A frequency division splicing interferometer

Abstract

This invention discloses a frequency-division splicing interferometer, characterized by comprising a multi-dimensional displacement stage, a mirror-to-be-tested attitude adjustment mechanism, an interferometer, two angle measuring devices, and a data processing unit; the interferometer, angle measuring devices, and mirror-to-be-tested attitude adjustment mechanism are located on the multi-dimensional displacement stage; the interferometer is used to acquire the surface shape of each sub-aperture of the mirror under test and send it to the data processing unit; the data unit is used to splice the surface shapes of each sub-aperture of the mirror under test to obtain the mirror surface shape h(x,y), perform low-pass filtering on h(x,y), and take a line in the filtered surface shape that satisfies y=y1; the first angle measuring device is used to translate along the y=y1 line to measure the slope of the low spatial frequency surface shape of the mirror under test and send it to the data processing unit; the second angle measuring device is used to monitor the motion angle of the first angle measuring device and send the monitoring data to the data processing unit; the data processing unit is used to calculate the two-dimensional surface shape of the mirror under test.

Description

Technical Field

[0001] This invention belongs to the fields of optical processing and testing, and synchrotron radiation optics, and specifically relates to a frequency-division splicing interferometer. Background Technology

[0002] In the field of synchrotron radiation, high-precision optical components are essential for the high-fidelity transmission of synchrotron radiation light. my country's fourth-generation synchrotron radiation facility, currently under construction, is the world's highest-performing synchrotron radiation facility, placing extremely high demands on the surface precision of optical components and on optical processing and testing. Reflectors, as one of the most important optical components in synchrotron radiation, are elongated in shape, such as... Figure 1 As shown, the length is usually 100 millimeters, and some are about 1 meter long.

[0003] Currently available surface shape inspection equipment, both domestically and internationally, such as large-aperture interferometers (hundreds of millimeters in diameter), can measure the surface shape of a large-sized mirror in a single measurement. However, large-aperture interferometers have low spatial resolution, which cannot meet the high-precision inspection requirements of X-ray mirrors. Small-aperture interferometers (commonly 6 inches and below) have high spatial resolution. Although they cannot obtain the surface shape of a large-sized mirror in a single measurement, they can measure the surface shape of multiple sub-apertures and stitch the measurement results together. In addition to stitching interferometers based on different methods, commonly used surface shape inspection equipment for X-ray mirror surface shape inspection includes various types of NOM (nanometer measurement instruments) and LTP (long-range surface shape analyzers).

[0004] Currently, high-precision detection of one-dimensional planes and one-dimensional curved surfaces of X-ray mirrors has been achieved both domestically and internationally, as well as high-precision detection of two-dimensional planes. However, high-precision detection of two-dimensional curved surfaces has not yet been solved and remains a global challenge. The difficulty lies in achieving high stability of the experimental system and eliminating system errors.

[0005] The two-dimensional curved surface detection of X-ray mirrors uses various splicing interferometers based on different methods. (1) Systematic errors in the interferometer: The reference mirror of the interferometer has surface shape error. When the reference mirror and the mirror under test are mismatched, there will be low-frequency backhaul error, which makes the beam reflected from the mirror under test unable to return along the original path. Therefore, the surface shape measured by the interferometer is not accurate enough at low spatial frequencies, but the surface shape at medium and high spatial frequencies is accurate. (2) Existing splicing interferometer technology at home and abroad and its problems: In traditional splicing interferometers, the relative attitude between sub-apertures is determined by the surface shape of the overlapping area. However, this traditional method will cause systematic errors to accumulate gradually during the splicing process, regardless of whether it is averaged. Whether the method used to homogenize the impact of reference mirror error or to remove the surface shape error of the reference mirror through absolute calibration, low-frequency backhaul error still cannot be eliminated and will continue to accumulate. RADSI at Osaka University in Japan introduced another reference mirror and used an interferometer to measure the attitude between adjacent sub-apertures, but it has extremely high requirements for the stability of the experimental setup and has not eliminated low-frequency backhaul error. There is also a type of ASI stitching interferometer based on angle measurement, which uses an angle measuring instrument to measure the attitude of adjacent sub-apertures, but the data within a sub-aperture uses the same angle information, which also does not solve the low-frequency backhaul error problem. Summary of the Invention

[0006] To address the technical problems existing in the prior art, the present invention aims to provide a frequency division and splicing interferometer, which consists of five main components: an interferometer, two angle measuring devices, a set of attitude adjustment mechanism for the mirror under test, a set of multidimensional displacement stage, and a data processing unit.

[0007] An interferometer is used to acquire the surface shape of each sub-aperture of the mirror under test. A first angle measuring device is used to acquire the surface slope of the mirror under test at low spatial frequencies. By combining this data with the interferometer data, the low-frequency backlash error present in the interferometer can be eliminated. A second angle measuring device is used to monitor the movement of the first angle measuring device during the measurement of the surface slope. The measured motion angle information of the first angle measuring device is returned to the data processing unit to compensate for any deviations from the linear motion of the first angle measuring device, thereby eliminating the motion angle error present in the measurement process. A mirror under test attitude adjustment mechanism can adjust the mirror under test to translate in the y-direction, rotate in the xy-plane, and rotate in the yz-plane. A multi-dimensional displacement stage integrates the various sub-components of the frequency division interferometer. The main motion dimensions are: the first translational sub-stage 1 and the second translational sub-stage 2 translate in the x-direction, the third translational sub-stage 3 translates in the z-direction, and the rotational sub-stage 4 rotates in the xz plane. Specifically, the first translational sub-stage 1 supports one interferometer, the second translational sub-stage 2 supports the first angle measuring device, the third translational sub-stage 3 supports the second angle measuring device, and the rotational sub-stage 4 supports the mirror under test and its attitude adjustment mechanism. Figure 2 As shown.

[0008] The technical solution of this invention is as follows:

[0009] A frequency division and splicing interferometer, characterized in that it includes a multi-dimensional displacement stage, a mirror attitude adjustment mechanism, an interferometer, two angle measuring devices, and a data processing unit; the interferometer, angle measuring devices, and mirror attitude adjustment mechanism are located on the multi-dimensional displacement stage;

[0010] The multidimensional displacement stage is used to control the interferometer and the first angle measuring device to translate in the x direction, control the second angle measuring device to adjust translation in the z direction, and control the mirror under test to rotate in the xz plane; the x direction is parallel to the surface shape of the mirror under test, the x, y, and z directions are perpendicular to each other, the normal direction of the center of the mirror under test is the z direction, and the plane containing the x and z directions is the xz plane;

[0011] The attitude adjustment mechanism of the mirror under test is used to adjust the mirror under test to translate in the y direction, rotate in the xy plane, and rotate in the yz plane;

[0012] The interferometer is used to acquire the surface shape of each sub-aperture of the mirror under test and send it to the data processing unit; the data unit is used to stitch together the surface shapes of each sub-aperture of the mirror under test to obtain the mirror surface shape h(x,y), perform low-pass filtering on h(x,y) according to a set spatial frequency a, and take a line F in the filtered surface shape that satisfies y = y1. 1a (x);

[0013] The first angle measuring device is used to translate along the line y=y1 to measure the low spatial frequency surface slope of the mirror under test and send it to the data processing unit;

[0014] The second angle measuring device is used to monitor the motion angle of the first angle measuring device and send the monitoring data to the data processing unit;

[0015] The data processing unit removes the motion angle error present in the measurement process of the first angle measuring device based on the monitoring data, and obtains the line F. 1a The slope of the surface shape (x) without motion angle error is low-pass filtered according to the set spatial frequency a to obtain the filtered surface shape L. 1a (x); then calculate the surface shape difference δ. 1a (x)=F 1a (x)-L 1a (x), let (x) be any coordinate point (x,y) on the mirror surface h(x,y). i ,y j The surface shape value h(x) at point ) i ,y j ) and δ 1a (x) have the same x-coordinate x i δ at the surface shape 1a (x i Subtracting the two values, we obtain the coordinates of the point (x,y) in the two-dimensional surface shape hC(x,y) of the mirror under test. i ,y j The surface shape value hC(x) at point ) i ,y j )=h(x i ,y j )-δ 1a (x i ).

[0016] Furthermore, from the surface shape after low-pass filtering of h(x,y), a line F of y = y2 is also selected. 2a (x); After adjusting the mirror under test to translate along the y-direction using the mirror under test attitude adjustment mechanism, the first angle measuring device translates along the y = y2 line to measure the low spatial frequency surface slope of the mirror under test and sends it to the data processing unit; the data processing unit removes the motion angle error present in the measurement process of the first angle measuring device based on the corresponding monitoring data to obtain the line F. 2a The slope of the surface shape (x) without motion angle error is low-pass filtered according to the set spatial frequency a to obtain the filtered surface shape L. 2a (x); then, following steps 21) to 23), the two-dimensional surface shape hC(x,y) of the mirror to be tested is generated:

[0017] 21) Let L1a (x) minus F 1a (x), perform a linear function fit on the obtained difference to obtain the first fitting result, and then L 1a The difference between (x) and the first fitting result is denoted as LC. 1a (x); Let L 2a (x) minus F 2a (x), perform a first-order function fitting on the obtained difference to obtain the second fitting result, and then L 2a The difference after subtracting the second fitting result from (x) is denoted as LC. 2a (x);

[0018] 22) Calculate δ 1a (x)=F 1a (x)-LC 1a (x), δ 2a (x)=F 2a (x)-LC 2a (x); then, perform a linear fit on the difference values ​​of the two surfaces corresponding to the same x-coordinate on the mirror surface to obtain the coefficient of the first term.

[0019] and zero-order coefficient

[0020] 23) Based on the fitting results, obtain the coordinates (x,y) of any point in the two-dimensional surface shape hC(x,y) of the mirror under test. i ,y j The surface shape value hC(x) at point ) i ,y j )=h(x i ,y j )-[k(x i )*y j +b(x i )];in, For δ 1a (x) x-coordinate i The surface shape difference value at the location, For δ 2a (x) x-coordinate i The surface shape difference value at the location.

[0021] Furthermore, N lines F are selected from the surface shape after low-pass filtering of h(x,y). 1a (x), F 2a (x), ..., F Na(x); After adjusting the mirror under test along the y-direction using the mirror under test attitude adjustment mechanism, the first angle measuring device measures the low spatial frequency surface slope of the mirror under test along each line and sends it to the data processing unit; the data processing unit removes the motion angle error present in the measurement process of the first angle measuring device according to the corresponding monitoring data, obtains the surface slope of each line without motion angle error, and performs low-pass filtering on it according to the set spatial frequency a, and the filtered surface is denoted as L. 1a (x), L 2a (x), ..., L Na (x); where L Na (x) represents the filtered surface shape corresponding to the nth line; then, following steps 31) to 33), the two-dimensional surface shape hC(x,y) of the mirror under test is generated:

[0022] 31) Let L na (x) minus F na (x), perform a linear function fit on the obtained difference to obtain the nth fitting result, and then L na The difference between (x) and the nth fitting result is denoted as LC. na (x);

[0023] 32) Calculate the surface shape difference value δ corresponding to the same abscissa. na (x)=F na (x)-LC na (x), n = 1 to N;

[0024] 33) Interpolate the surface shape difference values ​​obtained in step 32), using the same interpolation function for different ordinates under the same abscissa; then subtract the interpolation function from the surface shape h(x,y) to generate the two-dimensional surface shape hC(x,y) of the mirror to be tested.

[0025] Furthermore, the spatial frequency a satisfies the following: 1 / a must be greater than the beam spot diameter of the first angle measuring device and less than the surface stitching step of the sub-aperture.

[0026] Furthermore, the multidimensional displacement stage includes a first translational sub-displacement stage 1, a second translational sub-displacement stage 2, a third translational sub-displacement stage 3, and a rotational sub-displacement stage 4; the first translational sub-displacement stage 1 is used to support the interferometer, the second translational sub-displacement stage 2 is used to support the first angle measuring device, the third translational sub-displacement stage 3 is used to support the second angle measuring device, and the rotational sub-displacement stage 4 is used to support the mirror to be measured.

[0027] Furthermore, the line F 1a (x) represents the midline of the mirror surface to be tested.

[0028] The advantages of this invention are as follows:

[0029] The frequency-division stitching interferometer of this invention not only perfectly solves the world-class problem of high-precision detection of two-dimensional curved surfaces of X-ray mirrors—the removal of low-frequency backlash error—but also obtains high-precision full-frequency surface shapes. Full-frequency surface shapes are not only desirable in the field of optical processing, but are also highly beneficial for research on many important scientific issues in the field of synchrotron radiation. This frequency-division stitching interferometer can achieve high-precision surface shape detection of one-dimensional planes, one-dimensional curved surfaces, two-dimensional planes, and two-dimensional curved surfaces across the entire frequency band. Attached Figure Description

[0030] Figure 1 The front view of the mirror under test is shown;

[0031] Figure 2 The main structural components of the frequency division splicing interferometer are shown in the diagram.

[0032] Figure 3 The diagram shows the center line F of the mirror surface under test obtained using an interferometer. a (x), and the center line L of the mirror surface to be measured obtained using the first and second angle measuring devices. a (x);

[0033] Figure 4 The difference δ between the centerline data of the mirror surface under test is shown. a (x);

[0034] Figure 5 The diagram shows the two-dimensional surface shape of the interferometer minus the surface shape difference δ along the center line. a (x), resulting in a new two-dimensional surface shape;

[0035] Figure 6 The diagram shows the surface slope L of two lines on the surface of the mirror under test, obtained using the first and second angle measuring devices. 1a (x) and L 2a (x);

[0036] Figure 7 The paper demonstrates linear fitting of surface shape differences under the second data processing method.

[0037] Figure 8 The diagram shows that, under the second data processing method, a new two-dimensional surface shape is obtained by subtracting the surface shape difference from the two-dimensional surface shape of the interferometer.

[0038] Reference numerals in the attached figures: 1-first translational sub-stage, 2-second translational sub-stage, 3-third translational sub-stage, 4-rotational sub-stage. Detailed Implementation

[0039] 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.

[0040] The first translational stage 1 carries an interferometer to perform translational motion and acquire the surface shape of each sub-aperture of the mirror under test; the second translational stage 2 carries the first angle measuring device to perform translational motion and measure the slope of the low spatial frequency surface shape of the mirror under test. At the same time, the second angle measuring device continuously monitors the movement of the first angle measuring device.

[0041] The data processing unit receives three parts of data: data from the interferometer (i.e., the surface shape of each sub-aperture of the mirror under test), data from the first angle measuring device, and data from the second angle measuring device. Among them, the data from the first angle measuring device and the data from the second angle measuring device can be processed to form new data, which is the slope of the low spatial frequency surface shape of the mirror under test after removing motion angle errors.

[0042] Based on different detection requirements, three specific data processing methods are proposed to achieve full-band surface shape detection by removing low-frequency backlash errors.

[0043] The first method: combining interferometer data with the slope of a line's surface shape.

[0044] The surface shape of each sub-aperture of the mirror under test is obtained using an interferometer, and the surface shape of the entire mirror is obtained by splicing them together, denoted as h(x,y); then, according to the set spatial frequency a(mm)... -1 Apply a low-pass filter to h(x,y), and take the shape of the middle line of the filtered shape, denoted as F. a (x), such as Figure 3 As shown. Spatial frequency a (mm) -1 The value can be selected according to actual needs. In principle, 1 / a should be greater than the beam spot diameter of the angle measuring device and less than the interferometer splicing step size.

[0045] The slope of the surface of the mirror under test is obtained by using the first and second angle measuring devices along the middle line of the mirror surface, according to a(mm) -1 The spatial frequency is low-pass filtered, and the resulting surface shape is denoted as L. a (x), such as Figure 3 As shown.

[0046] Let F a (x) and L a The difference between (x) and (x) is denoted as δ. a (x), as described in formula (1), as Figure 4 As shown.

[0047] δ a (x)=F a (x)-L a (x) (1)

[0048] Then subtract the surface shape difference δ from the entire surface shape h(x,y). a (x), such as Figure 5 As shown, the resulting surface shape is denoted as hC(x,y), as described in formula (2), where (x i ,y j ) represents the coordinates of any point on the surface shape of the mirror to be measured; the surface shape hC(x,y) is the two-dimensional surface shape after removing low-frequency backlash error, and at the same time, a high-precision full-frequency surface shape is obtained through frequency division: the interferometer can accurately measure a(mm) -1 The surface shape above the spatial frequency, but due to the presence of low-frequency backflash error, a(mm) -1 Surface shape measurements below the spatial frequency are inaccurate; however, the frequency-division stitching interferometer, while eliminating low-frequency backlash errors, not only ensures accurate low-frequency surface shape results but also preserves the interferometer's a(mm) value. -1 Information above the spatial frequency.

[0049] hC(x i ,y j )=h(x i ,y j )-δ a (x i (2)

[0050] The aforementioned frequency division processing method includes frequency decomposition and integration. Frequency decomposition refers to performing low-pass filtering on the surface shape information obtained by the interferometer and the angle measuring device according to the same spatial frequency to obtain the low-frequency surface shape, and taking the difference between the original surface shape and the low-frequency surface shape as the high-frequency surface shape. Frequency integration refers to correcting the low frequency of the interferometer according to the result of the angle measuring device, removing the low-frequency backlash error of the interferometer, and obtaining a new surface shape, that is, the high frequency of the interferometer + the low frequency of the angle measuring device = a new surface shape hC(x,y) with high precision across the entire frequency band.

[0051] The second method: combining interferometer data with the slope of the surface shape of the two lines.

[0052] like Figure 6 As shown, the mirror under test is adjusted to translate along the y-direction using the mirror attitude adjustment mechanism. Data from two lines at positions y1 and y2 on the mirror surface are obtained through measurements from the first and second angle measuring devices, and then a(mm) is calculated. -1 Low-pass filtering of spatial frequencies, the filtered surface shapes are denoted as L. 1a (x) and L 2a (x).

[0053] The surface shape h(x,y) obtained by interferometer splicing is calculated according to a(mm) -1 The spatial frequency is low-pass filtered, and the surface shapes of the two lines at positions y1 and y2 on the filtered surface are taken, and denoted as F respectively. 1a(x) and F 2a (x).

[0054] Correction L 1a (x) and L 2a The orientation of (x): Let L 1a (x) minus F 1a (x), fit this difference using a linear function, and then let L 1a (x) minus the difference after fitting the linear function is denoted as LC. 1a (x); Let L 2a (x) minus F 2a (x), fit this difference using a linear function, and then let L 2a (x) minus the difference after fitting the linear function is denoted as LC. 2a (x).

[0055] Let F 1a (x) and LC 1a Let F be the difference between (x). 2a (x) and LC 2a The difference between (x) is denoted as δ. 1a (x) and δ 2a (x), as described in formulas (3) and (4); then, linearly fit the difference values ​​of the two surfaces corresponding to the same horizontal coordinate x on the mirror surface: substitute formulas (5) and (6) into formula (7), and solve for the coefficients k and b of the first and zero terms as described in formula (8). Different vertical coordinates under the same horizontal coordinate use the same linear fitting function, such as Figure 7 As shown: as x i The linear fit at z is i =k i y+b i For the same x i Although y is different, in x = x i Above, the linear fitting function for the surface shape difference is z. i =k i y+b i ;x p The linear fit at z is p =k p y+b p x q The linear fit at z is q =k q y+b q .

[0056] δ 1a (x)=F 1a (x)-LC 1a (x) (3)

[0057] δ 2a(x)=F 2a (x)-LC 2a (x) (4)

[0058]

[0059]

[0060] z = ky + b (7)

[0061]

[0062] The surface shape h(x,y) minus the difference surface shape after linear fitting, such as Figure 8 As shown, the obtained surface shape is denoted as hC(x,y). As described in formula (9), the surface shape hC(x,y) is a two-dimensional surface shape that has removed the low-frequency backlash error. At the same time, a high-precision full-frequency surface shape is obtained by frequency division.

[0063] hC(x i ,y j )=h(x i ,y j )-[k(x i )*y j +b(x i (9)

[0064] The second approach takes two lines and analyzes them in more detail, extending the results of the two lines to the entire mirror surface, or in other words, extending the influence of the results in the horizontal direction (i.e., the direction of the two lines, which is also the x-direction) to the vertical direction (perpendicular to the two lines, i.e., the y-direction). Specifically, for each x-coordinate, a point can be taken from each of the two lines, and the two points determine a straight line, which is a vertical line (along the y-direction). The two points taken for each x are different, which means that the length of each vertical line is different. That is, the slope k and intercept b of the fitted vertical line vary depending on x.

[0065] The third method: combining interferometer data with the slope of the surface shape of multiple lines.

[0066] The mirror under test is adjusted to move along the y-direction using the attitude adjustment mechanism of the mirror under test. After measurement by the first and second angle measuring devices, the y1, y2...y values ​​on the mirror surface are taken out. n Find the slope of the surface shape of n lines at position n, and apply it to a(mm). -1 Low-pass filtering of spatial frequencies, the filtered surface shapes are denoted as L. 1a (x), L 2a (x)……L na (x).

[0067] The surface shape h(x,y) obtained by interferometer splicing is calculated according to a(mm) -1 The spatial frequency is low-pass filtered, and the values ​​of y1, y2...y3 on the filtered shape are taken. n The shape of a surface with n lines at position is denoted as F. 1a (x), F 2a (x)……F na (x).

[0068] Correction L 1a (x), L 2a (x)……L na The orientation of (x): Let L 1a (x) minus F 1a (x), fit this difference using a linear function, and then let L 1a (x) minus the difference after fitting the linear function is denoted as LC. 1a (x); Let L 2a (x) minus F 2a (x), fit this difference using a linear function, and then let L 2a (x) minus the difference after fitting the linear function is denoted as LC. 2a (x); similarly, this applies to LC. na (x).

[0069] Let F 1a (x) and LC 1a The difference between (x) is denoted as δ. 1a (x), and similarly, this can be extrapolated to δ. na (x), as described in formula (10). There are n surface shape difference values ​​corresponding to the same horizontal coordinate on the mirror surface to be tested. The n surface shape difference values ​​are interpolated; for different vertical coordinates under the same horizontal coordinate, the same interpolation function is used. The surface shape h(x,y) is subtracted from the interpolation function, and the new surface shape hC(x,y) is the two-dimensional surface shape that has removed the low-frequency backlash error. At the same time, a high-precision full-frequency surface shape is obtained by frequency division.

[0070] δ na (x)=F na (x)-LC na (x) (10)

[0071] In actual engineering tasks, the purchased mirrors need to be inspected and tested. A large number of mirrors need to be tested in a short period of time. Experiments have shown that the first method is the most efficient. When the purchased mirrors are installed on the synchrotron radiation beamline, surface shape detection is also required for online assembly and adjustment. The first method is also the most efficient.

[0072] In order to improve the processing accuracy of optical components, a second and third scheme were proposed. Since optical processing involves processing the entire two-dimensional mirror surface, the second and third schemes would allow for more precise two-dimensional detection.

[0073] 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 frequency division stitching interferometer, characterized in that, The device comprises a multi-dimensional displacement table, a mirror posture adjusting mechanism, an interferometer, two angle measuring devices and a data processing unit. The multi-dimensional displacement table is used to control the interferometer and the first angle measuring device to move in the x direction, control the second angle measuring device to move in the z direction, and control the mirror to rotate in the x-z plane. The mirror posture adjusting mechanism is used to adjust the mirror to move in the y direction, rotate in the x-y plane and rotate in the y-z plane. The interferometer is used to acquire the surface shape of each sub-aperture of the mirror to be measured and send it to the data processing unit; the data unit is used to splice the surface shape of each sub-aperture of the mirror to be measured to obtain the mirror surface shape h(x, y), perform low-pass filtering on h(x, y) according to a set spatial frequency a, and take a line F in the filtered surface shape that satisfies y=y1 1a (x); The first angle measuring device is used to measure the low spatial frequency slope of the mirror surface along the y=y1 line and send the measurement result to the data processing unit. The second angle measuring device is used to monitor the movement angle of the first angle measuring device and send the monitoring data to the data processing unit. The data processing unit removes the motion angle error present in the measurement process of the first angle measuring device based on the monitoring data, and obtains the line F. 1a The slope of the surface shape (x) without motion angle error is low-pass filtered according to the set spatial frequency a to obtain the filtered surface shape L. 1a (x); then calculate the surface shape difference δ. 1a (x)=F 1a (x)-L 1a (x), let (x) be any coordinate point (x,y) on the mirror surface h(x,y). i ,y j The surface shape value h(x) at point ) i ,y j ) and δ 1a (x) have the same x-coordinate x i δ at the surface shape 1a (x i Subtracting the two values, we obtain the coordinates of the point (x,y) in the two-dimensional surface shape hC(x,y) of the mirror under test. i ,y j The surface shape value hC(x) at point ) i ,y j )=h(x i ,y j )-δ 1a (x i ).

2. The frequency division stitching interferometer of claim 1, wherein, a line F of y=y2 is selected from the low-pass filtered surface shape of h(x,y) 2a (x); after adjusting the panning of the mirror along the y direction by the mirror adjustment mechanism, the first angle measuring device measures the low spatial frequency surface shape slope of the mirror along the line y=y2 and sends it to the data processing unit; the data processing unit removes the motion angle error of the first angle measuring device during the measurement according to the corresponding monitoring data, and obtains the corresponding surface shape slope of the line F 2a (x) without motion angle error, and performs low-pass filtering on it according to the set spatial frequency a to obtain the filtered surface shape L 2a (x); then the two-dimensional surface shape hC(x,y) of the mirror is generated according to steps 21) to 23): 21) Let L 1a (x) - F 1a (x) be fitted to the resulting differences to obtain a first fit result, and let the difference between L 1a (x) and the first fit result be denoted by LC 1a (x); let L 2a (x) - F 2a (x) be fitted to the resulting differences to obtain a second fit result, and let the difference between L 2a (x) and the second fit result be denoted by LC 2a (x). 22) calculate delta 1a (x) = F 1a (x) - LC 1a (x), delta 2a (x) = F 2a (x) - LC 2a (x); and linearly fitting two surface profile difference values corresponding to the same horizontal coordinate x on the mirror surface profile, to obtain the first term coefficient and the zero term coefficient 23) Based on the fitting results, obtain the coordinates (x,y) of any point in the two-dimensional surface shape hC(x,y) of the mirror under test. i ,y j The surface shape value hC(x) at point ) i ,y j )=h(x i ,y j )-[k(x i )*y j +b(x i )];in, For δ 1a (x) x-coordinate i The surface shape difference value at the location, For δ 2a (x) x-coordinate i The surface shape difference value at the location.

3. The frequency division stitching interferometer of claim 1, wherein, N lines F are selected from the low-pass filtered surface shape of h(x, y) 1a (x), F 2a (x),..., F Na (x); after adjusting the panning of the mirror to be tested along the y direction by using the mirror adjustment mechanism to be tested, the first angle measuring device measures the low spatial frequency surface shape slope of the mirror to be tested along each line and sends it to the data processing unit; the data processing unit removes the motion angle error existing in the measurement process of the first angle measuring device according to the corresponding monitoring data, obtains the surface shape slope corresponding to each line without motion angle error, and performs low-pass filtering on it according to the set spatial frequency a, and obtains the filtered surface shape respectively denoted as L 1a (x), L 2a (x),..., L Na (x); wherein L Na (x) is the filtered surface shape corresponding to the nth line; then the two-dimensional surface shape hC(x, y) of the mirror to be tested is generated according to steps 31) ~ 33): 31) Let L na (x) minus F na (x), perform a linear function fit on the obtained difference to obtain the nth fitting result, and then L na The difference between (x) and the nth fitting result is denoted as LC. na (x); 32) Calculate the surface profile difference value δ for the same horizontal coordinate na (x) = F na (x) - LC na (x), n = 1 ~ N; 33) Interpolation is performed according to the surface difference value obtained in step 32), and the same interpolation function is used for different vertical coordinates at the same horizontal coordinate.

4. The frequency division stitching interferometer of claim 1 or 2 or 3, wherein, The spatial frequency a satisfies: 1 / a is greater than the beam spot diameter of the first angle measuring device and less than the surface stitching step length of the sub-aperture.

5. The frequency division stitching interferometer of claim 1 or 2 or 3, wherein, The multi-dimensional displacement table comprises a first translation sub-displacement table (1), a second translation sub-displacement table (2), a third translation sub-displacement table (3) and a rotation sub-displacement table (4). The first translation sub-displacement table (1) is used to carry the interferometer, the second translation sub-displacement table (2) is used to carry the first angle measuring device, the third translation sub-displacement table (3) is used to carry the second angle measuring device, and the rotation sub-displacement table (4) is used to carry the mirror.

6. The frequency division stitching interferometer of claim 1 or 2 or 3, wherein, The line F 1a (x) is the center line of the mirror surface of the mirror under test.

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