Calibration and reconstruction method and system of deflection technology based on light beam imaging model

Abstract

The invention relates to a calibration and reconstruction method and system of a deflection technology based on a light beam imaging model, and relates to the field of precision optical measurement. The method comprises the following steps: carrying out screen angle calibration on a screen; carrying out camera entrance pupil size calibration on the camera; performing camera target surface conjugate surface calibration on the camera; determining a conjugate point corresponding to the entrance pupil size based on a calibration result of the entrance pupil size calibration in combination with a geometrical optics principle; based on the corresponding condition of the conjugate point and the entrance pupil size, pupil weight function distribution is defined; generating an imaging model based on a distribution result of pupil weight function distribution; and performing surface shape reconstruction calibration on the to-be-measured piece through the imaging model to obtain a surface shape reconstruction calibration result. According to the method, the convolution effect determined by aberration in imaging can be directly described, additional precision equipment is not needed, measurement steps are not obviously increased, the method is suitable for various deflection measurement systems, and the deflection measurement precision of a complex curved surface can be improved on the premise that time and hardware cost are effectively controlled.

Description

Technical Field

[0001] This invention relates to the field of precision optical measurement, and in particular to a calibration and reconstruction method for deflection based on a beam imaging model. Background Technology

[0002] Deflectometry has become a highly competitive solution for measuring complex optical surfaces due to its advantages such as large dynamic range, low hardware cost, and strong anti-interference ability [J. Burke, A. Pak, S. Höfer, et al., "Deflectometry for specular surfaces: an overview," Adv. Opt. Technol. 12,1237687 (2023).]. However, since the cameras used in practice are not ideal pinhole imaging systems, the signals acquired in deflectometry will be affected by the point spread function of the imaging system composed of the camera, screen, and the surface under test. Especially when measuring complex curved surfaces, aberrations will cause the point spread function to exhibit significant spatial variation and asymmetric characteristics, affecting the pixel correspondence calculation based on the imaging results through convolution effects, thereby affecting the measurement accuracy.

[0003] In related technologies, the solution to this problem is mainly image filtering [Z. Niu, X. Zhang, J. Ye, et al., "Adaptive Phase Correction for Phase Measuring Deflectometry Based on Light Field Modulation," IEEE Trans. Instrum. Meas. 70, 7003610 (2021).], but it still has drawbacks such as requiring a large number of image acquisitions, insufficient numerical stability, and the use of overly simplified physical assumptions. Filtering based on the instrument transfer function [T. Su, A. Maldonado, P. Su, et al., "Instrument transferfunction of slope measuring deflectometry systems," Appl. Opt. 54, 2981-2990 (2015).] and signal acquisition based on binary fringe defocus [Y. Shi, C. Chang, X. Liu, et al., "Infrared phase measuring deflectometry by using defocused binary fringe," Opt. Lett. 46, 3091–3094 (2021).] can also be used to solve the measurement errors caused by the convolution effect mentioned above, but their applicability is relatively limited, especially in the measurement of complex curved surfaces, where effectiveness is difficult to guarantee. Transition imaging [Y.Chen, X. Zhang, T. Chen, et al., "Transition imaging phase measuring deflectometry for high-precision measurement of optical surfaces," Measurement 199, 111589 (2022).] is also a scheme to suppress convolution effects, but its measurement accuracy needs to be guaranteed through customized system design, and its versatility is insufficient.

[0004] In other words, there is currently a lack of a high-precision technique for measuring the deflection of complex curved surfaces. Summary of the Invention

[0005] This invention relates to a calibration and reconstruction method and system for deflection based on a beam imaging model, which can achieve high-precision measurement of deflection on complex curved surfaces. The technical solution is as follows.

[0006] On the one hand, a calibration and reconstruction method for deflection based on a beam imaging model is provided, which is applied to computer equipment in a deflection measurement system for complex optical surfaces; The system includes a camera, a screen, a device under test, and a computer device; The camera, the screen, and the device under test are communicatively connected to the computer device. The method includes: The screen angle is calibrated. The camera entrance pupil size is calibrated. The camera's target surface conjugate surface is calibrated. Based on the calibration results of the entrance pupil size calibration, and combined with the principles of geometric optics, the conjugate point corresponding to the entrance pupil size is determined; Based on the correspondence between the conjugate point and the entrance pupil size, a pupil weighting function is defined for allocation; An imaging model is generated based on the allocation results of the pupil weight function. The surface shape of the test piece is reconstructed and calibrated using the imaging model to obtain the surface shape reconstruction and calibration results.

[0007] In an optional embodiment, the screen angle calibration includes: Determine the relationship between the intensity of the screen-radiated light and the angle between the light ray and the screen normal vector; Based on the angle relationship between the light ray and the screen normal vector, the screen angle is calibrated.

[0008] In an optional embodiment, before calibrating the screen angle, the following steps are included: A sample screen image is acquired using a camera, and the sample screen image corresponds to at least two grayscale images; Based on the sample screen images, nonlinear response correction is performed on the camera and the screen.

[0009] In an optional embodiment, the step of calibrating the camera entrance pupil size includes: The camera is imaged through a reference imaging system to obtain a reference size relative to the camera's entrance pupil. The camera entrance pupil size is calibrated based on the aforementioned camera entrance pupil reference size.

[0010] In an optional embodiment, the reference imaging system is implemented as a dual telecentric imaging system.

[0011] In an optional embodiment, the calibration of the camera target surface conjugate surface includes: The camera is controlled to image the screen with at least two sample sinusoidal fringes to obtain at least two projected rays; Based on the imaging results, the screen pose is determined by combining the phase shift method, and the perspective projection relationship between the camera and the screen is fitted. At least two of the projected rays are fitted with a fringe modulation scheme to perform focus point fitting for camera target surface conjugate calibration.

[0012] In an optional embodiment, the pupil weighting function is implemented as an elliptic distribution function, or the pupil weighting function is implemented as a slanted normal distribution function.

[0013] In an optional embodiment, the generation of the imaging model based on the allocation result of the pupil weighting function includes: By combining precise grayscale calculation, the pixel grayscale of the camera is determined using the reverse tracing calculation method; Based on the pixel grayscale and the pupil weight allocation function, combined with an optimized image processing algorithm, the imaging model is generated.

[0014] In an optional embodiment, the method further includes: The imaging model is geometrically calibrated by combining visual methods and phase deviation.

[0015] On the other hand, a calibration and reconstruction system for deflection based on a beam imaging model is provided, which includes a camera, a screen, a device under test, and a computer device. The camera, the screen, and the device under test are communicatively connected to the computer device. The system is used to perform the calibration and reconstruction methods of deflection based on beam imaging models as described above.

[0016] The beneficial effects of the technical solution provided by this invention include at least the following: It achieves accurate modeling of the imaging process in deflection measurement, and can directly describe the convolution effect determined by aberration in imaging. It does not require additional precision equipment or significantly increase the measurement steps, and is applicable to various deflection measurement systems. It can improve the deflection measurement accuracy of complex curved surfaces while effectively controlling time and hardware costs. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1This illustration shows a structural block diagram of a deflection calibration and reconstruction system based on a beam imaging model, provided in an exemplary embodiment of this application.

[0019] Figure 2 The illustration shows a flowchart of a deflection calibration and reconstruction method based on a beam imaging model provided in an exemplary embodiment of this application.

[0020] Figure 3 This illustration shows a flowchart of another calibration and reconstruction method for deflection based on a beam imaging model provided in an exemplary embodiment of this application. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0022] Figure 1 This application shows a structural block diagram of a calibration and reconstruction system for deflection based on a beam imaging model, provided by an exemplary embodiment of the present application. The system includes a camera 110, a screen 120, a device under test 130, and a computer device 140.

[0023] The camera 110, screen 120, and device under test 130 are all connected to the computer device 140.

[0024] In combination with the above system, Figure 2 This illustration shows a flowchart of a calibration and reconstruction method for deflection based on a beam imaging model, provided in an exemplary embodiment of this application, demonstrating the application of this method to... Figure 1 Taking the computer equipment within the system shown as an example, the method includes: Step 201: Perform screen angle calibration.

[0025] Step 202: Calibrate the camera entrance pupil size.

[0026] Step 203: Perform camera target surface conjugate calibration on the camera.

[0027] Steps 201 to 203 are the preliminary adjustment and calibration process for the components within the system.

[0028] Step 204: Based on the calibration results of the entrance pupil size calibration, and combined with the principles of geometric optics, determine the conjugate point corresponding to the entrance pupil size.

[0029] Step 205: Based on the correspondence between the conjugate point and the entrance pupil size, define the pupil weighting function allocation.

[0030] Step 206: Generate an imaging model based on the allocation result of the pupil weight function.

[0031] Step 207: Perform surface reconstruction and calibration on the test piece using the imaging model to obtain the surface reconstruction and calibration results.

[0032] Optionally, step 207 illustrates the application of the corresponding imaging model.

[0033] Figure 3 This illustration shows a flowchart of another calibration and reconstruction method for deflection based on a beam imaging model provided in an exemplary embodiment of this application, demonstrating the application of this method to... Figure 1 Taking the computer equipment within the system shown as an example, the method includes: Step 301: Acquire a sample screen image using a camera.

[0034] In this embodiment of the application, the sample screen image corresponds to at least two grayscale images.

[0035] Step 302: Based on the sample screen image, perform nonlinear response correction on the camera and the screen.

[0036] In this embodiment of the application, before calibrating the screen angle, the screen displaying different grayscale images is directly photographed by the camera, the nonlinear response curve between the camera and the screen is fitted, and the grayscale value of the stripe pattern displayed on the screen is adjusted according to the curve so that the intensity of the stripe signal conforms to a sine function in the image captured by the camera. Step 303: Determine the relationship between the intensity of the screen radiated light and the angle between the light ray and the screen normal vector.

[0037] Step 304: Based on the angle relationship between the light ray and the screen normal vector, calibrate the screen angle.

[0038] That is, in the embodiments of this application, the deflection measurement system consists of a camera, a screen, and a device under test. Before constructing the measurement system, the screen displaying different grayscale images is directly photographed by the camera, the nonlinear response curve between the camera and the screen is fitted, and the grayscale value of the stripe pattern displayed on the screen is adjusted according to the curve so that the intensity of the stripe signal conforms to a sine function in the image captured by the camera.

[0039] Step 305: Image the camera lens using the reference imaging system to obtain the reference size relative to the camera entrance pupil.

[0040] Step 306: Calibrate the camera entrance pupil size based on the camera entrance pupil reference size.

[0041] It should be noted that the reference urban-rural system used in the embodiments of this application can be implemented as a dual telecentric imaging system.

[0042] This process is the process of obtaining the camera's entrance pupil size.

[0043] Step 307: Control the camera to image at least two sample sinusoidal fringes onto the screen to obtain at least two projected rays.

[0044] Step 308: Based on the imaging results, determine the screen pose using the phase-shifting method, and fit the perspective projection relationship between the camera and the screen.

[0045] Step 309: Fit the focus point to at least two projected rays with the fringe modulation to calibrate the conjugate surface of the camera target.

[0046] Steps 307 to 309 illustrate the process of conjugate surface calibration. Optionally, in this process, to ensure sufficient data volume and suppress the effect of defocus, the camera is imaged onto the screen displaying sinusoidal fringes at different poses. The phase is calculated using the phase-shifting method to determine the pixel correspondence, and the screen pose is calculated and the perspective projection relationship is fitted. On each projected ray, the optimal focus point is fitted according to the fringe modulation, for example, using a Gaussian function or a quadratic curve, and the conjugate surface of the camera target is fitted through the optimal focus point position, for example, using a quadratic surface. Sampling is performed on the entrance pupil based on the aforementioned entrance pupil size. For example, when set as the starting point of the reverse tracing ray, according to the principles of geometric optics, each group of rays corresponds to a camera pixel, and the direction in the object space points to the conjugate point of that camera pixel on the conjugate surface.

[0047] It should be noted that, in the embodiments of this application, the pupil weighting function is implemented as an elliptic distribution function, or the pupil weighting function is implemented as a skewed normal distribution function. Step 310: Combine precise grayscale calculation with reverse tracing calculation to determine the pixel grayscale of the camera.

[0048] Step 311: Based on pixel grayscale and pupil weight allocation function, combined with optimized image solving algorithm, generate imaging model.

[0049] In this embodiment of the application, in order to bypass the difficulty of accurate grayscale calculation, the grayscale of the camera pixels is calculated by reverse tracing based on the grayscale of the stripe pattern displayed on the screen at different poses. The phase shift method is used to eliminate the influence factors that can be regarded as consistent within a single set of light, and the calculated phase is used as the output of the imaging model modeling result.

[0050] Step 312: Combine visual methods and phase deviation to perform geometric calibration on the imaging model.

[0051] That is, in the embodiments of this application, a geometric calibration and surface reconstruction process is also included.

[0052] Geometric calibration can be performed using the same visual method as traditional deflection measurement, only the objective function of optimization needs to be replaced by the phase deviation calculated by the above imaging model instead of the conventional reprojection error; Since a single camera pixel corresponds to multiple light rays, it is difficult to directly calculate the normal vector at the measurement point. Therefore, basis functions, such as Zernike polynomials or B-splines, are used to parameterize the surface under test. The aforementioned phase deviation is used as the objective function to achieve convenient surface reconstruction in an optimized manner.

[0053] Optionally, in a specific example of this application, a deflection measurement system is constructed using a camera with a resolution of 1920×1200 pixels, a lens focal length of 75 mm, and a screen with a resolution of 2048×1536 pixels and a pixel size of 0.0784 mm. Using functions... y = a × x b + c The nonlinear response relationship between the camera and the screen was fitted. The relationship between the intensity of the screen radiant rays and the angle between the ray and the screen normal vector was fitted using a cosine function and a first-order polynomial. The camera captured fringe patterns displayed on the screen at 15 different poses. A four-step phase-shifting method was used to obtain the modulation and phase. The modulation map sequence in object space is as follows: Figure 2 As shown, where m represents the modulation index, a quadratic surface is used to fit the conjugate surface of the camera target based on this set of data. A hexapolar pattern with a light density of 6 is used for sampling on the entrance pupil, with each camera pixel corresponding to 127 sampled rays. The pupil weighting function is specified using a combination of an elliptic and a skewed normal distribution function, as shown... Figure 3 As shown, due to edge occlusion, the weights of the sampled rays at the entrance pupil edge are multiplied by 0.5 before optimization. To simplify the calculation, 25 pixels are uniformly selected on the camera target surface, and their corresponding pupil weight functions are calculated. The parameters of the remaining pupil weight functions are obtained through interpolation. The LM algorithm is used to jointly optimize all parameters to complete the imaging model calibration.

[0054] For a non-spherical surface, the radius of curvature of the best-fit sphere for its nominal surface shape is 25.2 mm. The reconstruction results of this method are based on the measurement results of the Taylor Hobson LUPHOScan profilometer. The root mean square value of the reconstruction error of the invented method is 0.31 μm, while the root mean square value of the reconstruction error using the traditional pinhole camera model is 3.03 μm. This shows that the invented method effectively improves the measurement accuracy for complex curved surfaces.

[0055] The above are merely optional embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calibration and reconstruction of deflection based on a beam imaging model, characterized in that, The method is applied to computer equipment within a deflection measurement system for complex smooth curved surfaces; The system includes a camera, a screen, a device under test, and a computer device; The camera, the screen, and the device under test are communicatively connected to the computer device. The method includes: The screen angle is calibrated. The camera entrance pupil size is calibrated. The camera's target surface conjugate surface is calibrated. Based on the calibration results of the entrance pupil size calibration, and combined with the principles of geometric optics, the conjugate point corresponding to the entrance pupil size is determined; Based on the correspondence between the conjugate point and the entrance pupil size, a pupil weighting function is defined for allocation; An imaging model is generated based on the allocation results of the pupil weight function. The surface shape of the test piece is reconstructed and calibrated using the imaging model to obtain the surface shape reconstruction and calibration results.

2. The method according to claim 1, characterized in that, The screen angle calibration includes: Determine the relationship between the intensity of the screen-radiated light and the angle between the light ray and the screen normal vector; Based on the angle relationship between the light ray and the screen normal vector, the screen angle is calibrated.

3. The method according to claim 2, characterized in that, Before calibrating the screen angle, the following steps are included: A sample screen image is acquired using a camera, and the sample screen image corresponds to at least two grayscale images; Based on the sample screen images, nonlinear response correction is performed on the camera and the screen.

4. The method according to claim 1, characterized in that, The step of calibrating the camera entrance pupil size includes: The camera is imaged through a reference imaging system to obtain a reference size relative to the camera's entrance pupil. The camera entrance pupil size is calibrated based on the aforementioned camera entrance pupil reference size.

5. The method according to claim 4, characterized in that, The reference imaging system is implemented as a dual telecentric imaging system.

6. The method according to claim 1, characterized in that, The calibration of the camera target surface conjugate surface includes: The camera is controlled to image the screen with at least two sample sinusoidal fringes to obtain at least two projected rays; Based on the imaging results, the screen pose is determined by combining the phase shift method, and the perspective projection relationship between the camera and the screen is fitted. At least two of the projected rays are fitted with a fringe modulation scheme to perform focus point fitting for camera target surface conjugate calibration.

7. The method according to claim 6, characterized in that, The pupil weighting function is implemented as an elliptic distribution function, or the pupil weighting function is implemented as a sloping normal distribution function.

8. The method according to claim 1, characterized in that, The imaging model generated from the allocation result based on the pupil weight function includes: By combining precise grayscale calculation, the pixel grayscale of the camera is determined using the reverse tracing calculation method; Based on the pixel grayscale and the pupil weight allocation function, combined with an optimized image processing algorithm, the imaging model is generated.

9. The method according to claim 1, characterized in that, The method further includes: The imaging model is geometrically calibrated by combining visual methods and phase deviation.

10. A calibration and reconstruction system for deflection based on a beam imaging model, characterized in that, The system includes a camera, a screen, a device under test, and a computer device; The camera, the screen, and the device under test are communicatively connected to the computer device. The system is used to perform the calibration and reconstruction method of the deflection technique based on the beam imaging model as described in any one of claims 1 to 9.

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