A method, medium, and apparatus for calibrating a plane reference mirror in a vertical interferometer.

Abstract

This invention relates to the field of optical measurement and calibration technology, and in particular to a method, medium, and apparatus for calibrating a plane reference mirror in a vertical interferometer. The method involves placing a calibration plate as a temporary mirror under test in the measurement optical path of a vertical Fizeau interferometer. At at least one measurement point, the calibration plate is continuously rotated around its own rotation center. The rotation centers at each measurement point are offset from the central optical axis of the plane reference mirror and equidistant. Multiple frames of surface shape measurement data are collected at each measurement point, and the absolute surface shape error of the plane reference mirror is obtained by arithmetic averaging of all measurement point data. This method, through the specific offset measurement point settings, systematically changes the spatial orientation of the calibration plate at different points, offsetting central symmetry errors and suppressing asymmetric errors and random noise. It achieves high-precision and robust absolute calibration without the need for complex algorithms. Compared with traditional methods, it combines accuracy, efficiency, and practicality, is suitable for various application scenarios, and provides a framework for subsequent efficiency optimization.

Description

Technical Field

[0001] This invention relates to the field of optical measurement and calibration technology, and in particular to a method, medium, and device for calibrating a plane reference mirror for a vertical interferometer. Background Technology

[0002] Fizeau laser interferometers are widely used for measuring the surface shape accuracy of optical components. Their basic principle is to obtain the optical path difference between a reference mirror and the mirror under test by comparing their wavefront information, thus determining the surface shape error. However, this measurement method couples the surface shape errors of the reference mirror and the mirror under test, directly affecting the accuracy of the final measurement result.

[0003] To improve measurement accuracy, the surface shape error of the reference mirror needs to be absolutely calibrated to isolate the systematic errors it introduces. Common calibration methods include:

[0004] Rotation averaging method: By rotating the reference mirror multiple times around the optical axis and averaging the measurement results, rotational asymmetry errors can be separated, but rotational symmetry errors (such as spherical aberration) cannot be effectively separated.

[0005] The rotation-translation method adds a translation operation to the rotation. By taking measurements at three different positions and combining them with computer algorithms, the reference mirror shape, including rotational symmetry errors, can be calculated. However, this method relies on complex algorithms, has a cumbersome implementation process, and requires a high level of technical skill from the operators. Summary of the Invention

[0006] To address one of the aforementioned technical problems, the present invention adopts the following technical solution:

[0007] According to one aspect of the present invention, a method for calibrating a plane reference mirror for a vertical interferometer is provided, comprising the following steps:

[0008] A calibration plate is placed in the measurement optical path of the vertical Fizeau interferometer as a temporary mirror to be measured.

[0009] At at least one measurement point, the calibration plate is driven to rotate continuously around its own rotation center, and multiple frames of surface shape measurement data are collected at each measurement point. The rotation center of each measurement point is off-axis from the central optical axis of the plane reference mirror, and the distance between the rotation center of each measurement point and the central optical axis of the plane reference mirror is equal.

[0010] The arithmetic mean of all surface measurement data collected from all measurement points is the absolute surface error of the plane reference mirror.

[0011] According to a second aspect of the present invention, a non-transitory computer-readable storage medium is provided, which stores a computer program that, when executed by a processor, implements the above-described method for calibrating a planar reference mirror for a vertical interferometer.

[0012] According to a third aspect of the present invention, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method for calibrating a planar reference mirror for a vertical interferometer.

[0013] This invention has at least one of the following beneficial effects:

[0014] This invention provides a method for calibrating a planar reference mirror for a vertical Fizeau interferometer. The method involves continuously rotating a calibration plate at at least one off-axis measurement point and acquiring multiple frames of surface shape data. The absolute surface shape error of the reference mirror is then obtained by globally averaging the measurement data from all points. The key to this method is that the rotation centers of all measurement points maintain the same off-axis distance from the central optical axis of the reference mirror, ensuring that the spatial orientation of the calibration plate relative to the reference mirror changes systematically at different points. This arrangement allows the calibration plate's own centrosymmetry errors (such as annular bands or central bulges) to be distributed at different angles at different points, effectively canceling them out during the global averaging process. Simultaneously, asymmetric errors and random noise (such as air noise) are sufficiently suppressed within a single point through averaging across a large number of rotating frames. The entire process requires no complex algorithms, relying solely on physical rotation, spatial offset, and basic averaging calculations to achieve high-precision and robust absolute calibration.

[0015] Compared to the limitations of traditional rotating average methods, which cannot eliminate rotational symmetry errors, and rotating translation methods, which rely on complex inversion algorithms, this invention combines accuracy, efficiency, and engineering practicality. On one hand, through a "equidistant multi-point + global averaging" mechanism, it comprehensively separates various error components introduced by the calibration plate, significantly improving the accuracy of the calibration results. On the other hand, the method has a clear structure, is easy to operate, and is applicable to vertical interferometers of different apertures, demonstrating strong versatility. More importantly, this scheme provides a basic framework for the subsequent introduction of adaptive judgment mechanisms (such as identifying symmetry errors through differential methods), allowing for dynamic selection of single-point or multi-point measurement modes while ensuring accuracy, further optimizing measurement efficiency. It is suitable for various application scenarios such as high-precision optical manufacturing, metrology calibration, and online testing. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart illustrating a method for calibrating a planar reference mirror in a vertical interferometer, provided as an embodiment of the present invention;

[0018] Figure 2 This is a schematic diagram of the calibration device corresponding to a planar reference mirror calibration method for a vertical interferometer provided in an embodiment of the present invention;

[0019] Figure 3 This is a schematic diagram of the connection structure of the base, motor, calibration plate and bearing balls in the calibration device provided in the embodiment of the present invention.

[0020] Figure 4 This is a schematic diagram illustrating the calibration effect of a planar reference mirror calibration method for a vertical interferometer provided in an embodiment of the present invention.

[0021] Figure 5 A schematic diagram illustrating the measurement results of the center-symmetric error at different measurement points provided in this embodiment of the invention;

[0022] Figure 6 The image shows the shape measurement results (left) of two adjacent error type detection positions provided in this embodiment of the invention, and the result after differentiation (right). Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] As one possible embodiment of the present invention, such as Figure 1 As shown, a method for calibrating a plane reference mirror for a vertical interferometer is provided, the method comprising the following steps:

[0025] S100: Place a calibration plate 1 in the measurement optical path of the vertical Fizeau interferometer as a temporary mirror under test. Specifically, the calibration plate 1 is a planar plate.

[0026] Specifically, such as Figure 2 and 3 As shown, the calibration device of the present invention may include the following components:

[0027] Base 4: Used to support the overall structure and can rotate around the optical axis of the reference mirror 5 to change the measurement point position;

[0028] Motor 3: Mounted on base 4, used to drive calibration plate 1 to rotate;

[0029] Calibration plate 1: As a temporary reflecting surface in interferometry, its surface shape does not need to be highly accurate;

[0030] Multiple evenly distributed bearing balls 2 are positioned between the motor 3 and the calibration plate 1 to ensure that the calibration plate 1 rotates smoothly without any wobble.

[0031] This device has a simple structure, requires no precision guide rails or translation mechanisms, and is suitable for vertical interferometers of different apertures. After installing the reference mirror 5 on the vertical interferometer, the device is placed below the vertical interferometer; the motor 3 is started to rotate the calibration plate 1, and the bearing ball 2 ensures smooth rotation, and then data acquisition and processing are performed.

[0032] S200: At at least one measurement point, the calibration plate 1 is driven to rotate continuously around its own rotation center, and multiple frames of surface shape measurement data are collected at each measurement point. The rotation center of each measurement point is offset from the central optical axis of the plane reference mirror 5, and the distance between the rotation center of each measurement point and the central optical axis of the plane reference mirror 5 is equal. The equal distance from the rotation center of all measurement points to the optical axis of the reference mirror 5 ensures that the error structure undergoes only pure orientation rotation at different points without introducing scale or deformation differences, thus guaranteeing the effectiveness of the averaging.

[0033] Specifically, in this step, data acquisition can be performed using the automatic sequence measurement function built into the laser interferometer for continuous measurement. After acquiring data at a certain measurement point, the entire device is rotated around the axis of the reference mirror 5 by a certain angle (e.g., 60 degrees), and the above acquisition steps are repeated.

[0034] Typically, planar calibration plates 1 commonly exhibit asymmetric surface shape errors (such as local protrusions, scratches, or uneven processing), while the probability of having centrally symmetric surface shape errors (such as annular bands or radially symmetric undulations) is relatively low. In the calibration scheme adopted in this invention, asymmetric errors can be effectively suppressed by driving the calibration plate 1 to rotate continuously at a single measurement point and collecting a large number of frame data using arithmetic averaging; while centrally symmetric errors, because they are constant during a single rotation, cannot be eliminated by single-point averaging. They must be eliminated by using multiple equidistant measurement points off-axis, causing them to exhibit spatial variations at different azimuth angles, and then by global averaging.

[0035] Based on the aforementioned differences in error characteristics, this invention can dynamically determine the number of measurement points required according to the actual error structure of the calibration plate 1: if only asymmetric errors exist, only one measurement point is needed to complete high-precision calibration; if centrally symmetric errors also exist, multiple equidistantly distributed measurement points are used. This strategy not only ensures calibration accuracy but also significantly improves measurement efficiency and avoids unnecessary data acquisition and processing overhead.

[0036] In other words, whether to set one or multiple measurement points can be determined based on the following:

[0037] When calibration plate 1 contains only asymmetric surface errors, there is one measurement point.

[0038] In this embodiment, the elimination mechanism for random and asymmetric errors is mainly the statistical dilution effect, which is explained in detail below:

[0039] At a single measurement point, calibration plate 1 rotates continuously, and the interferometer continuously acquires a large number of measurement frames (such as hundreds to thousands of times).

[0040] Such errors (such as local dust, instantaneous airflow disturbance, and minor scratches) are spatially localized and temporally random: they only appear in the interferometric field of view when the calibration plate 1 is rotated to a specific angle, and they occur at a very low frequency in all acquisition frames (for example, only 2–3 frames out of 100 frames are affected).

[0041] Since the vast majority of measurement frames do not contain this error, their data accurately reflect the surface shape of the reference mirror; while the few frames containing the error only introduce outliers in local areas. When the arithmetic mean is calculated for all frames, the outliers are "diluted" by a large number of normal values, and their contribution to the final average result approaches zero.

[0042] According to the law of large numbers, as the number of samples approaches infinity, the expected value of the random error tends to zero, and the average result converges to the error-free true surface shape. Therefore, simply collecting a large number of samples from a single location and averaging them is sufficient to effectively suppress random and asymmetric errors.

[0043] When calibration plate 1 contains not only asymmetric surface shape errors but also centrally symmetric surface shape errors, there are multiple measurement points.

[0044] In this embodiment, the mechanism for eliminating central symmetry error is mainly the spatial orientation randomization effect, which is explained in detail below:

[0045] Centrally symmetric errors (such as annular bands, central convex hulls, etc.) are rotationally invariant: at the same measurement point, no matter how the calibration plate 1 is rotated, the shape and position of the error in the interferogram remain unchanged, so it cannot be eliminated by averaging within a single point.

[0046] However, when the calibration plate 1 is moved to different measurement points (each point's rotation center is located on the same circle centered on the optical axis of the reference mirror 5), the spatial orientation of the calibration plate 1 relative to the reference mirror 5 changes. At this time, the originally fixed centrally symmetric error structure undergoes an overall rotation (i.e., "self-rotation") relative to the coordinate system of the reference mirror 5, and its ring-shaped characteristics appear as ring-shaped distributions at different angles in the interferogram.

[0047] For example, the annular error center acquired at point one is located at the top of the image, while at point two (after rotation by 60°) it is located at the upper right, and so on. Figure 5 As shown.

[0048] When all measurement data from all points are averaged, a high error value at a certain location will be compensated by a low error value or even no error value at other points at that location.

[0049] Since sampling and averaging a rotationally symmetric function at multiple equally spaced azimuth angles yields a result that approximates the radial mean of the function, and if the function itself is a non-ideal surface (such as a ring), it will be "flattened" to a constant or close to a plane after global averaging. Therefore, by using multi-point spatial offset and global averaging, the centrosymmetry error can be effectively eliminated.

[0050] Specifically, when there are multiple measurement points (≥2), the rotation centers of the multiple measurement points are located on a circle with the same radius centered on the optical axis of the plane reference mirror 5, and are distributed in a regular polygonal manner.

[0051] Preferably, the regular polygon is a regular hexagon, and the angular interval between adjacent measurement points is 60 degrees.

[0052] S300: The arithmetic mean of all surface measurement data collected from all measurement points is the absolute surface error of the plane reference mirror 5.

[0053] The principle of the method in this embodiment is as follows:

[0054] An ideal plane is generated by rotating the calibration plate 1 multiple times. The rotation center of the calibration plate 1 is changed, and the surface shape is detected multiple times at each rotation center. Finally, the results are averaged to eliminate the influence of the surface shape error of the rotating calibration plate 1 and environmental noise, thereby obtaining the absolute surface shape error of the calibration reference plane.

[0055] Specifically, for the nth measurement result W at the m-th rotation center mm ,have

[0056] ;

[0057] Where Ref represents the surface shape error of the reference mirror 5, and Tes mnThis is the nth measurement result of reference mirror 5 at the m-th rotation center.

[0058] By continuously rotating calibration plate 1 and averaging all measurement results, we can obtain:

[0059] ;

[0060] Where M is the total number of rotation centers, and N is the total number of measurements at each measurement point.

[0061] When calibration plate 1 rotates randomly, the last term in the above equation is approximately equal to the Mente-Carlo integral performed over the entire rotating calibration plate 1, i.e.:

[0062] ;

[0063] Therefore, the result after multiple averaging At this point, the surface shape error Ref of reference mirror 5 is obtained, thus completing the absolute calibration of the planar reference mirror 5.

[0064] Specifically, six measurement points were selected, each located at a vertex of a regular hexagon. 200 measurements were performed at each point to illustrate the effectiveness of this method, as shown below. Figure 4 As shown in the figure. Specifically, the nominal reference error in the figure is the actual error of reference mirror 5, and the error of the reference surface at the middle position is the error value of reference mirror 5 calculated using this method. As can be seen from the RMS values ​​shown in the first and second figures, the error value calculated by this method is extremely close to the actual error of reference mirror 5, achieving the effect of absolute calibration. Figure 4 The last figure shown, which is also the graph of the method residual, shows that after averaging, all asymmetric errors, symmetric errors, and random errors are effectively suppressed, thus minimizing the RMS value.

[0065] As another possible embodiment of the present invention, the method further includes the following steps before performing multi-point measurements:

[0066] S210: Perform surface shape measurements on calibration plate 1 at two adjacent error type detection positions to obtain two sets of measurement data. The two error type detection positions are radially distributed along the optical axis pointing to the center of the plane reference mirror 5. The translation distance between adjacent positions is small enough to ensure that the two measurement areas partially overlap, and the difference results can reflect the spatial gradient characteristics of the surface shape.

[0067] Specifically, in this step, two adjacent error type detection locations can be used, one of which can be the first measurement point, and the second can be a new point where a minimal displacement occurs in the radial direction.

[0068] S220: Perform differential processing on the two sets of measurement data.

[0069] Specifically, the differential processing includes:

[0070] S221: Perform pixel-by-pixel subtraction on the measurement data of calibration plate 1 at two adjacent positions to generate a difference image.

[0071] S222: Determine whether there is a centrally symmetric surface shape error by detecting whether there are annular stripes in the difference image.

[0072] This judgment principle is based on the preservation property of the spatial symmetry of surface error under difference operations, and the specific logic is as follows:

[0073] In this embodiment, the difference operation is essentially spatial differentiation. The specific method principle of this embodiment is explained as follows:

[0074] When interferometry is performed on calibration plate 1 at two adjacent and partially overlapping positions (with a very small radial translation Δx), two surface shapes W1(x,y) and W2(x,y) are obtained, and their difference results are as follows:

[0075] ;

[0076] When Δx is sufficiently small, this operation is approximately equivalent to taking the first-order partial derivative (i.e., spatial differential) of the surface shape function along the translation direction:

[0077] .

[0078] Based on the above, the following explanation addresses the fact that the rotational symmetry error still exhibits a circular characteristic after differentiation:

[0079] If the surface of calibration plate 1 has rotational symmetry errors (such as central protrusions, annular bands, spherical deviations, etc.), its surface shape function can be expressed as a function that is only related to the radial distance. The relevant form is W(r).

[0080] Find the spatial derivative of such functions (e.g.) The results still exhibit the gradient characteristics of a ring-shaped symmetrical distribution: the gradient is maximum at the edge of the ring error, and the gradients at the center and periphery approach zero, exhibiting an overall structure of one or more concentric rings, such as... Figure 6 As shown.

[0081] Therefore, the presence of clear annular stripes in the difference image indicates the existence of a radially symmetrical undulating structure in the original surface shape.

[0082] If the error is an asymmetric structure such as isolated bumps, scratches, or random noise, its local position is different in the two translation measurements. After differentiation, it will appear as local spots or irregular textures and will not form closed, concentric rings.

[0083] Systematic errors (such as the error of reference mirror 5) are exactly the same in both measurements and will be completely canceled out in the difference, leaving no residue.

[0084] S230: If a closed loop structure exists in the difference result, it is determined that there is a centrally symmetric surface shape error, and multi-point measurement is performed.

[0085] S240: If there is no closed loop structure in the difference result, then only rotation and multi-frame measurement are performed at one measurement point, and the obtained data are averaged to obtain the surface error of the reference mirror 5.

[0086] Therefore, the solution in this embodiment is the pre-judgment mechanism of the above embodiment. Through the pre-judgment mechanism, it is dynamically determined whether to enable multi-point measurement, thereby reducing unnecessary data collection and calculation and improving work efficiency.

[0087] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0088] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, mobile terminal, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0089] In an exemplary embodiment of this disclosure, an electronic device capable of implementing the above-described method is also provided.

[0090] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: entirely in hardware, entirely in software (including firmware, microcode, etc.), or in a combination of hardware and software, collectively referred to herein as “circuit,” “module,” or “system.”

[0091] An electronic device according to this embodiment of the invention. The electronic device is merely an example and should not be construed as limiting the functionality or scope of the embodiments of the invention.

[0092] Electronic devices are manifested in the form of general-purpose computing devices. Components of an electronic device may include, but are not limited to: at least one processor, at least one memory, and buses connecting different system components (including memory and processor).

[0093] The memory stores program code that can be executed by a processor, causing the processor to perform the steps described in the "Exemplary Methods" section above, according to various exemplary embodiments of the present invention.

[0094] The storage may include readable media in the form of volatile storage, such as random access memory (RAM) and / or cache memory, and may further include read-only memory (ROM).

[0095] The storage may also include programs / utilities having a set (at least one) of program modules, including but not limited to: an operating system, one or more applications, other program modules, and program data, each or some combination of these examples may include an implementation of a network environment.

[0096] A bus can represent one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus that uses any of the various bus architectures.

[0097] The electronic device can also communicate with one or more external devices (e.g., keyboards, pointing devices, Bluetooth devices, etc.), one or more devices that enable a user to interact with the electronic device, and / or any device that enables the electronic device to communicate with one or more other computing devices (e.g., routers, modems, etc.). This communication can be performed via input / output (I / O) interfaces. Furthermore, the electronic device can communicate with one or more networks (e.g., local area networks (LANs), wide area networks (WANs), and / or public networks, such as the Internet) via a network adapter. The network adapter communicates with other modules of the electronic device via a bus. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with the electronic device, including but not limited to: microcode, device drivers, redundant processors, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0098] In exemplary embodiments of this disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the methods described above is stored. In some possible embodiments, various aspects of the present invention may also be implemented as a program product comprising program code that, when the program product is run on a terminal device, causes the terminal device to perform the steps of the various exemplary embodiments of the present invention described in the "Exemplary Methods" section above.

[0099] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0100] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, apparatus, or device.

[0101] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0102] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0103] Furthermore, the accompanying drawings are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention and are not intended to be limiting. It is readily understood that the processes shown in the above drawings do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0104] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0105] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for planar reference mirror calibration for a vertical interferometer, characterized in that, The method comprises the following steps: placing a calibration plate in the measurement path of the vertical Fizeau interferometer as a temporary mirror to be measured; driving the calibration plate to continuously rotate around its own rotation center at at least one measurement point, and collecting multiple frames of surface shape measurement data at each measurement point, wherein the rotation center of each measurement point is arranged off-axis with respect to the central optical axis of the plane reference mirror, the rotation centers of the measurement points are located on a circle with the same radius and with the central optical axis of the plane reference mirror as the center, and the distance between the rotation center of each measurement point and the central optical axis of the plane reference mirror is equal; performing arithmetic averaging on all the collected surface shape measurement data of the measurement points, and the obtained average result is the absolute surface shape error of the plane reference mirror.

2. The method according to claim 1, wherein, when the calibration plate only contains asymmetric surface shape errors, the measurement point is one.

3. The method according to claim 1, wherein, when the calibration plate contains not only asymmetric surface shape errors but also center-symmetric surface shape errors, the measurement points are multiple.

4. The method of claim 3, wherein, The rotation centers of the multiple measurement points are located on a circle with the same radius and with the central optical axis of the plane reference mirror as the center, and are distributed in a regular polygonal manner.

5. The method of claim 4, wherein, The regular polygon is a regular hexagon, and the angle interval between adjacent measurement points is 60 degrees.

6. The method of claim 1, wherein, The calibration plate is a plane plate.

7. The method of claim 1, wherein, Before performing the multi-point measurement, the following steps are further included: performing surface shape measurement on the calibration plate at two adjacent error type detection positions respectively to obtain two groups of measurement data; the two error type detection positions are distributed along the radial direction of the central optical axis of the plane reference mirror; the translation distance between adjacent positions is small enough to make the two measurement regions partially overlap, and the difference result can reflect the spatial gradient characteristics of the surface shape; performing difference processing on the two groups of measurement data; if there is a closed ring structure in the difference result, it is determined that there is a center-symmetric surface shape error, and the multi-point measurement is performed; if there is no closed ring structure in the difference result, the rotation and multi-frame measurement are performed at only one measurement point, and the obtained data is averaged to obtain the surface shape error of the reference mirror.

8. The method of claim 7, wherein, The difference processing includes: performing pixel-by-pixel subtraction operation on the measurement data of the calibration plate at the two adjacent positions to generate a difference image; determining whether there is a center-symmetric surface shape error by detecting whether there is a ring-shaped fringe in the difference image. 9.A non-transitory computer-readable storage medium storing a computer program, the computer program comprising instructions causing a processor to perform the method according to any one of claims 1 to 8. The computer program, when executed by a processor, implements the plane reference mirror calibration method for a vertical interferometer according to any one of claims 1 to 8.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor, when executing the computer program, implements the plane reference mirror calibration method for a vertical interferometer according to any one of claims 1 to 8.

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