Rotation and translation absolute calibration method based on nerve radiation field, medium and equipment

Abstract

The invention relates to the technical field of optical precision measurement, in particular to a rotation and translation absolute calibration method based on a nerve radiation field, a medium and equipment. The method comprises the following steps: acquiring at least three groups of interference measurement data of a measured mirror under original, rotation and translation poses by using an interference measurement system to be calibrated, inputting pixel coordinates and position coding information in the data into a neural radiation field network, optimizing network parameters through a self-supervised training strategy, and completing calibration of a reference mirror surface shape. Compared with a traditional Zernike method, the scheme adopts a neural radiation field to construct a double-branch network, can adaptively learn complex surface shape space distribution, and improves medium-high frequency error separation precision; the error of the reference mirror and the measured mirror is synchronously and directly output by double branches without successive dependence, so that error transmission and accumulation are avoided; the self-supervised training mechanism implicitly compensates pose deviation and noise interference through redundancy constraint, and shows higher engineering robustness.

Description

Technical Field

[0001] This invention relates to the field of optical precision measurement technology, and in particular to a method, medium and device for absolute calibration of rotation and translation based on neural radiation fields. Background Technology

[0002] The Fizeau laser interferometer is currently the primary instrument for nanoscale ultra-precision optical surface measurement. It reconstructs surface topography by comparing the optical path difference between a reference surface and a test surface. Specifically, the Fizeau interferometer employs a common-path structure, consisting of a laser source, a beam splitter, a reference mirror, and the mirror under test. After beam splitting, one portion of the laser beam is reflected by a high-precision reference mirror, while the other portion is reflected by the mirror under test. The two reflected beams re-converge and interfere, forming an interference fringe image. Since the reference mirror theoretically has an ideal spherical (or planar) surface, while the mirror under test has actual manufacturing errors, there is a difference in the optical path lengths of the two beams. This optical path difference directly reflects the deviation of the mirror under test from the ideal surface shape, i.e., the surface shape error. Therefore, the Fizeau interferometer measurement results simultaneously contain surface shape error information from both the reference mirror and the mirror under test. To achieve higher precision measurements, it is necessary to separate the surface shape error of the interferometer's own reference mirror from the measurement results, thereby obtaining the true surface shape of the measured surface, i.e., "absolute calibration."

[0003] The rotation-translation method is currently the mainstream absolute calibration method. First, the surface shape of the test part is measured in its original position, rotation, and translation pose. Then, a calculation model is established based on the three sets of measurement data (such as formulas (1), (2), and (3)). Finally, the Zernike polynomial is used to fit and solve the test surface shape to obtain W. ref and W test This allows for the separation of errors between the reference surface and the measured surface, thereby indirectly deriving the shape of the reference surface.

[0004] Specifically, the current principle of laser interferometer surface shape measurement is as follows: For the original position measurement results (i.e., wavefront error) ,have: (1) For the rotational position measurement results (i.e., wavefront error) ,have: (2) For translational position measurement results (i.e., wavefront error) ,have: (3) Among them, W ref For reference, the mirror shape error, W testThis represents the error in the shape of the mirror being measured. Rot and Shift represent rotation and translation operations on the mirror surface, respectively. test Rot For the measured mirror shape error in rotational pose, W test Shift The error of the measured mirror shape is the result of translational pose.

[0005] However, Zernike polynomials have limited nonlinear representation capabilities for complex surface features such as mid-to-high frequency characteristics and local high-frequency defects, leading to difficulties in separating mid-to-high frequency errors and an inability to effectively characterize non-smooth mid-to-high frequency error features, resulting in fitting errors. Furthermore, because the Zernike method cannot directly fit and obtain W... test W test Rot or W test Shift However, it is not possible to directly output the reference mirror shape error, so it is necessary to perform indirect calculations based on a certain measurement result to obtain it (e.g., This further leads to the accumulation of mid-to-high frequency fitting errors in the calibration results, ultimately affecting the absolute measurement accuracy of subsequent optical components. Summary of the Invention

[0006] To address one of the aforementioned technical problems, the present invention adopts the following technical solution: According to one aspect of the present invention, a method for absolute calibration of rotation and translation based on neural radiation fields is provided, the method comprising the following steps: Using the interferometric measurement system to be calibrated, at least three sets of interferometric measurement data are acquired for the mirror under test in its original position, rotational pose, and translational pose. The interferometric measurement data are surface error distribution data obtained from the interferogram, in which each pixel exists in the form of pixel coordinates (x,y), surface height error z, and position encoding information corresponding to the pixel coordinates. The pixel coordinates and corresponding position encoding information from the three sets of interferometric data are input into the neural radiation field network to generate the reference mirror shape error W. ref The measured mirror surface shape error W test The measured mirror shape error W under rotational pose test Rot and the error W of the measured mirror surface shape in the translational pose test Shift Position encoding information is used to map pixel coordinates to a high-dimensional space. The neural radiation field network includes invariant surface branching networks and variable surface branching networks; Invariant surface branching networks are used to generate W based on the input information corresponding to the original position of the input. refInvariant surface branching networks include multi-layered sequentially connected fully connected networks, with at least one jumper structure in the network; The variable-face branch network is used to generate W based on the input information corresponding to the original position, rotation pose, and translation pose, respectively. test W test Rot and W test Shift ; Variable-faceted branching networks include multi-layered sequentially connected fully connected networks, with at least two jumper structures in the network; Based on the predicted face height error and the actual face height error corresponding to each pixel, the parameters of the neural radiation field network are optimized using a self-supervised training strategy; so that the predicted measurement result synthesized from the output results of the two branches approximates the actual measurement result. W obtained at the end of optimization ref This serves as the reference mirror shape error in the interferometric measurement system to be calibrated, in order to complete the calibration.

[0007] 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 absolute calibration of rotation and translation based on a neural radiation field.

[0008] 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 absolute calibration of rotation and translation based on a neural radiation field.

[0009] This invention has at least one of the following beneficial effects: Traditional Zernike methods rely on a finite number of manually designed low-frequency basis functions, which struggle to effectively characterize non-smooth surface features such as mid-frequency textures or high-frequency defects, leading to insufficient separation of mid- and high-frequency errors. In contrast, this approach employs a Neural Radiation Field (NeRF) network to construct a dual-branch network. Through a multi-layer fully connected structure and high-dimensional positional encoding, it achieves strong nonlinear function approximation, enabling adaptive learning of the spatial distribution of complex surface shapes. The network directly extracts features from the data without pre-setting basis functions, thus more accurately distinguishing the mid- and high-frequency error components of the reference and tested mirrors, significantly improving the reference surface error W. ref The separation accuracy is improved, effectively overcoming the fitting bottleneck of traditional methods in the high-frequency region.

[0010] The traditional Zernike method requires first fitting the error W of the measured mirror surface. testThis indirectly leads to the derivation of the reference mirror error, causing the fitting residual of the tested mirror to be passed on and accumulated in the reference mirror result, with a significant impact, especially in the mid-to-high frequency region. This scheme uses a dual-branch neural network to synchronously and directly output W. ref With W test Both are optimized in parallel during training, with no sequential dependency. The loss function directly constrains the consistency between the synthesized measurements and the real data, eliminating the need for intermediate derivation steps. This fundamentally breaks the error propagation chain, ensuring the accuracy of the reference mirror calibration results and providing a reliable benchmark for subsequent absolute measurements.

[0011] Traditional calibration methods are highly sensitive to the accuracy of rotation / translation operations and environmental stability; even minor pose deviations or vibration noise can easily distort the calculation results. This proposed solution employs a self-supervised training mechanism, jointly optimizing the errors between the reference mirror and the measured mirror using three sets of pose data to create redundant constraints. During training, the network automatically adjusts its parameters to minimize the overall reconstruction error, implicitly compensating for angle deviations, translation errors, and environmental noise interference during actual operation. This end-to-end global optimization strategy enables the system to maintain higher accuracy even under non-ideal experimental conditions, demonstrating engineering robustness far superior to traditional methods. Attached Figure Description

[0012] 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.

[0013] Figure 1 The flowchart illustrates a rotational and translational absolute calibration method based on a neural radiation field, as provided in an embodiment of the present invention.

[0014] Figure 2 This is a structural diagram of the interferometric measurement system to be calibrated provided in an embodiment of the present invention.

[0015] Figure 3 This is a schematic diagram of the neural radiation field network (NeRF) provided in an embodiment of the present invention.

[0016] Figure 4 This is a schematic diagram of the network structure of a variable surface branching network provided in an embodiment of the present invention.

[0017] Figure 5 This is a schematic diagram of the network structure of an invariant surface branching network provided in an embodiment of the present invention.

[0018] Figure 6The image provided in this embodiment of the invention shows a comparison between the calibrated surface shape of the mirror under test obtained by calibration using the method (NeRF) of this patent and the conventional Zernike method, and the actual measured surface shape result GT. Detailed Implementation

[0019] 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.

[0020] As one possible embodiment of the present invention, such as Figure 1 As shown, a rotational and translational absolute calibration method based on neural radiation fields is provided, which includes the following steps: S100: Using the interferometric measurement system to be calibrated, acquire at least three sets of interferometric measurement data for the mirror under test 2 in its original position, rotational pose, and translational pose. The interferometric measurement data is the surface error distribution data obtained from the interferogram, in which each pixel exists in the form of pixel coordinates (x,y), surface height error z, and position encoding information corresponding to the pixel coordinates.

[0021] Specifically, the setup of the interferometric measurement system to be calibrated can be referred to Figure 2 The setup is as shown. Reference mirror 1 and the mirror under test 2 are placed in their respective positions and fixed using their corresponding mounting fixtures. For example, mirror under test 2 is fixed using its corresponding fixture 3. Then, the corresponding interferometric measurement data is acquired. Rotational pose is mainly achieved by rotating the plane containing the pixel coordinates (i.e., the surface under test) around the optical axis; translational pose is mainly achieved by displacing the pixel coordinates along the x or y direction.

[0022] S100 includes: S101: For each orientation of the test mirror 2, acquire multiple frames of phase-shifted interferograms using a Fizeau laser interferometer.

[0023] In practice, phase-shifting interferometry (PSI) is used to acquire phase-shifting interferograms. Typically, 4 or 13 frames of phase-shifting interferograms are acquired, with a phase-shifting step size of λ / 4 (λ is the laser wavelength, such as 632.8 nm). This step is used to obtain sufficient information to demodulate the absolute phase, which is a prerequisite for subsequent quantitative surface shape reconstruction. Rotation and translation operations are performed separately after the pose adjustment of the tested mirror 2, ensuring that the three sets of data correspond to different spatial states of the same tested mirror 2.

[0024] S102: Phase demodulation of multiple phase-shifted interferograms based on phase-shifting interferometry to obtain a wrapped phase map.

[0025] The standard four-step algorithm or the least squares phase-shifting algorithm is used to convert the multi-frame interferogram into a wrapper phase value (range [0, 2π)) for each pixel. This step achieves a preliminary conversion from optical intensity image to phase information, but due to phase wrapping, it cannot yet reflect the true continuous surface shape.

[0026] S103: Perform phase unpacking on the wrapped phase map to obtain a continuous phase distribution.

[0027] In this step, phase expansion can be performed using Goldstein path tracing or the minimum norm method to eliminate 2π jumps and obtain a globally continuous phase field. This step improves robustness in regions with abrupt changes or noise, directly affecting the final surface accuracy, and is a crucial step in interferometric data processing.

[0028] S104: Convert the continuous phase distribution into surface height error data, and use the pixel coordinates and their corresponding surface height error data as the interferometric measurement data under this attitude.

[0029] According to the formula The phase is converted into height error (unit: nm), forming a two-dimensional array, with each element corresponding to the surface error value of a pixel. This generates interferometric measurement data for each pose, specifically the coordinates of each pixel, including the x and y coordinates of the pixel plane and the height error value z in the height direction. This data serves as the input to the subsequent neural network.

[0030] Prior to S200, the method also includes: S210: Normalize the original pixel coordinates (x,y) and surface height error z to linearly map them to the [0,1] interval.

[0031] Since the x and y coordinate range (approximately 50–60 mm) is much larger than the z coordinate (<100 μm), directly inputting the original values ​​would cause the network to become insensitive to changes in the z direction. Therefore, normalization is required. After normalization, the dimensions of each dimension are consistent, which significantly improves the convergence speed and stability of the fully connected network. This step is a standard data preprocessing step.

[0032] S220: A 10th-order sine and cosine coding is used to encode the normalized pixel coordinates (x, y), mapping the two-dimensional pixel coordinates into a 256-dimensional high-dimensional vector to enhance the neural network's ability to express mid-to-high frequency surface features.

[0033] The 10th-order sine and cosine encoding outputs a dimension of 256. This encoding enables the network to effectively perceive low-frequency, mid-frequency, and high-frequency features, thereby effectively extracting high-frequency details (such as scratches and ripples). Thus, the low-dimensional normalized pixel coordinates (x,y) are mapped to a high-dimensional space to enhance the neural network's ability to capture high-frequency details of complex surface morphology, which is the key to the successful application of the NeRF model in surface reconstruction.

[0034] S200: Input the pixel coordinates and corresponding position encoding information from the three sets of interferometric data into the neural radiation field network to generate the reference mirror shape error W. ref The measured mirror surface shape error W test The measured mirror shape error W under rotational pose test Rot and the error W of the measured mirror surface shape in the translational pose test Shift Position encoding information is used to map pixel coordinates to a high-dimensional space.

[0035] Among them, such as Figures 3 to 5 As shown, the neural radiation field network includes invariant surface branch networks and variable surface branch networks.

[0036] The invariant surface branch network is used to generate W based on the pixel coordinates corresponding to the original input position and the positional encoding information corresponding to the pixel coordinates. ref Invariant surface branching networks include multi-layered sequentially connected fully connected networks, with at least one jumper structure in the network.

[0037] Specifically, such as Figure 5 As shown, the invariant surface branching network comprises eight sequentially connected fully connected layers. A jumper structure is included in the network to directly pass the raw input to the input of the fifth fully connected layer. The network takes positional information and corresponding positional encoding information as input, and uses eight 256-dimensional fully connected layers to estimate a fixed wavefront error represented by the surface shape of the reference mirror 1. The jumper structure at the input of the fifth fully connected layer improves the overall performance of the network.

[0038] Each layer of the fully connected network is a 256-dimensional fully connected layer, and the output data structure of each fully connected network layer is B×256, where B is the number of pixels.

[0039] The invariant surface branch only receives the normalized pixel coordinates and encoded information of the original position as input, because its modeling object is the fixed-mounted reference mirror 1, which does not change with the pose of the measured mirror 2. The eight-layer fully connected structure (256 dimensions per layer) provides sufficient nonlinear expressive power; the jumper structure (input directly connected to the fifth layer) is used to alleviate gradient vanishing in deep networks, retain low-frequency global information, and ensure the accuracy of the overall surface shape trend of the reference mirror 1.

[0040] The variable surface branching network is used to generate W based on the pixel coordinates and corresponding position encoding information of the three sets of input interferometric data. test W test Rot and W test Shift Variable-faceted branching networks include multi-layered, sequentially connected fully connected networks, with at least two jumper structures within the network.

[0041] Specifically, such as Figure 4 As shown, the variable-faceted branching network consists of eight sequentially connected fully connected layers, with two jumper structures within the network. These two jumper structures are used to directly pass the original input to the input of the fifth fully connected layer and the output of the last fully connected layer, respectively.

[0042] Each fully connected layer is a 256-dimensional fully connected layer, and the output data structure of each fully connected layer is B×256, where B is the number of pixels. The weights of the variable-face branch network differ for different inputs.

[0043] The variable-face branch needs to process three types of inputs: original, rotated, and translated pixel coordinates and positional encoding information. Although the network structure is the same, the output naturally corresponds to the measured mirror shape under different poses due to the different transformations of the input coordinates. The two jumper structures (connecting to the fifth layer and the output layer respectively) not only preserve intermediate features but also strengthen the final output's dependence on the original coordinates, improving the ability to model local distortions. At the same time, although the network structure corresponding to the three sets of inputs is the same, the weight parameters of the network corresponding to each input are different, which allows for a better output of the measured mirror shape under different poses.

[0044] S300: Based on the predicted surface height error and the actual surface height error corresponding to each pixel, the parameters of the neural radiation field network are optimized using a self-supervised training strategy; so that the predicted measurement result synthesized from the output results of the two branches approximates the actual measurement result.

[0045] During training, after each training iteration, the invariant surface branch network can generate a new W. ref The variable-surface branching network generates a new W. test W test Rot and W test Shift Then, based on these generated results and referring to the three calculation formulas corresponding to the laser interferometer surface shape measurement principle in the background technology, the optimized W after this training can be calculated. s W s Rot and W s Shift The specific process is as follows: For the original position prediction result (i.e., the prediction wavefront error) W s ,have: (1) For the rotational position measurement result (i.e., wavefront error) W s Rot ,have: (2) For the translational position measurement result (i.e., wavefront error) W s Shift ,have: (3) Then, based on the results of the loss function described below, the network parameters are adjusted. After multiple rounds of training and optimization, the predicted measurement result synthesized from the outputs of the two branches is made to approximate the actual measurement result. Specifically, in the self-supervised training strategy, the loss function is the mean square error (MSE) between the predicted measurement result and the actual interferometric measurement data, and the loss function value MSE in the i-th training optimization is... i The following conditions must be met: The following conditions must be met: ; Among them, W si n W si Rot-n and W si Shift-n These represent the original position predicted surface height error, rotation pose predicted surface height error, and translation pose predicted surface height error, respectively, for the nth pixel during the i-th training and optimization. m n W m Rot-n and W m Shift-n These represent the actual surface height error at the original position, the actual surface height error at the rotated pose, and the actual surface height error at the translated pose, respectively, for the nth pixel; N is the total number of pixels, n = 1, 2, ..., N.

[0046] The following conditions can be used to determine whether self-supervised training optimization has ended: S301: If the loss function is less than the preset threshold, the self-supervised training optimization ends.

[0047] S302: If the loss function is greater than or equal to the preset threshold, then continue to the next round of self-supervised training optimization.

[0048] S400: W obtained at the end of optimization refThis serves as the reference mirror shape error in the interferometric measurement system to be calibrated, in order to complete the calibration.

[0049] Once W ref Once calibrated and stored, its W will remain in operation as long as reference mirror 1 is not disassembled or damaged. ref The calibration results can be used long-term without the need for repeated calibration. If a new mirror 2 arrives subsequently, all measurements can be performed via W. absolute =W meas -W ref Achieve absolute surface reconstruction. Due to W... ref It directly models and outputs the results, rather than indirectly deriving them from the surface shape error of the measured mirror, thus avoiding the error accumulation problem in the traditional Zernike method, and showing significant advantages, especially in the mid-to-high frequency region. The calibration results are valid for a long time as long as the reference mirror 1 remains undisassembled or undamaged, representing a substantial improvement.

[0050] Taking the Zygo F3.3 transmission spherical test mirror 2 as an example, the effects of the present invention will be explained, and the specific implementation steps are as follows: Data Acquisition: In a 2304×2304 pixel image, the effective region radius is set to 650 pixels. To improve data reliability, this method has the capability to process multiple sets of rotation and translation data: interference images are acquired under three rotations (27°, 45°, 90°) and two translations (-20 pixels each in the x and y directions), and the data is input into the algorithm described in this patent; to obtain the pixel coordinates (x, y) and surface height error z for each pixel.

[0051] Coordinate normalization: The pixel coordinates are normalized using a normalization algorithm; Position encoding: Perform 10th-order sine and cosine encoding on the input coordinates to obtain the position encoding information corresponding to the prime coordinates; Network training: Using the PyTorch framework, the network was trained for 500 epochs on an RTX 3080 GPU with an initial learning rate of 0.001, which was reduced to 0.0001 after the 451st epoch to complete the network training optimization. Output: After training, the invariant surface branch outputs the reference surface shape error W. ref Variable surface branch output test surface shape error W test ; Verification and evaluation: The calibration accuracy is evaluated by the average difference error and reconstruction error.

[0052] The NeRF method described in this patent was used to perform calculations on the results of the conventional Zernike method under the same input. The calibrated surface shape of the tested mirror 2 is shown below. Figure 6As shown, the surface shape results of the reference mirror 1 and the tested mirror 2 obtained by the calculation are re-synthesized by simulation measurement results and compared with the actual measurement results GT (Ground Truth). The values ​​in the figure are the differences (RMS error values) between the surface shape results obtained by the two methods and the actual measurement results.

[0053] Figure 6 In the image, the first row shows the absolute surface error of the reference mirror at 45 degrees, from left to right: the true value, the surface error calculated using the Zernike method, and the surface error calculated using the Neural Radiation Field (NeRF). The second row shows the difference between the latter two (Zernike and NeRF) and the true value.

[0054] As can be seen from the first row, the surface shape errors calculated using either Zernike or neural radiation field methods tend to align with the true values. However, the difference map distribution shows that the true surface shape calculated using the neural radiation field method has a smaller gap from the true value, and the two are closer, especially in the mid-frequency error distribution (i.e., the mottled image region in the figure). Conversely, the mid-frequency feature difference in the difference map obtained using the Zernike method is much greater.

[0055] Meanwhile, the RMS value of the difference map obtained from the neural radiation field method is smaller than that of the Zernike method, which quantitatively confirms that the actual surface shape calculated by the neural radiation field method is closer to the true value. The third and fourth rows show the same processing at 90 degrees, and the results are consistent with those in the first and second rows.

[0056] In summary, compared to the traditional Zernike method, the method proposed in this patent yields significantly smaller fitting residuals, and the mid-to-high frequency residuals are also significantly reduced. This demonstrates the superiority of this method over the original Zernike method.

[0057] 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.

[0058] 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.

[0059] In an exemplary embodiment of this disclosure, an electronic device capable of implementing the above-described method is also provided.

[0060] 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.”

[0061] 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.

[0062] Electronic devices are manifested in the form of general-purpose computing devices. The components of an electronic device may include, but are not limited to: at least one processor, at least one memory, and a bus connecting different system components (including memory and processor).

[0063] 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.

[0064] 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).

[0065] 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.

[0066] 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.

[0067] 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.

[0068] 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.

[0069] 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.

[0070] 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.

[0071] 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.

[0072] 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).

[0073] 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.

[0074] 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.

[0075] 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 rotational and translational absolute calibration method based on neural radiation fields, characterized in that, The method includes the following steps: Using the interferometric measurement system to be calibrated, at least three sets of interferometric measurement data are acquired for the mirror under test in its original position, rotational pose, and translational pose. The interferometric measurement data are surface error distribution data obtained from the interferogram, in which each pixel exists in the form of pixel coordinates (x,y), surface height error z, and position encoding information corresponding to the pixel coordinates. The pixel coordinates and corresponding position encoding information from the three sets of interferometric measurement data are input into the neural radiation field network to generate the reference mirror shape error W. ref The measured mirror surface shape error W test The measured mirror shape error W under rotational pose test Rot and the error W of the measured mirror surface shape in the translational pose test Shift ; The location encoding information is used to map pixel coordinates to a high-dimensional space; The neural radiation field network includes invariant surface branching networks and variable surface branching networks; The invariant surface branch network is used to generate W based on the input information corresponding to the original input position. ref The invariant surface branch network includes a multi-layered sequentially connected fully connected network, and the network has at least one jumper structure. The variable surface branch network is used to generate W according to the input information corresponding to the original position, rotation pose, and translation pose, respectively. test W test Rot and W test Shift The variable-face branch network includes a multi-layer sequentially connected fully connected network, with at least two jumper structures in the network. Based on the predicted face height error and the actual face height error corresponding to each pixel, the parameters of the neural radiation field network are optimized using a self-supervised training strategy; so that the predicted measurement result synthesized from the output results of the two branches approximates the actual measurement result. W obtained at the end of optimization ref This serves as the reference mirror shape error in the interferometric measurement system to be calibrated, in order to complete the calibration.

2. The method according to claim 1, characterized in that, The invariant surface branch network includes an eight-layer sequentially connected fully connected network, with a jumper structure in the network. The jumper structure is used to directly pass the original input to the input of the fifth layer fully connected network. Each layer of the fully connected network is a 256-dimensional fully connected layer, and the output data structure of each fully connected network layer is B×256, where B is the number of pixels.

3. The method according to claim 1, characterized in that, The variable-face branching network includes eight sequentially connected fully connected networks, with two jumper structures in the network; the two jumper structures are respectively used to directly pass the original input to the input of the fifth fully connected network and the output of the last fully connected network. Each layer of the fully connected network is a 256-dimensional fully connected layer, and the output data structure of each fully connected network is B×256, where B is the number of pixels; the weights of the variable surface branch network corresponding to different inputs are different.

4. The method according to claim 1, characterized in that, Using the interferometric measurement system to be calibrated, acquire at least three sets of interferometric measurement data for the mirror under test in its original position, rotational pose, and translational pose, including: For each orientation of the mirror under test, multiple frames of phase-shifted interferograms are acquired using a Fizeau laser interferometer; Phase demodulation of the multi-frame phase-shifted interferograms is performed using phase-shifting interferometry to obtain a wrap-around phase map; The packaged phase map is subjected to phase unrolling processing to obtain a continuous phase distribution; The continuous phase distribution is converted into surface height error data, and the pixel coordinates and their corresponding surface height error data are used as the interferometric measurement data under this attitude.

5. The method according to claim 1, characterized in that, Before inputting the three sets of interferometric measurement data into the neural radiation field network, the method further includes: The original pixel coordinates (x, y) and the surface height error z are normalized to linearly map to the [0, 1] interval.

6. The method according to claim 1, characterized in that, After normalizing the original pixel coordinates (x, y) and the surface height error z, the method further includes: A 10th-order sine-cosine coding method is used to encode the normalized pixel coordinates (x,y), mapping the two-dimensional pixel coordinates into a 256-dimensional high-dimensional vector to enhance the neural network's ability to express mid-to-high frequency surface features.

7. The method according to claim 1, characterized in that, In the self-supervised training strategy, the loss function is the mean square error (MSE) between the predicted measurement result and the actual interferometric measurement data, and the loss function value MSE optimized in the i-th training iteration is... i The following conditions must be met: ； Among them, W si n W si Rot-n and W si Shift-n These represent the original position predicted surface height error, rotation pose predicted surface height error, and translation pose predicted surface height error, respectively, for the nth pixel during the i-th training and optimization. m n W m Rot-n and W m Shift-n These represent the actual surface height error at the original position, the actual surface height error at the rotated pose, and the actual surface height error at the translated pose, respectively, for the nth pixel; N is the total number of pixels, n = 1, 2, ..., N.

8. The method according to claim 7, characterized in that, If the loss function is less than a preset threshold, the self-supervised training optimization ends.

9. A non-transitory computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a rotational and translational absolute calibration method based on a neural radiation field as described in 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, When the processor executes the computer program, it implements a rotational and translational absolute calibration method based on a neural radiation field as described in any one of claims 1 to 8.

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