Laser interferometer plane reflection mirror surface type error compensation method based on redundancy characteristics

Abstract

The invention discloses a laser interferometer plane reflection mirror surface type error compensation method based on redundancy characteristics. The method comprises the following steps of: establishing a composite compensation model containing a rotating surface type error and a translation surface type error based on a redundant measurement characteristic of an X / Y-direction measurement light beam on an Rz degree of freedom; the rotating surface type error model is constructed through Rz degree-of-freedom redundant data of a measurement light beam, and the translation surface type error model is established based on a geometrical relationship between a rotating error gradient and a measurement light beam interval. And compensating the two types of surface type errors to an interferometer measurement model by adopting a parameterization compensation mechanism, and realizing dynamic error correction through an iterative optimization algorithm. The method can effectively solve the problem of measurement precision caused by deformation of the reflector surface, and provides a reliable measurement basis for an ultra-precise motion control system.

Description

Technical Field

[0001] The present invention relates to a method for compensating the surface error of a plane reflective mirror in a laser interferometer based on redundant features. The method is specifically applied to compensating for mirror deformation caused by reflective mirror manufacturing errors, assembly stress deformation, and environmental factors (such as temperature gradients and vibration) in high-precision laser interferometer measurement systems. The method belongs to the field of precision measurement and motion control technology. Background Art

[0002] As a core device for high-precision displacement measurement, laser interferometers are susceptible to mirror surface errors. Residual stresses during manufacturing, mechanical stresses during assembly, and environmental factors such as temperature gradients and vibration can cause the mirror surface to deform, causing the actual surface to deviate from the ideal plane. This surface deviation introduces additional optical path differences, causing the interferometer-measured X / Y displacements and Rz rotation angles to systematically deviate from the actual motion stage's position, severely impacting nanometer-level measurement accuracy.

[0003] To address these issues, the present invention proposes a method for compensating for reflector surface errors based on redundant measurement. This method precisely measures and compensates for reflector surface errors by controlling a motion stage to scan the reflector surface along a specific path, leveraging the redundant nature of the X / Y measurement beams. Specifically, by controlling the motion stage to move along one axis while maintaining a constant position along another axis, surface data can be systematically acquired at different mirror positions.

[0004] In terms of error modeling and calculation, this invention calculates the rotational surface error of the reflector by analyzing the differences in the rotation angles of the measurement beams at different positions. Based on this rotational surface error data and combined with the spatial distribution of the measurement beams, the translational surface error of the reflector surface is derived. This processing method fully utilizes the principles of geometric optics to achieve the coordinated solution of rotational and translational surface errors.

[0005] The technical features of this invention are primarily reflected in the following three aspects: First, a redundant feature-based laser interferometer reflector surface error measurement and compensation scheme is proposed, ensuring the operability and accuracy of the compensation process from path planning to error correction. Second, an error calculation model based on geometric constraints is established, which can accurately fit the deformation characteristics of the reflector surface. Finally, it can quickly respond to changes in reflector errors and adjust compensation parameters. This method can improve the measurement accuracy and stability of laser interferometers, providing a highly efficient technical solution for the field of precision measurement and calibration. Summary of the Invention

[0006] The purpose of this invention is to provide a method for compensating for the surface error of a plane reflector in a laser interferometer based on redundancy features. This method addresses the problem of surface deformation caused by mirror manufacturing errors, assembly deviations, and environmental factors in existing laser interferometer measurement systems. By establishing a coordinated compensation mechanism for rotational and translational surface profiles, this method can systematically correct the surface error of the reflector, thereby significantly improving the measurement accuracy and reliability of the interferometer measurement system.

[0007] To achieve the above object, the present invention discloses a method for compensating the surface error of a plane reflector of a laser interferometer based on redundant features, which specifically includes the following steps:

[0008] In the method, the specific implementation process of step S1 measurement path planning is as follows: first, the Rz rotational degree of freedom of the motion stage is set to a zero position; then, a scanning path along the X / Y axis is planned, and the motion stage is controlled to perform reciprocating scanning motion along the other axis while maintaining an unchanged axial position, so that the scanning range covers the entire working area of ​​the reflector; at the same time, the other degrees of freedom (including the Z-axis displacement and the Rx and Ry rotational degrees of freedom) are ensured to remain stable.

[0009] In the method, the specific implementation process of step S2 for obtaining the X-direction reflector rotation surface data YRZ is as follows: controlling the motion stage to perform scanning motion along a preset path, controlling the motion stage to maintain a zero position in the X direction, and performing full-range motion along the preset path in the Y direction; after each measurement point is stabilized, synchronously collecting displacement data and Rz rotation angle data measured by the X / Y interferometer; and recording the difference in the Rz measurement value of each position point to obtain the value of the X-direction reflector rotation surface value YRZ at different Y positions.

[0010] In the method, the specific implementation process of step S2 of obtaining the Y-direction reflector rotation surface data XRZ is as follows: controlling the motion stage to perform scanning motion along a preset path, controlling the motion stage to maintain a zero position in the Y direction, and performing full-range motion along the preset path in the X direction; after each measurement point is stabilized, synchronously collecting displacement data and Rz rotation angle data measured by the X / Y interferometer; and recording the difference in the Rz measurement value of each position point to obtain the value of the Y-direction reflector rotation surface value XRZ at different X positions.

[0011] In the method, the specific implementation process of step S3 to obtain the X-direction reflector translation surface data YTX is as follows: the X-direction plane mirror translation surface is based on the rotation surface, and the local surface structure of the plane mirror is as follows: Figure 3 As shown in the figure, when the laser measurement beam X1 measures point i, X2 measures the surface value of point i+1. The interval between the two beams is dX. Based on the rotation surface value YRZ, the rotation surface value at point i can be expressed as: , then the X-direction reflector translation surface data YTX is expressed as:

[0012]

[0013] In the method, the specific implementation process of step S3 of obtaining the Y-axis reflector translation surface data XTY is as follows: when the laser measurement beam Y1 measures point j, Y2 measures the surface value of point j+1, and the interval between the two beams is dY, based on the rotation surface value XRZ, the rotation surface value at point j can be expressed as: , then the Y-direction reflector translation surface data XTY is expressed as:

[0014]

[0015] In the method, the specific implementation process of step S2 of obtaining the Y-direction reflector rotation surface data XRZ is as follows: controlling the motion stage to perform scanning motion along a preset path, controlling the motion stage to maintain a zero position in the Y direction, and performing full-range motion along the preset path in the X direction; after each measurement point is stabilized, synchronously collecting displacement data and Rz rotation angle data measured by the X / Y interferometer; and recording the difference in the Rz measurement value of each position point to obtain the value of the Y-direction reflector rotation surface value XRZ at different X positions.

[0016] In the method, the specific implementation process of step S4 of surface error compensation is as follows: the calculated XRZ / YRZ and XTY / YTX parameters are compensated into the interferometer measurement model to correct the measurement data. The compensation process adopts an iterative optimization algorithm.

[0017] In the method, the specific implementation process of step S5 compensation verification is as follows: controlling the motion stage to re-execute the complete scanning path and collect compensated measurement data; evaluating the compensation effect by analyzing the data residuals before and after compensation; if the requirements are not met, returning to step S3 to re-optimize the compensation parameters until the accuracy indicators are met.

[0018] The redundant feature-based surface error compensation method for a laser interferometer plane mirror proposed in the present invention has achieved a breakthrough improvement in measurement accuracy through a collaborative compensation mechanism of rotational surface shape and translational surface shape. It is particularly suitable for equipment fields such as lithography machines and ultra-precision machine tools that have extremely high requirements for measurement stability, and provides key surface error correction guarantees for high-precision motion control systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The present invention is a flow chart of a method for compensating the surface error of a plane reflective mirror of a laser interferometer based on redundant features.

[0020] Figure 2 This is the actual surface diagram of the interferometer mirror.

[0021] Figure 3It is a schematic diagram of the structure between the interferometer beam and the local surface shape. DETAILED DESCRIPTION

[0022] The present invention will be further described below with reference to specific embodiments.

[0023] See also Figure 1 Compensation method flow chart, Figure 2 Interferometer mirror actual surface diagram and Figure 3 Schematic diagram of the structure between the interferometer beam and the local surface shape. The present invention discloses a method for compensating the surface shape error of a laser interferometer plane reflector based on redundant features. The specific implementation process includes the following five key steps:

[0024] Step S1: Measurement path planning: Adjust the Rz rotational degree of freedom of the motion stage to zero to ensure initial position stability. Next, plan the X / Y scanning path, controlling the motion stage to perform reciprocating scanning along one axis while maintaining a fixed position in the other. The scanning range must cover the entire working area of ​​the reflector. At the same time, ensure that the other degrees of freedom (including Z-axis displacement and Rx and Ry rotational degrees of freedom) remain stable to avoid additional error interference.

[0025] Step S2: Obtain the mirror's rotational surface data in the X and Y directions based on the scanning path. The motion stage is controlled to maintain zero position in one direction and perform a full-range scan along the preset path in the other direction. After each scanning point stabilizes, the interferometer's X / Y displacement data and Rz rotation angle data are synchronously collected. By calculating the difference in Rz measurement values ​​at each point, the X-axis rotational surface data YRZ and the Y-axis rotational surface data XRZ at different positions on the Y axis are obtained.

[0026] Step S3: After obtaining the rotational surface data, the reflector's translational surface data in the X and Y directions is further calculated. The laser beam's measurement data at adjacent points in the X and Y directions, combined with the changing patterns of the rotational surface, are used to determine the reflector's translational characteristics in these two directions. Specifically, in the X direction, the laser beam performs a differential analysis of the surface values ​​at adjacent points, combining the effects of the rotational surface to recursively derive the translational surface data for the entire X-direction range. Similarly, in the Y direction, the laser beam performs a similar process on the surface values ​​at adjacent points, combining the calculation results of the rotational surface to derive the translational surface data for the entire Y-direction range.

[0027] Step S4: Integrate the rotational surface parameters (XRZ, YRZ) and translational surface parameters (XTY, YTX) obtained in the above steps into the interferometer measurement model to perform error compensation on the original measurement data. During the compensation process, an iterative optimization algorithm is used to continuously adjust the compensation parameters to ensure the accuracy and consistency of the correction results.

[0028] Step S5: Verify the compensation effect. After compensation is complete, re-execute the entire scan path and collect compensated measurement data. Compare the pre- and post-compensation measurement data, analyze the residual changes, and evaluate the compensation effect. If the compensated accuracy does not meet the expected requirements, return to the previous step and further optimize the compensation parameters until the accuracy requirements are met.

[0029] This invention provides a method for compensating for the surface errors of plane mirrors in a laser interferometer based on redundant features. By accurately collecting the mirror's rotational surface data (XRZ, YRZ) and translational surface data (XTY, YTX) during the scanning path, the redundant features are used to model, analyze, and compensate for the mirror's surface errors. By controlling the motion stage's degrees of freedom, rationally planning the scanning path, and combining recursive and optimization algorithms, this method efficiently and accurately compensates for the mirror's surface errors in the X and Y directions, significantly improving the laser interferometer's measurement accuracy and system reliability. This method is suitable for high-precision measurement equipment and has significant application value in scenarios with stringent requirements for the plane mirror's surface shape.

Claims

1. A method for compensating the surface error of a plane reflector of a laser interferometer based on redundant features, characterized in that include: A calculation model for the mirror's rotational surface error YRZ / XRZ is established using the redundant measurement data of the Rz degree of freedom from the X / Y measurement beam. A recursive calculation model for the mirror's translational surface error YTX / XTY is constructed based on the relationship between the gradient change of the rotational surface error and the spatial spacing of the measurement beams.

2. The rotation surface error compensation method according to claim 1, characterized in that: The method for solving the rotational surface error is as follows: by controlling the motion stage to perform single-degree-of-freedom motion along the X-axis and the Y-axis respectively, the Rz measurement data obtained by the X-axis interferometer during Y-axis scanning is used to solve the YRZ error component, and the Rz measurement data obtained by the Y-axis interferometer during X-axis scanning is used to solve the XRZ error component.

3. The translational surface error compensation method according to claim 1, characterized in that: The translational surface error is calculated by recursively solving the translational surface error components at each position on the reflector surface based on the discrete sampling data of the rotational surface error and the geometric relationship between the rotational error variation between adjacent measurement points and the measurement beam spacing.

4. The method for compensating the surface error of a plane reflector of a laser interferometer according to claims 1 to 3, characterized in that: The error compensation is achieved by compensating the calculated rotational surface error and translational surface error parameters to the interferometer measurement model, dynamically adjusting the compensation parameters through an iterative optimization algorithm, and analyzing and verifying the compensation effect.

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