A large-angle heterodyne interferometer wavefront angle error calibration method and system

Abstract

The present application relates to a kind of wide-angle heterodyne interferometer wavefront angle measurement error calibration method and system, belong to laser interferometry field, including: in the predetermined wide-angle measurement range Multiple standard angle input points are set, collect heterodyne interferometry data, extract wavefront parameter set and obtain original wavefront angle measurement result;According to standard angle input and original wavefront angle measurement result Calculation original angle measurement error;Based on original angle measurement error, original wavefront angle measurement result and wavefront parameter set Error calibration model is established, error parameter is identified and error calibration parameter set is generated;Subsequent measurement, according to error calibration parameter set, current original wavefront angle measurement result and corresponding wavefront parameter set Error correction amount is calculated, and modified wavefront angle measurement result is obtained.The present application can unify calibration and correction decoupling nonlinear error, periodic nonlinear error and wavefront parameter processing residual, improve wavefront angle measurement precision and linearity in wide-angle range.

Description

Technical Field

[0001] This invention relates to a method and system for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer, belonging to the field of laser interferometry technology. Background Technology

[0002] Heterodyne interferometry is a crucial technique for achieving high-resolution displacement and angle measurements. This technique typically obtains displacement, angle, or attitude information of the measured object by detecting the phase change of the heterodyne signal between a reference beam and a measurement beam. It features non-contact operation, high resolution, and suitability for dynamic measurements. For heterodyne interferometers that perform angle measurements based on wavefront information, changes in the angle of the measured object not only cause phase changes in the heterodyne signal but also alter the wavefront distribution, optical axis position, wavefront curvature, or receiver phase distribution of the interferometric light. Therefore, the angle measurement results of the measured object can be obtained through wavefront parameter extraction, spatial phase information processing, optical axis position parameter extraction, or angle decoupling.

[0003] In the wavefront angle measurement process of a large-angle heterodyne interferometer, the change in the measured angle typically manifests first as a change in the optical axis position, wavefront curvature, phase distribution, or spatial sampling parameters. The original wavefront angle measurement result is then obtained from the wavefront parameter set through angle decoupling, angle calculation, or equivalent angle measurement processing. This process involves heterodyne interference signal formation, wavefront state changes, wavefront parameter extraction, spatial sampling information processing, and angle decoupling, angle calculation, or equivalent angle measurement processing. In some systems, it may further involve optical axis position recovery, wavefront reconstruction, or wavefront restoration processing. The wavefront state change is used to characterize the correspondence between the change in the measured angle and the change in the state of the interferometric wavefront. Within a small angle range, the error relationship between the original wavefront angle measurement result and the standard angle is usually relatively simple, and zero-position calibration or proportional coefficient calibration can meet general measurement requirements.

[0004] However, as the angle measurement range increases, the nonlinear characteristics and error sensitivity in the mapping relationship between the wavefront state and the measured angle, as well as the angle calculation relationship, become significantly enhanced. Changes in beam propagation state, wavefront parameter extraction errors, optical axis position extraction errors, receiver surface spatial sampling errors, phase demodulation period errors, and system assembly deviations can all lead to zero-position deviations, proportional coefficient deviations, decoupling nonlinear errors, periodic nonlinear errors, and wavefront parameter processing residuals in the original wavefront angle measurement results. For systems involving wavefront reconstruction or wavefront restoration, these errors may also manifest as wavefront reconstruction residuals or restoration residuals. These errors are more pronounced at the large-angle end, easily causing increased end-angle measurement errors, decreased overall linearity, and local periodic residual fluctuations.

[0005] Currently, commonly used methods for handling angle measurement errors mainly include single-point zero-position correction, proportional coefficient correction, local linear fitting, or simple table lookup compensation based on a single output quantity. These methods can compensate for some fixed deviations, but they typically do not incorporate the original wavefront angle measurement results and wavefront parameter set into the error description, making it difficult to characterize the error variations caused by wavefront state changes, wavefront parameter extraction, spatial sampling information processing, and angle calculation over a large angle range. For systems involving wavefront reconstruction or wavefront restoration, it is also difficult to further characterize the impact of reconstruction or restoration residuals on the angle measurement results. Especially in large-angle heterodyne interferometer wavefront angle measurement scenarios, the angle measurement error often simultaneously includes decoupling nonlinearity error, periodic nonlinearity error, and wavefront parameter processing residuals; for systems involving optical axis position recovery, wavefront reconstruction, or wavefront restoration, it may also include corresponding restoration residuals, reconstruction residuals, or restoration residuals. Single error term correction or local calibration methods are insufficient to meet the requirements of high-precision angle measurement.

[0006] In summary, existing error calibration methods struggle to simultaneously address the diverse error correction requirements within a large-angle measurement range and the complexities of wavefront angle measurement information processing. Therefore, a method is needed to calibrate the error of wavefront angle measurement outputs from large-angle heterodyne interferometers. This method, without re-defining the specific optical path structure of the heterodyne interferometer, establishes an error calibration relationship between the original wavefront angle measurement results obtained from heterodyne interferometry data through wavefront parameter extraction, spatial sampling information processing, optical axis position recovery, wavefront reconstruction or restoration, and further angle decoupling or angle calculation, and generates calibration parameters for subsequent wavefront angle measurement result correction. This aims to improve the accuracy and linearity of wavefront angle measurement results over a large angle range. Summary of the Invention

[0007] This invention aims to solve the problem of inaccurate calibration and correction of angle measurement errors caused by angle decoupling nonlinearity, periodic nonlinearity, and residuals from wavefront parameter processing in large-angle heterodyne interferometers. It proposes a method and system for calibrating wavefront angle measurement errors in large-angle heterodyne interferometers.

[0008] Technical solution one is as follows:

[0009] A method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer includes:

[0010] S1. Set multiple standard angle input points within a predetermined large angle measurement range, and control the standard angle input device to sequentially output the standard angles corresponding to the multiple standard angle input points;

[0011] S2. Collect heterodyne interferometric measurement data output by the large-angle heterodyne interferometer at each of the aforementioned standard angle input points;

[0012] S3. Extract the wavefront parameter set corresponding to each of the standard angle input points based on the heterodyne interferometry data, and obtain the corresponding original wavefront angle measurement result from the wavefront parameter set through angle decoupling processing, angle calculation processing or equivalent angle measurement processing;

[0013] S4. Calculate the original angle measurement error at each of the standard angle input points based on the standard angle and the original wavefront angle measurement results;

[0014] S5. Based on the original angle measurement error, the original wavefront angle measurement result, and the wavefront parameter set corresponding to the original wavefront angle measurement result, establish an error calibration model with the original wavefront angle measurement result and the wavefront parameter set as input variables.

[0015] The error calibration model includes an angle error term related to the original wavefront angle measurement result and a wavefront parameter processing residual term related to the wavefront parameter set. The angle error term includes at least one of a zero-position error term, a proportional error term, a decoupling nonlinear error term, and a periodic nonlinear error term, and includes at least a decoupling nonlinear error term or a periodic nonlinear error term.

[0016] S6. Identify the error parameters in the error calibration model and generate an error calibration parameter set;

[0017] S7. Generate an error calibration table, an error correction file, or a callable error correction model based on the set of error calibration parameters.

[0018] S8. In subsequent measurements, based on the error calibration table, error correction file, or callable error correction model, and in conjunction with the original wavefront angle measurement results currently output by the large-angle heterodyne interferometer and its corresponding wavefront parameter set, calculate the error correction amount, correct the original wavefront angle measurement results, and obtain the corrected wavefront angle measurement results.

[0019] Specifically, the set of wavefront parameters includes at least one of the following: optical axis position parameter, wavefront curvature parameter, phase distribution parameter, spatial phase parameter, phase difference parameter, spatial sampling parameter, interference contrast parameter, optical axis position recovery residual parameter, wavefront reconstruction residual parameter, and wavefront restoration residual parameter.

[0020] Specifically, the error calibration model is expressed as follows:

[0021] ,

[0022] in, Original wavefront angle measurement results and wavefront parameter set The corresponding calibration error, For the zero-position error term, This is the proportional error term. To decouple the nonlinear error term, For periodic nonlinear error terms, The residual terms are processed for the wavefront parameters.

[0023] Specifically, the error calibration model is expressed as follows:

[0024] ,

[0025] in, For zero-position error parameters, This is the proportional error parameter. To decouple nonlinear error parameters, and For periodic nonlinear error parameters, The periodic error angular frequency parameter, For the set of wavefront parameters The relevant wavefront parameters are used to process the residual terms.

[0026] Specifically, the wavefront parameter processing residual term is determined by at least one of the following methods: optical axis position residual, phase distribution residual, wavefront curvature residual, spatial sampling residual, wavefront fitting residual, optical axis position recovery residual, wavefront reconstruction residual, and wavefront restoration residual, combined with table lookup, piecewise interpolation, residual fitting, or experimental calibration.

[0027] Specifically, in S6, the error parameters in the error calibration model are identified:

[0028] S61. Identify the error parameters in the error calibration model based on the original angle measurement error, the original wavefront angle measurement result and the wavefront parameter set at each of the standard angle input points.

[0029] S62. Determine whether the identified model residuals meet the preset residual threshold.

[0030] If the model residual does not meet the preset residual threshold, the wavefront parameter of the angle error term in the error calibration model is adjusted to process the residual term, and the error parameter identification is performed again.

[0031] If the model residuals meet the preset residual threshold, then the set of error calibration parameters is output.

[0032] Specifically, when the large-angle heterodyne interferometer outputs angle results in two directions simultaneously, error calibration models in the two directions are established respectively, or a vector-form error calibration model containing directional coupling error terms is established.

[0033] The directional coupling error term is used to characterize the influence of the angle input in one direction on the original wavefront angle measurement result in another direction.

[0034] Specifically, in subsequent measurement processes, it is determined whether the original wavefront angle measurement result and its corresponding wavefront parameter set are within the effective calibration range corresponding to the error calibration model;

[0035] When the original wavefront angle measurement result and its corresponding wavefront parameter set are within the effective calibration range, the error calibration table, error correction file or callable error correction model are called for correction.

[0036] When the original wavefront angle measurement result or its corresponding wavefront parameter set exceeds the effective calibration range, an out-of-range prompt, a reduced confidence flag, or the output of the corrected wavefront angle measurement result is stopped.

[0037] Technical Solution 2 is as follows: A large-angle heterodyne interferometer wavefront angle measurement error calibration system, used to execute the large-angle heterodyne interferometer wavefront angle measurement error calibration method described in Technical Solution 1, including a standard angle input module, a heterodyne interferometry data acquisition module, a wavefront parameter extraction module, a raw wavefront angle measurement result reading module, an error calculation module, an error calibration model establishment module, an error parameter identification module, a calibration parameter storage module, and an angle measurement result correction module;

[0038] The standard angle input module is connected to the error calculation module, the heterodyne interferometry data acquisition module is connected to the wavefront parameter extraction module, the wavefront parameter extraction module is connected to the original wavefront angle measurement result reading module, the wavefront parameter extraction module is connected to the error calibration model establishment module, the original wavefront angle measurement result reading module is connected to the error calculation module, the original wavefront angle measurement result reading module is connected to the error calibration model establishment module, and the original wavefront angle measurement result reading module is connected to the angle measurement result correction module. The error calculation module, the error calibration model establishment module, the error parameter identification module, the calibration parameter storage module, and the angle measurement result correction module are connected in sequence.

[0039] A standard angle input module is used to receive or control a standard angle input device to sequentially output multiple standard angles within a predetermined large angle measurement range;

[0040] The heterodyne interferometry data acquisition module is used to acquire heterodyne interferometry data output by the large-angle heterodyne interferometer at each of the aforementioned standard angles.

[0041] The wavefront parameter extraction module is used to extract a set of wavefront parameters corresponding to each of the standard angles based on the heterodyne interferometry data.

[0042] The original wavefront angle measurement result reading module is used to read or calculate the original wavefront angle measurement result obtained by angle decoupling processing, angle calculation processing or equivalent angle measurement processing of the wavefront parameter set;

[0043] The error calculation module is used to calculate the original angle measurement error based on the standard angle and the original wavefront angle measurement result;

[0044] An error calibration model establishment module is used to establish an error calibration model with the original wavefront angle measurement result and the wavefront parameter set corresponding to the original wavefront angle measurement result as input variables, based on the original angle measurement error, the original wavefront angle measurement result, and the wavefront parameter set corresponding to the original wavefront angle measurement result. The error calibration model includes an angle error term related to the original wavefront angle measurement result and a wavefront parameter processing residual term related to the wavefront parameter set. The angle error term includes at least one of a zero-position error term, a proportional error term, a decoupling nonlinear error term, and a periodic nonlinear error term, and includes at least a decoupling nonlinear error term or a periodic nonlinear error term.

[0045] The error parameter identification module is used to identify the error parameters in the error calibration model and generate an error calibration parameter set.

[0046] The calibration parameter storage module is used to store error calibration tables, error correction files, or callable error correction models according to the set of error calibration parameters.

[0047] The angle measurement result correction module is used to calculate the error correction amount and correct the original wavefront angle measurement result in subsequent measurement processes, based on the error calibration table, error correction file or callable error correction model, and in combination with the original wavefront angle measurement result currently output by the large-angle heterodyne interferometer and its corresponding wavefront parameter set, to obtain the corrected wavefront angle measurement result.

[0048] The beneficial effects of this invention are:

[0049] This invention addresses the wavefront angle measurement output of large-angle heterodyne interferometers. It establishes an error calibration model corresponding to the wavefront angle measurement process to address the errors generated during wavefront parameter extraction, spatial sampling information processing, optical axis position recovery, wavefront reconstruction, wavefront restoration, angle decoupling, or angle calculation. This improves the specificity and completeness of the description of large-angle wavefront angle measurement errors.

[0050] This invention can incorporate zero-position error, proportional error, decoupling nonlinear error, periodic nonlinear error and wavefront parameter processing residual into the same calibration framework, and is suitable for angle measurement scenarios where multiple error terms act together over a large angle range.

[0051] This invention establishes an error calibration relationship by combining standard angle input, wavefront parameter set, and original wavefront angle measurement results. It can calibrate the error distribution within a large angle measurement range and generate an error calibration parameter set, error calibration table, error correction file, or callable error correction model, providing a basis for subsequent angle measurement result correction.

[0052] This invention can calibrate and correct the original wavefront angle measurement results without changing the specific optical path structure of the heterodyne interferometer. Therefore, it does not limit the specific wavefront control method, receiving method, angle decoupling method or angle calculation method of the heterodyne interferometer, and has good applicability.

[0053] This invention can reduce the angle measurement residuals caused by decoupling nonlinearity, periodic nonlinearity and wavefront parameter processing residuals during large-angle angle measurement, thereby improving the linearity, repeatability and measurement accuracy of the wavefront angle measurement results of large-angle heterodyne interferometers. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the overall process for the wavefront angle measurement error calibration method of the large-angle heterodyne interferometer described in this invention;

[0055] Figure 2 This is a schematic diagram of the error term composition of the angle measurement error calibration model described in this invention;

[0056] Figure 3 This is a schematic diagram of the error parameter identification and calibration parameter generation process described in this invention;

[0057] Figure 4 This is a schematic diagram of the functional modules of the large-angle heterodyne interferometer wavefront angle measurement error calibration system described in this invention;

[0058] In the diagram, 1-Standard angle input module, 2-Heterodyne interferometry data acquisition module, 3-Wavefront parameter extraction module, 4-Original wavefront angle measurement result reading module, 5-Error calculation module, 6-Error calibration model establishment module, 7-Error parameter identification module, 8-Calibration parameter storage module, and 9-Angle measurement result correction module. Detailed Implementation

[0059] Example 1:

[0060] This embodiment provides a method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer, such as... Figures 1-4 As shown, it includes the following steps:

[0061] Multiple standard angle input points are set within a predetermined large angle measurement range, and the standard angle input device is controlled to sequentially output the standard angle input corresponding to the multiple standard angle input points.

[0062] Furthermore, the multiple standard angle input points can be set at equal intervals within a predetermined large angle measurement range, or they can be set at non-equal intervals according to the error variation characteristics of the large-angle heterodyne interferometer; in the angle range where the error changes rapidly, the density of the standard angle input points can be increased. For a large-angle heterodyne interferometer measuring angles in both directions, the standard angle input points can be set according to a two-dimensional angle grid, and standard angle inputs in both directions can be obtained respectively.

[0063] Collect heterodyne interferometric measurement data output by the large-angle heterodyne interferometer at each of the aforementioned standard angle input points.

[0064] Based on the heterodyne interferometry data, extract the wavefront parameter set corresponding to each of the standard angle input points, and obtain the corresponding original wavefront angle measurement result from the wavefront parameter set through angle decoupling processing, angle calculation processing, or equivalent angle measurement processing.

[0065] In this embodiment, the large-angle heterodyne interferometer can employ a heterodyne interferometric measurement system capable of outputting raw wavefront angle measurement results. The heterodyne interferometric measurement system can obtain the raw wavefront angle measurement results through wavefront state change detection, wavefront parameter extraction, spatial sampling information processing, optical axis position recovery, wavefront reconstruction, wavefront restoration, angle decoupling, or angle calculation. This invention does not limit the specific optical path structure of the large-angle heterodyne interferometer; as long as it can output raw wavefront angle measurement results, the error calibration method described in this invention can be used.

[0066] The original angle measurement error at each of the standard angle input points is calculated based on the standard angle input and the original wavefront angle measurement results.

[0067] Based on the original angle measurement error, the original wavefront angle measurement result, and the wavefront parameter set corresponding to the original wavefront angle measurement result, an error calibration model is established with the original wavefront angle measurement result and the wavefront parameter set as input variables.

[0068] The error calibration model includes an angle error term related to the original wavefront angle measurement result and a wavefront parameter processing residual term related to the wavefront parameter set. The angle error term includes at least a decoupling nonlinear error term or a periodic nonlinear error term.

[0069] The error parameters in the error calibration model are identified to generate a set of error calibration parameters.

[0070] An error calibration table, an error correction file, or a callable error correction model can be generated based on the set of error calibration parameters.

[0071] In subsequent measurements, based on the error calibration table, error correction file, or callable error correction model, and combined with the original wavefront angle measurement results currently output by the large-angle heterodyne interferometer and its corresponding wavefront parameter set, the error correction amount is calculated to correct the original wavefront angle measurement results, thereby obtaining the corrected wavefront angle measurement results.

[0072] Furthermore, such as Figure 2 As shown, the wavefront angle measurement information processing process of a large-angle heterodyne interferometer includes heterodyne interferometric measurement data, wavefront parameter set, original wavefront angle measurement result, and corrected wavefront angle measurement result. The heterodyne interferometric measurement data is processed by wavefront parameter extraction to obtain a wavefront parameter set. This set undergoes angle decoupling, angle calculation, or equivalent angle measurement processing to obtain the original wavefront angle measurement result. Error calculation module 5 calculates the original angle measurement error based on the standard angle input and the original wavefront angle measurement result. Error calibration model establishment module 6 establishes an error calibration model based on the original angle measurement error, the original wavefront angle measurement result, and the wavefront parameter set. Error parameter identification module 7 identifies the parameters in the error calibration model to obtain the error calibration parameter set. During subsequent measurements, angle measurement result correction module 9 calculates the error correction amount based on the error calibration parameter set and the current original wavefront angle measurement result and its corresponding wavefront parameter set, correcting the original wavefront angle measurement result to obtain the corrected wavefront angle measurement result.

[0073] Specifically, the standard angle input is generated by a standard angle station. The standard angle station sequentially outputs multiple standard angles θ1, θ2, ..., θ3 within a predetermined angular measurement range. M Where M is the number of standard angle points. The large-angle heterodyne interferometer outputs the corresponding heterodyne interferometry measurement data at each standard angle point, and the wavefront parameter extraction module 3 extracts the wavefront parameter set P1, P2, ..., P... M The original wavefront angle measurement result reading module 4 obtains the original wavefront angle measurement result θ based on the wavefront parameter set through angle decoupling processing, angle calculation processing, or equivalent angle measurement processing. m,1 θ m,2 、…、θ m,M Error calculation module 5 calculates the original angle measurement error at each standard angle point.

[0074] In this embodiment, the wavefront parameter set includes at least one of the following: optical axis position parameter, wavefront curvature parameter, phase distribution parameter, spatial phase parameter, phase difference parameter, spatial sampling parameter, interference contrast parameter, optical axis position recovery residual parameter, wavefront reconstruction residual parameter, and wavefront restoration residual parameter.

[0075] Furthermore, let θ be the standard angle corresponding to the j-th standard angle input. j The original wavefront angle measurement result output by the large-angle heterodyne interferometer at this standard angle is θ.m,j Then the original angular measurement error e at the j-th standard angle point j Represented as:

[0076]

[0077] Where, θ j Let θ be the j-th standard angle. m,j For the original wavefront angle measurement result at the j-th standard angle, e j This represents the corresponding original angle measurement error.

[0078] Furthermore, let P be the set of wavefront parameters extracted under the j-th standard angle input. j The original wavefront angle measurement result can be expressed as:

[0079]

[0080] Among them, P j Let F be the set of wavefront parameters for the j-th standard angle input. d For angle decoupling function, angle calculation function, or equivalent angle measurement function, θ m,j This refers to the original wavefront angle measurement result obtained from the wavefront parameter set through angle decoupling, angle calculation, or equivalent angle measurement processing. The angle decoupling function, angle calculation function, or equivalent angle measurement function can be determined by the wavefront angle measurement model of the heterodyne interferometer.

[0081] Furthermore, the error calibration model is used to describe the error relationship between the original wavefront angle measurement results, the wavefront parameter set, and the standard angle input.

[0082] In this embodiment, the error calibration model is expressed as:

[0083]

[0084] Where, E(θ) m P) represents the original wavefront angle measurement result θ m The calibration error corresponding to the wavefront parameter set P, E0 is the zero-position error term, E s (θ m E represents the proportional error term. d (θ m E represents the decoupling nonlinear error term. p (θ m ) represents the periodic nonlinear error term. The residual terms are processed for the wavefront parameters.

[0085] like Figure 3As shown, the error calibration model includes a zero-position error term, a proportional error term, a decoupling nonlinear error term, a periodic nonlinear error term, and a wavefront parameter processing residual term. The error calibration model may also include a direction coupling error term to correct the mutual influence between two angular measurement directions.

[0086] Furthermore, the zero-position error term is used to characterize the initial bias of the original wavefront angle measurement output; the proportional error term is used to characterize the deviation of the angle measurement sensitivity or angle conversion proportional coefficient; the decoupling nonlinearity error term is used to characterize the error caused by the nonlinearity of the wavefront parameter set and the angle decoupling relationship; the periodic nonlinearity error term is used to characterize the periodic residual error caused by heterodyne phase demodulation, periodic variation of interference signal, polarization mixing, or periodic error of optical devices; and the wavefront parameter processing residual term is used to characterize the residual error caused by errors in wavefront parameter extraction, spatial sampling information processing, optical axis position recovery, wavefront reconstruction, wavefront restoration, or receiver phase distribution processing.

[0087] Specifically, the zero-position error term is used to correct the initial bias of the original wavefront angle measurement result; the proportional error term is used to correct the deviation of the angle measurement proportional coefficient; the decoupling nonlinear error term is used to correct the nonlinear deviation caused by the decoupling relationship between the wavefront parameters and the angle over a large angle range; the periodic nonlinear error term is used to correct the periodic residual error that occurs with the change of angle; the wavefront parameter processing residual term is used to correct the residual error caused by wavefront parameter extraction, spatial sampling information processing, optical axis position recovery, wavefront reconstruction, wavefront restoration, or receiver phase distribution processing; and the directional coupling error term is used to correct the influence of a change in one angular direction on the original wavefront angle measurement result in another direction.

[0088] In this embodiment, the error calibration model can also take the following form:

[0089]

[0090] Where a0 is the zero-position error parameter, a1 is the proportional error parameter, a2 is the decoupling nonlinear error parameter, b1 and c1 are the periodic nonlinear error parameters, ω is the periodic error angular frequency parameter, and R... w (P) represents the wavefront parameter processing residuals associated with the wavefront parameter set P.

[0091] Specifically, when the error calibration model adopts the above form, the quadratic term is used to represent the main decoupling nonlinear error over a large angle range; the sine and cosine terms are used to represent the periodic nonlinear error; and the wavefront parameter processing residual term is used to represent the residual error related to the wavefront parameter set. Based on the actual calibration residual, some error terms can be omitted, or the error calibration model can be represented using piecewise calibration and table lookup correction.

[0092] Furthermore, the wavefront parameter processing residual term Rw (P) can be determined based on the optical axis position residual, phase distribution residual, wavefront curvature residual, spatial sampling residual, wavefront fitting residual, optical axis position recovery residual, wavefront reconstruction residual, wavefront restoration residual, or a combination thereof. The wavefront parameter processing residual term can be represented by table lookup, piecewise interpolation, residual fitting, or experimental calibration. The error calibration model can be represented by fewer error terms, a piecewise model, a table lookup model, or a hybrid model based on the calibration residual.

[0093] Furthermore, the standard angle input device can be a standard angle table, a standard turntable, an angle calibration device, a standard attitude adjustment device, or other devices capable of providing known angle changes. The standard angle input can be a unidirectional angle input or an angle input in two mutually perpendicular directions.

[0094] Furthermore, the error parameter identification process includes:

[0095] Select multiple standard angle points within the predetermined large-angle measurement range;

[0096] The control standard angle input device sequentially outputs the plurality of standard angle points;

[0097] Collect large-angle heterodyne interferometry measurement data at each standard angle point;

[0098] Extract the set of wavefront parameters at each standard angle point and calculate the corresponding original wavefront angle measurement results;

[0099] The original angle measurement error is calculated based on the standard angle input and the original wavefront angle measurement results.

[0100] Based on the original angle measurement error, the original wavefront angle measurement result, and the wavefront parameter set, the error parameters in the error calibration model are identified.

[0101] Determine whether the identified model residuals meet the preset residual threshold;

[0102] If the model residuals do not meet the preset residual threshold, the error terms, segmentation ranges, or wavefront parameters in the error calibration model are adjusted to process the residual terms, and the error parameters are re-identified.

[0103] If the model residuals meet the preset residual threshold, then the set of error calibration parameters will be output.

[0104] like Figure 4As shown, the error parameter identification and calibration parameter generation process includes: inputting standard angle data; acquiring heterodyne interferometry measurement data; extracting the wavefront parameter set; reading or calculating the original wavefront angle measurement results; calculating the original angle measurement error; selecting error model terms; identifying error parameters; determining whether the residual meets the preset threshold; if not, adjusting the error model terms, segmentation range, or wavefront parameters to process the residual terms and then re-identifying; if satisfied, generating and saving the error calibration parameter set.

[0105] Furthermore, assuming the set of error calibration parameters is Λ, the error parameter identification can be achieved using the following objective function:

[0106]

[0107] Where M is the number of standard angle points, e j Let E(θ) be the original angle measurement error at the j-th standard angle point. m,j ,P j; Λ) represents the model error corresponding to the j-th standard angle point of the error calibration model, and Λ represents the set of error calibration parameters to be identified.

[0108] Specifically, the error parameter identification module 7 can obtain the set of error calibration parameters based on the above objective function. In this way, the residual between the model error and the actual original angle measurement error at each standard angle point of the error calibration model can be minimized, thereby obtaining the error calibration parameters suitable for the current angle measurement state of the large-angle heterodyne interferometer.

[0109] Furthermore, in subsequent measurements, let θ be the original wavefront angle measurement result output by the large-angle heterodyne interferometer. m The corresponding wavefront parameter set is P, and the error correction amount obtained from the error calibration model is E. c (θ m,P If θ is the corrected angle measurement result, then... c Represented as:

[0110]

[0111] Where, θ c To correct the wavefront angle measurement results, E c (θ m P) is the error correction amount calculated based on the set of error calibration parameters.

[0112] After the error calibration parameter set is generated, the calibration parameter storage module 8 saves it as an error calibration parameter file, an error calibration table, or an error correction model. During subsequent measurements, the angle measurement result correction module 9 corrects the angle measurement result θ based on the current original wavefront angle measurement result. mAnd when the error correction model includes wavefront parameter processing residual terms, it combines the current wavefront parameter set P and calls the corresponding error correction amount E. c (θ m The function outputs the corrected wavefront angle measurement result θ (P). c .

[0113] Furthermore, when the large-angle heterodyne interferometer simultaneously outputs angle results in two directions, error calibration models can be established for each of the two directions, or a vector-form error calibration model including directional coupling error terms can be established. The directional coupling error terms characterize the influence of the angle input in one direction on the original wavefront angle measurement result in the other direction.

[0114] Furthermore, the two-dimensional error calibration model may include zero-position error, proportional error, decoupling nonlinear error, periodic nonlinear error, wavefront parameter processing residual, and directional coupling error for each of the two angular directions.

[0115] Furthermore, the error calibration model can be stored in the form of a parametric model, a lookup table model, a piecewise interpolation model, or a hybrid model, and can be called in subsequent measurement processes to calculate the error correction. The set of error calibration parameters can be stored in an electronic signal processing unit, a host computer, a controller, an angle measurement data processing module, or a calibration parameter file.

[0116] Furthermore, the error calibration method may include determining the effective calibration range. During subsequent measurements, when the original wavefront angle measurement result and its corresponding wavefront parameter set are within the effective calibration range corresponding to the error calibration model, the angle measurement result correction module 9 calls the error correction model, error calibration table, or error correction file for correction; when the original wavefront angle measurement result or its corresponding wavefront parameter set exceeds the effective calibration range, the angle measurement result correction module 9 outputs an out-of-range prompt, a reduced confidence flag, or stops outputting the corrected wavefront angle measurement result.

[0117] Furthermore, the error calibration method can be performed during the factory calibration stage, experimental calibration stage, maintenance calibration stage, readjustment stage, or after optical component replacement of the large-angle heterodyne interferometer. After re-executing the error calibration process, the error calibration parameter set and error calibration model can be updated.

[0118] As an example, a large-angle heterodyne interferometer was set within a 20 mrad angle measurement range, and multiple standard angle points were selected for error calibration. The 20 mrad is merely an example of the angle measurement range in one implementation; the predetermined large-angle measurement range can be set according to the heterodyne interferometer structure, wavefront parameter extraction method, and angle decoupling method. Before calibration, the original wavefront angle measurement results exhibited nonlinear errors and local periodic residual errors at the large angle end. After generating error calibration parameters using the error calibration model described in this invention and performing corrections, the corrected wavefront angle measurement residuals were significantly reduced. Under these example conditions, the corrected wavefront angle measurement error can reach the order of 1 μrad. This example is used to illustrate the error calibration effect of this invention and does not constitute a limitation on the scope of protection of this invention.

[0119] Example 2:

[0120] This embodiment provides a large-angle heterodyne interferometer wavefront angle measurement error calibration system, such as... Figures 2-4 As shown, the method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer as described in Example 1 includes a standard angle input module 1, a heterodyne interferometry data acquisition module 2, a wavefront parameter extraction module 3, a raw wavefront angle measurement result reading module 4, an error calculation module 5, an error calibration model establishment module 6, an error parameter identification module 7, a calibration parameter storage module 8, and an angle measurement result correction module 9.

[0121] The standard angle input module 1 is connected to the error calculation module 5, the heterodyne interferometry data acquisition module 2 is connected to the wavefront parameter extraction module 3, the wavefront parameter extraction module 3 is connected to the original wavefront angle measurement result reading module 4, the wavefront parameter extraction module 3 is connected to the error calibration model establishment module 6, the original wavefront angle measurement result reading module 4 is connected to the error calculation module 5, the original wavefront angle measurement result reading module 4 is connected to the error calibration model establishment module 6, the original wavefront angle measurement result reading module 4 is connected to the angle measurement result correction module 9, and the error calculation module 5, the error calibration model establishment module 6, the error parameter identification module 7, the calibration parameter storage module 8, and the angle measurement result correction module 9 are connected in sequence;

[0122] The standard angle input module 1 is used to receive or control the standard angle input device to sequentially output multiple standard angle inputs within a predetermined large angle measurement range.

[0123] The heterodyne interferometry data acquisition module 2 is used to acquire heterodyne interferometry data output by the large-angle heterodyne interferometer at each of the standard angles.

[0124] The wavefront parameter extraction module 3 is used to extract a set of wavefront parameters corresponding to each of the standard angles based on the heterodyne interferometry measurement data.

[0125] The original wavefront angle measurement result reading module 4 is used to read or calculate the original wavefront angle measurement result obtained by angle decoupling processing, angle calculation processing or equivalent angle measurement processing of the wavefront parameter set.

[0126] The error calculation module 5 is used to calculate the original angle measurement error based on the standard angle input and the original wavefront angle measurement result.

[0127] The error calibration model establishment module 6 is used to establish an error calibration model with the original wavefront angle measurement result and the wavefront parameter set corresponding to the original wavefront angle measurement result as input variables, based on the original angle measurement error, the original wavefront angle measurement result, and the wavefront parameter set corresponding to the original wavefront angle measurement result.

[0128] The error calibration model includes an angle error term related to the original wavefront angle measurement result and a wavefront parameter processing residual term related to the wavefront parameter set. The angle error term includes at least a decoupling nonlinear error term or a periodic nonlinear error term.

[0129] The error parameter identification module 7 is used to identify the error parameters in the error calibration model and generate an error calibration parameter set.

[0130] The calibration parameter storage module 8 is used to store error calibration tables, error correction files, or callable error correction models according to the error calibration parameter set.

[0131] The angle measurement result correction module 9 is used to calculate the error correction amount and correct the original wavefront angle measurement result in subsequent measurement processes, based on the error calibration table, error correction file or callable error correction model, and in combination with the original wavefront angle measurement result currently output by the large-angle heterodyne interferometer and its corresponding wavefront parameter set, to obtain the corrected wavefront angle measurement result.

Claims

1. A method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer, characterized in that, include: S1. Set multiple standard angle input points within a predetermined large angle measurement range, and control the standard angle input device to sequentially output the standard angles corresponding to the multiple standard angle input points; S2. Collect heterodyne interferometric measurement data output by the large-angle heterodyne interferometer at each of the aforementioned standard angle input points; S3. Extract the wavefront parameter set corresponding to each of the standard angle input points based on the heterodyne interferometry data, and obtain the corresponding original wavefront angle measurement result from the wavefront parameter set through angle decoupling processing, angle calculation processing or equivalent angle measurement processing; S4. Calculate the original angle measurement error at each of the standard angle input points based on the standard angle and the original wavefront angle measurement results; S5. Based on the original angle measurement error, the original wavefront angle measurement result, and the wavefront parameter set corresponding to the original wavefront angle measurement result, establish an error calibration model with the original wavefront angle measurement result and the wavefront parameter set as input variables. The error calibration model includes an angle error term related to the original wavefront angle measurement result and a wavefront parameter processing residual term related to the wavefront parameter set. The angle error term includes at least one of a zero-position error term, a proportional error term, a decoupling nonlinear error term, and a periodic nonlinear error term, and includes at least a decoupling nonlinear error term or a periodic nonlinear error term. S6. Identify the error parameters in the error calibration model and generate an error calibration parameter set; S7. Generate an error calibration table, an error correction file, or a callable error correction model based on the set of error calibration parameters. S8. In subsequent measurement processes, based on the error calibration table, error correction file or callable error correction model, and combined with the original wavefront angle measurement result currently output by the large-angle heterodyne interferometer and its corresponding wavefront parameter set, calculate the error correction amount, correct the original wavefront angle measurement result, and obtain the corrected wavefront angle measurement result. The set of wavefront parameters includes at least one of the following: optical axis position parameters, wavefront curvature parameters, phase distribution parameters, spatial phase parameters, phase difference parameters, spatial sampling parameters, interference contrast parameters, optical axis position recovery residual parameters, wavefront reconstruction residual parameters, and wavefront restoration residual parameters.

2. The method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer according to claim 1, characterized in that, The error calibration model is expressed as follows: ， Where, E(θ) m P) represents the original wavefront angle measurement result θ m The calibration error corresponding to the wavefront parameter set P, E0 is the zero-position error term, E s (θ m E represents the proportional error term. d (θ m E represents the decoupling nonlinear error term. p (θ m ) represents the periodic nonlinear error term. The residual terms are processed for the wavefront parameters.

3. The method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer according to claim 2, characterized in that, The error calibration model is expressed as follows: ， Where a0 is the zero-position error parameter, a1 is the proportional error parameter, a2 is the decoupling nonlinear error parameter, b1 and c1 are the periodic nonlinear error parameters, ω is the periodic error angular frequency parameter, and R... w (P) represents the wavefront parameter processing residuals associated with the wavefront parameter set P.

4. The method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer according to any one of claims 1 to 3, characterized in that, The wavefront parameter processing residual term is determined by at least one of the following methods: optical axis position residual, phase distribution residual, wavefront curvature residual, spatial sampling residual, wavefront fitting residual, optical axis position recovery residual, wavefront reconstruction residual, and wavefront restoration residual, combined with table lookup, piecewise interpolation, residual fitting, or experimental calibration.

5. The method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer according to any one of claims 1 to 3, characterized in that, In step S6, the error parameters in the error calibration model are identified: S61. Identify the error parameters in the error calibration model based on the original angle measurement error, the original wavefront angle measurement result and the wavefront parameter set at each of the standard angle input points. S62. Determine whether the identified model residuals meet the preset residual threshold. If the model residual does not meet the preset residual threshold, the angle error term or wavefront parameter in the error calibration model is adjusted to process the residual term, and the error parameter identification is performed again. If the model residuals meet the preset residual threshold, then the set of error calibration parameters is output.

6. The method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer according to any one of claims 1 to 3, characterized in that, When the large-angle heterodyne interferometer outputs angle results in two directions simultaneously, error calibration models are established in the two directions respectively, or a vector-form error calibration model containing directional coupling error terms is established. The directional coupling error term is used to characterize the influence of the angle input in one direction on the original wavefront angle measurement result in another direction.

7. The method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer according to any one of claims 1 to 3, characterized in that, In subsequent measurements, it is determined whether the original wavefront angle measurement results and their corresponding wavefront parameter set are within the effective calibration range of the error calibration model. When the original wavefront angle measurement result and its corresponding wavefront parameter set are within the effective calibration range, the error calibration table, error correction file or callable error correction model are called for correction. When the original wavefront angle measurement result or its corresponding wavefront parameter set exceeds the effective calibration range, an out-of-range prompt, a reduced confidence flag, or the output of the corrected wavefront angle measurement result is stopped.

8. A wavefront angle measurement error calibration system for a large-angle heterodyne interferometer, characterized in that, The method for calibrating the wavefront angle measurement error of a large-angle heterodyne interferometer as described in any one of claims 1-3 includes a standard angle input module (1), a heterodyne interferometry data acquisition module (2), a wavefront parameter extraction module (3), a raw wavefront angle measurement result reading module (4), an error calculation module (5), an error calibration model establishment module (6), an error parameter identification module (7), a calibration parameter storage module (8), and an angle measurement result correction module (9). The standard angle input module (1) is connected to the error calculation module (5), the heterodyne interferometry data acquisition module (2) is connected to the wavefront parameter extraction module (3), the wavefront parameter extraction module (3) is connected to the original wavefront angle measurement result reading module (4), the wavefront parameter extraction module (3) is connected to the error calibration model establishment module (6), the original wavefront angle measurement result reading module (4) is connected to the error calculation module (5), the original wavefront angle measurement result reading module (4) is connected to the error calibration model establishment module (6), the original wavefront angle measurement result reading module (4) is connected to the angle measurement result correction module (9), and the error calculation module (5), the error calibration model establishment module (6), the error parameter identification module (7), the calibration parameter storage module (8), and the angle measurement result correction module (9) are connected in sequence. A standard angle input module is used to receive or control a standard angle input device to sequentially output multiple standard angles within a predetermined large angle measurement range; The heterodyne interferometry data acquisition module is used to acquire heterodyne interferometry data output by the large-angle heterodyne interferometer at each of the aforementioned standard angles. The wavefront parameter extraction module is used to extract a set of wavefront parameters corresponding to each of the standard angles based on the heterodyne interferometry data. The original wavefront angle measurement result reading module is used to read or calculate the original wavefront angle measurement result obtained by angle decoupling processing, angle calculation processing or equivalent angle measurement processing of the wavefront parameter set; The error calculation module is used to calculate the original angle measurement error based on the standard angle and the original wavefront angle measurement result; An error calibration model establishment module is used to establish an error calibration model with the original wavefront angle measurement result and the wavefront parameter set corresponding to the original wavefront angle measurement result as input variables, based on the original angle measurement error, the original wavefront angle measurement result, and the wavefront parameter set corresponding to the original wavefront angle measurement result. The error calibration model includes an angle error term related to the original wavefront angle measurement result and a wavefront parameter processing residual term related to the wavefront parameter set. The angle error term includes at least one of a zero-position error term, a proportional error term, a decoupling nonlinear error term, and a periodic nonlinear error term, and includes at least a decoupling nonlinear error term or a periodic nonlinear error term. The error parameter identification module is used to identify the error parameters in the error calibration model and generate an error calibration parameter set. The calibration parameter storage module is used to store error calibration tables, error correction files, or callable error correction models according to the set of error calibration parameters. The angle measurement result correction module is used to calculate the error correction amount and correct the original wavefront angle measurement result in subsequent measurement processes, based on the error calibration table, error correction file or callable error correction model, and in combination with the original wavefront angle measurement result currently output by the large-angle heterodyne interferometer and its corresponding wavefront parameter set, to obtain the corrected wavefront angle measurement result.

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