiece, serving as the reference beam. The other parallel beam was reflected by the two mirrors under test and served as the measurement beam. The distance between the light stripes formed by the two beams on the CCD was obtained through image processing, and the relative vibration of the two mirrors was calculated. Figure 2 (b) shows a capacitance sensor measurement method that installs the capacitance sensor between two crystal monochromators and adjusts the distance and parallelism between the two ends of the capacitance sensor to achieve a non-optical angle measurement method.

[0005] Angle measurement solutions based on commercial autocollimators or laser interferometers are quite mature. However, when measuring the angular vibration of a dual-mirror system with a very small mirror spacing, the autocollimator is too large to be directly fixed to one of the mirrors being measured, thus preventing the measurement of the relative rotation of the other mirror. Secondly, the typical exit spot size of an autocollimator is 50mm, while the mirror spacing in a synchrotron X-ray dual-mirror system is usually much smaller than 50mm. The autocollimator beam incident upstream of the beamline will be blocked by the mirrors, preventing it from passing through both mirrors and thus making measurement impossible. Therefore, Figure 2 The measurement method using a double slit and CCD camera shown in (a) improves upon the autocollimator method by using slits to change the shape and size of the collimating light source, thus solving the problem of light obstruction due to two reflections on the measured mirror surface. However, the spacing of the double slits in this scheme needs to be adjusted according to different measured mirrors. Different spacing double slit devices need to be used for different applications, therefore this method cannot simultaneously meet the angle measurement requirements of all dual-mirror systems. Figure 1 (b) The laser interferometer-based angle measurement method requires fixing the angle interferometer and the cornerstone prism to one of the mirrors under test in the dual-mirror system to achieve relative angle measurement. However, installing the angle interferometer in a very small space is extremely difficult. Although small-volume laser interferometers and capacitive sensor-based measurement methods exist, they still require connecting a part of the measuring device to the mirror under test. This contact affects the actual vibration of the mirror, which is detrimental to the measurement. Therefore, there is an urgent need for a relative angle vibration measurement method to achieve the assembly and testing of X-ray close-spaced dual-mirror systems. Summary of the Invention

[0006] To address the technical problems existing in the prior art, the present invention aims to provide a high-precision measurement device and method for the relative angular vibration of X-ray dual-mirror systems. This invention focuses on solving the problem of high-precision measurement of the relative angular vibration of optical components in closely spaced dual-mirror systems used for X-ray imaging in synchrotron radiation beamlines.

[0007] The main contents of this invention include:

[0008] 1. High-precision measurement method for relative angular vibration of X-ray close-interval dual-mirror system.

[0009] 1.1 The device of the present invention consists of a laser with a fixed relative position, a position-sensitive detector (PSD), a plane mirror, and a focusing lens, with the dual-mirror system to be tested placed between the laser and the plane mirror.

[0010] 1.2 This invention can measure the relative angular vibration of a dual-mirror system. When the dual-mirror system is close together (only needing to be larger than the size of the laser beam), angle measurement can also be achieved.

[0011] 1.3 In this invention, the beam emitted by the laser passes through the dual-mirror system twice, which improves the measurement resolution by 4 times.

[0012] 2. Measurement Error Analysis of X-ray Close-Interval Dual-Mirror System

[0013] 2.1 The relationship between the distance between the two mirrors and the measurement error was analyzed, and it was concluded that the larger the distance between the two mirrors, the smaller the error.

[0014] 2.2 The relationship between lens focal length and measurement error was analyzed, and it was concluded that the larger the lens focal length, the smaller the error.

[0015] 2.3 The relationship between the initial tilt angle of the mirror under test and the measurement error was analyzed, concluding that the influence of the initial angle on the measurement has opposite trends in the positive and negative directions. When measuring in the positive direction, the smaller the initial angle, the smaller the error; when measuring in the negative direction, the smaller the initial angle, the larger the error.

[0016] 2.4 The relationship between the position of the dual-mirror system in the measurement system and the measurement error was analyzed, and it was found that the closer the dual-mirror system is to the laser side, the smaller the measurement error.

[0017] 2.5 Based on the analysis results, guide the placement of the dual-mirror system and the selection of optical components in actual measurements to improve measurement accuracy.

[0018] 3. A measurement error correction method based on simplified functions is proposed.

[0019] 3.1 The measurement error of the system is subjected to Taylor expansion to simplify the error expression, correct the measurement error, and improve the measurement accuracy.

[0020] 3.2 Estimate the initial parameters of the measurement system, including the distance between the two mirrors, the focal length of the lens, the initial tilt angle of the mirror under test, and the position of the two mirror system in the measurement system. Substitute these parameters into the simplified error expression to obtain the error function curves under different measurement conditions.

[0021] 3.3 The influence of the estimation errors of four parameters—the distance between the two mirrors, the focal length of the lens, the initial tilt angle of the mirror under test, and the position of the two-mirror system in the measurement system—on the error correction was analyzed.

[0022] 3.4 The impact of errors in the initial tilt angle of the simulated mirror and the position of the dual-mirror system in the measurement system on the accuracy correction is investigated. It is found that when the deviation of these two estimates is within a reasonable range (less than 10% error), the measurement error correction method based on the simplified function can still achieve effective error correction for the measurement system.

[0023] The technical solution of this invention is as follows:

[0024] A high-precision measurement device for relative angular vibration of an X-ray dual-mirror system, characterized in that it includes a laser, a focusing unit, a beam splitting unit, a reflector, a position detection sensor, and a data processing unit; the optical path between the focusing unit and the reflector is the focal length f of the focusing unit;

[0025] The laser beam output from the laser is incident on the dual-mirror system to be measured through the beam splitting unit, and is reflected sequentially by the first and second mirrors under test of the dual-mirror system to reach the reflecting mirror;

[0026] The reflector is used to reflect the incident light beam to the dual-mirror system, and then reflect it sequentially through the second test mirror and the first test mirror into the beam splitting unit;

[0027] The beam splitting unit is used to direct the light beam reflected by the first mirror under test onto the focusing unit, forming parallel light and directing it onto the position-sensitive detector.

[0028] The position detection sensor is used to generate a monitoring image based on the received incident beam and send it to the data processing unit;

[0029] The data processing unit is used to obtain the angular vibration result Δα of the dual-mirror system based on the monitoring image, the parameters of the dual-mirror system, and the focal length f. final .

[0030] Furthermore, the data processing unit first obtains the position offset Δy of the light signal based on the monitoring image, and then calculates the initial relative vibration value between the first and second mirrors under test. Then according to The angular vibration result Δα was obtained. final The error formula Error(Δα) is expanded to f(Δα) at ​​zero using a fourth-order Taylor expansion. The first and second test mirrors are initially parallel and tilted at an angle of θ. D1 is the distance from the first test mirror to the center of the focusing unit, and ΔD is the interval between the first and second test mirrors.

[0031] Furthermore, the closer the dual-mirror system is to the focusing unit, the higher the measurement accuracy.

[0032] Furthermore, the larger the distance ΔD between the first and second mirrors under test, the higher the measurement accuracy.

[0033] Furthermore, the initial tilt angle θ of the first and second mirrors under test has opposite effects on accuracy in the positive and negative directions. When measuring in the positive direction, the smaller θ is, the smaller the error; when measuring in the negative direction, the smaller θ is, the larger the error.

[0034] Furthermore, the larger the focal length f, the higher the measurement accuracy.

[0035] Furthermore, the focusing unit is a convex lens.

[0036] Furthermore, the beam-splitting unit is a beam-splitting prism.

[0037] An angle vibration measurement method based on a high-precision relative angle vibration measurement device of the aforementioned X-ray dual-mirror system includes the following steps:

[0038] 1) Place the dual-mirror system to be measured between the beam splitter and the reflector, measure the monitoring image of the dual-mirror system in its initial state, and send it to the data processing unit;

[0039] 2) Acquire the monitoring image of the dual-mirror system at the current moment and send it to the data processing unit;

[0040] 3) The data processing unit calculates the initial relative vibration values ​​between the first and second mirrors under test based on the positional offset Δy of the light signal in the monitored image and the focal length f. Then according to The angular vibration result Δα was obtained. final The error formula Error(Δα) is expanded to f(Δα) at ​​zero using a fourth-order Taylor expansion. The first and second test mirrors are initially parallel and tilted at an angle of θ. D1 is the distance from the first test mirror to the center of the focusing unit, and ΔD is the interval between the first and second test mirrors.

[0041] The advantages of this invention are as follows:

[0042] This patent proposes a method for measuring the relative angle of an X-ray dual-mirror system, solving the problem of relative angle measurement in closely spaced dual-mirror structures. It avoids the issue of wide-beam collimating light sources being unable to pass through the narrow slits of the closely spaced mirrors, and the problem of measurement components such as reflectors and capacitive sensors coming into contact with the mirror under test, causing the measurement results to not fully reflect the relative vibration of the two mirrors. This method is also universally applicable to general dual-mirror structures. Furthermore, this patent performs error analysis on the measurement method, correcting fundamental errors in the measurement principle by simplifying the error function, thus achieving high-precision angle measurement of dual-mirror structures. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the angle measurement principle.

[0044] (a) Schematic diagram of angle measurement principle of autocollimator, (b) Schematic diagram of angle measurement principle of laser interferometer.

[0045] Figure 2 Diagram of a dual-mirror angle measurement system;

[0046] (a) Schematic diagram of the dual-slit and CCD camera dual-mirror angle measurement system, (b) Schematic diagram of the capacitive sensor dual-mirror angle measurement system.

[0047] Figure 3 This is a schematic diagram of the measurement principle of an X-ray close-spaced dual-mirror system.

[0048] Figure 4 This is a diagram of the optical propagation path.

[0049] Figure 5 This is a flowchart of the measurement process.

[0050] Figure 6 The figure shows the simulation results of the error varying with Δα;

[0051] (a) Relationship between error and the distance between the tested mirrors; (b) Relationship between error and the focal length of the lens.

[0052] (c) Relationship between error and initial tilt angle of the mirror under test, (d) Relationship between error and placement of the mirror under test.

[0053] Figure 7 The graph shows the effect of the error in the value of D1 on f(Δα) within the range of -0.1 to 0.1 rad.

[0054] (a) The values ​​of f are different, and (b) The values ​​of θ are different.

[0055] Figure 8 The effect of the error in the value of ΔD within the range of -0.1 to 0.1 rad on f(Δα);

[0056] (a) The values ​​of f are different, and (b) The values ​​of θ are different.

[0057] Figure 9 The effect of the error in the value of θ within the range of -0.1 to 0.1 rad on f(Δα);

[0058] (a) The values ​​of f are different, (b) The values ​​of θ are different, (c) The values ​​of D1 are different, and (d) The values ​​of ΔD are different.

[0059] Figure 10 The effect of the error in the value of f within the range of -0.1 to 0.1 rad on f(Δα);

[0060] (a) The values ​​of f are different, (b) The values ​​of θ are different, (c) The values ​​of D1 are different, and (d) The values ​​of ΔD are different.

[0061] Figure 11 The simulation results are for groups one through six in Table 1;

[0062] (a) Simulation results of Group 1, (b) Simulation results of Group 2, (c) Simulation results of Group 3, (d) Simulation results of Group 4, (e) Simulation results of Group 5, (f) Simulation results of Group 6. Detailed Implementation

[0063] The present invention will now be described in further detail with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0064] This patent designs a measurement method for an X-ray close-range dual-mirror system, the measurement principle diagram is as follows: Figure 3 As shown, the measuring device consists of a laser, a convex lens, a beam splitter, a plane mirror, and a position sensor (PSD). The first and second mirrors under test form a dual-mirror system, and the relative angular vibration between them is the angular vibration of the dual-mirror system under test. Before starting the measurement, to improve the measurement accuracy, the components need to be selected and placed according to certain requirements. First, the lens focal length f is selected, based on the measurement range of the PSD, i.e., the maximum value of Δy. maxSubstituting into formula (7), the range of the measured angle Δα can be derived. The larger f is, the smaller the angle measurement range. According to the description in 2.2, the larger f is, the smaller the measurement error. Therefore, within the range that meets the angle measurement requirements, considering the space for component placement, a lens with the largest possible focal length should be selected. Secondly, after the lens focal length f is determined, the distance from the virtual focusing lens to the plane mirror, that is, the distance from the focusing lens to the beam splitter and the distance from the beam splitter to the plane mirror, is then determined to be f. Then, according to 2.4, for the dual-mirror system under test, the dual-mirror system consisting of the first and second mirrors under test should be placed close to the beam splitter within the space where it can be placed, and the beam splitter should be placed close to the focusing lens within the space where it can be placed, so that the distance from the dual-mirror system to the focusing lens is as small as possible. Then, if the distance between the first and second mirrors under test in the dual-mirror system is not adjustable, the dual-mirror system is directly placed into the measurement optical path; otherwise, the distance ΔD between the first and second mirrors under test needs to be adjusted and increased as much as possible while meeting the usage requirements. Finally, adjust the laser beam to be perpendicular to the plane mirror, the PSD to be parallel to the focusing lens, and the beam to fall on the center of the PSD. For example... Figure 3 As shown, except for the dual-mirror system, the components constituting the measuring device are fixed in relative positions. The optical propagation path is as follows: Figure 4 As shown, the light beam emitted by the laser passes through a beam splitter, is reflected by the first and second test mirrors at points A and B, respectively, and then reaches a plane mirror. The plane mirror reflects the light again, which is then reflected by the first and second test mirrors at points D and E, respectively. The outgoing light is reflected by the beam splitter to the focusing lens, forming parallel light, and finally received by the PSD position-sensitive detector. If there is no angular vibration, A and E coincide, B and D coincide, the beam falls on the center of the PSD, and Δy equals 0.

[0065] Measurement process as follows Figure 5 As shown, the initial value Δα of the relative angular vibration is calculated based on the position offset Δy of the light signal detected by the PSD in the measuring device and the focal length f of the focusing lens. Error analysis is performed on the measuring device to obtain a complete and complex error calculation function, as shown in formula (23), denoted by Error. Taylor expansion is performed on the complex error calculation result (formula (23)) to obtain a simplified cubic function, as shown in formula (25), denoted by f(Δα). Based on the lens focal length f, the parameters of each component of the dual-mirror system, including the positions D1 and D2 of the dual-mirror system in the coordinate system, the distance ΔD between the two mirrors, and the initial tilt angle θ of the mirrors, can all be obtained in advance through calibration or measurement. Substituting into the simplified cubic function f(Δα), the correction value f(Δα) at ​​the initial value Δα is obtained. The initial measurement value Δα is corrected to obtain the final angular vibration result Δα. final .

[0066] according to Figure 5The measurement principle of this measuring device, as well as the error analysis and correction method, are key to obtaining high-precision relative angular vibration of the dual-mirror system.

[0067] 4.1 Measurement Principle

[0068] World coordinate system definition as follows Figure 3 As shown, the y-axis points vertically upwards, and the z-axis aligns with the direction of the laser beam output. The origin of the coordinate system is at the center O of the virtual focusing lens. The virtual focusing lens and PSD are rotationally symmetrical with respect to the real focusing lens and PSD about the beam splitter. The incident light V... in The normal vector is [0 0 1]. T Initially, the first and second mirrors are parallel, and after rotating by an angle θ around the x-axis, their normal vectors are:

[0069]

[0070] Let the vibration angle of the first test mirror around the x-axis be α1, the vibration angle of the second test mirror around the x-axis be α2, and the vibration angle relative to the first test mirror around the x-axis be Δα.

[0071] α2-α1=Δα (2)

[0072] Then, the normal vectors of the first and second mirrors under test are as shown in formula (3). Furthermore, the normal vector of the plane mirror is [0 0 -1]. T .

[0073]

[0074] If the normal vector of the mirror is [α β γ] T The transfer matrix of the light reflection process by the plane mirror is expressed as:

[0075]

[0076] Let the transfer matrices of the first mirror under test, the second mirror under test, and the plane mirror be M, respectively. m1 M m2 、and M m The incident light rays pass through the first and second test mirrors, then to the plane mirror, and are reflected back to the second and first test mirrors. The reflection transmission matrix after five reflections is as follows:

[0077]

[0078] The normal vector V of the ray L6 emitted to the focusing lens L6 for:

[0079] V L6 =M5V in =[0 -sin(4Δα) -cos(4Δα)]T (6)

[0080] The outgoing light normal vector rotates about the x-axis by -4Δα relative to the incident light. The plane mirror is located at the position of the lens imaging and is a distance f from the lens. Therefore, the relative vibration Δα between the first and second mirrors under test satisfies formula (7). This method can improve the measurement resolution by 4 times.

[0081]

[0082] 4.2 Error Analysis

[0083] This patent analyzes measurement errors. The process is as follows: Figure 5 As shown in the dashed box, firstly, based on the equations of light rays and the plane equation of the mirror, the coordinates of the reflection points A, B, C, D, and E of the plane mirror in steps 1 to 5 are calculated. Then, the actual coordinate position P of the light received by the PSD in step 6 is calculated. Finally, the error is calculated. The direction vector V of the light rays L1, L2, L3, L4, L5, and L6 is also shown. in V L2 V L3 V L4 V L5 V L6 Represented as:

[0084]

[0085] Given that the normal vectors of the first and second mirrors under test are V1 and V2 respectively, and the distance from the plane mirror to the origin is f, the plane equations of the first and second mirrors under test and the plane mirror are constructed as shown in formula (9). Let D1 and D2 represent the distances from the first and second mirrors under test to the origin O (the center of the focusing lens).

[0086]

[0087] Step 1: Solve the equations of the straight line L1 and the plane of the first mirror being measured, plane1, to obtain the coordinates of point A, P. A [P AX P AY P AZ ] T .

[0088] The equation of the initial ray L1 is expressed as formula (10), and the result of combining the equations is shown in formula (11).

[0089]

[0090]

[0091] Step 2: Solve the equations of the straight line of ray L2 and the plane of the second measured mirror, plane2, to obtain the coordinates of point B, P. B [P BX P BY P BZ ] T The equation of the line L2 is expressed as formula (12), and the result of solving the equation simultaneously is shown in formula (13).

[0092]

[0093]

[0094] Step 3: Solve the equations of the linear ray L3 and the plane of the plane mirror (plane3) to obtain the coordinates of point C (P). C [P CX P CY P CZ ] T The equation of line L3 is expressed as formula (14), and the result of solving the equation simultaneously is shown in formula (15).

[0095]

[0096]

[0097] Step 4: Combine the equations of the linear ray L4 and the plane of the second measured mirror (plane2) to obtain the coordinates of point D (P). D [P DX P DY P DZ ] T The equation of line L4 is expressed as formula (16), and the result of solving the equation simultaneously is shown in formula (17).

[0098]

[0099]

[0100] Step 5: Combine the equations of the linear ray L5 and the plane of the first measured mirror (plane1) to obtain the coordinates of point E (P). E [P EX P EY P EZ ] T The equation of line L5 is expressed as formula (18), and the result of solving the equation simultaneously is shown in formula (19).

[0101]

[0102]

[0103] Step 6: Combine the equations of ray L6 with those of the XY plane to obtain the coordinates of point P.X P Y P Z ] T The equation of line L6 is expressed as formula (20), and the result of solving the equation simultaneously is shown in formula (21).

[0104]

[0105]

[0106] make

[0107]

[0108] Where ΔD represents the double-mirror interval, then P y The complete expression is as follows:

[0109]

[0110] Step 7: Calculate the measurement error, as shown in formula (23). According to formula (22) and formula (23), it can be seen that the measurement error is related to D1, ΔD, f, and θ. These four parameters correspond to the placement position of the dual-mirror system, the distance between the two mirrors, the focal length, and the initial tilt angle, respectively.

[0111]

[0112] To more intuitively illustrate the error analysis, Δα is represented by 100 points at equal intervals from -0.1 to 0.1 rad. Figure 6 The results of the error analysis are presented, from Figure 6 As can be seen, the measurement error increases with the increase of the absolute value of Δα. Figure 6 In (a), D1 is taken as 400 mm, θ as 0.007 rad, and f as 2000 mm. The figure shows the error results for ΔD ranging from 5 mm to 505 mm in 100 mm intervals. Figure 6 As can be seen from (a), the larger ΔD is, that is, the larger the distance between the two mirrors, the smaller the measurement error. Figure 6 In (b), D1 is taken as 400 mm, ΔD as 5 mm, and θ as 0.007 rad. The figure shows the error results for f ranging from 1000 mm to 2000 mm in 200 mm intervals. Figure 6 As can be seen from (b), the larger the focal length f of the lens, the smaller the error. Figure 6 In (c), D1 is 400 mm, ΔD is 5 mm, and f is 2000 mm. The figure shows the error results for θ ranging from 0.007 rad to 0.057 rad, with an interval of 0.01 rad. Figure 6As can be seen in (c), the influence of the initial angle θ on the measurement error has opposite trends when Δα is positive or negative. When Δα is positive, the angle measurement error increases with the increase of θ, and when Δα is negative, it decreases with the increase of θ. Figure 6 As can be seen from (d), with ΔD = 5 mm, θ = 0.007 rad, and f = 2000 mm, the figure shows the error results for D1 ranging from 400 mm to 900 mm in 100 mm increments. Figure 6 As can be seen from (d), the smaller D1 is, the smaller the distance between the dual-mirror system and the virtual lens, and the smaller the error. Therefore, when using this device to measure the angular vibration of a dual-mirror structure, if the distance between the first and second mirrors under test in the dual-mirror system is adjustable, within the range that meets the usage requirements, in order to improve the measurement accuracy, it is necessary to try to increase the distance between the two mirrors, increase the focal length of the lens, and bring the dual-mirror system under test closer to the lens end.

[0113] 4.3 Error Correction

[0114] To further improve measurement accuracy, this patent proposes an error correction method based on simplified function fitting. The fourth-order Taylor expansion of the error formula (24) at zero is obtained as follows:

[0115]

[0116] R n The higher-order terms are negligible. Therefore, a cubic function can be used to simplify the complex error expression. If D1, ΔD, f, and θ are known before measurement, the measurement results can be corrected, thereby reducing the measurement error. For a two-mirror system to be measured, the selected lens f is known, the distance L from the first mirror to the lens is easy to measure, and usually, the initial angle θ between the mirror and the XZ plane and the distance ΔD between the two mirrors are known. Therefore, the parameters of D1 and D2 can be estimated.

[0117]

[0118] Therefore, the measurement results are corrected as follows:

[0119]

[0120] In this correction method, the errors in the values ​​of D1, ΔD, f, and θ affect the accuracy of the measurement results. The partial derivatives of f(Δα) in formula (25) with respect to D1, ΔD, f, and θ are calculated respectively, and the results are as follows. Formulas (28) to (31) represent the influence of the differences in the values ​​of D1, ΔD, f, and θ on the error.

[0121]

[0122]

[0123]

[0124]

[0125] Figure 7 The function curve of formula (28) is shown to illustrate the effect of the error in the value of D1 on the correction accuracy. Figure 7 In (a), the different line curves represent the results with θ = 0.007 rad and f = 1000 mm to 2000 mm, with an interval of 200 mm. Figure 7 (b) shows the results of different line types with f = 2000 mm and θ = 0.007 rad to 0.057 rad, with an interval of 0.01 rad. When the parameters θ and f are determined, the influence of D1 on the error is only related to Δα, and the error increases with the increase of the absolute value of Δα. The overall influence of D1 on the error is relatively small.

[0126] Figure 8 The function curve of formula (29) is shown to illustrate the effect of the error in the value of ΔD on the accuracy of the correction. Figure 8 In (a), the different line curves represent the results with θ = 0.007 rad and f = 1000 mm to 2000 mm, with an interval of 200 mm. Figure 8 (b) shows the results of different line types where f is 2000 mm and θ is 0.007 rad to 0.057 rad, with an interval of 0.01 rad. When the parameters θ and f are determined, the influence of ΔD on the error is only related to Δα, and the error decreases as the absolute value of Δα increases. The overall influence of ΔD on the error is relatively small.

[0127] Figure 9 The function curve of formula (30) is shown to illustrate the effect of the error in the value of θ on the correction accuracy. Figure 9 In (a), the different line type curves represent the results when θ is 0.007 rad, D1 is 400 mm, ΔD is 5 mm, and f is 1000 mm to 2000 mm with an interval of 200 mm. Figure 9 (b) The different line type curves represent the results when f is 2000 mm, D1 is 400 mm, ΔD is 5 mm, and θ is 0.007 rad to 0.057 rad, with an interval of 0.01 rad. The six curves in the figure almost overlap. Figure 9 (c) shows the results of different line type curves with f = 2000 mm, ΔD = 5 mm, θ = 0.007 rad, and D1 = 400 mm to 900 mm with an interval of 100 mm. Figure 9 (d) shows the results of different line types where f is 2000 mm, θ is 0.007 rad, D1 is 400 mm, and ΔD ranges from 5 mm to 505 mm in 100 mm intervals. From formula (30) and... Figure 9 As can be seen, the effect of θ on the error is approximately a linear curve, monotonically increasing. The slope varies with the values ​​of D1, ΔD, and f, but it is not sensitive to θ.

[0128] Figure 10 The function curve of formula (31) is shown to illustrate the effect of the error in the value of f on the correction accuracy. Figure 10 In (a), the different line type curves represent the results when θ is 0.007 rad, D1 is 400 mm, ΔD is 5 mm, and f is 1000 mm to 2000 mm with an interval of 200 mm. Figure 10 (b) shows the results of different line types with f = 2000 mm, D1 = 400 mm, ΔD = 5 mm, and θ = 0.007 rad to 0.057 rad, with an interval of 0.01 rad. Figure 10 (c) shows the results of different line type curves with f = 2000 mm, ΔD = 5 mm, θ = 0.007 rad, and D1 = 400 mm to 900 mm with an interval of 100 mm. Figure 10 (d) shows the results of different line types where f is 2000 mm, θ is 0.007 rad, D1 is 400 mm, and ΔD ranges from 5 mm to 505 mm in 100 mm intervals. From formula (30) and... Figure 9 As can be seen from this, the influence of f on the error is related to a variety of factors, and the error decreases as the absolute value of Δα increases.

[0129] To more intuitively demonstrate the effect of the cubic function fitting method on improving accuracy, six different sets of values ​​for D1, ΔD, f, and θ were simulated, as shown in Table 1. These six sets of values ​​include several combinations of two-mirror systems. Table 1 also provides the estimated values ​​for D1 and θ. The error between D1 and θ is 10%, which is taken as positive. The estimated values ​​of f and ΔD are considered accurate. The actual values ​​and estimated values ​​are shown in Table 1. The results of the error estimation equations for these six sets of values ​​are as follows: Figure 11 As shown, Figures (a) to (f) correspond to respectively Figure 6 The results for the six groups are shown in the diagram. The thin solid line represents the actual measurement error, and the dotted line represents the error based on the results obtained using data with errors. The prediction errors of f and θ based on cubic function fitting are shown, with the thick solid line representing the corrected error. The average actual errors for groups one through six within the range of Δα from -0.1 to 0.1 rad are 4.242, 4.241, 4.081, 14.874, 14.872, and 14.552 mrad, respectively. The average corrected errors are 0.230, 0.229, 0.236, 0.803, 0.802, and 0.816 mrad, representing reductions of 4.013, 4.012, 3.845, 14.072, 14.070, and 13.736 mrad, respectively. Figure 11 As shown, even if there are reasonable deviations in the estimates of D1 and θ, this method can still achieve a good correction effect.

[0130] Table 1 shows the actual and estimated values ​​of D1, D2, f, and θ for 6 groups.

[0131]

[0132] Although specific embodiments of the invention have been disclosed for illustrative purposes to aid in understanding and implementing the invention, those skilled in the art will understand that various substitutions, variations, and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the content disclosed in the preferred embodiments, and the scope of protection claimed by the invention is defined by the claims.

Claims

1. A high-precision measuring device for the relative angular vibration of an X-ray dual-mirror system, characterized in that, It includes a laser, a focusing unit, a beam-splitting unit, a reflector, a position detection sensor, and a data processing unit; the optical path between the focusing unit and the reflector is the focal length of the focusing unit. f ; The laser beam output from the laser is incident on the dual-mirror system to be measured through the beam splitting unit, and is reflected sequentially by the first and second mirrors under test of the dual-mirror system to reach the reflecting mirror; The reflector is used to reflect the incident light beam to the dual-mirror system, and then reflect it sequentially through the second test mirror and the first test mirror into the beam splitting unit; The beam splitting unit is used to direct the light beam reflected by the first mirror under test onto the focusing unit, forming parallel light and directing it onto the position detection sensor; The position detection sensor is used to generate a monitoring image based on the received incident beam and send it to the data processing unit; The data processing unit is used to process the monitored image, the parameters of the dual-mirror system, and the focal length. f The angular vibration result Δ of the dual-mirror system was obtained. α final ; The data processing unit first obtains the position offset Δ of the light signal based on the monitoring image. y Then, the initial relative vibration value Δ between the first and second mirrors under test is calculated. α Then according to Δ α final The angular vibration result Δ is obtained. α final Among them, the error formula Error (Δ α A fourth-order Taylor expansion at zero point yields... The error formula , The first and second mirrors under test are initially parallel and tilted at an angle of _____. θ , D 1 represents the distance from the first mirror under test to the center of the focusing unit, and Δ represents the distance from the first mirror under test to the center of the focusing unit. D The interval between the first and second mirrors under test.

2. The apparatus according to claim 1, characterized in that, The closer the dual-mirror system is to the focusing unit, the higher the measurement accuracy.

3. The apparatus according to claim 1, characterized in that, The distance Δ between the first and second mirrors under test D The larger the value, the higher the measurement accuracy.

4. The apparatus according to claim 1, characterized in that, Initial tilt angles of the first and second test mirrors θ The effects of positive and negative directions on accuracy have opposite trends. When measuring in the positive direction, θ The smaller the value, the smaller the error; when measuring in the negative direction, θ The smaller the value, the greater the error.

5. The apparatus according to claim 1, characterized in that, The focal length f The larger the value, the higher the measurement accuracy.

6. The apparatus according to claim 1, characterized in that, The focusing unit is a convex lens.

7. The apparatus according to claim 1, characterized in that, The beam-splitting unit is a beam-splitting prism.

8. An angle vibration measurement method based on the high-precision relative angle vibration measurement device of the X-ray dual-mirror system according to claim 1, comprising the following steps: 1) Place the dual-mirror system to be measured between the beam splitter and the reflector, measure the monitoring image of the dual-mirror system in its initial state, and send it to the data processing unit; 2) Acquire the monitoring image of the dual-mirror system at the current moment and send it to the data processing unit; 3) The data processing unit adjusts the position offset Δ of the light signal in the monitored image. y and focal length f The initial relative vibration value Δ between the first and second mirrors under test was calculated. α Then according to Δ α final The angular vibration result Δ is obtained. α final Among them, the error formula Error (Δ α A fourth-order Taylor expansion at zero point yields... The error formula , The first and second mirrors under test are initially parallel and tilted at an angle of _____. θ , D 1 represents the distance from the first mirror under test to the center of the focusing unit, and Δ represents the distance from the first mirror under test to the center of the focusing unit. D The interval between the first and second mirrors under test.

9. The method according to claim 8, characterized in that, The focusing unit is a convex lens, the beam splitting unit is a beam splitting prism, and the reflecting mirror is a plane reflecting mirror.

Images