A method and system for multi-surface phase-shifting interferometry based on LSTM

Abstract

The application belongs to the field of optical precision measurement, and provides a multi-surface phase shift interferometry method and system based on LSTM, which comprises the following steps: placing a test mirror at a distance of alpha from a reference mirror, sampling the interferometer optical path at a preset sampling timing when wavelength tuning is performed, calculating the phases corresponding to the first interference cavity, the second interference cavity and the third interference cavity based on the central wavelength, calculating the light intensity at the receiving end of the interferometer based on the phases, and obtaining a light intensity matrix; inputting the light intensity matrix as a training data set and the phases as labels into a neural network based on LSTM for training, and obtaining a solving network after the training is completed; placing a mirror to be measured at a distance of alpha from the reference mirror, collecting an interference pattern photo and converting it into a gray scale matrix, inputting the gray scale matrix into the solving network, obtaining a phase value, unwrapping the phase value, and obtaining the surface shape of the mirror to be measured. Compared with the prior art, the application provides a method for accurately reconstructing the surface shape under non-ideal phase shift conditions.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical precision measurement, and in particular to a multi-surface phase shift interferometry method and system based on LSTM. BACKGROUND

[0002] Traditional phase shift interferometry algorithms were designed to solve the surface shape of a single surface in the early stage, which often achieves phase shift by moving the reference plane. For the surface shape detection of optical devices containing multiple nearly parallel surfaces, it is usually necessary to smear Vaseline or other substances on the non-measurement surface to cause scattering of the reflected light of the non-measurement surface to avoid affecting the main interference signal. In view of this inconvenience, another multi-surface phase shift interferometry method is proposed. In order to solve the signal separation and accurate calculation problem in multi-surface phase shift interferometry, researchers have proposed various improved methods. For example, in the frequency domain analysis field, Fourier transform combined with window function can effectively separate the interference signal in the frequency domain, thereby simplifying the complexity of equation solving and enhancing the harmonic suppression performance to reduce the influence of phase shift error.

[0003] At present, in actual measurement, in order to facilitate surface shape solving, it is usually required to achieve equal step phase shift as much as possible, that is, to ensure the stability of the laser wavelength modulation rate, the accuracy of image sampling, and to meet the uniformity of phase shift interval as much as possible, so as to reduce the influence of phase shift error. However, in actual operation, we often encounter non-ideal phase shift conditions. For example, due to the nonlinear response of the device or environmental interference, the phase shift amount of each step may deviate from the expectation, showing constant offset or random fluctuation. Such deviation will cause distortion of the phase information in the interference pattern, thereby affecting the accuracy of the final surface shape calculation. The traditional phase shift interferometry calculation method usually assumes ideal phase shift conditions, and lacks effective error compensation ability for such deviation, so it cannot accurately reconstruct the surface shape under non-ideal phase shift conditions. SUMMARY

[0004] In order to overcome the defect that the prior art cannot accurately reconstruct the surface shape under non-ideal phase shift conditions, the present application provides a multi-surface phase shift interferometry method and system based on LSTM.

[0005] In order to achieve the above technical effects, the technical solutions of the present application are as follows:

[0006] A multi-surface phase shift interferometry method based on LSTM, comprising the following steps:

[0007] Place the test mirror at a distance of alpha from the reference mirror, and the interference light path passes through the reference mirror, the first plane of the test mirror and the second plane of the test mirror in turn; the first interference cavity is formed between the reference mirror and the first plane of the test mirror; wherein the second interference cavity is formed between the reference mirror and the second plane of the test mirror; the first plane and the second plane of the test mirror form the third interference cavity;

[0008] When wavelength tuning is performed, the interference light path is sampled at a preset sampling timing, the phases corresponding to the first interference cavity, the second interference cavity and the third interference cavity are calculated based on the center wavelength, the light intensity at the receiving end of the interferometer is calculated based on the phases, and a light intensity matrix is obtained;

[0009] The light intensity matrix is taken as a training data set, the phase of the first interference cavity corresponding to the light intensity matrix is taken as a label and input into the LSTM-based neural network for training, and an algorithm network is obtained after training is completed;

[0010] The test mirror is placed at a distance of alpha from the reference mirror, an interference pattern photo is collected and converted into a gray scale matrix, the gray scale matrix is input into the algorithm network, a phase value is obtained, the phase value is unwrapped, and a surface profile of the test mirror is obtained.

[0011] The application further provides a multi-surface phase shift interferometry system based on LSTM.

[0012] The training data acquisition module samples the interference light path at a preset sampling timing and calculates the phases corresponding to the interference cavities and the light intensity on the receiving light path;

[0013] The model training module is loaded with an LSTM-based neural network, the data collected by the training data acquisition module is input into the LSTM-based neural network for training, and an algorithm network is obtained after training is completed;

[0014] The measurement module collects an interference pattern photo of the test mirror and converts it into a gray scale matrix, inputs the gray scale matrix into the algorithm network, obtains a phase value, unwraps the phase value, and obtains a surface profile of the test mirror.

[0015] The application further provides an electronic device, which comprises a memory, a processor, a computer program stored in the memory and executable on the processor, and the processor implements the multi-surface phase shift interferometry method based on LSTM as described in the application when executing the computer program.

[0016] The application further provides a computer readable storage medium, which stores a computer program, and the computer program is executable on the processor to implement the multi-surface phase shift interferometry method based on LSTM as described in the application.

[0017] Compared with the prior art, the present application has the beneficial effects of:

[0018] The present application learns the phase information of the interference pattern from the input data by the LSTM neural network. Since the random phase shift factor usually exists in different ways in the training sample, the trained model can generalize this change pattern and automatically compensate for these errors in the inference stage. Secondly, the LSTM neural network can capture long-term trends from the gray change sequence, while the random phase shift factor usually exists in the form of noise, which is manifested as short-term deviation or disturbance. The LSTM neural network can ignore these short-term random fluctuations by capturing the main trend characteristics, so that the final phase calculation is not sensitive to the random phase shift factor. In addition, in the training process of the LSTM neural network, it directly learns the relationship between the phase and the gray change from the gray sequence without relying on the assumption of the phase shift step or error in the traditional method. Therefore, when the network processes the interference pattern under the condition of random phase shift, it can directly map to the phase value through the learned weight without relying on the accurate step or phase shift condition as in the traditional method. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 A flowchart of a multi-surface phase shift interferometry method based on LSTM.

[0020] Figure 2 A placement diagram of the reference mirror and the test mirror.

[0021] Figure 3 A wavelength response curve of the laser and a fitted response curve.

[0022] Figure 4 An architecture diagram of the LSTM-based neural network.

[0023] Figure 5 An architecture diagram of a multi-surface phase shift interferometry system based on LSTM.

[0024] Figure 6 A Fizeau interferometer optical path set up in Example 6.

[0025] Figure 7 A surface shape measurement result of the multi-surface phase shift interferometry method based on LSTM.

[0026] Figure 8 A surface shape measurement result of the 45-step algorithm.

[0027] Figure 9 A surface shape diagram measured by the present application and the 45-step algorithm under the condition of random phase shift. DETAILED DESCRIPTION

[0028] The drawings are only for illustrative purposes and cannot be understood as limiting the present application;

[0029] It is understood by those skilled in the art that some well-known descriptions in the drawings can be omitted.

[0030] The technical solutions of the present application will be further described below in combination with the drawings and examples.

[0031] Example 1

[0032] This embodiment proposes a multi-surface phase shift interferometry method based on LSTM, as shown in Figure 1 The flowchart of the multi-surface phase shift interferometry method based on LSTM of this embodiment is shown in

[0033] The multi-surface phase shift interferometry method based on LSTM proposed in this embodiment includes the following steps:

[0034] Place the test mirror at a distance of a from the reference mirror, and the interference light path passes through the reference mirror, the first plane of the test mirror and the second plane of the test mirror in turn; wherein the reference mirror and the first plane of the test mirror form a first interference cavity; the reference mirror and the second plane of the test mirror form a second interference cavity; the first plane and the second plane of the test mirror form a third interference cavity;

[0035] When wavelength tuning is performed, the interferometer light path is sampled at a preset sampling timing, the phases corresponding to the first interference cavity, the second interference cavity and the third interference cavity are calculated based on the center wavelength, the light intensity at the receiving end of the interferometer is calculated based on the phases, and a light intensity matrix is obtained;

[0036] The light intensity matrix is used as a training data set, and the phase of the first interference cavity corresponding to the light intensity matrix is used as a label to input into a neural network based on LSTM for training, and after training, a solving network is obtained;

[0037] Place the test mirror at a distance of a from the reference mirror, collect an interference pattern photo and convert it into a gray scale matrix, input the gray scale matrix into the solving network, obtain a phase value, unwrap the phase value, and obtain a surface profile of the test mirror.

[0038] In this embodiment, the LSTM neural network is used to extract the phase information of the interferogram from the input data. Since the random phase shift factor in the training samples exists in a variety of ways, the trained model can effectively learn and generalize these change patterns, thereby automatically compensating for the errors caused thereby in the inference stage. In addition, the LSTM neural network has the ability to capture long-term trends in the gray scale change sequence, while the random phase shift factor usually behaves as a short-term disturbance or offset. By focusing on the main trend features, the LSTM neural network can effectively ignore these short-term random fluctuations, thereby improving the robustness of the phase calculation to the random phase shift factor. Further, in the training process of the LSTM neural network, the network directly learns the internal relationship between the phase and the gray scale change from the gray scale sequence without relying on the assumptions of the phase shift step or error in the traditional method. Therefore, when processing the interferogram with a random phase shift condition, the model can directly map the input data to the phase value through the learned weights without relying on the precise step or specific phase shift condition as in the traditional method.

[0039] As an example, the test mirror is a transparent parallel plate.

[0040] As shown in FIG. 1, the placement diagram of the reference mirror and the test mirror is shown. Wherein, r is the reference mirror, u is the first plane of the test mirror, and d is the second plane of the test mirror. Figure 2

[0041] Specifically, three interference cavities are generated by the transparent parallel plate, and the second and third interference cavities can be regarded as interference signals. By taking the phase information of the first interference cavity as a label, the LSTM neural network can directly learn the nonlinear mapping relationship between the input gray scale sequence and the target phase. Although the interference signals generated by the second and third interference cavities will affect the overall interferogram, through the end-to-end learning ability of the LSTM neural network, the neural network can identify and ignore these secondary interference signals, focus on the phase features of the first interference cavity, and ensure the accuracy and reliability of the measurement results. Through this design, the system can adapt to various configurations of different test mirrors such as transparent parallel plates, and is suitable for complex optical measurement scenarios.

[0042] In an optional embodiment, the step of sampling the optical path of the interferometer at a preset sampling timing includes: performing a fourth-order polynomial fitting on a wavelength response curve of the laser, and sampling the fitted curve at a preset sampling timing.

[0043] As shown in FIG. 2, the wavelength response curve of the laser and the fitted response curve are shown. Figure 3

[0044] ​​In this embodiment, through the operation of fitting, the discrete signal is approximately converted into a continuous signal. The high-order phase shift error is derived from the nonlinearity when the wavelength of the laser is tuned. The sampling points are obtained on the response curve after fitting, which is equivalent to considering the nonlinear factor in the training set, thereby eliminating the influence of the high-order phase shift error from the root.

[0045] In an optional embodiment, the method further comprises: changing the cavity length of the interference cavity, and calculating the corresponding phase and light intensity on the test mirror under different cavity lengths to obtain a plurality of light intensity matrices; and taking the plurality of light intensity matrices as training data, and taking the first interference cavity length corresponding to any matrix as a label to input into the LSTM-based neural network for training.

[0046] Specifically, the interference signal light intensity I(x, y) received at a certain pixel point in the imaging system of the interferometer can be represented as:

[0047]

[0048] where I0(x, y) is the background light intensity, I1, I2, and I3 are the modulation amplitudes of the interference signals generated by the first interference cavity, the second interference cavity, and the third interference cavity, respectively; and φ1(x, y), φ2(x, y), and φ3(x, y) are the initial phases of the three groups of interference signals.

[0049] φ1(x, y) = 2kL ru (x, y)

[0050] φ2(x, y) = 2k[L ru (x, y) + nL rd (x, y)]

[0051] φ3(x, y) = 2knL ud (x, y)

[0052] where L ru is the first interference cavity, L rd is the second interference cavity, and L ud is the third interference cavity; k = 2π / λ, and n is the refractive index of the material to be measured.

[0053] In this embodiment, by changing the cavity length of the interference cavity and calculating the corresponding phase and light intensity on the test mirror under different cavity lengths, the diversity of the training data can be significantly increased, the training set data can be greatly increased, a wider phase distribution characteristic can be covered, and thus the generalization ability and robustness of the neural network model can be improved. This way not only reduces the dependence on real data collection, effectively reduces the experimental cost and time overhead, but also enhances the adaptability of the model to complex environments and random noise.

[0054] Further optionally, the step of changing the cavity length of the interference cavity comprises changing the fluctuation of the mirror surface of the test mirror; and the cavity length calculation formula of the interference cavity is as follows:

[0055] L ru (x,y) = L1(x,y) + Z u0 (x,y)

[0056] L rd (x,y) = L2(x,y) + Z d0 (x,y)

[0057] L ud (x,y) = L2(x,y) - L1(x,y)

[0058] wherein (x,y) represents an arbitrary point on the test mirror, L1 is the interval distance between the first plane of the test mirror and the reference mirror, L2 is the interval distance between the second plane of the test mirror and the reference mirror, Z u0 (x,y) is the fluctuation of the first plane of the test mirror, Z d0 (x,y) is the fluctuation of the second plane of the test mirror, L ru , L rd and L ud are the first interference cavity, the second interference cavity and the third interference cavity respectively.

[0059] As an example, the magnitude of Z u0 (x,y) and Z d0 (x,y) is nanometer to micrometer.

[0060] In an optional embodiment, the step of changing the fluctuation of the mirror surface of the test mirror comprises adjusting and randomly combining the fluctuation of the first plane of the test mirror and the fluctuation of the second plane of the test mirror within a preset range.

[0061] Specifically, Z u0 (x,y) and Z d0 (x,y) are valued within a preset range and randomly combined to obtain a plurality of collocation combinations of three initial phase values φ1(x,y), φ2(x,y) and φ3(x,y), and the corresponding light intensity is calculated, the sequence of the phase φ1(x,y) is taken modulo 2π, and the obtained remainder is numbered in order of size, and the number is input into the neural network as a simplified label value.

[0062] In this embodiment, by changing the fluctuation of the test mirror surface, the cavity length of the interference cavity can be flexibly adjusted on a micro scale, thereby generating diversified phase data under different cavity lengths, significantly increasing the richness of the training data and covering a wider range of phase distribution. In addition, the generated micro fluctuation change can also simulate the interference cavity characteristics under various actual measurement scenarios, enabling the neural network to have stronger adaptability and still maintain high-precision phase calculation performance when processing interference patterns in complex or random environments, thereby providing a guarantee for the accuracy and stability of optical measurement.

[0063] Further optionally, the LSTM-based neural network contains a plurality of LSTM layers, each LSTM layer contains a plurality of neurons, and an activation layer is placed after each neuron.

[0064] As shown in FIG. 1, an architecture diagram of the LSTM-based neural network is shown. Figure 4

[0065] In this embodiment, the deep features are extracted layer by layer through the multi-layer LSTM structure, which more accurately models the time correlation and nonlinear relationship in the interference pattern data. Meanwhile, the introduction of the activation layer alleviates the gradient vanishing problem and optimizes the gradient flow and training stability of the network, thereby accelerating the convergence and improving the training efficiency.

[0066] Embodiment 2

[0067] This embodiment improves the LSTM-based multi-surface phase shift interference measurement method proposed in Embodiment 1.

[0068] In an optional embodiment, the method further comprises: when using laser wavelength tuning to perform phase shifting, introducing a plurality of constant phase shift offsets, training the phase calculated based on each constant phase shift offset and the light intensity input in the LSTM-based neural network, and obtaining a plurality of calculation networks after the training is completed; inputting the number of the plurality of calculation networks as a label into the LSTM-based neural network for training to obtain a judgment network; the judgment network measures the phase shift offset based on the gray scale change matrix of the to-be-measured mirror, and selects a suitable calculation network according to the size of the phase shift offset.

[0069] In this embodiment, by introducing a plurality of constant phase shift offsets, the coverage range of the training data can be effectively expanded, and diversified data sets under different offset conditions can be generated, thereby improving the adaptability and robustness of the neural network to constant offsets. Further, compared with a single network model, the plurality of calculation networks obtained through training have more targeted calculation performance, which can significantly improve the accuracy and efficiency of phase calculation. In addition, through the judgment network, it can select the most suitable calculation network for the current environment and specific conditions according to the gray scale matrix features of the to-be-measured mirror, thereby improving the flexibility of the system in complex measurement scenarios and optimizing the stability and accuracy of the calculation process.​

[0070] In an optional embodiment, the step of introducing a plurality of constant phase shift offsets comprises: presetting a plurality of constant phase shift offsets, changing the sampling interval of the sampling timing according to the size of the phase shift offset, and obtaining the light intensity matrix and the phase corresponding to different phase shift offsets.

[0071] As an exemplary illustration, the time interval is set to 0.1 s, 50 samples are taken for the interference optical path to obtain the initial light intensity matrix, then the sampling time interval is increased or decreased, the step of change is 1%, the upper and lower limits are ±25%, 50 samples are taken for each time interval, and a total of 51 light intensity matrices with different constant phase shift offsets are obtained. In this embodiment, by sampling the time interval, a plurality of constant offset phase shift conditions can be dynamically generated on the time axis, enriching the diversity of the training data set and covering more diversified phase and light intensity change characteristics. Further, by combining the multi-solution network and the judgment network, the flexibility and reliability of the method in complex optical measurement tasks are strongly supported.

[0072] Embodiment 3

[0073] This embodiment proposes a multi-surface phase shift interference measurement system based on LSTM, which applies the multi-surface phase shift interference measurement method based on LSTM proposed in embodiments 1 and 2. As shown in

[0074] , it is the architecture diagram of the multi-surface phase shift interference measurement system based on LSTM of this embodiment. Figure 5

[0075] This embodiment proposes a multi-surface phase shift interference measurement system based on LSTM, which includes:

[0076] The training data acquisition module samples the optical path of the laser in time and calculates the phase corresponding to the interference cavity and the light intensity on the test mirror;

[0077] The model training module has a neural network based on LSTM, inputs the data collected in the training data acquisition module into the neural network based on LSTM for training, and obtains a solution network after training.

[0078] The measurement module collects the interference pattern photo of the mirror to be measured and converts it into a gray scale matrix, inputs the gray scale matrix into the solution network, obtains the phase value, unwraps the phase value, and obtains the surface profile of the mirror to be measured.

[0079] It can be understood that the system of this embodiment corresponds to the method of embodiments 1 and 2 described above, and the options in embodiments 1 and 2 described above are also applicable to this embodiment, so they will not be described here. ​

[0080] Example 4

[0081] This embodiment proposes a computer device, including a memory and a processor. The memory stores computer-readable instructions, which, when executed by the processor, cause the processor to perform the steps of the LSTM-based multi-surface phase-shifting interferometry method proposed in Embodiments 1 and 2.

[0082] Example 5

[0083] This embodiment proposes a storage medium storing computer-readable instructions, wherein when the computer-readable instructions are executed by a processor, they implement the steps of the LSTM-based multi-surface phase-shifting interferometry method proposed in Embodiments 1 and 2.

[0084] By way of example, the storage medium includes, but is not limited to, USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks or optical disks, and other media capable of storing program code.

[0085] By way of example, the instructions, programs, code sets, or instruction sets may be implemented using conventional programming languages.

[0086] By way of example, the processor includes, but is not limited to, smartphones, personal computers, servers, network devices, etc., for performing all or part of the steps of the LSTM-based multi-surface phase-shift interferometry method based on staged learning described in Examples 1 and 2.

[0087] Example 6

[0088] This embodiment uses a multi-surface phase-shifting interferometry measurement method based on LSTM proposed in embodiments 1 to 5 to measure the mirror under test.

[0089] like Figure 6 The image shows the optical path of the Fizeau interferometer constructed in this embodiment.

[0090] like Figure 7 The figure shows the surface shape measurement results of the LSTM-based multi-surface phase-shifting interferometry method.

[0091] like Figure 8 The image shows the surface measurement results of the 45-step algorithm.

[0092] 45-step algorithm is a phase extraction technique used in interferometry. It combines Fourier transform and phase shifting techniques to accurately calculate the phase information by collecting interferograms at multiple stepped phases. Figure 7 With Figure 8 It can be seen that the measurement results of the present method are close to the 45-step algorithm, and the main three-dimensional topographic features of the object surface can be captured.

[0093] Then, a linear phase shift factor ε0 and a random phase shift factor M are introduced respectively. As shown in Table 1, for different linear phase shifts ε0, the PV values and RMS values of the present application and the 45-step algorithm are shown. Smaller PV values indicate smaller surface topography or wavefront error, and smaller RMS values indicate that the overall level of surface or wavefront error is lower, and the overall is smoother or closer to the ideal state. As can be seen from Table 1, the present application has excellent insensitivity in the range of ε0=0% to-25%, and as ε0 increases, the PV values and RMS values of the 45-step algorithm increase, while the values of the present scheme remain relatively stable.

[0094] Table 1 PV values and RMS values under linear phase shift conditions

[0095]

[0096] As shown in Table 2, for different random phase shift factors M, the PV values and RMS values of the present application and the 45-step algorithm are shown. As can be seen from Table 1, as M increases, the PV values of the 45-step algorithm gradually increase, while the calculated values of the present scheme remain relatively stable. In addition, the present application can also maintain stability in RMS values.

[0097] Table 2 PV values and RMS values under random phase shift conditions

[0098]

[0099] As Figure 9 As shown, under random phase shift conditions, the present application and the 45-step algorithm measure the surface topography, where a-d are the surface topography measured by the present method, and e-h are the surface topography measured by the 45-step algorithm. As can be seen, as the amplitude of the random phase shift increases, the surface topography obtained by using the 45-step algorithm gradually distorts, while the surface topography measured by the present application still has the main three-dimensional topographic features.

[0100] The terms in the drawings are only used for illustrative purposes and cannot be understood as limiting the present patent;

[0101] Obviously, the above embodiments of the present application are merely exemplary but not intended to limit the embodiments of the present application. Based on the above description, any other variations or changes can be made by those skilled in the art without departing from the spirit and principles of the present application. It is not necessary to list all the embodiments here. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present application shall fall within the scope of the claims of the present application.

Claims

1. A multi-surface phase-shift interferometry measurement method based on LSTM, characterized in that, Includes the following steps: The test mirror is placed at a distance α from the reference mirror, and the interference light path passes sequentially through the reference mirror, the first plane of the test mirror, and the second plane of the test mirror; wherein, the reference mirror and the first plane of the test mirror form a first interference cavity; the reference mirror and the second plane of the test mirror form a second interference cavity; and the first plane and the second plane of the test mirror form a third interference cavity. During wavelength tuning, the interferometer optical path is sampled according to a preset sampling sequence. The phases corresponding to the first, second, and third interferometer cavities are calculated based on the center wavelength. The light intensity at the interferometer receiver is calculated based on the phases to obtain the light intensity matrix. The light intensity matrix is ​​used as a training dataset, and the phase of the first interferometer cavity corresponding to the light intensity matrix is ​​used as a label input into the LSTM-based neural network for training. After training, the solution network is obtained. The mirror under test is placed at a distance α from the reference mirror. An interference pattern photograph is acquired and converted into a grayscale matrix. The grayscale matrix is ​​input into the solution network to obtain the phase value. The phase value is unwrapped to obtain the surface shape of the mirror under test.

2. The LSTM-based multi-surface phase-shift interferometry measurement method according to claim 1, characterized in that, The step of sampling the interferometer optical path according to a preset sampling time sequence includes: performing fourth-order polynomial fitting on the wavelength response curve of the laser, and sampling the fitted curve according to a preset sampling time sequence.

3. The multi-surface phase-shift interferometry measurement method based on LSTM according to claim 1, characterized in that, The method further includes: changing the cavity length of the interference cavity, calculating the phase and light intensity on the test mirror corresponding to different cavity lengths to obtain several light intensity matrices, using the several light intensity matrices as training data, and using the first interference cavity length corresponding to any matrix as a label input into an LSTM-based neural network for training.

4. The LSTM-based multi-surface phase-shift interferometry measurement method according to claim 3, characterized in that, The step of changing the length of the interference cavity includes: changing the undulation of the test mirror surface; the formula for calculating the length of the interference cavity is as follows: L ru (x,y)=L1(x,y)+Z u0 (x,y) L rd (x,y)=L2(x,y)+Z d0 (x,y) L ud (x,y)=L2(x,y)-L1(x,y) Where (x, y) represents any point on the test mirror, L1 is the distance between the first plane of the test mirror and the reference mirror, L2 is the distance between the second plane of the test mirror and the reference mirror, and Z... u0 (x,y) represents the undulation of the first plane of the test mirror, Z d0 (x,y) represents the undulation of the second plane of the test mirror, L ru L rd and L ud These are the first interference cavity, the second interference cavity, and the third interference cavity, respectively.

5. The LSTM-based multi-surface phase-shift interferometry measurement method according to claim 4, characterized in that, The method of changing the undulation of the test mirror surface includes: adjusting and arbitrarily arranging the undulation of the first plane and the second plane of the test mirror within a preset range.

6. A multi-surface phase-shift interferometry method based on LSTM according to any one of claims 1 to 5, characterized in that, The method further includes: when using laser wavelength tuning for phase shifting, introducing several constant phase shift offsets, calculating the phase and light intensity based on any constant phase shift offset, constructing an LSTM-based neural network for any constant phase shift offset, and inputting the phase and light intensity for training, and obtaining several solution networks after training. Construct an LSTM-based judgment network and input the numbers of several solution networks as labels into the judgment network for training; The judgment network measures the phase shift offset based on the grayscale matrix of the mirror under test, and selects an appropriate solution network according to the magnitude of the phase shift offset.

7. The LSTM-based multi-surface phase-shift interferometry measurement method according to claim 6, characterized in that, The step of introducing several constant phase shift offsets includes: presetting several constant phase shift offsets, changing the sampling interval of the sampling time sequence according to the magnitude of the phase shift offsets, and obtaining the light intensity matrix and phase corresponding to different phase shift offsets.

8. A multi-surface phase-shifting interferometry system based on LSTM, applied to the multi-surface phase-shifting interferometry method based on LSTM as described in any one of claims 1 to 7, characterized in that, The system includes: Training data acquisition module: During wavelength tuning, the interferometer optical path is sampled according to a preset sampling sequence, and the phase corresponding to the interference cavity and the light intensity on the receiving optical path are calculated; Model training module: It is equipped with an LSTM-based neural network. The data collected in the training data acquisition module is input into the LSTM-based neural network for training. After training, the solution network is obtained. Measurement module: Acquires an interference pattern photograph of the mirror under test and converts it into a grayscale matrix. Inputs the grayscale matrix into the solution network to obtain the phase value. Unwraps the phase value to obtain the surface shape of the mirror under test.

9. 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 the LSTM-based multi-surface phase-shifting interferometry method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the LSTM-based multi-surface phase-shifting interferometry method as described in any one of claims 1-7.

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