Neural-radiance-field-based rotational and translational absolute calibration method, medium and device

Abstract

The present application relates to the field of optical precision measurement, in particular to a rotation and translation absolute calibration method based on neural radiation field, medium and equipment. The method steps are: obtaining at least three groups of interference measurement data of the measured mirror under the original, rotation and translation pose of the to-be-calibrated interference measurement system, inputting the pixel coordinates and position coding information in the data into the neural radiation field network, optimizing the network parameters through the self-supervised training strategy, and completing the calibration of the reference mirror surface. Compared with the traditional Zernike method, the present scheme adopts a neural radiation field to construct a double-branch network, can adaptively learn the complex surface shape space distribution, and improve the separation accuracy of medium and high frequency errors; the double-branch synchronously directly outputs the errors of the reference mirror and the measured mirror, without dependence on the sequence, avoiding error transmission and accumulation; the self-supervised training mechanism implicitly compensates the pose deviation and noise interference through redundant constraints, and shows higher engineering robustness.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical precision measurement, in particular to a rotation-translation absolute calibration method based on a neural radiation field, a medium and equipment. BACKGROUND

[0002] Fizeau laser interferometer is the main instrument for nanometer ultra-precision optical surface measurement at present, which reconstructs the surface topography by comparing the optical path difference between the reference surface and the test surface. Specifically, the Fizeau interferometer adopts a common optical path structure, which is composed of a laser source, a light splitting element, a reference mirror and a measured mirror. After being split by the light splitting element, part of the laser beam is reflected on the high-precision reference mirror, and the other part is reflected on the measured mirror. The two reflected beams recombine and interfere to form an interference fringe image. Since the surface of the reference mirror is theoretically an ideal spherical surface (or a plane), and the measured mirror has actual machining errors, there is a difference in the optical path of the two beams. This optical path difference directly reflects the deviation of the measured mirror from the ideal surface, i.e. the surface error. Therefore, the measurement result of the Fizeau interferometer contains the surface error information of both the reference mirror and the measured mirror. To achieve higher precision measurement, the surface error of the interferometer reference mirror needs to be separated from the measurement result, so as to obtain the true surface of the measured surface, i.e. "absolute calibration".

[0003] The rotation-translation method is the current mainstream absolute calibration method. First, the measured part is measured in the original position, rotation and translation positions respectively, and then an operation model (such as formulas (1), (2) and (3)) is established based on the three sets of measurement data obtained, and the test surface is fitted and solved by using Zernike polynomials, and finally W ref and W test are obtained, realizing the error separation of the reference surface and the measured surface, and then the reference surface is indirectly deduced.

[0004] Specifically, the principle of laser interferometer surface measurement is as follows:

[0005] For the original position measurement result (i.e. wavefront error) , there is:

[0006] ; (1)

[0007] For the rotation position measurement result (i.e. wavefront error) , there is:

[0008] ; (2)

[0009] For the translation position measurement result (i.e. wavefront error) , there is:

[0010] (3)

[0011] wherein, W ref is the reference surface shape error, W test is the measured surface shape error. Rot and Shift represent the rotation and translation operations on the surface, respectively, W test Rot is the measured surface shape error of the rotated pose, W test Shift is the measured surface shape error of the translated pose.

[0012] However, the Zernike polynomial has limited nonlinear representation capability for complex surface shape characteristics such as medium-high frequency characteristics and local high-frequency defects, resulting in difficulty in separating medium-high frequency errors, and being unable to effectively represent non-smooth medium-high frequency error characteristics, thereby generating fitting errors. At the same time, since the Zernike method can only directly fit to obtain W test , W test Rot or W test Shift , and cannot directly output the reference surface shape error, an indirect operation based on a measurement result is required to obtain (such as ), which further leads to the accumulation of medium-high frequency fitting errors in the calibration result, and finally affects the absolute measurement accuracy of the subsequent optical elements. SUMMARY

[0013] In view of one of the above technical problems, the technical scheme adopted by the present application is as follows:

[0014] According to one aspect of the present application, a rotation and translation absolute calibration method based on a neural radiation field is provided, the method comprising the following steps:

[0015] using a to-be-calibrated interferometric measurement system, obtaining at least three sets of interferometric measurement data of the measured mirror at an original position, a rotated pose and a translated pose; the interferometric measurement data is surface shape error distribution data obtained from an interference pattern, wherein each pixel point exists in the form of pixel coordinates (x, y), surface shape height error z and position encoding information corresponding to the pixel coordinates;

[0016] inputting the pixel coordinates and corresponding position encoding information in the three sets of interferometric measurement data into a neural radiation field network to generate a reference surface shape error W ref , a measured surface shape error W test , a measured surface shape error of the rotated pose W test Rot and a measured surface shape error of the translated pose W test Shift ; the position encoding information is used to map the pixel coordinates to a high-dimensional space;

[0017] The neural radiation field network includes invariant surface branching networks and variable surface branching networks;

[0018] Invariant surface branching networks are used to generate W based on the input information corresponding to the original position of the input. ref Invariant surface branching networks include multi-layered sequentially connected fully connected networks, with at least one jumper structure in the network;

[0019] 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;

[0020] 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.

[0021] 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.

[0022] 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.

[0023] 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.

[0024] This invention has at least one of the following beneficial effects:

[0025] 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 precision effectively overcomes the fitting bottleneck of the traditional method in the high-frequency region.

[0026] The traditional Zernike method needs to fit the measured mirror surface error W test , and then indirectly derive the reference mirror error, which causes the fitting residual of the measured mirror to be transmitted and accumulated into the reference mirror result, especially in the medium and high frequency regions. The present scheme directly outputs W ref and W test through a double-branch neural network, and the two are optimized in parallel in the training without any dependence. The loss function directly constrains the consistency of the synthesized measurement value and the real data, without the need for intermediate derivation steps, which fundamentally breaks the error transmission chain and ensures the accuracy of the reference mirror calibration result, providing a reliable benchmark for subsequent absolute measurement.

[0027] The traditional calibration method is highly sensitive to the accuracy of rotation / translation operation and environmental stability, and slight pose deviation or vibration noise can easily cause distortion of the calculation result. The present scheme uses a self-supervised training mechanism to jointly optimize the reference mirror and measured mirror errors through three sets of attitude data, forming redundant constraints. The network automatically adjusts the parameters to minimize the overall reconstruction error during training, implicitly compensating for angle deviation, translation error and environmental noise interference in actual operation. This end-to-end global optimization strategy enables the system to maintain higher accuracy under non-ideal experimental conditions, and exhibits much better engineering robustness than the traditional method. BRIEF DESCRIPTION OF DRAWINGS

[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0029] Figure 1 A flowchart of a neural radiation field-based rotation and translation absolute calibration method is provided for the embodiments of the present application.

[0030] Figure 2 A structural diagram of an interferometric measurement system to be calibrated is provided for the embodiments of the present application.

[0031] Figure 3 A network structure diagram of a neural radiation field network (NeRF) is provided for the embodiments of the present application.

[0032] Figure 4 A network structure diagram of a variable surface branch network is provided for the embodiments of the present application.

[0033] Figure 5A network structure schematic diagram of the invariant surface branch network provided for the embodiment of the present application is shown.

[0034] Figure 6 The comparison diagram of the calibrated surface shape result of the measured mirror and the real measurement surface shape result GT after calibration using the above method (NeRF) and the traditional Zernike method of the present application respectively is shown. DETAILED DESCRIPTION

[0035] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0036] As a possible embodiment of the present application, as shown in Figure 1 a neural radiation field-based rotation-translation absolute calibration method is provided, and the method comprises the following steps:

[0037] S100: using a to-be-calibrated interferometric measurement system, at least three groups of interferometric measurement data of the measured mirror 2 in original position, rotation pose and translation pose are obtained; the interferometric measurement data is surface shape error distribution data obtained according to an interference figure, wherein each pixel point exists in the form of pixel coordinates (x, y), surface shape height error z and position coding information corresponding to the pixel coordinates.

[0038] Specifically, the to-be-calibrated interferometric measurement system can be built according to the content shown in Figure 2 After the reference mirror 1 and the measured mirror 2 are respectively placed in the corresponding positions and fixed through the respective corresponding mounting clamps, such as the measured mirror 2 is fixed through the corresponding measured mirror clamp 3, the corresponding interferometric measurement data is obtained. The rotation pose is mainly realized by rotating the plane where the pixel coordinates are located (i.e. the measured surface) around the optical axis; the translation pose is mainly realized by displacing the pixel coordinates in the x or y direction.

[0039] S100 comprises:

[0040] S101: for the measured mirror 2 in each pose, a plurality of phase shift interference figures are collected through a Fizeau laser interferometer.

[0041] In actual operation, phase shift interferometry (PSI) is adopted to collect phase shift interferograms, usually 4 or 13 frames of phase shift interferograms can be collected, and the phase shift step is λ / 4 (λ is the wavelength of laser, such as 632.8 nm). This step is used to obtain sufficient information to demodulate the absolute phase, which is the premise of subsequent quantitative surface reconstruction. The rotation and translation operations are respectively performed after the pose adjustment of the measured mirror 2 is completed, to ensure that the three groups of data correspond to different spatial states of the same measured mirror 2.

[0042] S102: Phase demodulation is performed on the multiple frames of phase shift interferograms based on phase shift interferometry to obtain a wrapped phase image.

[0043] The standard four-step algorithm or the least square phase shift algorithm is adopted to convert the multiple frames of interferograms into wrapped phase values (range [0, 2π)) of each pixel point. This step realizes the preliminary conversion from the optical intensity image to the phase information, but the real continuous surface shape cannot be reflected due to the phase wrapping.

[0044] S103: Phase unwrapping processing is performed on the wrapped phase image to obtain a continuous phase distribution.

[0045] In this step, the Goldstein path tracking or the minimum norm method can be used for phase unwrapping to eliminate the 2π jump and obtain a global continuous phase field. This step can improve the robustness in the presence of abrupt changes or noise regions and directly affects the final surface shape accuracy, which is a key link in the processing of interference data.

[0046] S104: The continuous phase distribution is converted into surface height error data, and the pixel coordinates and the corresponding surface height error data are taken as the interference measurement data under the pose.

[0047] According to the formula The phase is converted into height error (unit: nm) to form a two-dimensional array, and each element corresponds to the surface error value of a pixel point. From this, the corresponding interference measurement data under each pose can be generated, and the specific coordinates corresponding to each pixel point include the x and y of the pixel plane and the height error value z in the height direction. This data is the input target of the subsequent neural network.

[0048] Before S200, the method further includes:

[0049] S210: The original pixel coordinates (x, y) and the surface height error z are respectively subjected to coordinate normalization processing to be linearly mapped to the [0, 1] interval.

[0050] Since the x, y coordinate range (about 50-60mm) is much larger than z (<100um), directly inputting the original value will cause the network to be insensitive to the change in the z direction. Therefore, normalization processing is needed, and after normalization, the dimensions of each dimension are consistent, which significantly improves the convergence speed and stability of the fully connected network. This step belongs to the standard data preprocessing step.

[0051] S220: The normalized pixel coordinates (x, y) are position encoded using 10-order sine-cosine encoding, and the two-dimensional pixel coordinates are mapped to a 256-dimensional high-dimensional vector to enhance the expression ability of the neural network for medium-high frequency surface feature.

[0052] The output dimension of 10-order sine-cosine encoding is 256. This encoding enables the network to effectively perceive low, medium and high frequency features, and thus effectively extract high frequency details (such as scratches and ripples). Therefore, 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 topography, which is a key to the successful application of the NeRF model to surface reconstruction.

[0053] S200: The pixel coordinates and corresponding position encoding information in the three sets of interferometric measurement data are input into the neural radiation field network to generate the reference mirror surface error W ref , the measured mirror surface error W test , the measured mirror surface error W test of the rotation pose, and the measured mirror surface error W Rot of the translation pose. test Shift Position encoding information is used to map pixel coordinates to a high-dimensional space.

[0054] As shown in Figures 3 to 5 , the neural radiation field network includes an invariant surface branch network and a variable surface branch network.

[0055] The invariant surface branch network is used to generate W ref from the input original position corresponding pixel coordinates and position encoding information corresponding to the pixel coordinates. The invariant surface branch network includes multiple layers of sequentially connected fully connected networks, and at least one skip structure is provided in the network.

[0056] Specifically, as shown in Figure 5 , the invariant surface branch network includes eight layers of sequentially connected fully connected networks, and one skip structure is provided in the network, which is used to directly pass the original input to the input of the fifth fully connected network. The network uses position information and corresponding position encoding information as input, uses 8 fully connected layers of 256 dimensions to estimate the fixed wavefront error represented by the reference mirror 1 surface, and uses a skip structure at the input end of the fifth fully connected layer to improve the overall performance of the network.

[0057] 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.

[0058] 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.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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.

[0063] 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.

[0064] During training, after each training iteration, the invariant surface branch network can generate a new W.ref The variable face branch network corresponds to generate a new W test , W test Rot , and W test Shift Then, according to the three calculation formulas corresponding to the principle of laser interferometer surface shape measurement in the background art, the W s , W s Rot , and W s Shift after this training optimization can be calculated, and the specific process is as follows:

[0065] For the original position prediction result (that is, the predicted wavefront error) W s , we have:

[0066] ; (1)

[0067] For the rotation position measurement result (that is, the wavefront error) W s Rot , we have:

[0068] ; (2)

[0069] For the translation position measurement result (that is, the wavefront error) W s Shift , we have:

[0070] ; (3)

[0071] Then, according to the results of the following loss function, the parameters of the network are adjusted, and after multiple rounds of training optimization, the predicted measurement result synthesized by the output results of the two branches approximates 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 i of the i-th training optimization satisfies the following conditions:

[0072] satisfies the following conditions:

[0073] ;

[0074] where W si n , W si Rot-n , and W si Shift-n are the original position prediction surface height error, the rotation pose prediction surface height error, and the translation pose prediction surface height error corresponding to the n-th pixel point obtained at the i-th training optimization, respectively; W mn , W m Rot-n and W m Shift-n respectively represent the original position actual surface height error, the rotation pose actual surface height error and the translation pose actual surface height error corresponding to the nth pixel point; N represents the total amount of pixel points, n = 1, 2, …, N.

[0075] Whether the self-supervised training optimization is completed can be judged according to the following conditions:

[0076] S301: If the loss function is less than a preset threshold, the self-supervised training optimization is completed.

[0077] S302: If the loss function is greater than or equal to the preset threshold, the next round of self-supervised training optimization is continued.

[0078] S400: The W ref obtained at the end of the optimization is taken as the reference mirror surface error in the interferometric measurement system to be calibrated, so as to complete the calibration.

[0079] Once the W ref is calibrated and stored, as long as the reference mirror 1 is not disassembled or damaged, the W ref calibration result can be used for a long time without repeated calibration. When a new measured mirror 2 comes in later, all measurements can be realized by W absolute = W meas - W ref to realize absolute surface reconstruction. Since W ref is directly modeled and output, rather than indirectly derived through the measured mirror surface error, the error accumulation problem in the traditional Zernike method is avoided, especially in the medium and high frequency regions. The calibration result is long-term effective under the premise that the reference mirror 1 is not disassembled or damaged, which greatly improves.

[0080] Taking the Zygo F3.3 transmission spherical measured mirror 2 as an example, the effect of the present application is described, and the specific implementation steps are as follows:

[0081] Data acquisition: In the 2304x2304 pixel image, the effective area radius is set to 650 pixels. In order to improve the data reliability, the present method has the processing capability of multiple rotation and translation data: 3 times of rotation (27°, 45°, 90°) and 2 times of translation (x, y direction each-20 pixels) under the interference image, the data is input into the algorithm described in the present patent; In order to obtain each pixel point in pixel coordinates (x, y) and surface height error z.

[0082] Coordinate normalization: the pixel coordinates are normalized by using a normalization algorithm;

[0083] Position encoding: 10-order sine-cosine encoding is performed on the input coordinates to obtain the position encoding information corresponding to the primitive coordinates.

[0084] Network training: using the PyTorch framework, training 500 rounds on an RTX 3080 GPU, the initial learning rate is 0.001, and after the 451st round, it is reduced to 0.0001, and the network training optimization is completed.

[0085] Output result: after training, the invariant surface branch outputs the reference surface shape error W ref , and the variable surface branch outputs the test surface shape error W test .

[0086] Verification and evaluation: the calibration accuracy is evaluated by the average difference error and the reconstruction error.

[0087] The above method (NeRF) of the present patent is used respectively, and the same input is operated with the traditional Zernike method. The calibrated surface shape result of the measured mirror 2 is as shown in Figure 6 . The surface shape results of the reference mirror 1 and the measured mirror 2 obtained by operation are re-simulated to synthesize the measurement results, and compared with the real measurement results GT (Ground Truth). The values in the figure are the difference (RMS error value) between the surface shape results obtained by the two methods and the real measurement results.

[0088] Figure 6 In the first row, the first row is the absolute surface shape error of the reference mirror at 45 degrees, and from left to right, the true value, the surface shape error obtained by using the Zernike method, and the surface shape error obtained by using the neural radiation field are shown. The second row is the difference between the latter two (Zernike and NeRF) and the true value.

[0089] From the first row, it can be seen that whether using Zernike or neural radiation field, the calculated surface shape error is consistent with the true value. However, from the difference distribution, the real surface shape after the neural radiation field method is closer to the true value, especially the error distribution of the middle frequency (i.e. the mottled image area in the figure). On the contrary, the difference in the middle frequency of the difference graph obtained by using the Zernike method is farther away.

[0090] At the same time, the value in the upper left corner (the RMS of the difference graph) is smaller than that of the Zernike method, which quantitatively verifies that the real surface shape after the neural radiation field method is closer to the true value. The third and fourth rows are the same processing at 90 degrees, and the conclusions obtained are consistent with those of the first and second rows.

[0091] In summary, compared with the traditional Zernike method, the fitting residual obtained by the method proposed in the patent is significantly smaller in numerical value, and the medium and high frequency residual is significantly reduced. It is proved that the method is superior to the original Zernike.

[0092] In addition, although the various steps of the methods in the present disclosure are described in a particular order in the accompanying drawings, this does not require or imply that the steps must be performed in this particular order, or that all of the steps shown must be performed to achieve the desired result. Additionally or alternatively, certain steps can be omitted, multiple steps can be combined into one step, and / or one step can be divided into multiple steps, etc.

[0093] From the above description of the embodiments, those skilled in the art can easily understand that the example embodiments described herein can be implemented by software, or by software in combination with necessary hardware. Therefore, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a U disk, a mobile hard disk, etc.) or a network, and includes a number of instructions to make a computing device (which can be a personal computer, a server, a mobile terminal, or a network device, etc.) execute the methods according to the embodiments of the present disclosure.

[0094] In the example embodiments of the present disclosure, an electronic device capable of implementing the above method is also provided.

[0095] Those skilled in the art can understand that each aspect of the present disclosure can be implemented as a system, a method or a program product. Therefore, each aspect of the present disclosure can be embodied in the form of a complete hardware embodiment, a complete software embodiment (including firmware, microcode, etc.), or an embodiment combining hardware and software aspects, which can be collectively referred to as "circuitry", "module" or "system" herein.

[0096] The electronic device according to this embodiment of the present disclosure. The electronic device is only an example, and should not bring any limitation to the function and use range of the embodiments of the present disclosure.

[0097] The electronic device is in the form of a general computing device. The components of the electronic device can include but are not limited to the above-mentioned at least one processor, the above-mentioned at least one storage, a bus connecting different system components (including storage and processor).

[0098] The storage stores program code, which can be executed by the processor, so that the processor executes the steps according to various example embodiments of the present disclosure described in the above "example method" section of the specification.

[0099] The storage can include a readable medium in the form of volatile storage such as random access memory (RAM) and / or cache memory, and can further include a non-volatile storage such as read only memory (ROM).

[0100] The storage can also include a program / utility, having a set of program modules, which are configured to carry out the processes of the subject matter described herein, including an operating system, one or more application programs, other program modules, and program data, each or some combination thereof, which may

[0101] The bus can represent one or more of several types of bus structures, including a storage bus or bus controller, a peripheral bus, a graphics bus, a processor or local bus using any of a variety of bus architectures.

[0102] The electronic device can also communicate with one or more external devices such as a keyboard or a pointing device, through an I / O interface. Additionally, the electronic device can communicate with one or more devices that enable a user to interact with the electronic device through an input device or devices 110. The input device(s) 110 can include, for example, a microphone, a camera, a button, a switch, an infrared port, a USB port, a Bluetooth® interface, a memory card slot, a wireless radio frequency interface, or any combination thereof. The input device(s) 110 can also include a display for conveying information, such as a video display unit, a CRT screen, a flat-panel display, a television, a computer monitor, a projection device, or any combination thereof. The electronic device can also include an output device, such as a speaker, a printer, a television, a flat-panel display, a computer monitor, a projection device, or any combination thereof. The electronic device can further include a network interface 112 for interfacing the electronic device with one or more other electronic devices or a network.

[0103] In exemplary embodiments of the present disclosure, a computer readable storage medium having stored thereon a program product capable of implementing the above-described methods of the present specification is also provided. In some possible implementations, various aspects of the present disclosure can also be implemented in the form of a program product including program code, which, when executed on a terminal device, causes the terminal device to perform the steps described in the above-mentioned “Exemplary Methods” section according to various exemplary embodiments of the present disclosure.

[0104] A program product can take any combination of one or more computer-readable media. The computer-readable media can be a computer-readable storage medium or a computer-readable signal medium. The computer-readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the above. More specific examples (a non-exhaustive list) of the computer-readable storage medium include an electrical connection having one or more wires, a portable disc, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0105] The computer-readable signal medium can include a computer-readable storage medium that is propagated as a carrier wave in a baseband or propagated as part of a propagated data signal in a carrier, such as a propagated signal. The propagated signal can take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer-readable signal medium can be any computer-readable medium that is not a computer-readable storage medium and that can communicate, propagate, or transport programming for use by or in connection with an instruction execution system, apparatus, or device.

[0106] The program code embodied on the computer-readable media can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical, RF, etc., or any suitable combination of the above.

[0107] Program code used by or in connection with the described embodiments can be written in any of a number of suitable programming languages and implementing methods, including an object-oriented programming language such as Java, C++, or the like, and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computing device, partly on the user's computing device, as a stand-alone software package, partly on the user's computing device and partly on a remote computing device or entirely on the remote computing device or server. In the latter scenario, the remote computing device can be connected to the user's computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computing device such as through the Internet using an Internet Service Provider. The application program code can be downloaded to the user's computing device from an external computer or external storage located in a location remote from the user computing device, through the Internet, or from any other remote source using, for example, a modem, a cellular protocol (e.g., Global System for Mobile Communications (GSM), Code Division Multiple Access (CDMA), Long-Term Evolution (LTE), etc.), or other protocol.

[0108] Furthermore, the accompanying drawings merely show the illustrative embodiments of the method according to the present application and are therefore not restrictive in nature. It will be readily understood that the processing shown in the accompanying drawings does not indicate or limit the chronological order of the processes. In addition, it will be readily understood that the processes can be executed, for example, synchronously or asynchronously in a plurality of modules.

[0109] It should be noted that, although several modules or units of the devices for action execution are mentioned in the foregoing detailed description, such division into modules or units is not mandatory. Indeed, according to an embodiment of the present disclosure, features and functions of two or more of the above-described modules or units can be embodied in one module or unit. Conversely, features and functions of one module or unit described above can be further divided into plural modules or units.

[0110] The above merely shows the specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any changes or replacements within the technical scope disclosed by the present application can be easily conceived by those skilled in the art, and should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A neural-radiance-field-based rotation-translation absolute calibration method, characterized in that, The method comprises the following steps: Using the interferometric measurement system to be calibrated, at least three sets of interferometric measurement data of the measured mirror at the original position, the rotating pose and the translating pose are acquired; the interferometric measurement data is the surface shape error distribution data acquired according to the interferogram, wherein each pixel point exists in the form of pixel coordinates (x, y), surface shape height error z and position encoding information corresponding to the pixel coordinates; inputting pixel coordinates and corresponding position encoding information in the three groups of interferometric measurement data into a neural radiation field network to generate reference mirror surface error W ref , measured mirror surface error W test , measured mirror surface error W of the rotation pose test Rot , and measured mirror surface error W of the translation pose test Shift ; The position encoding information is used for mapping the pixel coordinates to a high-dimensional space; The neural radiation field network comprises an invariant surface branch network and a variable surface branch network; The invariant surface branch network is used for generating W ref The invariant surface branch network comprises a plurality of layers of sequentially connected full connection networks, and at least one skip structure is arranged in the network. The variable-face branch network is used for generating W test , W test Rot and W test Shift respectively corresponding to the input information of the input original position, the rotation pose and the translation pose respectively. The variable-face branch network comprises a plurality of layers of sequentially connected full connection networks, and at least two jump structures are arranged in the network. According to the predicted surface shape height error and the actual surface shape height error corresponding to each pixel point, the parameters of the neural radiation field network are optimized by a self-supervised training strategy; and the predicted measurement result synthesized by the output results of the two branches is made to approximate the actual measurement result. The W obtained at the end of the optimization is used as the reference mirror figure error in the interferometry system to be calibrated to complete the calibration. ref , as the reference mirror figure error in the interferometry system to be calibrated to complete the calibration.

2. The method of claim 1, wherein, The invariant surface branch network comprises eight sequentially connected fully connected networks, and a jump structure is arranged in the network; the jump structure is used for directly transmitting the original input to the input of the fifth fully connected network. The fully connected network of each layer is a 256-dimensional fully connected layer, and the output data structure of each fully connected network is Bx256, wherein B is the number of pixels.

3. The method of claim 1, wherein, The variable surface branch network comprises eight sequentially connected fully connected networks, and two jump structures are arranged in the network; the two jump structures are respectively used for directly transmitting the original input to the input of the fifth fully connected network and the output of the last fully connected network. The fully connected network of each layer is a 256-dimensional fully connected layer, and the output data structure of each fully connected network is Bx256, wherein B is the number of pixels; the weights of the variable surface branch network corresponding to different inputs are different.

4. The method of claim 1, wherein, Using the interferometric measurement system to be calibrated, at least three sets of interferometric measurement data of the measured mirror at the original position, the rotating pose and the translating pose are acquired, comprising: For the measured mirror at each pose, a plurality of phase shift interferograms are collected by a Fizeau laser interferometer; The plurality of phase shift interferograms are phase demodulated based on phase shift interferometry to obtain wrapped phase maps; The wrapped phase maps are subjected to phase unwrapping processing to obtain continuous phase distributions; The continuous phase distributions are converted into surface shape height error data, and the pixel coordinates and the corresponding surface shape height error data are taken as the interferometric measurement data at the pose.

5. The method of claim 1, wherein, Before the three sets of interferometric measurement data are input into the neural radiation field network, the method further comprises: The original pixel coordinates (x, y) and the surface shape height error z are subjected to coordinate normalization processing respectively, so as to be linearly mapped to the [0, 1] interval.

6. The method of claim 1, wherein, After the original pixel coordinates (x, y) and the surface shape height error z are subjected to coordinate normalization processing respectively, the method further comprises: The normalized pixel coordinates (x, y) are subjected to position encoding by adopting a 10th-order sine cosine coding, so as to map the two-dimensional pixel coordinates into a 256-dimensional high-dimensional vector, so as to enhance the expression ability of the neural network to the medium and high frequency surface shape features.

7. The method of claim 1, wherein, In the self-supervised training strategy, a loss function is a mean square error (MSE) between the predicted measurement result and the actual interferometric measurement data, and a loss function value MSE of the i-th training optimization i satisfies the following conditions: ； wherein, W si n , W si Rot-n and W si Shift-n are the original position predicted surface height error, the rotation pose predicted surface height error and the translation pose predicted surface height error of the nthpixel point corresponding to the ithtraining optimization, respectively; W m n , W m Rot-n and W m Shift-n are the original position actual surface height error, the rotation pose actual surface height error and the translation pose actual surface height error of the nthpixel point, respectively; N is the total amount of pixel points, and n = 1, 2, …, N.

8. The method of claim 7, wherein, If the loss function is less than a preset threshold value, the self-supervised training optimization is ended. 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 is executed by the processor to realize the neural radiation field-based rotating and translating absolute calibration method 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 implements the neural-radiance-field-based rotation-translation absolute calibration method according to any one of claims 1-8 when executing the computer program.

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