A grating scale measurement error compensation method

Abstract

The present invention provides a method for compensating the measurement error of a grating scale, comprising the following steps: S1: constructing an initial error compensation model and a multi-dimensional bounded optimization model; S2: extracting a sub-pixel track positioning map from the input grating image by a sub-pixel level positioning network; S3: constructing a regression tree in the task space according to the sub-pixel track positioning map, outputting a regression result associated with each interference factor and migrating the regression result to the multi-dimensional bounded optimization model; S4: feeding back compensation conditions to the sub-pixel level positioning network by the multi-dimensional bounded optimization model according to the regression result; S5: extracting a new sub-pixel track positioning map by the sub-pixel level positioning network according to the compensation conditions and inputting the new sub-pixel track positioning map into a decoding layer, and outputting a decoding result as an accurate measurement result, thereby completing the compensation of the measurement error of the grating scale. The present invention provides a method for compensating the measurement error of a grating scale, which solves the problem that the measurement accuracy of the grating scale is often affected by various error factors.

Description

Technical Field

[0001] The present invention relates to the technical field of precision measurement, and more specifically, to a method for compensating the measurement error of a grating scale. Background Art

[0002] Ultra-precision manufacturing and processing in the micro-nano field are the objects of the national key field breakthrough development research plan, and are one of the important prerequisites for China to transform from a manufacturing power to a manufacturing powerhouse. As the core measurement device of micro-nano ultra-precision processing equipment, the grating scale is inevitably affected by multiple interference factors during the measurement process, which seriously restricts its measurement accuracy reliability and accuracy improvement.

[0003] The measurement accuracy of the grating scale is often affected by various error factors. The common errors generally include the following four categories: optoelectronic system error, vibration error, tooling error, and temperature error. The more common method for correcting the measurement accuracy of the grating scale is to separately separate and correct these four types of errors. In addition, some methods have been proposed that the geometric error, vibration, or thermal non-uniformity of the grating scale will cause relative displacement and mechanical deformation of the structural components, resulting in measurement errors. Therefore, a numerical simulation algorithm is proposed to estimate the measurement errors. However, this type of method only compares the numerical results with the theoretical values and is difficult to be effective in essence. There are also some methods that quantitatively describe the grating pair error, guide rail error, and workbench error, establish a total error model of the grating measurement system, and experimentally verify that this model can improve the accuracy of the grating measurement system; however, this model assumes that the contributions of each error to the system accuracy are the same. Therefore, the model only simply linearly superimposes each error term and then adds a random error term. In reality, the contribution degrees of each error to the system accuracy are often not equal and cannot be a simple linear superposition relationship.

[0004] Therefore, for the measurement accuracy error of the grating scale caused by multiple error factors, there is currently no good error compensation method. Summary of the Invention

[0005] In order to overcome the technical defect that the measurement accuracy of the grating scale is often affected by various error factors, the present invention provides a method for compensating the measurement error of the grating scale.

[0006] To solve the above technical problems, the technical solution of the present invention is as follows:

[0007] A method for compensating the measurement error of a grating scale, comprising the following steps:

[0008] S1: Construct an initial error compensation model and a multi-dimensional bounded optimization model;

[0009] The initial error compensation model includes a sub-pixel level positioning network, a decoding layer, and a task space.

[0010] The multi-dimensional bounded optimization model is established with the objective function of minimizing the coupling error of multiple interference factors;

[0011] S2: The sub-pixel level positioning network extracts the sub-pixel code track positioning map according to the input grating image;

[0012] S3: In the task space, a regression tree is constructed according to the sub-pixel code track positioning map, the regression results associated with each interference factor are output, and the regression results are transferred to the multi-dimensional bounded optimization model;

[0013] S4: The multi-dimensional bounded optimization model feeds back the compensation conditions to the sub-pixel level positioning network according to the regression results;

[0014] S5: The sub-pixel level positioning network extracts a new sub-pixel code track positioning map according to the compensation conditions and inputs it into the decoding layer, and the output decoding result is used as the accurate measurement result to complete the measurement error compensation of the grating scale.

[0015] In the above solution, an initial error compensation model and a multi-dimensional bounded optimization model are constructed, and the initial error compensation model and the multi-dimensional bounded optimization model are fused through parameter transfer. During measurement, the regression results associated with each interference factor are obtained according to the grating image, then the corresponding compensation conditions are fed back by the multi-dimensional bounded optimization model, and finally the accurate measurement result is obtained according to the compensation conditions, realizing the error compensation of multiple interference factors in the measurement of the grating scale.

[0016] Preferably, the sub-pixel code track positioning map is extracted from the input grating image through the following steps:

[0017] A1: Extract multi-scale feature sub-maps from the input grating image;

[0018] A2: Perform coarse positioning of the code track according to the multi-scale feature sub-maps to obtain the coarse code track positioning map;

[0019] A3: Obtain the sub-pixel code track positioning map according to the multi-scale feature sub-maps and the coarse code track positioning map.

[0020] Preferably, the decoding layer obtains the decoding result by means of table lookup.

[0021] Preferably, the reward function for constructing the regression tree is:

[0022]

[0023]

[0024] Among them, R i represents the reward function value at the current moment, R i-1 represents the reward function value at the previous moment, P π represents the conversion function between the task space and the feature set under the current policy, Denotes the mathematical transpose of the conversion function, π R Denotes the R-dimensional representation of parameter s, a denotes the error value corresponding to parameter s at the current moment, and D denotes the set of image features.

[0025] Preferably, a source task iteration strategy is introduced to accelerate transfer learning:

[0026] Q t+τ (s t , ′ ) = (1 - a ′ )Q t (s t + ′ )

[0027] + ′ [Q(S t , ′ ) + (S t+a , ′ ) + … + (s t+τ-1 , ′ ) /

[0028] Where Q t+τ (s t , ′ ) denotes the action value function of the target grating scale error compensation model, t denotes the number of iterations, s t denotes the state quantity at the t-th iteration, a ′ denotes the proportionality coefficient of the assigned action value function, Q t (s t + a′) denotes the action value function of the source grating scale error compensation model, α′ denotes the action, Q(·) denotes the value function, S t+1 denotes the state quantity at the (t + 1)-th moment, s t+τ-1 denotes the state quantity at the previous moment, and τ denotes the number of subtasks.

[0029] Preferably, the interference factors include temperature error and vibration error.

[0030] Preferably, the multi-dimensional bounded optimization model is:

[0031]

[0032] s.t. t1 ≥ T ≥ t2

[0033] f1 ≥ F ≥ f2

[0034] a1 ≥ A ≥ a2

[0035] Among them, C′(·) represents the coupling error of multiple interference factors, e1(T) represents the temperature error, e2(A,F) represents the vibration error, T represents the temperature of the working environment of the grating scale, A represents the vibration amplitude of the working environment of the grating scale, F represents the vibration frequency of the working environment of the grating scale, t1 represents the upper bound of the temperature of the working environment of the grating scale, t2 represents the lower bound of the temperature of the working environment of the grating scale, f1 represents the upper bound of the vibration frequency of the working environment of the grating scale, f2 represents the lower bound of the vibration frequency of the working environment of the grating scale, a1 represents the upper bound of the vibration amplitude of the working environment of the grating scale, and a2 represents the lower bound of the vibration amplitude of the working environment of the grating scale.

[0036] Preferably, it further includes optimizing the constraint conditions of the multi-dimensional bounded optimization model, specifically:

[0037] Based on the K-means clustering method, divide the interference factor intervals, calculate the errors for temperature, frequency, and amplitude respectively, calculate their support and confidence for the errors respectively, measure the sluggish candidate interval set between the interference factors and the errors, and select the intervals that significantly suppress the grating scale errors from them.

[0038] Preferably, it further includes the following steps:

[0039] Under the optimized constraint conditions, transform the multi-dimensional bounded optimization model into the following unconstrained optimization problem:

[0040]

[0041]

[0042] Among them, I α (·) represents the penalty function, t i represents the upper or lower bound of the temperature of the working environment of the grating scale, f i represents the upper or lower bound of the frequency of the working environment of the grating scale, a i represents the upper or lower bound of the vibration amplitude of the working environment of the grating scale, u represents the calculation parameter of the penalty function, and α represents the Indicator function approximation factor.

[0043] Preferably, the regression result S n is a set of error parameters including temperature error and vibration error.

[0044] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0045] The present invention provides a method for compensating the measurement error of a grating scale, constructs an initial error compensation model and a multi-dimensional bounded optimization model, fuses the initial error compensation model and the multi-dimensional bounded optimization model through parameter migration, obtains the regression results related to various interference factors according to the grating image during measurement, then the multi-dimensional bounded optimization model feeds back the corresponding compensation conditions, and finally obtains accurate measurement results according to the compensation conditions, realizing the error compensation of multiple interference factors in the grating scale measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flowchart of the implementation steps of the technical solution of the present invention;

[0047] Figure 2 It is a schematic diagram of the construction process of the regression tree in the present invention;

[0048] Figure 3 It is a flowchart of optimizing the constraint conditions of the multi-dimensional bounded optimization model in the present invention;

[0049] Figure 4 It is a schematic diagram of the multi-dimensional dense measurement compensation matrix in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] The drawings are only for illustrative purposes and should not be construed as a limitation of this patent;

[0051] To better illustrate this embodiment, some components in the drawings are omitted, enlarged or reduced, and do not represent the dimensions of the actual product;

[0052] For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0053] The technical solution of the present invention will be further described below with reference to the drawings and embodiments.

[0054] Embodiment 1

[0055] As Figure 1 shown, a method for compensating the measurement error of a grating scale includes the following steps:

[0056] S1: Construct an initial error compensation model and a multi-dimensional bounded optimization model;

[0057] The initial error compensation model includes a sub-pixel level positioning network, a decoding layer and a task space,

[0058] The multi-dimensional bounded optimization model is established with the objective function of minimizing the coupling error of multiple interference factors;

[0059] S2: The sub-pixel level positioning network extracts a sub-pixel code track positioning map according to the input grating image;

[0060] S3: Construct a regression tree in the task space according to the sub-pixel track positioning map, output the regression results associated with various interference factors, and transfer the regression results to the multi-dimensional bounded optimization model;

[0061] S4: The multi-dimensional bounded optimization model feeds back the compensation conditions to the sub-pixel level positioning network according to the regression results;

[0062] S5: The sub-pixel level positioning network extracts a new sub-pixel track positioning map according to the compensation conditions and inputs it into the decoding layer. The output decoding result is used as the accurate measurement result to complete the measurement error compensation of the grating scale.

[0063] In the specific implementation process, an initial error compensation model and a multi-dimensional bounded optimization model are constructed, and the initial error compensation model and the multi-dimensional bounded optimization model are fused through parameter transfer. During measurement, the regression results associated with various interference factors are obtained according to the grating image, and then the corresponding compensation conditions are fed back by the multi-dimensional bounded optimization model. Finally, accurate measurement results are obtained according to the compensation conditions to achieve the measurement error compensation of the grating scale for multiple interference factors.

[0064] Embodiment 2

[0065] A method for measuring error compensation of a grating scale, comprising the following steps:

[0066] S1: Construct an initial error compensation model and a multi-dimensional bounded optimization model;

[0067] The initial error compensation model includes a sub-pixel level positioning network, a decoding layer, and a task space.

[0068] More specifically, the decoding layer obtains the decoding result by looking up a table; the encoding layer in the decoding layer generates corresponding codes based on the laser etching method of the absolute encoding stripes on the glass substrate.

[0069] The multi-dimensional bounded optimization model is established with the coupling error of multiple interference factors minimized as the objective function;

[0070] S2: The sub-pixel level positioning network extracts a sub-pixel track positioning map according to the input grating image;

[0071] More specifically, the sub-pixel track positioning map is extracted from the input grating image through the following steps:

[0072] A1: Extract multi-scale feature sub-maps from the input grating image;

[0073] A2: Perform rough track positioning on the multi-scale feature sub-maps to obtain a rough track positioning map;

[0074] A3: Obtain the sub-pixel track positioning map according to the multi-scale feature sub-maps and the rough track positioning map.

[0075] S3: Construct a regression tree in the task space according to the sub-pixel code track positioning map, output the regression results associated with various interference factors, and transfer the regression results to the multi-dimensional bounded optimization model;

[0076] In the specific implementation process, as Figure 2 shown, the regression tree is constructed by dividing the task space through iterative steps, and the features of the task space are extracted by using the Markov process through optimization steps. The iterative steps perform regression operations on different error types in the task space, and linearly regress each group of data into their corresponding temperature errors, vibration errors, and amplitude errors; the optimization steps perform feature extraction on the input image, including but not limited to tilt angle, jitter degree, image clarity, etc., to prepare the parameters for the next step of fusion with the multi-dimensional bounded constraint model - that is, transfer learning. Among them, the task nodes included in the subtask are various image representations, the root task is the decoding task in the new environment, and the subtask is equivalent to splitting the root task to improve the task processing speed.

[0077] More specifically, the reward function for constructing the regression tree is:

[0078]

[0079]

[0080] Among them, R i represents the reward function value at the current moment, R i-1 represents the reward function value at the previous moment, P π represents the conversion function between the task space and the feature set under the current policy, represents the mathematical transpose of the conversion function, π R represents the R-dimensional representation of the parameter s, a represents the error value corresponding to the parameter s at the current moment, and D represents the set of image features.

[0081] More specifically, introduce the source task iteration strategy to accelerate transfer learning:

[0082] Q t+τ (s t , ′ ) = (1 - a ′ )Q t (s t + ′ )

[0083] + ′ [Q(S t , ′ ) + (S t+1 , ′ ) + … + (s t+τ-1 , ′ ) /

[0084] Among them, Q t+τ (s t , ′ ) represents the action value function of the target grating scale error compensation model, t represents the number of iterations, s t represents the state quantity at the t-th iteration, a ′ represents the proportional coefficient of the allocated action value function, Q t (s t + ′ ) represents the action value function of the source grating scale error compensation model, α ′ represents the action, Q(·) represents the value function, S t+1 represents the state quantity at the (t + 1)-th moment, s t+τ-1 represents the state quantity at the previous moment, and τ represents the number of subtasks.

[0085] In the specific implementation process, the above action acceleration function is used to evaluate the goodness of the correction of the model parameters by the new reward function.

[0086] S4: The multi-dimensional bounded optimization model feeds back the compensation conditions to the sub-pixel level positioning network according to the regression results;

[0087] S5: The sub-pixel level positioning network extracts a new sub-pixel code track positioning map according to the compensation conditions and inputs it into the decoding layer, and the output decoding result is used as the accurate measurement result to complete the grating scale measurement error compensation.

[0088] Embodiment 3

[0089] A grating scale measurement error compensation method includes the following steps:

[0090] S1: Construct an initial error compensation model and a multi-dimensional bounded optimization model;

[0091] The initial error compensation model includes a sub-pixel level positioning network, a decoding layer, and a task space.

[0092] More specifically, the decoding layer obtains the decoding result by means of table lookup; the encoding layer in the decoding layer generates corresponding codes based on the laser etching method of the absolute encoding stripes on the glass substrate.

[0093] The multi-dimensional bounded optimization model is established with the objective function of minimizing the coupling error of multiple interference factors;

[0094] More specifically, the interference factors include temperature error and vibration error.

[0095] More specifically, the multi-dimensional bounded optimization model is:

[0096]

[0097] s.t.t1≥T≥t2

[0098] f1 ≥ F ≥ f2

[0099] a1 ≥ A ≥ a2

[0100] Among them, ′ (·) represents the coupling error of multiple interference factors, e1() represents the temperature error, e2(,F) represents the vibration error, T represents the temperature of the working environment of the grating scale, A represents the vibration amplitude of the working environment of the grating scale, F represents the vibration frequency of the working environment of the grating scale, t1 represents the upper bound of the temperature of the working environment of the grating scale, t2 represents the lower bound of the temperature of the working environment of the grating scale, f1 represents the upper bound of the vibration frequency of the working environment of the grating scale, f2 represents the lower bound of the vibration frequency of the working environment of the grating scale, a1 represents the upper bound of the vibration amplitude of the working environment of the grating scale, and a2 represents the lower bound of the vibration amplitude of the working environment of the grating scale.

[0101] More specifically, as Figure 3 shown, it also includes optimizing the constraint conditions of the multi-dimensional bounded optimization model, specifically:

[0102] Based on the K-means clustering method, divide the interference factor intervals, calculate the errors for temperature, frequency, and amplitude respectively, calculate their support degrees and confidence degrees for the errors, measure the sluggish candidate interval set between the interference factors - errors, and select the intervals that significantly suppress the grating scale errors from them.

[0103] More specifically, it also includes the following steps:

[0104] Under the optimized constraint conditions, transform the multi-dimensional bounded optimization model into the following unconstrained optimization problem:

[0105]

[0106]

[0107] Among them, I α (·) represents the penalty function, t i represents the upper or lower bound of the temperature of the working environment of the grating scale, f i represents the upper or lower bound of the frequency of the working environment of the grating scale, α i represents the upper or lower bound of the amplitude of the working environment of the grating scale, u represents the calculation parameter of the penalty function, and α represents the Indicator function approximation factor.

[0108] In the specific implementation process, use the method of solving the unconstrained optimization problem to solve the above formula, complete the decoupling of the grating scale measurement error coupling model, find the optimal error suppression experimental conditions for the grating scale measurement, provide a data-based explanation for the action mechanism of multiple interference factors on the grating scale measurement accuracy NSFC 2020, reveal the high-dimensional nonlinear coupling mechanism of the grating scale measurement error, and provide a theoretical basis for the grating scale measurement error compensation.

[0109] S2: The sub-pixel track positioning map is extracted from the input raster image by the sub-pixel level positioning network;

[0110] More specifically, the sub-pixel track positioning map is extracted from the input raster image through the following steps:

[0111] A1: Extract multi-scale feature sub-maps from the input raster image;

[0112] A2: Coarse positioning of the track is performed based on the multi-scale feature sub-maps to obtain a coarse track positioning map;

[0113] A3: Obtain the sub-pixel track positioning map based on the multi-scale feature sub-maps and the coarse track positioning map.

[0114] S3: Construct a regression tree in the task space according to the sub-pixel track positioning map, output the regression results associated with each interference factor, and transfer the regression results to the multi-dimensional bounded optimization model;

[0115] More specifically, the regression result S n is a set of error parameters including temperature error and vibration error.

[0116] More specifically, the reward function for constructing the regression tree is:

[0117]

[0118]

[0119] where, R i represents the reward function value at the current moment, R i-1 represents the reward function value at the previous moment, P π represents the conversion function between the task space and the feature set under the current policy, represents the mathematical transpose of the conversion function, π R represents the R-dimensional representation of the parameter s, a represents the error value corresponding to the parameter s at the current moment, and D represents the set of image features.

[0120] More specifically, introduce the source task iteration strategy to accelerate transfer learning:

[0121] Q t+τ (s t , ′ ) = (1 - a ′ )Q t (s t + ′ )

[0122] + ′ [Q(S t , ′ ) + (St+1 , ′ ) + … + (s t+τ-1 , ′ ) /

[0123] where Q t+τ (s t , ′ ) represents the action value function of the target grating scale error compensation model, t represents the number of iterations, s t represents the state quantity at the t-th iteration, a ′ represents the proportionality coefficient of the assigned action value function, Q t (s t + ′ ) represents the action value function of the source grating scale error compensation model, α ′ represents the action, Q(·) represents the value function, S t+1 represents the state quantity at the (t + 1)-th moment, s t+τ-1 represents the state quantity at the previous moment, and τ represents the number of subtasks.

[0124] S4: The multi-dimensional bounded optimization model feeds back the compensation conditions to the sub-pixel level positioning network according to the regression result;

[0125] S5: The sub-pixel level positioning network extracts a new sub-pixel code track positioning map according to the compensation conditions and inputs it into the decoding layer, and the output decoding result is used as the accurate measurement result to complete the grating scale measurement error compensation.

[0126] In the specific implementation process, construct a multi-dimensional dense measurement compensation matrix as shown in Figure 4 . When the grating scale measures, it searches for the corresponding measurement compensation matrix according to the regression result S n (current working environment) for feedback and image correction, so as to achieve accurate error compensation.

[0127] Obviously, the above embodiments of the present invention are merely examples for clearly explaining the present invention, rather than limiting the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made on the basis of the above description. It is not necessary and impossible to list all the implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A grating scale measurement error compensation method, characterized in that, It includes the following steps: S1: Construct an initial error compensation model and a multi-dimensional bounded optimization model; The initial error compensation model includes a sub-pixel positioning network, a decoding layer, and a task space. The multi-dimensional bounded optimization model is established with the coupling error of multiple interference factors minimized as the objective function. S2: The sub-pixel positioning network extracts a sub-pixel code track positioning map from the input grating image. S3: In the task space, a regression tree is constructed based on the sub-pixel code track positioning map, the regression results associated with each interference factor are output, and the regression results are transferred to the multi-dimensional bounded optimization model. S4: The multi-dimensional bounded optimization model feeds back the compensation conditions to the sub-pixel positioning network according to the regression results. S5: The sub-pixel positioning network extracts a new sub-pixel code track positioning map according to the compensation conditions and inputs it into the decoding layer. The output decoding result is used as the accurate measurement result, completing the measurement error compensation of the grating scale.

2. A grating scale measurement error compensation method according to claim 1, characterized in that The sub-pixel code track positioning map is extracted from the input grating image through the following steps: A1: Extract multi-scale feature sub-maps from the input grating image. A2: Perform coarse code track positioning based on the multi-scale feature sub-maps to obtain a coarse code track positioning map. A3: Obtain the sub-pixel code track positioning map according to the multi-scale feature sub-maps and the coarse code track positioning map.

3. A grating scale measurement error compensation method according to claim 1, characterized in that, The decoding layer obtains the decoding result by means of table lookup.

4. A grating scale measurement error compensation method according to claim 1, characterized in that The reward function for constructing the regression tree is: Among them, R i represents the reward function value at the current moment, and R i-1 represents the reward function value at the previous moment. P π represents the transformation function between the task space and the feature set under the current policy, represents the mathematical transpose of the transformation function, and π R represents the R-dimensional representation of the parameter s, a represents the error value corresponding to the parameter s at the current moment, and D represents the set of image features.

5. A grating scale measurement error compensation method according to claim 1, characterized in that Introduce a source task iteration strategy to accelerate transfer learning: Q t+τ (s t ,a′) = (1 - a′)Q t (s t + a′) + α′[Q(S t ,a′) + Q(S t+1 ,a′) + … + Q(s t+τ-1 ,a′)] / τ Among them, Q t+τ (s t , a′) represents the action value function of the target grating scale error compensation model, t represents the number of iterations, s t represents the state quantity at the t-th iteration, a′ represents the proportional coefficient of the assigned action value function, Q t (s t +a′) represents the action value function of the source grating scale error compensation model, α′ represents the action, Q(·) represents the value function, S t+1 represents the state quantity at the (t + 1)-th moment, s t+τ-1 represents the state quantity at the previous moment, and τ represents the number of subtasks.

6. A grating scale measurement error compensation method according to claim 1, characterized in that, The interference factors include temperature error and vibration error.

7. A grating scale measurement error compensation method according to claim 6, characterized in that The multi-dimensional bounded optimization model is: s.t.t1≥T≥t2 f1≥F≥f2 a1≥A≥a2 Where, C′(·) represents the coupling error of multiple interference factors, e1(T) represents the temperature error, e2(A, F) represents the vibration error, T represents the temperature of the working environment of the grating scale, A represents the vibration amplitude of the working environment of the grating scale, F represents the vibration frequency of the working environment of the grating scale, t1 represents the upper bound of the temperature of the working environment of the grating scale, t2 represents the lower bound of the temperature of the working environment of the grating scale, f1 represents the upper bound of the vibration frequency of the working environment of the grating scale, f2 represents the lower bound of the vibration frequency of the working environment of the grating scale, a1 represents the upper bound of the vibration amplitude of the working environment of the grating scale, and a2 represents the lower bound of the vibration amplitude of the working environment of the grating scale.

8. A grating scale measurement error compensation method according to claim 7, characterized in that, It also includes optimizing the constraint conditions of the multi-dimensional bounded optimization model, specifically: Based on the K-means clustering method, divide the interference factor intervals, calculate the error for temperature, frequency, and amplitude respectively, calculate their support and confidence for the error respectively, measure the sluggish candidate interval set between the interference factors and the error, and select the interval that significantly suppresses the grating scale error from it.

9. A grating scale measurement error compensation method according to claim 8, characterized in that, It also includes the following steps: Under the optimized constraint conditions, transform the multi-dimensional bounded optimization model into the following unconstrained optimization problem: Among them, I α (·) represents a penalty function, t i represents the upper or lower bound of the temperature of the working environment of the grating scale, f i represents the upper or lower bound of the frequency of the working environment of the grating scale, a i represents the upper or lower bound of the amplitude of the working environment of the grating scale, u represents the calculation parameter of the penalty function, and α represents the Indicator function approximation factor.

10. A grating scale measurement error compensation method according to claim 6, characterized in that, Regression result S n represents a set of error parameters including temperature error and vibration error.

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