Single-frame speckle deflection measurement method based on subarea wavefront correction

Abstract

A single-frame speckle deflection measurement method based on subarea wavefront correction belongs to the technical field of optical measurement, and comprises the following steps: based on a monocular deflection measurement system, projecting a standard speckle image to a to-be-measured mirror surface from a screen, and collecting a single-frame deformed speckle image reflected by the to-be-measured mirror surface; processing the reflected image by using a Zernike polynomial projection distortion correction method based on a mark point, and correcting the projection distortion of the reflected image caused by a non-orthogonal light path; obtaining sub-pixel mapping of the reflection image and the standard image based on a sub-region wavefront fitting correction and iterative registration algorithm; and based on system calibration and camera calibration, establishing a spatial incident light model and a spatial reflected light model, obtaining surface gradient distribution of the to-be-measured mirror surface, and reconstructing a three-dimensional shape of the to-be-measured mirror surface. According to the method, a reference plane is not needed, high-reflection surface shape measurement of only collecting a single-frame image can be achieved, the dynamic range and precision of speckle deflection measurement are improved through subarea wavefront correction, and the surface reconstruction precision can reach hundreds of nanometers.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical measurement, and particularly relates to a single-frame speckle deflection measurement method based on sub-region wavefront correction. Background Art

[0002] In the ultra-precision machining and alignment process of high-end optical components, fast and high-precision in-situ detection technology can provide real-time feedback on surface shape errors and significantly improve machining efficiency. Compared with traditional interferometer detection, deflection measurement technology has a larger dynamic range, stronger versatility, and better environmental anti-interference ability, making it more suitable for integration with processing equipment.

[0003] When traditional phase deflectometry uses sinusoidal fringe coding technology, it is necessary to solve phase information through multi-step phase-shifting method and multi-frequency heterodyne method. At least 6-8 images need to be taken during measurement. This not only requires light stability to ensure the accuracy of the solution, is sensitive to image noise, but also takes a long time for multi-frame shooting measurement, making it difficult to meet the real-time detection requirements of dynamic scenes and limiting its applicability in industrial fields.

[0004] Speckle deflectometry based on random speckle structured light uses the local displacement characteristics of random speckles. Through local uniqueness and sub-pixel tracking ability, it is theoretically possible to solve the surface shape with only a single-frame image, making it more suitable for dynamic monitoring. However, existing speckle deflection schemes still have certain defects: First, multi-camera systems are usually used, which require multi-camera collaborative calibration, resulting in high costs and limited volume. Second, in a simple monocular system, the existing moving speckle deflectometry sacrifices the single-frame measurement ability, and the scheme introducing a reference plane is prone to introduce accuracy errors and positioning errors in the production of the reference plane. In addition, a monocular measurement scheme that directly compares reflected speckles with projected standard speckles requires a strict orthogonal optical path layout. Otherwise, the reflected speckles cannot be directly registered with the standard speckles due to projection distortion. Moreover, the distortion of the reflected wavefront caused by non-planar components also makes the local deformation of the reflected speckles too large, resulting in a decrease in registration accuracy. Therefore, the application scope of this scheme is limited. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a single-frame speckle deflection measurement method based on sub-region wavefront correction, which realizes three-dimensional reconstruction of mirror elements with high precision and large dynamic range through a single-frame image.

[0006] To achieve the above object, the present invention provides a single-frame speckle deflection measurement method based on sub-region wavefront correction, including: S1. System setup and calibration S1.1 Set up a monocular speckle deflection measurement system, including: An LCD screen for projecting a standard marker point pattern and a random speckle pattern; A CCD camera for collecting deformed speckle images reflected by the mirror to be measured; The mirror surface to be measured and the mechanical adjustment device are used to adjust the position and pose of the mirror surface to be measured to ensure that the reflected image completely covers the camera field of view.

[0007] S1.2 Camera calibration and system calibration: Obtain the internal parameters and external parameters of the camera through camera calibration; Establish the conversion relationship between the screen pixel coordinate system, the camera coordinate system and the world coordinate system; S2. Project a standard marker point pattern on the LCD screen, adjust the mirror surface to be measured so that the reflected image of the mirror surface to be measured contains the marker points, and receive it by the CCD camera. Calculate the projection distortion parameters of the mirror surface reflected image through the Zernike polynomial projection distortion correction method based on the marker points; S3. Project a standard digital random speckle pattern on the LCD screen, and collect the deformed speckle pattern reflected by the mirror surface to be measured with the CCD camera; S4. Correct the deformed speckle pattern based on the obtained projection distortion parameters to obtain a restored image. Perform sub-pixel point registration on the restored image and the standard image using the sub-region wavefront fitting correction and iterative registration algorithm. Based on the point mapping relationship between the deformed image and the restored image during the projection distortion correction process, finally obtain the sub-pixel point mapping relationship between the deformed image and the standard image; S5. Based on the system calibration results and pixel mapping, construct a spatial light model in the world coordinate system, calculate the surface gradient distribution of the mirror surface to be measured, and reconstruct the three-dimensional surface shape.

[0008] The Zernike polynomial projection distortion correction steps described in S2 include: (1) Generate a binary pattern of white background and black marker points as the standard marker point image and project it on the LCD screen; (2) Adjust the position and pose of the mirror surface to be measured so that the CCD camera can receive the complete marker point pattern; (3) Perform binarization, morphological image processing, connected region extraction and screening on the reflected image, and extract the marker point centers; (4) Denote the deviation of the marker point centers between the reflected image and the standard image as R, establish the matrix equation MC = R, where M is the Zernike polynomial matrix, and solve the polynomial coefficient C by the least squares method; (5) Calculate the deviation of all pixels between the reflected image and the standard image based on the coefficient C to correct the distortion, and fill in the missing pixels with bicubic interpolation.

[0009] Preferably, the binary pattern of the marker points is the vertices and the center point of a regular polygon, and the number of points must be not less than the number of polynomial terms.

[0010] Preferably, the Zernike polynomial matrix is: Each row is the first n circular Zernike polynomials. When the number of marked points is m, this matrix has m rows.

[0011] Preferably, the digital random speckle pattern described in S3 is an RGB color three-channel image, and the gray value of any pixel point in the single-channel speckle pattern satisfies: where is the maximum light intensity, is the standard deviation of the Gaussian speckle, is the coordinate of the k-th randomly generated speckle center. There are N random speckles, making the duty cycle of the single-channel speckle approximately 50%, that is: A sub-region wavefront fitting correction and iterative registration algorithm described in S4 includes: (1) Divide the reflected deformed image and the standard image into several sub-images correspondingly; (2) For a single pair of sub-images, the deformed sub-image F and the standard sub-image G, based on maximizing the rewritten multi-channel ZNCC criterion, perform pixel-by-pixel registration to obtain the pixel mapping matrix of F and G; (3) Based on the Zernike polynomial wavefront fitting method with the optimal number of terms, use the pixel mapping point cloud data as the wavefront measurement data to fit the wavefront of the deformed sub-image; (4) Reverse-correct the deformed sub-image based on the fitted wavefront to obtain Fnew; (5) Let F = Fnew, and calculate the similarity difference between F, Fnew and the standard sub-image G respectively based on the multi-channel ZNCC criterion , as the convergence criterion, iterate the processes of (2) and (3) until is less than the allowable error, and output the final pixel mapping matrix of F and G; (6) Stitch the pixel mapping results of the sub-images.

[0012] The rewritten multi-channel ZNCC criterion is specifically: where is a pixel to be registered in the deformed sub-image F, is its possible registered pixel in the standard sub-image G.

[0013] Furthermore, an optimal number of terms Zernike polynomial wavefront fitting method includes: using the number of terms of the Zernike polynomial for wavefront fitting as the optimization variable, using the ZNCC value between the deformed image and the standard image after wavefront fitting correction as the objective function, selecting a suitable number of terms interval, and adopting the one-dimensional search algorithm - the golden section method to obtain the optimal number of terms that maximizes the objective function, and output the correction result.

[0014] Compared with the prior art, the beneficial effects of the present invention include: (1) Only a single-frame image is required to complete the measurement. Compared with the traditional phase deflectometry, the influence of factors such as ambient light fluctuation and mechanical vibration is effectively avoided, and it is suitable for rapid detection in complex working conditions such as industrial sites; (2) It can realize real-time dynamic monitoring of the surface shape of highly reflective objects, providing technical support for the alignment of optical systems and on-line quality inspection of mirrors; (3) There is no need to introduce a reference plane or a binocular camera. The rotation, shear and resolution differences caused by the non-orthogonal optical path of the system are directly eliminated through the projection distortion correction algorithm, significantly reducing the strict restrictions on the optical path layout and expanding the applicable range of the monocular system; (4) Based on the local distortion adaptive registration technology of sub-region wavefront fitting correction, it can adaptively process the deformation differences in different curvature regions of the measured surface and support high-dynamic range measurement of non-planar components; (5) The surface topography reconstruction accuracy reaches the order of hundreds of nanometers, meeting the detection requirements in the rough polishing stage of precision optical components. Description of the Drawings

[0015] Figure 1 It is a schematic diagram of the optical path of a monocular speckle deflectometry measurement system Figure 2 It is a schematic diagram of a kind of marker point pattern Figure 3 It is a flow chart of Zernike polynomial projection distortion correction based on marker points Figure 4 It is a flow chart based on sub-region wavefront fitting correction and iterative registration algorithm Figure 5 It is the measurement result of the interferometer of the optical component in the embodiment Figure 6 It is the measurement result of the optical component in the embodiment based on the method of the present invention Detailed Embodiments The present invention will be further described below with reference to the embodiments and the drawings.

[0016] The surface measurement result by using a Zygo commercial interferometer is as Figure 5 , which is, PV: 13073.457 nm, RMS: 2623.149 nm.

[0017] A single-frame speckle deflectometry measurement method based on sub-region wavefront correction includes the following steps: Step 1. System setup and calibration 1.1 System setup, as Figure 1 shown, a monocular speckle deflectometry measurement system is adopted, including: LCD screen, with a resolution of 3840*2160 and a pixel pitch of 0.369mm, used for projecting standard marker point patterns and random speckle patterns; CCD camera, with a resolution of 2448*2048 and a pixel size of 3.45 , and a lens focal length of 50mm, used for collecting the speckle images reflected by the mirror surface to be measured.

[0018] Mirror surface to be measured. In this embodiment, an optical element made of K9 material is selected, with an effective clear aperture of 100mm, and the surface roughness needs to meet the requirements of reflection imaging.

[0019] Mechanical adjustment device (not shown in the figure): used to accurately adjust the pose of the mirror surface to be measured. 1.2 System calibration of the mirror surface to be measured: Obtain the internal parameters and external parameters of the camera through camera calibration, and establish the conversion model between the screen pixel coordinate system, the camera coordinate system and the world coordinate system.

[0020] In this embodiment, the Zhang Zhengyou calibration method is adopted. Using a standard checkerboard calibration plate, the internal parameters (such as focal length, distortion coefficient) and external parameters (such as the spatial pose relationship between the screen and the camera) of the camera are obtained by shooting from multiple angles; After calibration, establish the conversion relationship from the screen pixel coordinate system to the world coordinate system (rotation matrix R s and translation vector T s ), and the conversion matrix M c from the camera coordinate system to the world coordinate system.

[0021] Step 2: Projection distortion correction, see Figure 3 Generate a binary marker point pattern with a resolution of 3840*2160. Among them, the marker point pattern is generated based on the vertices and the center point of a regular pentagon. For example, Figure 2 , a total of 6 dots with a diameter of 20 pixels, and the binary contrast is black dots on a white background.

[0022] Project the standard marker point pattern on the LCD screen, adjust the mirror surface to be measured so that the reflected image of the mirror surface to be measured contains the marker points, and receive them with the CCD camera. Extract the center of the marker points from the reflected image received by the CCD, and calculate the projection distortion parameters of the mirror surface reflected image through the Figure 3 marker point-based Zernike polynomial projection distortion correction method shown. In this example, the first 6 terms of the circular domain Zernike polynomial are used.

[0023] Step 3: Collect deformed speckle patterns Generate a standard three-channel color speckle pattern with a resolution of 3840*2160. The color speckle pattern is a single Gaussian speckle =1, and the duty cycle is 50%. After projecting the standard speckle pattern on the screen, the camera collects the reflected deformed speckle images.

[0024] Step 4: Based on the sub-region wavefront fitting correction and iterative registration algorithm, obtain the sub-pixel point mapping between the reflected image and the standard image. Refer to Figure 4 Use the calculated projection distortion parameters to correct the deformed image and output the restored image.

[0025] Divide both the restored image and the standard speckle image into 12*12 sub-regions with a sub-region size of 85*85 pixels. Perform sub-region registration based on the multi-channel ZNCC criterion, with a registration sub-window size of 21*21 pixels. And perform the optimal term number sub-region wavefront fitting correction iteration as shown in Figure 4 below, with the optimal term number search range from 3 to 28 terms. The iteration convergence threshold is 0.001. Finally, perform global stitching, and based on the pixel mapping between the deformed image and the restored image in the projection correction, obtain the pixel mapping between the deformed image and the standard speckle image.

[0026] Step 5: Ray modeling and integral reconstruction Based on camera calibration and system calibration, convert the mapping relationship into the corresponding incident and reflected rays in the world coordinate system, establish a surface gradient equation, and reconstruct the surface topography by the integration method. The results are as Figure 6 shown. The PV value of the speckle deflection measurement result is 14965.885 nm, and the RMS value is 2912.378 nm.

[0027] This embodiment verifies the measurement ability of the method, indicating that the method can achieve sub-micron surface shape detection with single-frame imaging, meeting the requirements of rapid detection in industrial fields.

Claims

1. A single-frame speckle deflection measurement method based on sub-region wavefront correction, characterized in that It includes the following steps: S1. Build a monocular speckle deflection measurement system, including an LCD screen and a CCD camera, and perform camera calibration and system calibration to obtain the internal and external parameters of the camera, and establish the transformation relationships between the screen pixel coordinate system and the world coordinate system, and between the camera coordinate system and the world coordinate system; S2. Project a standard marker point pattern on the LCD screen, adjust the pose of the mirror to be measured so that the reflected image of the mirror to be measured contains the marker points and is collected by the CCD camera; based on the reflected image, use the Zernike polynomial projection distortion correction method to calculate the projection distortion parameters of the mirror reflected image; S3. Project a standard digital random speckle pattern on the LCD screen, and collect the deformed speckle pattern reflected by the mirror to be measured by the CCD camera; S4. Use the projection distortion parameters obtained in step S2 to correct the deformed speckle pattern and generate a restored image; Divide the restored image and the standard speckle image into several sub-regions, use the multi-channel zero-mean normalized cross-correlation criterion for sub-pixel registration, and combine the Zernike polynomial wavefront fitting and iterative optimization algorithm to obtain the global sub-pixel mapping relationship; S5. Based on the system calibration parameters and the sub-pixel mapping relationship, construct a spatial incident light and reflected light model in the world coordinate system, calculate the surface gradient distribution of the mirror to be measured, and reconstruct the three-dimensional surface shape through an integral algorithm.

2. The single-frame speckle deflection measurement method based on sub-region wavefront correction according to claim 1, wherein The Zernike polynomial projection distortion correction method in step S2 includes: 2.1 Generate a binary marker point pattern including the vertices and center point of a regular polygon, and the number of marker points is not less than the number of terms of the Zernike polynomial; 2.2 Perform binary, morphological image processing, connected region extraction and screening on the reflected image to obtain the center coordinates of the marker points; 2.3 Calculate the center deviation R of the marked points between the reflection image and the standard image, and establish a matrix equation , where M is the Zernike polynomial matrix. Solve the polynomial coefficients C by the least squares method, and calculate the deviation of all pixels between the reflection image and the standard image using C to correct the distortion. The missing pixels are filled by bicubic interpolation.

3. The single-frame speckle deflection measurement method based on sub-region wavefront correction according to claim 2, wherein The Zernike polynomial matrix is: Each row is the first n terms of the circular domain Zernike polynomial. When the number of marker points is m, the matrix has m rows.

4. The single-frame speckle deflection measurement method based on sub-region wavefront correction according to claim 1, characterized in that The digital random speckle pattern in step S3 is an RGB color three-channel image, where the gray value of any pixel point in a single-channel speckle pattern satisfies: Among them, is the maximum light intensity, is the standard deviation of the Gaussian speckle, is the center coordinate of the k-th randomly generated speckle. There are N random speckles, making the duty cycle of the single-channel speckle approximately 50%, that is: 。 5. The single-frame speckle deflection measurement method based on sub-region wavefront correction according to claim 1, wherein Step S4 specifically includes: (4.1) Correspondingly divide the reflected deformed image and the standard image into several sub-images; (4.2) For a single pair of sub-images, the deformed sub-image F and the standard sub-image G, based on the maximization of the rewritten multi-channel ZNCC criterion, perform pixel-by-pixel registration to obtain the pixel mapping matrix of F and G; (4.3) Based on the Zernike polynomial wavefront fitting method with the optimal number of terms, use the pixel mapping point cloud data as the wavefront measurement data to fit the wavefront of the deformed sub-image; (4.4) Reverse-correct the deformed sub-image based on the deviation between the fitted wavefront and the standard wavefront to obtain Fnew; (4.5) Let \(F = F_{new}\), and calculate the difference in the similarity between \(F\), \(F_{new}\) and the standard sub - graph \(G\) based on the multi - channel ZNCC criterion , as the convergence criterion, iterate the process of (4.2) and (4.3) until is less than the allowable error, and output the pixel mapping matrix of the final \(F\) and \(G\); (4.6) Stitch the sub-image pixel mapping results.

6. The single-frame speckle deflection measurement method based on sub-region wavefront correction according to claim 5, wherein The rewritten multi-channel ZNCC criterion is specifically: Among them is a pixel to be registered in the deformed sub - figure F and is its possible registered pixel in the standard sub - figure G 7. The single-frame speckle deflection measurement method based on sub-region wavefront correction according to claim 5, characterized in that Step 4.3 specifically includes: using the number of terms of the Zernike polynomial used for wavefront fitting as the optimization variable, using the ZNCC value between the deformed image and the standard image after wavefront fitting correction as the objective function, selecting a suitable number of terms interval, and using the one-dimensional search algorithm - the golden section method to obtain the optimal number of terms that maximizes the objective function and output the correction result.

8. The single-frame speckle deflection measurement method based on sub-region wavefront correction according to claim 5, characterized in that, During the sub-region wavefront fitting and iterative registration process, weighted averaging is used for global stitching to eliminate the gaps at the sub-region boundaries.

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