Ritchey-Commann surface shape detection method and system based on two-angle Power iterative fitting

Abstract

The invention discloses a Ritchey-Commann surface shape detection method and system based on two-angle Power iterative fitting. Belongs to the technical field of optical detection and particularly relates to the technical field of large-aperture plane mirror surface shape error detection. The objective of the invention is to efficiently process detection data of Ritchey, Common and Miwn angles and calculate an accurate and reliable real surface shape of a plane mirror. Under the condition that the defocusing error amount is unknown, the optimal Power coefficient is calculated automatically and iteratively, the detection operation process is effectively simplified, the dependence of data processing on accurate measurement of the length value of the system is reduced, and meanwhile, the precision of plane mirror surface shape recovery solution is ensured.

Description

Technical Field

[0001] This invention belongs to the field of optical testing technology, specifically relating to the field of large-aperture planar mirror shape error detection technology. Background Technology

[0002] The Rickie-Common method is an effective method for detecting the surface shape error of a large-aperture plane mirror using a small-aperture interferometer. The principle is shown in Figure 1. The interferometer and the standard spherical mirror are in a confocal position. The plane mirror under test is inserted obliquely into the interference light path at the Rickie angle θ. The spherical beam is reflected by the plane mirror to the spherical mirror, and then returns along the original light path to interfere. Finally, the surface shape error of the plane mirror under test can be calculated based on the interference wavefront data.

[0003] Traditional single-angle detection methods directly measure various parameters of the optical path to establish a simulation model containing systematic errors, and then solve for the plane mirror shape. However, since the system power error is highly sensitive to the defocusing amount, accurate simulation requires high-precision measurement of the optical path length (i.e., parameter d in Figure 1). Another method, the rapid Richmond measurement method suitable for the manufacturing process, introduces a plane mirror with a known shape to calibrate the position of the optical path without systematic defocusing, and then replaces the plane mirror under test into the fixture for inspection. This method simplifies the process, but it is difficult to ensure the consistency of the plane mirror position during actual disassembly and assembly, and additional power errors are easily introduced before and after. Therefore, it is only suitable for scenarios with low inspection accuracy requirements.

[0004] In the Richter-Common detection optical path, there is a coupling relationship between the total length of the optical path and the defocus term of the interference wavefront. Without knowing the precise length error, it becomes impossible to separate the system-introduced defocus (power) error from the wavefront detection results, thus failing to obtain the true surface shape of the plane mirror. To solve this problem, the Richter-Common two-angle detection method is typically used. The principle is as follows: Figure 2 As shown, firstly, interferometric detection is performed separately at two Rickey angles θ1 and θ2. The obtained wavefront and normalized pupil defocus term are restored to the plane mirror coordinates. Then, the plane mirror data and error term (Power and astigmatism combination data) distributions at the two angles are subtracted. The defocus term coefficient is calculated based on the least squares fitting method. Finally, the corresponding error distribution is removed from the plane mirror data to obtain the true surface shape of the plane mirror.

[0005] In terms of both angles, the solution proposed by the ZYGO system also requires keeping the distance between the plane mirror and the interferometer constant. Figure 2When d1=d2, rotating the plane mirror changes the Rickey angle. If the Power error is known to be consistent, the true surface shape can be easily calculated. The problem with this method is the same as the fast Rickey-Common method: it cannot guarantee that the optical path length before and after rotating the plane mirror is completely consistent. Another method involves reconstructing the plane mirror surface shape using the influence matrix. This method simulates and analyzes the coefficient matrix of each Zernike term from the surface shape to the system wavefront aberration, and then uses least squares to fit the Zernike coefficients of the tested plane. This method avoids complex matrix calculations on the wavefront, but due to the limited number of analytical terms, it ignores the influence of higher-order Zernike terms and loses mid-frequency information in the surface shape.

[0006] It can be observed that in current RCKM inspection systems, the removal of system power errors relies on high-precision measurement of system length or consistency of plane mirror positions, which can be limited by hardware conditions and measurement accuracy in engineering applications. There are also issues with insufficient accuracy and information loss in data processing and reconstruction. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention proposes a Richcomb surface shape detection method and system based on two-angle Power iterative fitting. It can automatically iteratively calculate the optimal Power coefficient even when the defocusing error is unknown, effectively simplifying the detection operation process, reducing the dependence of data processing on accurate measurement of system length values, and simultaneously ensuring the accuracy of planar mirror surface shape reconstruction.

[0008] The method described in this invention is specifically as follows: S1. Obtain the two-angle interference detection wavefronts W1 and W2 of Rickie-Command, and measure the optical path lengths d1 and d2 as well as the Rickie angles θ1 and θ2; S2. Based on parameters d1, d2, θ1 and θ2, perform wavefront-surface transformation on the two angular wavefronts W1 and W2 to restore the two angular restored surface shapes S1 and S2. S3. Based on the Rickey angles θ1 and θ2, transform the Power error distribution to the plane mirror coordinates of the two angles, and the distribution is P1 and P2. S4. Calculate the difference distribution of the surface shape recovered from two angles. ,in and The Power error coefficients are introduced for the two angles respectively; S5. Perform Power iterative optimization fitting, calculate Power fitting using the least squares method, and perform Power coefficient iterative optimization fitting. Calculate the final surface shape after removing Power based on the fitting results, and further obtain the final solved surface shape.

[0009] Furthermore, after obtaining the two-angle interferometric detection wavefronts W1 and W2 from Richcomb, W1 and W2 need to be preprocessed, including selecting the elliptical aperture and removing invalid data.

[0010] Furthermore, when performing wavefront-surface shape transformation on the two angular wavefronts W1 and W2, coordinate transformation and amplitude transformation are performed sequentially. The coordinate transformation converts the elliptical data on the pupil plane coordinates to the coordinates on the surface of the measured plane mirror, restoring it to a circle. The amplitude transformation restores the wavefront to its surface shape based on the cosine relationship.

[0011] Furthermore, step S5 specifically includes: S51. Power fitting solution based on least squares method, let the formula... In Rewritten as ,in This represents the ratio of the Power coefficient at the two angles; in determining... After the value is obtained, it is obtained through least squares fitting. ; S52, Perform Power Coefficient Iterative optimization fitting, initial ,Will Substitution Least square fitting yields Calculate the residual error ; S53. Increase the initial coefficients by a certain step size. ,Right now Then perform least squares fitting again to obtain Calculate the residual error ; S54. Calculate the residual error evaluation function. and And compare, if Then continue iterating. Then stop iterating and obtain the final coefficients. Values ​​and fitted values ; S55, based on and The final surface shape after removing the Power is calculated, and the final solved surface shape is obtained.

[0012] Furthermore, in steps S52 to S54, the iteration direction needs to be determined when starting the iterative fitting. At that time, to determine the direction of iteration, first let To approximate a positive value of 0, calculate and ,calculate and If a comparison is made, The direction is correct, therefore the step size parameter... Take positive values ​​and negative values, and then... Perform an iterative process.

[0013] Furthermore, based on and The final solution surface shapes obtained from the two angles after removing the power are calculated as follows: ; ; The final solved surface shape is obtained further: 。

[0014] The system of the present invention includes an interferometer equipped with a standard spherical lens, a plane mirror and its supporting fixture, a rotating base for the plane mirror fixture, a spherical mirror and its fixture, and a laser tracker for measuring optical path parameters.

[0015] Furthermore, during the detection, the positions of the components are first adjusted at the first angle. The components to be adjusted include the interferometer (1), the plane mirror and its supporting fixture (2), and the spherical mirror and its fixture (4) to ensure that the optical path is effectively aligned. The interference wavefront of the system is measured, and after removing the spherical lens error and the spherical mirror surface shape error, the detection wavefront W1 is obtained. The actual Rickey angle θ1 and the distance d1 from the interferometer focus to the center of the plane mirror are measured using a laser tracker. Then, the plane mirror and its supporting fixture are rotated to the second angle using the rotating base of the plane mirror fixture. At the same time, the interferometer is moved to the corresponding position, and the positions of each component of the system are finely adjusted for interference detection. The same operation is used to obtain the detection wavefront W2, the actual Rickey angle θ2, and the distance d2 from the interferometer focus to the center of the plane mirror.

[0016] The beneficial effects of the method described in this invention are as follows: (1) The technical route for plane mirror surface shape detection is the Richcon Mang two-angle method. Compared with the traditional single-angle detection, it can separate the system defocus error, thereby obtaining the true surface shape of the plane mirror being tested.

[0017] (2) Based on the two-angle Power iterative fitting algorithm, the defocus error is separated without relying on the accurate measurement of the system defocus amount. Compared with other processing methods, the detection process is simpler and more efficient.

[0018] (3) The data processing steps do not involve low-order aberration fitting, retain mid-frequency information, and have high surface shape calculation accuracy.

[0019] The beneficial effects of the system described in this invention are as follows: It proposes a two-angle detection optical path system for Richcomb, employing a method of adjusting a horizontally rotating plane mirror and a moving interferometer to switch between the two-angle detection states. This avoids the risk of changes in the surface shape of the spherical mirror caused by movement, facilitating efficient detection in engineering applications. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the detection optical path of the Richconm in an embodiment of the present invention; Figure 2 The ray path diagram of the two-angle method of Rickie-Comman in the embodiment of the present invention is shown, where (1) is the first Rickie angle and (2) is the second Rickie angle; Figure 3 This is a flowchart of the method described in an embodiment of the present invention; Figure 4 This is a system structure diagram as described in an embodiment of the present invention. Detailed Implementation

[0021] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0022] Example 1 This embodiment provides a Richmond surface shape detection method based on two-angle Power iterative fitting. This method aims to efficiently process Richmond two-angle detection data and calculate the accurate and reliable true surface shape of a plane mirror. A surface shape calculation method based on two-angle Power iterative fitting is proposed, which can automatically iteratively calculate the optimal Power coefficient even when the defocusing error is unknown. This effectively simplifies the detection operation process, reduces the dependence of data processing on accurate measurement of system length values, and ensures the accuracy of the plane mirror surface shape reconstruction calculation.

[0023] like Figure 3 As shown, the method includes the following steps: 1. Obtain the wavefronts W1 and W2 of the two-angle interference detection of the Rickie-Common interferometer, and measure the optical path lengths (distance from the interferometer focal point to the center of the plane mirror) d1 and d2 and the Rickie angles θ1 and θ2.

[0024] 2. Preprocess the two-angle wavefront data, including selecting the elliptical aperture and removing invalid data.

[0025] 3. Based on parameters d and θ, perform wavefront-surface shape transformation on the two angular wavefronts W1 and W2 to restore the two angular restored surface shapes S1 and S2. Coordinate transformation and amplitude transformation are required sequentially. The coordinate transformation converts the elliptical data on the pupil plane coordinates to the coordinates of the measured plane mirror surface, restoring it to a circle; the amplitude transformation restores the wavefront to its surface shape based on the cosine relationship.

[0026] 4. Based on the Rickey angle θ, transform the Power error distribution to the plane mirror coordinates of the two angles, resulting in distributions P1 and P2.

[0027] 5. Calculate the difference distribution of the surface shape recovered from two angles. Theoretically, ignoring other errors, the final plane mirror shape obtained from the two angles should be identical. The error is caused by the linear superposition of the two angle power errors alone. (1) in , The Power error coefficients are introduced for the two angles respectively.

[0028] 6. Power fitting solution based on least squares method. Let the equation (1) Rewritten as: (2) in This represents the ratio of the Power coefficient at the two angles. In determining... After the value is obtained, it can be obtained through least squares fitting. .

[0029] 7. Perform Power coefficient calculation Iterative optimization fitting, ,Will Substitution Least square fitting yields Calculate the residual error: .

[0030] 8. Increase the initial coefficients by a certain step size, i.e. Substituting into the formula and performing least squares fitting again yields... Calculate the residual error: .

[0031] 9. Calculate the residual error evaluation function. and Furthermore, depending on the circumstances, the error function can be set as the residual error RMS, or the coefficients of certain Zernike terms in the residual error, etc. E ( δ A smaller value indicates a more ideal fit. Then continue iterating. Then stop iterating and obtain the final coefficients. Values ​​and fitted values .

[0032] 10. Based on and The final surface shape after removing the power is calculated, and the solved surface shapes obtained from the two angles are as follows: ; The final solved surface shape is obtained further: 。

[0033] Example 2 This embodiment further defines Embodiment 1. In steps 7-9, the iteration direction needs to be determined when starting the iterative fitting. That is, when... To determine the direction of iteration, we can first let To approximate a positive value of 0, calculate and .calculate and If a comparison is made, The direction is correct, therefore the step size parameter... Take positive values ​​and negative values, and then... The iterative process is then implemented. The iterative optimization method involved in steps 7-9 is the fixed step size method. In the actual algorithm process, more efficient methods such as binary descent and gradient iterative descent can be used to achieve similar results.

[0034] Example 3 This embodiment provides a Richcomb surface shape detection system for the above-described detection method, such as... Figure 4As shown, the system includes an interferometer 1 equipped with a standard spherical lens, a plane mirror and its supporting fixture 2, a rotating base 3 for the plane mirror fixture, a spherical mirror and its fixture 4, and a laser tracker 5 for measuring optical path parameters. During testing, the positions of the components are first adjusted at the first angle. The components to be adjusted include the interferometer 1, the plane mirror and its supporting fixture 2, and the spherical mirror and its fixture 4, to effectively align the optical path. The interference wavefront of the system is measured. After removing the errors of the spherical lens and the surface shape of the spherical mirror, the detection wavefront W1 is obtained. The actual Rickey angle θ1 and the distance d1 from the focus of the interferometer 1 to the center of the plane mirror are measured using the laser tracker 5. Then, the plane mirror and its supporting fixture 2 are rotated to the second angle using the rotating base 3 of the plane mirror fixture. At the same time, the interferometer 1 is moved to the corresponding position, and the poses of each component of the system are finely adjusted for interference testing. The same operation is used to obtain the detection wavefront W2, the actual Rickey angle θ2, and the distance d2 from the focus of the interferometer 1 to the center of the plane mirror.

Claims

1. A Richcomb surface shape detection method based on two-angle Power iterative fitting, characterized in that, The method includes the following steps: S1. Obtain the two-angle interference detection wavefronts W1 and W2 of Rickie-Command, and measure the optical path lengths d1 and d2 as well as the Rickie angles θ1 and θ2; S2. Based on parameters d1, d2, θ1 and θ2, perform wavefront-surface transformation on the two angular wavefronts W1 and W2 to restore the two angular restored surface shapes S1 and S2. S3. Based on the Rickey angles θ1 and θ2, transform the Power error distribution to the plane mirror coordinates of the two angles, and the distribution is P1 and P2. S4. Calculate the difference distribution of the surface shape recovered from two angles. ,in and The Power error coefficients are introduced for the two angles respectively; S5. Perform Power iterative optimization fitting, calculate Power fitting using the least squares method, and perform Power coefficient iterative optimization fitting. Calculate the final surface shape after removing Power based on the fitting results, and further obtain the final solved surface shape.

2. The Richmond surface shape detection method based on two-angle Power iterative fitting according to claim 1, characterized in that, After obtaining the two-angle interferometric detection wavefronts W1 and W2 from Richcomb, W1 and W2 need to be preprocessed, including selecting the elliptical aperture and removing invalid data.

3. The Richmond surface shape detection method based on two-angle Power iterative fitting according to claim 2, characterized in that, When performing wavefront-surface shape transformation on two angular wavefronts W1 and W2, coordinate transformation and amplitude transformation are performed sequentially. The coordinate transformation converts the elliptical data on the pupil plane coordinates to the coordinates on the surface of the measured plane mirror, restoring it to a circle. The amplitude transformation restores the wavefront to its surface shape based on the cosine relationship.

4. The Richmond surface shape detection method based on two-angle Power iterative fitting according to claim 3, characterized in that, Step S5 is as follows: S51. Power fitting solution based on least squares method, let the formula... In Rewritten as ,in , representing the ratio of the Power coefficient at the two angles; In determining After the value is obtained, it is obtained through least squares fitting. ; S52, Perform Power Coefficient Iterative optimization fitting, initial ,Will Substitution Least square fitting yields Calculate the residual error ; S53. Increase the initial coefficients by a certain step size. ,Right now Then perform least squares fitting again to obtain Calculate the residual error ; S54. Calculate the residual error evaluation function. and And compare, if Then continue iterating. Then stop iterating and obtain the final coefficients. Values ​​and fitted values ; S55, based on and The final surface shape after removing the Power is calculated, and the final solved surface shape is obtained.

5. The Richmond surface shape detection method based on two-angle Power iterative fitting according to claim 4, characterized in that, In steps S52 to S54, the iteration direction needs to be determined when starting the iterative fitting. At that time, to determine the direction of iteration, first let To approximate a positive value of 0, calculate and ,calculate and If a comparison is made, The direction is correct, therefore the step size parameter... Take positive values ​​and negative values, and then... Perform an iterative process.

6. The Richmond surface shape detection method based on two-angle Power iterative fitting according to claim 5, characterized in that, based on and The final solution surface shapes obtained from the two angles after removing the power are calculated as follows: ； ； The final solved surface shape is obtained further: 。 7. A Richcomb surface shape detection system for use in the method of any one of claims 1-6, characterized in that, The system includes an interferometer (1) equipped with a standard spherical lens, a plane mirror and its supporting fixture (2), a rotating base (3) for the plane mirror fixture, a spherical mirror and its fixture (4), and a laser tracker (5) for measuring optical path parameters.

8. The Richcomb surface shape detection system according to claim 7, characterized in that, During the test, the positions of the components are first adjusted at the first angle. The components to be adjusted include the interferometer (1), the plane mirror and its supporting fixture (2), and the spherical mirror and its fixture (4) to ensure that the optical path is effectively aligned. The interference wavefront of the system is measured. After removing the spherical lens error and the spherical mirror surface shape error, the detection wavefront W1 is obtained. The actual Rickey angle θ1 and the distance d1 from the focus of the interferometer (1) to the center of the plane mirror are measured using the laser tracker (5). Then, the plane mirror and its supporting fixture (2) are rotated to the second angle using the rotating base (3) of the plane mirror fixture. At the same time, the interferometer (1) is moved to the corresponding position. The positions of each component of the system are finely adjusted for interference detection. The same operation is used to obtain the detection wavefront W2, the actual Rickey angle θ2, and the distance d2 from the focus of the interferometer (1) to the center of the plane mirror.

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