Multi-pose robust error separation stitching detector flatness measurement method

Abstract

The application provides a multi-pose robust error separation splicing detector flatness measurement method, and relates to the technical field of optical flatness measurement. Synchronous differential observation data is obtained; synchronous differential observation data of a calibration mirror in multiple pose states is obtained, a pose mapping relationship is established and coordinate correlation is performed to form multi-pose constraint data; a robust error separation model containing a system error field, a calibration mirror surface shape and a pose drift term is established according to the multi-pose constraint data; the robust error separation model is robustly solved to obtain the system error field; actual measurement differential observation data of a splicing detector is obtained, compensation is performed according to the system error field, and a flatness measurement result is obtained. The application can effectively separate instrument fixed errors and calibration mirror surface shapes, and improve the stability and reliability of the splicing detector flatness measurement result.

Description

Technical Field

[0001] This application relates to the field of optical flatness measurement technology, and more specifically to a method for measuring the flatness of a spliced ​​detector with multi-pose robust error separation. Background Technology

[0002] The mosaic detector is a crucial component of the focal plane array system in large-aperture telescopes, requiring multiple detector units to form a nearly coplanar focal plane in space. The spatial consistency and focal plane geometry accuracy of the mosaic detector directly impact image plane registration, focal plane adjustment, and overall field-of-view imaging quality. Defocusing, height differences, and thermal loads causing surface shape variations can lead to image inhomogeneity and decreased measurement accuracy. Therefore, flatness testing of the mosaic detector is a critical step in the development and adjustment of large-aperture, wide-field-of-view telescopes.

[0003] Existing flatness detection methods mainly include interferometry, single-probe scanning measurement, and dual-probe differential measurement. Among them, interferometry has high accuracy in surface shape detection, but it has high requirements for the reflection characteristics of the measured surface, environmental stability, and installation posture. Single-probe scanning measurement has a simple structure, but its results easily include platform motion errors, system drift, and the measured surface shape simultaneously, making it difficult to distinguish them directly during the scanning process. The dual-probe differential measurement method synchronously acquires information from the standard surface and the measured surface through two measurement sensors, which can offset the common platform drift and slowly varying environmental errors to a certain extent, making it suitable for scanning surface shape detection of spliced ​​detectors or large-size planar components.

[0004] In the flatness testing of spliced ​​detectors based on the principle of synchronous measurement with dual probes, commonly used measurement structures include the shared-frame parallel type and the top-bottom symmetrical clamping type. The shared-frame parallel structure is simple to install, with both the standard surface and the measured surface in a natural supporting state, eliminating the need for clamping the spliced ​​detector and reducing the impact of clamping stress and gravitational deformation on the measurement results. Simultaneously, the two measurement surfaces are located on the same side of the measurement space, facilitating coordinate unification and regional registration. However, in the shared-frame parallel dual-probe differential measurement structure, the two probes do not act at exactly the same spatial position. The vertical straightness error, pitch angle error, and roll error of the connecting frame are superimposed on the outputs of the two probes with different weights, leaving residual systematic errors in the differential results, manifesting as low-order trend terms. Furthermore, transmission chain thrust fluctuations, cogging effects, and periodic angular motion cause periodic changes in the attitude of the connecting frame. This error manifests as periodic fringes in the scanning results, often overlapping with the true surface shape and difficult to distinguish.

[0005] To address the aforementioned issues, most existing error compensation methods rely on single-attitude calibration or simple planar subtraction, making it difficult to distinguish between fixed instrument errors and the surface shape of the calibration mirror itself. This can easily lead to misclassification of the calibration mirror's surface shape as a systematic error and its subtraction, or leave the systematic error remaining in the measured surface shape. Furthermore, existing error compensation methods often depend on fixed lookup tables or low-order models, resulting in insufficient stability when dealing with local anomalies, boundary defects, and different measurement regions. They also struggle to simultaneously suppress low-order trend terms and periodic fringe errors.

[0006] Therefore, there is an urgent need for a method to measure the flatness of a spliced ​​detector that can distinguish between the fixed error of the instrument and the surface shape of the calibration mirror itself, and suppress low-order trend terms and periodic stripe errors, under a co-mounted parallel dual-probe synchronous differential measurement structure. Summary of the Invention

[0007] The purpose of this application is to provide a method for measuring the flatness of a stitched detector with multi-pose robust error separation, which can solve at least one of the technical problems mentioned above. The specific solution is as follows: According to a specific embodiment of this application, this application provides a method for measuring the flatness of a stitched detector with multi-pose robust error separation, comprising the following steps: Acquire synchronous differential observation data; Acquire multiple synchronous differential observation data corresponding to the calibration mirror in multiple attitude states, and establish an attitude mapping relationship between the instrument coordinate system and the calibration mirror coordinate system based on the position change relationship of the calibration mirror relative to the instrument coordinate system in different attitude states. Based on the attitude mapping relationship, the synchronous differential observation data under different attitude states are associated according to the coordinate position of the calibration mirror to form multi-attitude constraint data; A robust error separation model is established based on the multi-attitude constraint data. The robust error separation model includes: system error field, calibration mirror shape, and attitude drift term. The system error field is obtained by robustly solving the system error field, the calibration mirror shape, and the attitude drift term according to the robust error separation model. Obtain the measured differential observation data corresponding to the spliced ​​detector, and compensate the measured differential observation data according to the system error field to obtain the flatness measurement result of the spliced ​​detector.

[0008] Furthermore, the acquisition of synchronous differential observation data includes: Obtain the height information of the standard surface and the calibration mirror at the same measurement location; The synchronous differential observation data is obtained based on the difference between the height information of the calibration mirror and the height information of the standard surface.

[0009] Furthermore, multiple synchronous differential observation data are acquired, including: The calibration mirror is controlled to translate and rotate relative to the instrument coordinate system to obtain the synchronous differential observation data under different attitude states; Record the translation amount and flip direction of different posture states relative to the initial posture state, and determine the posture mapping relationship corresponding to different posture states based on the translation amount and the flip direction.

[0010] Furthermore, the formation of multi-pose constraint data includes: Based on the attitude mapping relationship corresponding to different attitude states, the measurement position in the instrument coordinate system under different attitude states is mapped to the calibration mirror coordinate system; The synchronous differential observation data mapped to the same calibration mirror coordinate position under different attitude states are correlated to form cross-attitude constraint data.

[0011] Furthermore, the establishment of the robust error separation model includes: Based on the measurement positions corresponding to the synchronous differential observation data under different attitude states, establish the correspondence between the synchronous differential observation data and the system error component, calibration mirror shape component, and attitude drift component; Based on the positional correspondence of the system error components in the instrument coordinate system and the positional correspondence of the calibration mirror shape components in the calibration mirror coordinate system, the robust error separation model is established.

[0012] Furthermore, the attitude drift components include multi-parameter forms such as constant drift, tilt drift, and weakly coupled drift; The drift coefficient corresponding to the attitude drift component is determined based on the normalized coordinates of each measurement position in the instrument coordinate system.

[0013] Furthermore, the robust solution of the system error field, the calibration mirror shape, and the attitude drift term includes: The robust weights are determined based on the residuals between the synchronous differential observation data and the current prediction results of the robust error separation model. The residuals are weighted according to the robust weights, and the system error field, the calibration mirror shape, and the attitude drift term are updated alternately using the weighted residuals. The residuals are recalculated based on the updated system error field, the calibration mirror shape, and the attitude drift term, and then iteratively solved based on the recalculated residuals.

[0014] Further, the alternating update of the system error field and the calibration mirror shape includes: The system error field is updated based on the residuals and robust weights of multiple attitude data corresponding to the same instrument coordinate position; The data after deducting the system error field and the attitude drift term is mapped to the calibration mirror coordinate system, and the calibration mirror shape is updated according to the residuals and robust weights of multiple attitude data corresponding to the same calibration mirror coordinate position.

[0015] Furthermore, during the iterative update process of the system error field and the calibration mirror shape, the updated system error field and the calibration mirror shape are respectively subjected to neighborhood smoothing processing, and the system error field and the calibration mirror shape after neighborhood smoothing processing are subjected to mean removal processing. Whether to stop iteration is determined based on the relationship between the system error field and the adjacent iteration changes of the calibrated mirror shape and the corresponding convergence threshold.

[0016] Further, the compensation of the measured differential observation data based on the system error field includes: Acquire the measured differential observation data corresponding to each measurement point during the actual measurement phase of the splicing detector; Based on the distribution of the system error field in the instrument coordinate system, spatial interpolation is performed on the positions of each measuring point corresponding to the measured differential observation data to obtain the system error compensation amount corresponding to each measuring point. Subtract the corresponding system error compensation amount from the measured differential observation data corresponding to each measuring point to obtain the correction value of each measuring point; The mean value of each measuring point is processed to obtain the flatness measurement result of the splicing detector.

[0017] Compared with the prior art, the above-described solutions of this application have at least the following beneficial effects: 1. This application provides a method for measuring the flatness of a spliced ​​detector with multi-pose robust error separation. By controlling the translation and flipping of the calibration mirror relative to the instrument coordinate system during the calibration stage, an attitude mapping relationship is established between the instrument coordinate system and the calibration mirror coordinate system. The synchronous differential observation data under different attitude states are associated according to the coordinate position of the calibration mirror to form multi-pose constraint data. This makes the systematic error field fixed in the instrument coordinate system and the calibration mirror surface shape fixed in the calibration mirror coordinate system exhibit different variation laws under different attitude states. This solves the technical problem that the systematic error field and the calibration mirror surface shape cannot be distinguished under a single attitude because they are both fixed in their respective coordinate systems. It avoids misjudging the calibration mirror surface shape as a systematic error or leaving systematic errors in the measured surface shape.

[0018] 2. This application provides a method for measuring the flatness of a stitched detector with robust error separation based on multi-pose constraints. It establishes a robust error separation model based on multi-pose constraint data, including observation equations, attitude drift parameterization, and zero-mean constraints. Huber-type robust weights are used to weight the residuals and alternately update the system error field, calibration mirror shape, and attitude drift term. Robust weights reduce the impact of local outliers and random impulse noise on system error estimation. The multi-parameter form of the attitude drift term absorbs the clamping and adjustment deviations specific to each pose. Neighborhood smoothing constraints and mean removal improve the spatial continuity of the estimation results and suppress boundary noise. This method solves the technical problems of insufficient stability and difficulty in convergence of existing error compensation methods when facing local outliers, missing boundaries, and different measurement regions, thus improving the accuracy of error separation and the numerical stability of the solution process.

[0019] 3. This application provides a method for measuring the flatness of a stitched detector with robust multi-pose error separation. After obtaining the systematic error field during the multi-pose calibration stage, spatial interpolation is used during the actual measurement stage to map the systematic error field to the measured point position and subtract it from the measured differential observation data. After mean-free normalization, the flatness measurement result of the stitched detector is output. The whole method does not change the hardware composition of the existing co-mounted parallel dual-probe synchronous differential measurement structure. It only needs to add a multi-pose calibration process and data processing algorithm, which is easy to implement on the existing scanning measurement platform. It can simultaneously suppress the low-order trend term along the scanning direction and the periodic fringe error modulated along the other direction, effectively improving the repeatability and reliability of the shape measurement results after correction. Attached Figure Description

[0020] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings: Figure 1 This is a schematic flowchart illustrating a method for measuring the flatness of a spliced ​​detector with multi-pose robust error separation, provided in an embodiment of this application.

[0021] Figure 2 This is a schematic diagram of three-dimensional scatter points obtained when a spliced ​​detector flatness measurement method without using a multi-pose robust error separation method is not used, as provided in the embodiments of this application.

[0022] Figure 3 This is a schematic diagram of three-dimensional scatter points obtained when using a multi-pose robust error separation splicing detector flatness measurement method provided in an embodiment of this application.

[0023] Figure 4 This is a schematic diagram of the surface shape of the object under test measured in a high-precision measuring instrument, as provided in the embodiments of this application. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0025] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a product or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a product or device. Without further limitation, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the product or device that includes that element.

[0026] This application provides a method for measuring the flatness of a spliced ​​detector based on multi-pose robust error separation. This method is applied to a co-mounted parallel dual-probe synchronous differential measurement system. The co-mounted parallel dual-probe synchronous differential measurement system includes a mechanical scanning module and an electronically controlled data processing module.

[0027] The mechanical scanning module includes a two-dimensional motion platform, a mounting table, a shared connecting frame, a first measuring probe, a second measuring probe, a standard surface, and the workpiece under test (DUT). The two-dimensional motion platform is fixed to the mounting table, providing X-axis and Y-axis scanning motion for the measurement system. The shared connecting frame is fixed to the two-dimensional motion platform, simultaneously supporting both the first and second measuring probes, which maintain a fixed relative position on the frame. The standard surface, serving as a differential standard surface, is fixed at a preset position within the measurement system. The DUT is mounted on a measurement station opposite the standard surface. During calibration, the DUT acts as a calibration mirror; during actual measurement, it functions as a stitching detector. The first measuring probe acquires height information from the standard surface, and the second measuring probe acquires height information from the DUT.

[0028] The electronic control data processing module includes a synchronous trigger acquisition unit, a subsequent data processing unit, and a result output unit. The synchronous trigger acquisition unit is electrically connected to both the first and second measuring probes, and is used to uniformly control the sampling times of the first and second measuring probes, ensuring that they acquire their respective height data synchronously at the same time. The subsequent data processing unit is connected to the synchronous trigger acquisition unit and is used to perform coordinate registration, differential construction, error separation, spatial interpolation, and surface shape output on the acquired data. The result output unit is connected to the subsequent data processing unit and is used to output the corrected surface shape diagram, residual diagram, peak-to-valley values, root mean square value, periodic error amplitude, trend slope, and repeatability evaluation index.

[0029] like Figure 1 As shown, the method for measuring the flatness of a stitched detector with multi-pose robust error separation provided in this application includes the following steps: S1. Acquire synchronous differential observation data, which means completing the acquisition of synchronous differential observation data in the initial attitude state. In the technical solution of this application embodiment, the synchronous differential observation data includes: the difference data between the standard surface measurement information and the calibration mirror measurement information corresponding to the same measurement position.

[0030] The calibration mirror is installed at the test piece position in the measurement system. A two-dimensional motion platform drives the shared connecting frame and its first and second measuring probes to scan along the X and Y directions. At each measurement position, the first measuring probe acquires the height information of the standard surface, and the second measuring probe acquires the height information of the calibration mirror. A synchronous acquisition unit uniformly controls the sampling time of the two probes, ensuring that both probes acquire their respective height data at the same time.

[0031] To avoid confusion in differential directions, the embodiments of this application employ the same differential convention in both the calibration and measurement stages. Let the instrument coordinates of the i-th measurement point under the r-th calibration attitude be... ,in, This represents the coordinate value of the i-th measuring point in the X direction of the instrument coordinate system; This represents the coordinate value of the i-th measuring point in the Y direction of the instrument coordinate system.

[0032] The output of the first measuring probe is: The output of the second measuring probe is Then, the difference observation data are defined. The expression is: .in, This indicates the height information of the standard surface at the i-th measuring point; This indicates the height information of the calibration mirror at the i-th measuring point; This represents the height difference measured by the second measuring probe relative to the first measuring probe. By traversing all measurement positions in the r-th attitude state and calculating the differential observables at each measuring point, a set of synchronous differential observable data corresponding to all measuring points in the r-th attitude state is obtained. }

[0033] During actual measurement, the first and second measuring probes will be subject to common platform drift at the same time. The impact of public platform drift This will have a combined effect on the outputs of the first and second measuring probes. Among them, This indicates the amount of common drift.

[0034] Let the independent noise of the first measuring probe be... The independent noise of the second measuring probe is Then the expression for the output of the first measuring probe is: The expression for the output of the second measuring probe is: .

[0035] in, This represents the geometric response of the first measuring probe along the corresponding measuring path; This indicates the geometric response of the second measuring probe along the corresponding measuring path; This indicates the relative information of the calibration mirror surface acquired by the second measuring probe.

[0036] The technical solution of this application embodiment constructs a differential observable by subtracting the output of the first measurement probe from the output of the second measurement probe, thus mitigating common platform drift. The effects of environmental variations and platform drift on the measurement results were effectively offset, thus eliminating the influence of these factors. However, residual terms resulting from path differences between the first and second measurement probes and motion structure errors still require further calibration and compensation in subsequent steps.

[0037] The technical solution of this application embodiment solves the technical problem in dual-probe differential measurement where environmental gradual variation errors and platform common drift cannot be effectively offset due to the inconsistent sampling times of the two probes. This is achieved by acquiring the standard surface height information and calibration mirror height information at the same time at each measurement location, and constructing differential observation data by subtracting the outputs of the first and second measurement probes. The errors are canceled out in the differential operation, thus eliminating the influence of environmentally variable errors and platform common drift on the measurement results, and providing a high signal-to-noise ratio observation data basis for subsequent error separation.

[0038] S2. Acquire multiple synchronous differential observation data corresponding to the calibration mirror in multiple attitude states. Based on the positional change relationship of the calibration mirror relative to the instrument coordinate system in different attitude states, establish the attitude mapping relationship between the instrument coordinate system and the calibration mirror coordinate system.

[0039] After achieving the zero-position attitude and completing the synchronous differential observation data acquisition in the initial attitude state, the calibration mirror is controlled to undergo attitude transformation relative to the instrument coordinate system. This involves translational changes along the X and Y directions of the instrument coordinate system, as well as rotational changes around the X and Y directions of the calibration mirror coordinate system. The attitude state of the calibration mirror in space can be represented as a combination of translational amount and rotational direction relative to the initial attitude state.

[0040] In the embodiments of this application, the selection of translation amount and flip direction in each posture state follows the following principles: The selection principle for translation amount. To ensure sufficient difference in the rearrangement relationship between instrument coordinates and calibration mirror coordinates under different attitude states, and to ensure sufficient overlap between measurement areas of adjacent attitudes to form effective cross-attitude constraints, the translation amount for each attitude state is typically taken as 10% to 30% of the effective aperture of the calibration mirror. Too small a translation amount will result in excessive overlap of measurement areas under different attitude states, leading to convergence of the rearrangement relationship between instrument coordinates and calibration mirror coordinates, reducing the distinguishability of the system error field and the calibration mirror surface shape; too large a translation amount will result in insufficient overlap of measurement areas under different attitude states, making it difficult to form sufficient cross-attitude constraints, affecting the solution stability of the robust error separation model.

[0041] The selection principle for the flipping direction is as follows: It should include at least two orthogonal flipping directions: a 180-degree flip around the X-direction of the calibration mirror coordinate system and a 180-degree flip around the Y-direction of the calibration mirror coordinate system, to separate the error components in the two orthogonal directions. If only a single-direction flip is performed, the systematic error and calibration mirror shape in the other direction cannot be effectively separated, resulting in underdetermined observation equations for the robust error separation model.

[0042] The selection principle for the number of attitudes. Too few attitudes will lead to insufficient cross-attitude constraints, underdetermined observation equations in the robust error separation model, and inability to uniquely determine the system error field and calibration mirror shape; too many attitudes will increase the measurement time in the calibration stage and reduce measurement efficiency. In the embodiments of this application, the number of attitudes is usually selected to be 4 to 6, which ensures both error separation accuracy and measurement efficiency.

[0043] Attitude independence is guaranteed. Sufficient pose differences are required between each attitude state to allow multiple sets of observation data to be obtained from the same calibration mirror position at different instrument coordinate positions, thereby enhancing the constraint relationship between the system error field and the calibration mirror shape. If the combination of transformation parameters corresponding to different attitude states results in the calibration mirror having the same or approximately the same final pose in space, then these attitude states do not provide new independent constraints and cannot improve the identifiability of error separation.

[0044] Furthermore, the attitude combination should cover the entire measurement area to ensure sufficient observation information in each area. In this embodiment, the translation attitude along the X and Y directions of the instrument coordinate system is used to change the correspondence between the calibration mirror position and the instrument coordinate position, so that the systematic error fixed in the instrument coordinate system exhibits different influence patterns under different attitude states; the 180-degree flip attitude around the X and Y axes of the calibration mirror coordinate system is used to change the mapping direction of the calibration mirror shape relative to the instrument coordinate system, further improving the separability of systematic error and surface shape error. Therefore, the attitude settings need to meet the requirements of sufficient spatial coverage, independent error constraints, and stable and reliable measurement. Specific attitude parameters can be adjusted according to the measurement range and system structure characteristics.

[0045] After the zero position, multiple attitude states can be set sequentially, such as the attitude of translating a first distance along the positive X direction of the instrument coordinate system, the attitude of translating a second distance along the negative X direction of the instrument coordinate system, the attitude of rotating 180 degrees around the X axis of the calibration mirror coordinate system, and the attitude of rotating 180 degrees around the Y axis of the calibration mirror coordinate system.

[0046] In the technical solution of this application embodiment, the translation amount of the calibration mirror is denoted as... ,in, This represents the total translation of the calibration mirror in the r-th pose; This represents the translation along the X direction of the instrument coordinate system in the r-th posture; This represents the translation along the Y direction of the instrument coordinate system in the r-th posture.

[0047] The flip direction of the calibration mirror is determined by the flip matrix. To describe, .in, This indicates the flip state of the calibration mirror coordinate system in the X direction; represents the flip state of the calibration mirror coordinate system in the Y direction; diag represents the diagonal matrix.

[0048] when A value of +1 indicates that the calibration mirror has not flipped in the X direction of the calibration mirror coordinate system. A value of -1 indicates that the calibration mirror has undergone a 180-degree flip in the X direction of the calibration mirror coordinate system. A value of +1 indicates that the calibration mirror has not flipped in the Y direction of the calibration mirror coordinate system. A value of -1 indicates that the calibration mirror has been flipped 180 degrees in the Y direction of the calibration mirror coordinate system.

[0049] Based on the translation amount and flip direction of the current attitude state, the attitude mapping relationship corresponding to the current attitude state can be uniquely determined. Attitude mapping relationship It reflects the coordinate transformation rules between the instrument coordinate system and the calibration mirror coordinate system.

[0050] For each posture state, repeat the data acquisition process in step one, that is, control the two-dimensional motion platform to scan along the X and Y directions of the instrument coordinate system in the current posture state, simultaneously acquiring the height data of the first and second measuring probes at each measuring point, and according to... The synchronous differential observation data corresponding to each measuring point is constructed in a certain way. By traversing all preset attitude states and performing data acquisition respectively, synchronous differential observation data of the calibration mirror in multiple attitude states are obtained.

[0051] The technical solution of this application embodiment solves the technical problem that the system error field and the calibration mirror shape cannot be distinguished under a single attitude because they are both fixed in their respective coordinate systems. By controlling the calibration mirror to generate translational changes along the X and Y directions of the instrument coordinate system and flipping changes around the X and Y directions of the calibration mirror coordinate system, and recording the translational amount and flipping direction corresponding to each attitude state to determine the attitude mapping relationship, the solution addresses the technical problem that the system error field and the calibration mirror shape cannot be distinguished under a single attitude. By introducing spatial rearrangement constraints through multi-attitude calibration, the same measurement point position in the instrument coordinate system corresponds to different positions in the calibration mirror coordinate system under different attitude states. This creates conditions for distinguishing the system error field and the calibration mirror shape in the subsequent error separation model. At the same time, it does not require changing the existing dual-probe synchronous measurement hardware structure, and can be implemented by only adding a calibration process.

[0052] S3. Based on the attitude mapping relationship Synchronous differential observation data under different attitude states are correlated according to the coordinate position of the calibration mirror to form multi-attitude constraint data.

[0053] For each attitude state, based on the attitude mapping relationship corresponding to the current attitude state, each measurement position in the instrument coordinate system under the current attitude state is mapped to the corresponding position in the calibration mirror coordinate system.

[0054] The coordinates of a measurement position in the instrument coordinate system under the r-th attitude state are: The corresponding position of the i-th measuring point in the calibration mirror coordinate system is denoted as . According to the attitude mapping relationship The coordinate mapping can be represented as: in, The flip matrix representing the current attitude state; The translation vector represents the current attitude state.

[0055] By using coordinate mapping, the coordinates of the measuring points in the instrument coordinate system are flipped according to the flipping direction of the calibration mirror, and then translated according to the translation amount of the calibration mirror, so as to obtain the position of the i-th measuring point in the calibration mirror's own coordinate system.

[0056] After completing the coordinate mapping of each measuring point from the instrument coordinate system to the calibration mirror coordinate system under all attitude states, for any grid position in the calibration mirror coordinate system... Find all attitude states mapped to a specific mesh location. The measurement points. Because the correspondence between the measurement position in the instrument coordinate system and the grid position in the calibration mirror coordinate system differs under different attitude states, the same calibration mirror coordinate grid position... Different attitude states may correspond to different measuring points in the instrument coordinate system.

[0057] Map different attitude states to the same calibration mirror coordinate grid position. All synchronous differential observation data are correlated, that is, these data are assigned to the calibration mirror coordinate grid position. Corresponding data set .

[0058] By associating differential observation data mapped to the same calibration mirror coordinate grid position under all attitude states, the synchronous differential observation data originally collected separately under different attitude states are uniformly organized according to the spatial position in the calibration mirror coordinate system. Each calibration mirror grid position has observation data from multiple attitude states, and all the associated data form cross-attitude measurement constraint data.

[0059] The technical solution of this application addresses the problem that data collected in different attitude states cannot be directly used for error separation due to inconsistencies in coordinate systems. It maps the measurement positions in the instrument coordinate system to corresponding positions in the calibration mirror coordinate system based on attitude mapping relationships, and associates synchronous differential observation data mapped to the same calibration mirror coordinate grid position under different attitude states. Furthermore, it establishes cross-attitude measurement constraint data, ensuring that each calibration mirror grid position has observation data from multiple attitude states. This provides data support for separating the systematic error field and the calibration mirror surface shape in the robust error separation model according to the fixed rules of their respective coordinate systems.

[0060] S4. Establish a robust error separation model based on the multi-attitude constraint data. The robust error separation model includes: a system error field, a calibration mirror shape, and an attitude drift term. The system error field is fixed in the instrument coordinate system, and the calibration mirror shape is fixed in the calibration mirror coordinate system.

[0061] In the technical solution of this application embodiment, the robust error separation model includes three components: observation equation, attitude drift parameterization, and zero mean constraint.

[0062] For the i-th measurement position in the r-th attitude state, the synchronous differential observation data corresponding to the i-th measurement position in the r-th attitude state. This involves the cumulative effect of multiple error sources. In the embodiments of this application, Represented as systematic error components Calibrate the mirror shape component Attitude drift components and random noise components The sum of these, the expression for the observation equation is: in, This represents the systematic error field fixed in the instrument coordinate system; This represents the shape of the calibration mirror surface fixed in the calibration mirror coordinate system; This represents the attitude drift term caused by clamping, zero-point drift, and low-frequency tilt in the r-th attitude. It varies depending on the posture and state; This indicates random measurement noise.

[0063] In the technical solution of this application embodiment, when the position of the measuring point in the instrument coordinate system When determined, systematic error At the measuring point location The systematic error value at this point is a fixed value that does not change with the attitude of the calibration mirror. The systematic error value includes the vertical straightness error, pitch angle error, and roll error of the scanning platform, exhibiting a systematic deviation with a fixed spatial distribution in the instrument coordinate system. This is when the grid position in the calibration mirror coordinate system... When determining, calibrate the mirror shape. In grid location The surface height value is an inherent property of the calibration mirror itself and does not change with the orientation of the calibration mirror in space.

[0064] Due to the system error field Fixed in the instrument coordinate system, when the calibration mirror is translated or flipped, the position of the same measuring point in the instrument coordinate system... Calibration mirror coordinates under different attitude states Different, therefore the systematic error field and calibrated mirror shape The different patterns of change under different posture states provide a basis for mathematically distinguishing between the two. The posture drift term... It estimates independently for each attitude state to absorb the clamping and adjustment biases specific to the current attitude state.

[0065] In order to more accurately describe the characteristics of attitude drift as a function of spatial position, the embodiments of this application represent attitude drift as a multi-parameter form that includes constant drift, tilt drift and weakly coupled drift, i.e., attitude drift parameterization.

[0066] For the measurement position in the instrument coordinate system , coordinate and Normalization is performed to obtain normalized coordinates. and The expression is: in, and These represent the normalized coordinate values ​​of the i-th measuring point in the X and Y directions of the instrument coordinate system, respectively. This represents the maximum coordinate value in the X direction of the instrument coordinate system; This represents the minimum coordinate value in the X direction of the instrument coordinate system; This represents the maximum coordinate value in the Y direction of the instrument coordinate system; This represents the minimum coordinate value in the Y direction of the instrument coordinate system; This represents the average value of the coordinates of all measuring points in the X direction of the instrument coordinate system; This represents the average coordinate of all measuring points in the Y-direction of the instrument coordinate system. Through the above normalization process, the coordinate values ​​of each measuring point are mapped to a uniform numerical range.

[0067] Based on normalized coordinates, attitude drift term It can be represented as: in, Let be the constant drift term coefficients in the r-th attitude state. This represents the overall zero-position offset in the r-th attitude state. Let be the tilt drift coefficient along the X direction of the instrument coordinate system in the r-th attitude state. This indicates the degree of tilt of the measurement plane in the X direction of the instrument coordinate system under the r-th attitude state. Let be the tilt drift coefficient along the Y-direction of the instrument coordinate system in the r-th attitude state. This indicates the degree of inclination of the measurement plane in the Y direction of the instrument coordinate system under the r-th attitude state. Let be the coefficients of the weakly coupled terms in the r-th attitude state. Used to absorb the coupling background term caused by assembly and attitude changes.

[0068] Due to the system error field 1. Calibrate the mirror shape There is a non-uniqueness of the reference between the constant drift term and the system error field. While adding a constant, the calibrated mirror shape is also given Subtracting the same constant does not change the predicted value of the observation equation. To address this issue, the technical solution of this application applies a zero-mean constraint to the robust error separation model: a constraint is applied to the system error field. Apply constraints to the calibrated mirror shape Where, mean represents the operation of averaging the variable across all measurement locations; This represents the estimated value of the calibration mirror shape at the j-th grid position. The mean of the systematic error field and the mean of the calibration mirror shape at all measurement points are zero. The zero-mean constraint is only used to determine the relative zero point of the decomposition result and does not change the spatial distribution of the systematic error field and the calibration mirror shape.

[0069] Thus, the robust error separation model of this embodiment is constituted by the observation equation, the parameterized form of attitude drift, and the zero-mean constraint.

[0070] The technical solution of this application, by establishing a robust error separation model that includes observation equations, attitude drift parameterization, and zero-mean constraints, decomposes mixed synchronous differential observation data into a system error field fixed in the instrument coordinate system, a calibration mirror shape fixed in the calibration mirror coordinate system, and an attitude drift term that varies with attitude. This solves the technical problems of existing error compensation algorithms, which struggle to distinguish between fixed instrument errors and the calibration mirror's own surface shape, and are prone to misjudging the calibration mirror shape as a system error or leaving system errors in the measured surface shape. On one hand, the attitude drift term adopts a multi-parameter form including constant drift, tilt drift, and weakly coupled drift, which can more accurately absorb the clamping and adjustment deviations unique to each attitude, avoiding the erroneous inclusion of weakly coupled background terms in the fixed system error. On the other hand, the zero-mean constraint eliminates the non-uniqueness of the reference between the system error field and the calibration mirror shape, making the decomposition result have a unique physical meaning and improving the accuracy of error separation.

[0071] S5. Based on the robust error separation model, the system error field, calibration mirror shape, and attitude drift term are robustly solved to obtain the system error field.

[0072] To reduce the impact of local outliers and random impulse noise on error field estimation, the technical solution of this application introduces Huber-type robust weights.

[0073] Assign initial values ​​to the observation data at each measurement location and set initial values ​​for iteration. For the i-th measurement point in the r-th attitude state, the system error field... The initial value is set to zero to calibrate the mirror shape. The initial value is set to zero, and the attitude drift term is... The initial value is set to zero. The iterative solution process begins.

[0074] In the t-th iteration, based on the system error field of the current iteration step 1. Calibrate the mirror shape and attitude drift Calculate the predicted values ​​of the robust error separation model under the current parameters, and compare the predicted values ​​with the actual observed values. Subtracting the values ​​yields the residual at the i-th measurement point in the r-th attitude state. The expression is: in, This represents the residual at the i-th measurement point in the r-th attitude state. This represents the remaining amount of observational data that the current model cannot explain; Represents the systematic error field in the t-th iteration; This represents the calibration mirror shape in the t-th iteration; This represents the attitude drift term in the t-th iteration.

[0075] After obtaining the residuals for each measurement point, the robust weights for each measurement point are determined based on the absolute value of the residuals. In this embodiment, the robust weights are determined based on the residuals between the synchronous differential observation data and the current prediction results of the robust error separation model, specifically using a Huber-type robust weighting function. For measurement points with smaller residuals, it is assumed that these points conform to a normal data distribution and are given higher weights. For measurement points with larger residuals, it is assumed that these points may be affected by local outliers or random impulse noise and are given lower weights to reduce the impact of these larger residuals on the estimation results.

[0076] Let δ be a preset robustness threshold, which can be set according to the noise level of the measurement system. For the i-th measurement point in the r-th attitude state during the t-th iteration, the Huber-type robust weight of the i-th measurement point in the r-th attitude state is... Determined according to the following rules: When the absolute value of the residual At δ, ; When the absolute value of the residual At δ, .

[0077] That is, measurement points with smaller residuals participate in the estimation with full weight, while the weight of measurement points with larger residuals decreases inversely as the absolute value of the residuals increases.

[0078] Based on Huber-type robust weights, the system error field, calibration mirror shape, and attitude drift term are updated alternately.

[0079] Update the system error field At that time, the system error field is updated based on the residuals and robust weights of multiple attitude data corresponding to the same instrument coordinate position. For a fixed measurement point position in the instrument coordinate system... There may be multiple attitude states corresponding to the fixed measurement point position. The observation data. Subtract the current calibrated mirror shape from the observation data under multiple attitude states. and attitude drift The residuals are then weighted according to their corresponding robust weights to obtain the updated system error value. The expression is: in, In the (t+1)th iteration The systematic error value at that location. That is, for the same position in the instrument coordinate system. After deducting the calibration mirror shape and the attitude drift from all the observation data across attitudes, the common component of all the observation data across attitudes is the system error, which is extracted by robust weighted averaging.

[0080] When updating the attitude drift term, for the r-th attitude state, the drift coefficient vector of the r-th attitude state... It is obtained through robust minimization, that is, finding a set of drift coefficients such that, in the r-th attitude state, all measurement points after subtracting the system error field... and calibrated mirror shape The deviation between the residual and the attitude drift model is minimized. The drift coefficient vector corresponding to the r-th attitude state. The update is achieved through a minimization process, expressed as: in, This represents the drift coefficient vector that has the smallest value in the (t+1)th iteration. This represents the Huber robust loss function. Corresponding to Huber robust weights, it is used to reduce the impact of measurement points with large residuals on the estimation of drift coefficients; Let represent the row vector formed by the normalized coordinates of the i-th measurement point. The minimization process is solved using an iterative weighted least squares method, that is, in each iteration, the robust weights are updated according to the current residuals, and then the weighted least squares problem is solved based on the updated weights until the drift coefficients converge.

[0081] When updating the calibration mirror shape, the data after deducting the system error field and attitude drift term is transformed to the calibration mirror coordinate system according to the attitude mapping relationship. The calibration mirror shape is updated based on the residuals and robust weights of multiple attitude observation data mapped to the same calibration mirror coordinate grid position.

[0082] For a fixed grid position in the calibration mirror coordinate system Map all attitude states to fixed mesh positions The set of measurement points is denoted as For the set of measurement points The measurement points in the data will have the systematic error field deducted. and attitude drift The residuals are then weighted according to their corresponding robust weights to obtain the updated calibration mirror shape value: in, In the (t+1)th iteration The calibrated mirror shape value at the location; This indicates that after attitude mapping, the positions fall within the same calibration mirror mesh location. The complete set of measurement points.

[0083] For the same grid position in the calibration mirror coordinate system After deducting systematic errors and attitude drift, the common component of all observation data across attitudes is the calibration mirror shape, which is extracted by robust weighted averaging.

[0084] Through the aforementioned alternating update process, the system error field component fixed in the instrument coordinate system gradually increases during attitude averaging, while the calibration mirror shape component fixed in the calibration mirror coordinate system gradually increases during mirror coordinate rearrangement. The two components gradually separate during the alternating iterations. After each complete update, the residuals are recalculated based on the updated parameters, and the solution is iteratively performed based on the recalculated residuals.

[0085] To further improve the spatial continuity of the estimation results and suppress boundary noise, in this embodiment, after each iteration, during the iterative update of the system error field and the calibration mirror shape, neighborhood smoothing is performed on the updated system error field and the calibration mirror shape, and mean removal is performed on the neighborhood smoothed system error field and the calibration mirror shape, subtracting the average value of all data from each data point to make the overall mean value after processing zero.

[0086] The neighborhood window size is determined comprehensively based on the spatial variation characteristics of the error components, the measurement sampling interval, and the scale of surface details to be preserved. The systematic error field mainly originates from the straightness error, attitude error, and motion structure error of the scanning platform. Its spatial variation frequency is low, exhibiting continuous and slow changes. Therefore, a smaller neighborhood window is used for smoothing to suppress random noise while preserving the trend of systematic error changes. The calibration mirror shape is an inherent surface shape of the optical element, with strong spatial continuity. Therefore, a larger neighborhood window is used for smoothing to improve the stability of surface shape estimation. When the neighborhood window is too small, the number of data points participating in smoothing is insufficient, reducing noise suppression capability; when the neighborhood window is too large, excessive spatial averaging weakens the true error variation characteristics, causing loss of local surface details. Therefore, in this embodiment, a 3×3 neighborhood window is used for the systematic error field, and a 5×5 neighborhood window is used for the calibration mirror shape to achieve a balance between error smoothing and feature preservation.

[0087] For the systematic error field after the (t+1)th iteration update of the systematic error field The system error field With the system error field The 3×3 neighborhood smoothing results are weighted and fused, with the fusion weight being... That is, the systematic error field of (1- The weights retain their original values. The weights are derived from the neighborhood smoothing results. Then, a mean-removing operation is performed on the fused results to make the overall mean of the fused system error field zero. The expression is as follows: in, (·) represents a smoothing operator that takes the average of the variable to be processed within a 3×3 neighborhood window; The smoothing weights are for the system error field; This indicates that the variable to be processed is subjected to mean removal, that is, the average value of all positions is subtracted from the value at each position.

[0088] For the calibration mirror shape updated in the (t+1)th iteration , to calibrate the mirror shape With the calibrated mirror shape The 5×5 neighborhood smoothing results are weighted and fused, with the fusion weight being... Then, a mean-removing operation is performed on the fusion result, expressed as: in, This represents a smoothing operator that takes the average value of the variable to be processed within a 5×5 neighborhood window; The smoothing weight is assigned to the calibrated mirror shape.

[0089] In the technical solution of this application embodiment, the criterion for determining iterative convergence is: the changes in adjacent iterations of the system error field and the calibration mirror shape are both less than their respective preset convergence thresholds. Whether to stop iteration is determined based on the relationship between the changes in adjacent iterations of the system error field and the corresponding convergence thresholds.

[0090] For a systematic error field, the Frobenius norm of the change in the systematic error field between adjacent iterations is calculated. The Frobenius norm reflects the overall change in the systematic error field from the t-th iteration to the (t+1)-th iteration. The F-norm is then normalized. If the normalized change is less than a preset convergence threshold... Then the system error field has converged, and the expression is: in, This represents the system error field after the t-th iteration update; Let F represent the system error field after the (t+1)th iteration update; F represents the Frobenius norm. This indicates a small quantity to prevent the denominator from being zero; This represents the preset convergence threshold of the system error field.

[0091] Similarly, for a calibrated mirror shape, if the normalized value of its adjacent iteration changes is less than the preset convergence threshold... If the calibrated mirror shape has converged, then it is considered that the calibrated mirror shape has converged. in, This represents the calibration mirror shape after the t-th iteration update; This represents the calibration mirror shape after the (t+1)th iteration update; The preset convergence threshold is used to calibrate the mirror shape.

[0092] The iteration stops when both the systematic error field and the calibration mirror shape satisfy the convergence condition, at which point the final systematic error field is obtained. .

[0093] The robust solution proposed in this application addresses the technical problems of insufficient stability and difficulty in convergence of existing error compensation algorithms when faced with local outliers, missing boundaries, and different measurement regions. This is achieved by employing Huber-type robust weights to weight the residuals, alternately updating the system error field and calibration mirror shape, and incorporating neighborhood smoothing constraints and mean removal. Huber robust weights reduce the impact of local outliers and random impulse noise on system error estimation, improving the robustness of error extraction. The alternate update strategy gradually strengthens the system error field component fixed in the instrument coordinate system during cross-attitude averaging, while the calibration mirror shape component fixed in the calibration mirror coordinate system gradually strengthens during mirror coordinate rearrangement. These two components gradually separate during alternating iterations, achieving effective separation of the two error components. Neighborhood smoothing constraints and mean removal improve the spatial continuity of the estimation results and suppress boundary noise. Convergence is determined by the change in adjacent iterations, ensuring the reliability and numerical stability of the solution process.

[0094] S6. Obtain the measured differential observation data corresponding to the splicing detector, compensate the measured differential observation data according to the system error field, and obtain the flatness measurement result of the splicing detector.

[0095] After completing the calibration phase and obtaining the systematic error field Next, the calibration mirror is removed from the measurement system, and the stitched detector to be tested is installed at the position of the test piece, thus entering the actual measurement stage. The stitched detector is composed of multiple detector units spliced ​​together. The stitched detector needs to form an approximately coplanar focal plane in space, and the height consistency of each detector unit is the flatness measured.

[0096] The two-dimensional motion platform is started to scan along the X and Y directions of the instrument coordinate system to obtain the measured differential observation data corresponding to each measurement point in the actual measurement stage of the splicing detector.

[0097] During the actual measurement phase, the standard surface height information of the first measuring probe at each measuring point was collected simultaneously. The height information of the spliced ​​detector at each measuring point of the second measuring probe. For the i-th measuring point in the actual measurement phase, the position of the i-th measuring point in the instrument coordinate system is denoted as... Measured differential observation data Constructed using the same difference convention as in the calibration phase, the expression is: in, This indicates the height information of the standard surface at the i-th measuring point during the actual measurement phase; This represents the height information of the measured surface at the i-th measurement point during the actual measurement phase; This indicates the height difference measured by the second measuring probe relative to the first measuring probe during the actual measurement phase.

[0098] After obtaining the measured differential observation data for all measuring points, it is necessary to subtract the systematic error field obtained during the calibration stage from the measured differential observation data. Since the positions of the measuring points in the actual measurement stage may not completely coincide with the positions of the calibration grid in the calibration stage, the systematic error value cannot be directly read from the calibration grid. The technical solution of this application embodiment performs spatial interpolation on the positions of each measuring point corresponding to the measured differential observation data based on the distribution of the systematic error field in the instrument coordinate system, thereby obtaining the systematic error compensation amount corresponding to each measuring point.

[0099] For the actual measured point location Using the systematic error field obtained during the calibration phase The distribution on the calibration grid is used to calculate the location of the measured points using spatial interpolation operators. The system error estimate at point , expressed as: in, This represents the estimated system error obtained by interpolation at the location of the i-th measured point, which is also the compensation amount. Represents the systematic error field Interpolation operators for performing spatial interpolation operations; This represents the position coordinates of the i-th measuring point in the instrument coordinate system during the actual measurement phase.

[0100] In the technical solution of this application embodiment, spatial interpolation can be performed using linear interpolation or spline interpolation methods. The system error value at any measured location is estimated based on the system error value on the calibration grid points. The system error field obtained during the calibration stage is used to calculate the corresponding system error compensation amount at the measured point location through spatial interpolation.

[0101] After obtaining the system error compensation amount for each measuring point, subtract the corresponding system error compensation amount from the measured differential observation data for each measuring point to obtain the correction value for each measuring point, expressed as: in, This represents the correction value of the i-th measured point after deducting the system error compensation. This reflects the height deviation of the splicing detector at the i-th measuring point relative to the standard surface.

[0102] The technical solution in this embodiment outputs a relative surface shape rather than an absolute height value, requiring mean-reduction processing of the correction values ​​for all measuring points. Assume there are a total of [number missing] points in the actual measurement phase. For each measurement point, the correction value for the i-th measurement point is... Use the correction value of the i-th measuring point Subtracting the average of all measurement point correction values ​​yields the final mean-reduced correction result, expressed as: in, This represents the final surface shape result of the i-th measured point after mean-free normalization; This indicates the total number of measurement points during the actual measurement phase; This represents the summation of correction values ​​for all measured points.

[0103] The mean-removal process ensures that the final output of the spliced ​​detector flatness measurement results has a relative surface shape characteristic with zero mean, eliminating the influence of the system zero point on the measurement results.

[0104] The technical solution of this application adopts measured data correction. By interpolating the systematic error field obtained in the calibration stage to the measured point position and subtracting it from the measured differential observation data, it solves the technical problem that the systematic error cannot be directly matched and subtracted when the measured point position in the actual measurement stage does not completely coincide with the grid position in the calibration stage. Spatial interpolation is used to obtain the systematic error compensation amount corresponding to each measured point position, ensuring the integrity and continuity of systematic error compensation. Through zero-mean normalization processing, the relative surface shape result with the influence of the system zero point is removed, eliminating the influence of the system zero point on the measurement result. This effectively suppresses low-order ramp errors along the scanning direction and periodic fringe errors modulated along the other direction, improving the stability and repeatability of the corrected surface shape.

[0105] To verify the effectiveness of the technical solution proposed in the embodiments of this application, a simulation verification experiment was conducted. In the simulation verification, multiple sets of data were constructed, including a standard surface, a calibration mirror, the actual surface shape of the measured part, and the systematic errors of the measuring device. The actual surface shape of the measured detector was obtained using the standard surface shape measured by a high-precision profilometer as the simulation input true value. Systematic errors included the downward slope trend in the positive X direction of the instrument coordinate system, periodic fringes in the Y direction of the instrument coordinate system, weak coupling disturbances in the X and Y directions of the instrument coordinate system, and local weak distortions. Data was generated using a fixed grid, and different measurement ranges, peak-valley differences for different calibration mirrors, and peak-valley true values ​​for different measured part surface shapes were set, forming multiple sets of comparison samples. The comparison of results before and after compensation is shown in Table 1.

[0106] Table 1 Comparison of evaluation indicators before and after compensation like Figure 2 and Figure 3 As shown in the figure, the horizontal axis represents the position of the measurement area along the X direction of the instrument coordinate system, the vertical axis represents the position along the Y direction of the instrument coordinate system, and the color and height direction represent the differential height value at the corresponding measurement point. Figure 2The three-dimensional scatter plot obtained without adopting the technical solution of this application shows an overall tilting trend along the X direction. This change is mainly manifested in the monotonically decreasing height of the entire measurement area along the X direction, reflecting the low-order trend terms introduced by the vertical straightness error and attitude error of the scanning platform. At the same time, there is a periodic undulating structure along the Y direction, which is manifested as a regularly distributed wavy change, corresponding to the periodic stripe error caused by the periodic error of the motion mechanism. Figure 3 This is a three-dimensional scatter plot after compensation using the technical solution of this application. Compared to... Figure 2 The overall height distribution is more uniform, and the continuous tilting trend along the X-direction is significantly reduced, indicating that the low-order trend terms in the system error field are effectively separated and compensated. Simultaneously, the amplitude of the periodic ripples along the Y-direction decreases, indicating that the periodic error component is suppressed. The PV change rate, X-direction trend slope change rate, and Y-direction periodic error reduction rate in Table 1 are all calculated from measurement data before and after compensation. PV is used to evaluate the overall height variation range, the X-direction trend slope is used to evaluate the change in low-order tilt error, the Y-direction periodic error amplitude is used to evaluate the periodic error suppression effect, and the repeatability index is used to evaluate the stability of the error field extraction after multi-pose calibration. Therefore, Figure 2 , Figure 3 The spatial distribution variation shown corresponds to the quantitative evaluation results in Table 1, which together verify the effectiveness of the technical solution of this application in separating and compensating for system errors.

[0107] Figure 4 This refers to the standard surface shape of the measured component in this embodiment, measured by a high-precision profilometer. The standard surface shape serves as the true value input for the surface shape of the measured part in simulation verification. Figure 2 , Figure 3 , Figure 4 The comparison shows that the three-dimensional surface distribution before compensation is affected by systematic errors, exhibiting a significant tilting trend and periodic fluctuations, deviating considerably from the true surface features of the measured component. The three-dimensional surface distribution after compensation maintains the same overall trend as the reference standard surface, both showing a continuous curved surface feature with a higher central region and gradually decreasing edge region. This indicates that after systematic error field separation and compensation, the measurement results can accurately retain the main morphological features of the measured surface. Simultaneously, the overall tilting trend, local fluctuations, and periodic error structures in the compensation results are significantly suppressed, resulting in a smoother surface distribution that more closely approximates the spatial variation law of the reference standard surface. These results demonstrate that the technical solution proposed in this application can effectively separate the error components introduced by the measurement system, reduce the impact of systematic errors on the surface reconstruction results, and improve the accuracy and reliability of the flatness measurement results of the stitched detector.

[0108] In summary, the embodiments of this application provide a method for measuring the flatness of a stitched detector based on multi-pose robust error separation. This method acquires multi-pose synchronous differential observation data during the calibration phase, establishes an attitude mapping relationship between the instrument coordinate system and the calibration mirror coordinate system, and associates synchronous differential observation data under different attitude states according to the calibration mirror coordinate position to form multi-pose constraint data. Based on the multi-pose constraint data, a robust error separation model is established, including observation equations, attitude drift parameterization, and zero-mean constraints. The synchronous differential observation data is decomposed into a system error field fixed in the instrument coordinate system, a calibration mirror surface shape fixed in the calibration mirror coordinate system, and an attitude drift term that varies with attitude. A Huber-type robust weight is used for alternating iterative solution, and a stable system error field is obtained through neighborhood smoothing constraints and Frobenius norm convergence criteria. During the actual measurement phase, the system error field is mapped to the measured measurement point position through spatial interpolation and subtracted from the measured differential observation data. After mean-free normalization processing, the flatness measurement result of the stitched detector is output. While maintaining the advantages of synchronous relative measurement with dual probes, the technical solution effectively separates the fixed error of the instrument from the surface shape of the calibration mirror itself, suppresses low-order trend terms and periodic fringe errors, and improves the stability and reliability of the measurement results after calibration.

[0109] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0110] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for measuring the flatness of a spliced ​​detector with multi-pose robust error separation, characterized in that, Includes the following steps: Acquire synchronous differential observation data; Acquire multiple synchronous differential observation data corresponding to the calibration mirror in multiple attitude states, and establish the attitude mapping relationship between the instrument coordinate system and the calibration mirror coordinate system based on the position change relationship of the calibration mirror relative to the instrument coordinate system in different attitude states. Based on the attitude mapping relationship, the synchronous differential observation data under different attitude states are associated according to the coordinate position of the calibration mirror to form multi-attitude constraint data; A robust error separation model is established based on the multi-attitude constraint data. The robust error separation model includes: system error field, calibration mirror shape, and attitude drift term. The system error field is obtained by robustly solving the system error field, the calibration mirror shape, and the attitude drift term according to the robust error separation model. Obtain the measured differential observation data corresponding to the spliced ​​detector, and compensate the measured differential observation data according to the system error field to obtain the flatness measurement result of the spliced ​​detector.

2. The method for measuring the flatness of a spliced ​​detector according to claim 1, characterized in that, The acquisition of synchronous differential observation data includes: Obtain the height information of the standard surface and the calibration mirror at the same measurement location; The synchronous differential observation data is obtained based on the difference between the height information of the calibration mirror and the height information of the standard surface.

3. The method for measuring the flatness of a spliced ​​detector according to claim 1, characterized in that, Acquiring multiple synchronous differential observation data, including: The calibration mirror is controlled to translate and rotate relative to the instrument coordinate system to obtain the synchronous differential observation data under different attitude states; Record the translation amount and flip direction of different posture states relative to the initial posture state, and determine the posture mapping relationship corresponding to different posture states based on the translation amount and the flip direction.

4. The method for measuring the flatness of a spliced ​​detector according to claim 1, characterized in that, The formation of multi-pose constraint data includes: Based on the attitude mapping relationship corresponding to different attitude states, the measurement position in the instrument coordinate system under different attitude states is mapped to the calibration mirror coordinate system; The synchronous differential observation data mapped to the same calibration mirror coordinate position under different attitude states are correlated to form cross-attitude constraint data.

5. The method for measuring the flatness of a spliced ​​detector according to claim 4, characterized in that, The robust error separation model is established by: Based on the measurement positions corresponding to the synchronous differential observation data under different attitude states, establish the correspondence between the synchronous differential observation data and the system error component, calibration mirror shape component, and attitude drift component; Based on the positional correspondence of the system error components in the instrument coordinate system and the positional correspondence of the calibration mirror shape components in the calibration mirror coordinate system, the robust error separation model is established.

6. The method for measuring the flatness of a spliced ​​detector according to claim 5, characterized in that, The attitude drift components include: constant drift, tilt drift and weakly coupled drift in multi-parameter form; The drift coefficient corresponding to the attitude drift component is determined based on the normalized coordinates of each measurement position in the instrument coordinate system.

7. The method for measuring the flatness of a spliced ​​detector according to claim 1, characterized in that, Robust solution of the system error field, the calibration mirror shape, and the attitude drift term includes: The robust weights are determined based on the residuals between the synchronous differential observation data and the current prediction results of the robust error separation model. The residuals are weighted according to the robust weights, and the system error field, the calibration mirror shape, and the attitude drift term are updated alternately using the weighted residuals. The residuals are recalculated based on the updated system error field, the calibration mirror shape, and the attitude drift term, and then iteratively solved based on the recalculated residuals.

8. The method for measuring the flatness of a spliced ​​detector according to claim 7, characterized in that, Alternating updates to the system error field and the calibrated mirror shape include: The system error field is updated based on the residuals and robust weights of multiple attitude data corresponding to the same instrument coordinate position; The data after deducting the system error field and the attitude drift term is mapped to the calibration mirror coordinate system, and the calibration mirror shape is updated according to the residuals and robust weights of multiple attitude data corresponding to the same calibration mirror coordinate position.

9. The method for measuring the flatness of a spliced ​​detector according to claim 7, characterized in that, During the iterative update process of the system error field and the calibration mirror shape, the updated system error field and the calibration mirror shape are respectively subjected to neighborhood smoothing processing, and the system error field and the calibration mirror shape after neighborhood smoothing processing are subjected to mean removal processing. Whether to stop iteration is determined based on the relationship between the system error field and the adjacent iteration changes of the calibrated mirror shape and the corresponding convergence threshold.

10. The method for measuring the flatness of a spliced ​​detector according to claim 1, characterized in that, Compensation is performed on the measured differential observation data based on the system error field, including: Acquire the measured differential observation data corresponding to each measurement point during the actual measurement phase of the splicing detector; Based on the distribution of the system error field in the instrument coordinate system, spatial interpolation is performed on the positions of each measuring point corresponding to the measured differential observation data to obtain the system error compensation amount corresponding to each measuring point. Subtract the corresponding system error compensation amount from the measured differential observation data corresponding to each measuring point to obtain the correction value of each measuring point; The mean value of each measuring point is processed to obtain the flatness measurement result of the splicing detector.

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