Predictive surface shape multi-angle rotation iterative reconstruction method and device for monocular phase deflection

Abstract

The invention discloses a predictive surface shape multi-angle rotation iterative reconstruction method and device for monocular phase deflection. The method comprises the steps that a checkerboard calibration plate and a displayer are used for displaying a black and white checkerboard calibration displayer, the position relation of a camera and a world coordinate system and internal parameters of the camera; a coordinate correspondence mechanism between a display screen and a camera is established by writing a sine structured light pattern, and sub-pixel-level matching of a display screen pixel array and camera imaging pixels is realized through double processes of light field modulation and image decoding; based on the predicted surface shape, simulating a predicted surface shape equation and a preset height, and adopting ray tracing to reconstruct a light path; on the basis of a predictive surface shape equation, a preset height and a tracing reconstruction light path, an inclination direction and an angle are added as variables, and PV is taken as a target value to carry out nonlinear optimization so as to obtain an optimal height, an inclination direction and an angle, thereby obtaining a to-be-measured surface shape morphology. According to the invention, the problem of depth information acquisition by a traditional monocular is solved.

Description

Technical Field

[0001] This invention belongs to the field of precision measurement technology in machine vision, specifically relating to a method and apparatus for multi-angle rotational iterative reconstruction of a known surface shape using monocular phase deflection. Background Technology

[0002] Aspherical elements in optical components, with their greater design freedom, can not only more effectively correct various aberrations, but also simultaneously meet some theoretically mutually restrictive design requirements. As a result, they are widely used in precision instruments, and their surface accuracy requirements have reached the nanometer level. For example, the "diffraction-limited aspherical lens" currently sold by Thorlabs in the United States adopts the MRF technology of QED in the United States, and its root mean square value of surface shape is better than 55 nm. Surface shape detection technology is the means to ensure the processing quality of aspherical elements and is also the key to ensuring that aspherical optical systems can work properly.

[0003] If interferometry or contact measurement methods are used to inspect aspherical optical components, there are problems such as potential damage to the surface of the optical components, excessively high inspection costs, and demanding inspection environment requirements, making it difficult to promote in large-scale industrial production.

[0004] Phase-deflection refraction, also known as the fringe reflection method, transforms the projector in a fringe projection system into a display screen. A camera records the image of structured light fringes on the screen reflected in the mirror under test. Due to variations in the surface topography of the optical element under test, the fringes recorded by the camera will be deformed, and this deformation is related to the three-dimensional topography of the mirror surface. In measuring specular reflective optical elements, phase-deflection refraction uses a surface light source, unlike the fringe projection method which uses a projector as a point light source to project patterns. The camera can observe the light source through the specular reflection characteristics of the target object. This solves the problems of overexposure and feature matching errors caused by excessively high light intensity from projectors and specular reflection in the fringe projection method.

[0005] Phase measurement deflection techniques are currently classified into three types: single-camera single-screen method, dual-camera single-screen method (stereo deflection), and single-camera dual-screen method (dual-plane deflection). Each of these three techniques establishes the mapping relationship between phase and gradient in different ways. Among them, dual-plane deflection is relatively cumbersome due to the need for multiple displays or semi-reflective lenses, and the high precision required for display movement can easily affect calibration and measurement accuracy. Monocular phase measurement deflection, lacking depth information, results in high gradient ambiguity. While stereo phase measurement deflection solves the depth information acquisition problem through binocular vision, the addition of a camera increases the difficulty and accuracy of calibration, as well as the associated cost. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a method and apparatus for multi-angle rotation iterative reconstruction of a known surface shape using monocular phase deflection. Unlike traditional monocular algorithms, which rely solely on an initial preset height to reconstruct the surface shape, this proposed algorithm introduces height h, tilt direction az, and tilt angle alpha. It then optimizes the PV using nonlinear least squares to obtain the optimal PV, thereby reconstructing the surface shape.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for multi-angle rotational iterative reconstruction of a known surface shape for monocular phase deflection includes the following steps: Step 1: Use a checkerboard calibration board and a monitor to display a black and white checkerboard calibration display, and obtain the positional relationship between the camera and the world coordinate system and the camera intrinsic parameters; Step 2: Based on the positional relationship between the camera and the world coordinate system and the camera's intrinsic parameters, a coordinate correspondence mechanism between the display screen and the camera is established by writing a sinusoidal structured light pattern. Through the dual processes of light field modulation and image decoding, sub-pixel-level matching between the display screen pixel array and the camera imaging pixels is achieved. Step 3: Based on the sub-pixel matching of the display pixel array and the camera imaging pixels, combined with the known surface shape, simulate the known surface shape equation, preset the height, and use ray tracing to reconstruct the optical path; Step 4: Based on the known surface shape equation, preset height, and tracing reconstruction optical path, add tilt direction and angle as variables, and use PV as the target value to perform nonlinear optimization to obtain the optimal height, tilt direction, and angle, thereby obtaining the surface shape to be measured.

[0008] A further improvement of this invention is that the specific implementation method of step 1) is as follows: Step 1.1: Construct a monocular phase deflection measurement system consisting of a monocular camera and a monitor; Step 1.2: Obtain camera intrinsic parameters using checkerboard calibration; Step 1.3: The monitor displays a black and white checkerboard pattern. The calibrated positional relationship between the monitor and the camera is obtained by continuously adjusting the standard plane mirror.

[0009] A further improvement of the present invention is that the specific implementation method of step 2) is as follows: Step 2.1: The monitor screen displays four sinusoidal fringe patterns with different phase differences. The folded phase is obtained using the four-step phase shift method, as shown in the following formula:

[0010] in, Here, represents the grayscale value of the fringe pattern, and N is the set total number of phase-shift steps. The backlight intensity of the monitor; Modulation intensity; The desired wrapping phase; This indicates the current phase shift step number;

[0011] Taking n = 4, we get the following expression:

[0012] Step 2.2: Since the range of the arctangent function can only be restricted to an interval, the phase is wrapped within a period. The dual-frequency method is used to unwrap the phase and obtain the expanded phase, so as to achieve sub-pixel matching between the display pixel array and the camera imaging pixels.

[0013] A further improvement of the present invention is that the specific implementation method of step 3) is as follows: Step 3.1: Simulate the predicted surface equation based on the surface shape to be measured; Step 3.2: The surface to be measured is a plane mirror, that is, the plane is reconstructed in the world coordinate system according to the preset height h to obtain the preset surface shape; Step 3.3: The surface to be measured is a concave reflector. Based on the preset height h, the lowest point of the preset surface shape in the world coordinate system is obtained by finding the intersection of the pixel plane center and the optical center. The concave surface is then reconstructed based on this point. Step 3.4: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system using intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display.

[0014] A further improvement of this invention is that the specific implementation method of step 4) is as follows: Step 4.1: The surface to be tested is a plane mirror, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The preset plane is simulated by the normal direction. Step 4.2: The surface to be tested is a concave reflector, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The x and y coordinates remain unchanged to obtain the preset concave surface. Step 4.3: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system through intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display. Step 4.4: Set the initial height h, tilt direction az and tilt angle alpha, and set the upper and lower limits. Obtain the gradients in the x and y directions through the reconstructed optical path, and reconstruct the surface shape based on the gradient data using Zernike polynomials.

[0015] in, It is the height value. It is the first The Zernike polynomial is represented in rectangular coordinates. and These are the coefficients of the 0th and i-th Zenic polynomials, respectively; Step 4.5: Compare the fitted surface shape with the standard surface shape; use the difference between the maximum and minimum residual values ​​as PV, take PV as the target value, and optimize it through nonlinear least squares method to obtain the optimal h, az and alpha, thereby obtaining the reconstructed surface shape and the corresponding PV and RMS.

[0016] A device for multi-angle rotational iterative reconstruction of a known surface shape for monocular phase deflection includes: The display unit is calibrated using a checkerboard calibration plate and a display showing a black and white checkerboard calibration display, to obtain the positional relationship between the camera and the world coordinate system and the camera intrinsic parameters. The subpixel-level matching unit, based on the positional relationship between the camera and the world coordinate system and the camera's intrinsic parameters, establishes a coordinate correspondence mechanism between the display screen and the camera by writing sinusoidal structured light patterns. Through the dual processes of light field modulation and image decoding, it achieves subpixel-level matching between the display screen pixel array and the camera imaging pixels. The simulation unit, based on the sub-pixel matching of the display pixel array and the camera imaging pixels, combined with the known surface shape, simulates the known surface shape equation, presets the height, and reconstructs the optical path using ray tracing; The nonlinear optimization unit, based on the known surface shape equation, preset height, and tracing reconstruction optical path, adds tilt direction and angle as variables, and uses PV as the target value to perform nonlinear optimization to obtain the optimal height, tilt direction, and angle, thereby obtaining the surface shape to be measured.

[0017] A further improvement of this invention is that the specific implementation method for calibrating the display unit is as follows: Step 1.1: Construct a monocular phase deflection measurement system consisting of a monocular camera and a monitor; Step 1.2: Obtain camera intrinsic parameters using checkerboard calibration; Step 1.3: The monitor displays a black and white checkerboard pattern. The calibrated positional relationship between the monitor and the camera is obtained by continuously adjusting the standard plane mirror.

[0018] A further improvement of this invention lies in the following specific implementation method of the sub-pixel level matching unit: Step 2.1: The monitor screen displays four sinusoidal fringe patterns with different phase differences. The folded phase is obtained using the four-step phase shift method, as shown in the following formula:

[0019] in, Here, represents the grayscale value of the fringe pattern, and N is the set total number of phase-shift steps. The backlight intensity of the monitor; Modulation intensity; The desired wrapping phase; This indicates the current phase shift step number;

[0020] Taking n = 4, we get the following expression:

[0021] Step 2.2: Since the range of the arctangent function can only be restricted to an interval, the phase is wrapped within a period. The dual-frequency method is used to unwrap the phase and obtain the expanded phase, so as to achieve sub-pixel matching between the display pixel array and the camera imaging pixels.

[0022] A further improvement of this invention is that the specific implementation method of the simulation unit is as follows: Step 3.1: Simulate the predicted surface equation based on the surface shape to be measured; Step 3.2: The surface to be measured is a plane mirror, that is, the plane is reconstructed in the world coordinate system according to the preset height h to obtain the preset surface shape; Step 3.3: The surface to be measured is a concave reflector. Based on the preset height h, the lowest point of the preset surface shape in the world coordinate system is obtained by finding the intersection of the pixel plane center and the optical center. The concave surface is then reconstructed based on this point. Step 3.4: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system using intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display.

[0023] A further improvement of this invention lies in the following specific implementation method of the nonlinear optimization unit: Step 4.1: The surface to be tested is a plane mirror, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The preset plane is simulated by the normal direction. Step 4.2: The surface to be tested is a concave reflector, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The x and y coordinates remain unchanged to obtain the preset concave surface. Step 4.3: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system through intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display. Step 4.4: Set the initial height h, tilt direction az and tilt angle alpha, and set the upper and lower limits. Obtain the gradients in the x and y directions through the reconstructed optical path, and reconstruct the surface shape based on the gradient data using Zernike polynomials.

[0024] in, It is the height value. It is the first The Zernike polynomial is represented in rectangular coordinates. and These are the coefficients of the 0th and i-th Zenic polynomials, respectively; Step 4.5: Compare the fitted surface shape with the standard surface shape; use the difference between the maximum and minimum residual values ​​as PV, take PV as the target value, and optimize it through nonlinear least squares method to obtain the optimal h, az and alpha, thereby obtaining the reconstructed surface shape and the corresponding PV and RMS.

[0025] Compared with the prior art, the present invention has at least the following beneficial technical effects: The present invention provides a method and apparatus for multi-angle rotation and iterative reconstruction of a known surface shape for monocular phase deflection. The method initializes the known surface shape in three aspects: height, tilt direction, and tilt angle. It constructs an optical path based on the intersection of the line and the surface, reconstructs the surface shape, and performs nonlinear optimization of the PV to obtain the optimal parameters, thereby reconstructing the accurate surface shape of the surface to be measured.

[0026] Compared with traditional monocular phase measurement deflection techniques, this invention innovatively considers multiple aspects of the initial iterative surface shape and incorporates tilt variables into the reconstructed optical path. This solves the problem of depth information acquisition in traditional monocular methods. At the same time, it achieves the measurement accuracy of stereo phase measurement deflection techniques using only one camera, improving detection precision and reducing costs. Attached Figure Description

[0027] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of the measurement platform that has been built.

[0029] Figure 2 This is a highly iterative simulation diagram.

[0030] Figure 3 To add the tilt direction and angle to the iterative simulation diagram.

[0031] Figure 4 This is a schematic diagram of the reconstructed surface.

[0032] Figure 5 This is a schematic diagram of the residuals.

[0033] Figure 6 This is a flowchart of the method of the present invention.

[0034] Figure 7 This is a structural block diagram of the device of the present invention. Detailed Implementation

[0035] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0036] In the description of this invention, it should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0037] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0038] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0039] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0040] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0041] Example 1 like Figure 6 As shown, the method for multi-angle rotation and iterative reconstruction of a known surface shape for monocular phase deflection provided by the present invention includes the following steps: Step 1: Use the checkerboard calibration board and monitor to display the black and white checkerboard calibration display, the positional relationship between the camera and the world coordinate system, and the camera intrinsic parameters; Step 1.1: Construct a monocular phase deflection measurement system consisting of a monocular camera and a display, such as... Figure 1 As shown; Step 1.2: Use the checkerboard pattern and Zhang's calibration method to calibrate the camera's intrinsic and extrinsic parameters.

[0042] Step 1.3: Display a black and white checkerboard pattern on the monitor. By continuously adjusting the standard plane mirror, obtain the calibration pose relationship between the virtual monitor and the camera. Obtain the pose relationship between the real monitor and the camera using the following formula.

[0043]

[0044] and Let the rotation matrix and translation vector be the camera and the display. and Let be the rotation matrix and translation vector of the virtual images of the camera and display; n be the unit normal vector of the reference plane mirror; d be the distance from the optical center to the reference plane mirror; and I be the third-order identity matrix. Step 2: By writing a sinusoidal structured light pattern, a coordinate correspondence mechanism between the display screen and the camera is established. Through the dual processes of light field modulation and image decoding, sub-pixel-level matching between the display screen pixel array and the camera imaging pixels is achieved. Step 2.1: The monitor screen displays four sinusoidal fringe patterns with different phase differences. The folded phase is obtained using the four-step phase shift method, as shown in the following formula:

[0045] in, Here, represents the grayscale value of the fringe pattern, and N is the set total number of phase-shift steps. The backlight intensity of the monitor; Modulation intensity; The desired wrapping phase; This indicates the current number of phase shift steps.

[0046]

[0047] Taking n = 4, we get the following expression:

[0048] Step 2.2: Since the range of the arctangent function can only be restricted to an interval, the phase is wrapped within one period. The two-frequency method is used to unwrap the phase and obtain the expanded phase.

[0049] Step 3: Based on the known surface shape, simulate the equation of the known surface shape, preset the height, and reconstruct the light path using ray tracing; Step 3.1: Simulate the predicted surface equation based on the surface shape to be measured; Step 3.2: The surface to be measured is a plane mirror, that is, the plane is reconstructed in the world coordinate system according to the preset height h to obtain the preset surface shape; Step 3.3: The surface to be tested is a concave reflector. Based on the preset height h, the lowest point of the preset surface shape in the world coordinate system is obtained by finding the intersection of the pixel plane center and the optical center. The concave surface is reconstructed based on this point using the following formula.

[0050] in , , Represents the three-dimensional coordinates of a point on a concave surface. , Here are the x and y coordinates of the lowest point. The preset spherical radius.

[0051] Step 3.4: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system using intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated optical path is established by mapping the intersection points of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display. Figure 2 As shown; Step 4: Based on Step 3, add the tilt direction and angle as variables, and use PV as the target value to perform nonlinear optimization to obtain the optimal height, tilt direction and angle, thereby obtaining the surface morphology to be measured.

[0052] Step 4.1: The surface to be tested is a plane mirror, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The preset plane is simulated by the normal direction. Step 4.2: The surface to be tested is a concave reflector, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The x and y coordinates remain unchanged to obtain the preset concave surface. Step 4.3: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system using intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. Establish the simulated optical path by mapping the intersection points of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display. Reconstruct the simulated optical path as follows: Figure 3 As shown; Step 4.4: Set the initial height h, tilt direction az, and tilt angle alpha, and set upper and lower limits. Obtain the gradients in the x and y directions through the reconstructed optical path. Reconstruct the surface shape based on the gradient data using Zernike polynomials, as shown below. Figure 4 As shown; The Zernike gradient reconstruction method uses Zernike polynomials to fit the unknown surface shape through gradients. For ease of calculation, it is represented in a rectangular coordinate system as follows:

[0053] in For surface shape, For the first The Zernike polynomial is represented in rectangular coordinates. Let be the coefficient of the k-th term.

[0054] Calculate the gradient in the x-direction gradient in the y-direction Then, it can be obtained through the following two formulas. :

[0055]

[0056] Step 4.5: Substitute the obtained coefficient matrix into the surface shape equation to obtain the fitted surface shape, and compare it with the standard surface shape; use the difference between the maximum and minimum residual values ​​as PV, and use PV as the objective value to optimize through nonlinear least squares method to obtain the optimal h, az, and alpha, thus obtaining the reconstructed surface shape and the corresponding PV and RMS, as shown below. Figure 5 As shown, the PV of the reconstructed plane mirror is 605.16 nm, the RMS is 158.68 nm, and the ZYGO measurement data is 441.54 nm.

[0057] Example 2 like Figure 7 As shown, the device for multi-angle rotation and iterative reconstruction of a known surface shape for monocular phase deflection provided by the present invention includes: The display unit is calibrated using a checkerboard calibration plate and a display showing a black and white checkerboard calibration display, to obtain the positional relationship between the camera and the world coordinate system and the camera intrinsic parameters. The subpixel-level matching unit, based on the positional relationship between the camera and the world coordinate system and the camera's intrinsic parameters, establishes a coordinate correspondence mechanism between the display screen and the camera by writing sinusoidal structured light patterns. Through the dual processes of light field modulation and image decoding, it achieves subpixel-level matching between the display screen pixel array and the camera imaging pixels. The simulation unit, based on the sub-pixel matching of the display pixel array and the camera imaging pixels, combined with the known surface shape, simulates the known surface shape equation, presets the height, and reconstructs the optical path using ray tracing; The nonlinear optimization unit, based on the known surface shape equation, preset height, and tracing reconstruction optical path, adds tilt direction and angle as variables, and uses PV as the target value to perform nonlinear optimization to obtain the optimal height, tilt direction, and angle, thereby obtaining the surface shape to be measured.

[0058] In this embodiment, the specific implementation method for calibrating the display unit is as follows: Step 1.1: Construct a monocular phase deflection measurement system consisting of a monocular camera and a monitor; Step 1.2: Obtain camera intrinsic parameters using checkerboard calibration; Step 1.3: The monitor displays a black and white checkerboard pattern. The calibrated positional relationship between the monitor and the camera is obtained by continuously adjusting the standard plane mirror.

[0059] In this embodiment, the specific implementation method of the sub-pixel level matching unit is as follows: Step 2.1: The monitor screen displays four sinusoidal fringe patterns with different phase differences. The folded phase is obtained using the four-step phase shift method, as shown in the following formula:

[0060] in, Here, represents the grayscale value of the fringe pattern, and N is the set total number of phase-shift steps. The backlight intensity of the monitor; Modulation intensity; The desired wrapping phase; This indicates the current phase shift step number;

[0061] Taking n = 4, we get the following expression:

[0062] Step 2.2: Since the range of the arctangent function can only be restricted to an interval, the phase is wrapped within a period. The dual-frequency method is used to unwrap the phase and obtain the expanded phase, so as to achieve sub-pixel matching between the display pixel array and the camera imaging pixels.

[0063] In this embodiment, the specific implementation method of the simulation unit is as follows: Step 3.1: Simulate the predicted surface equation based on the surface shape to be measured; Step 3.2: The surface to be measured is a plane mirror, that is, the plane is reconstructed in the world coordinate system according to the preset height h to obtain the preset surface shape; Step 3.3: The surface to be measured is a concave reflector. Based on the preset height h, the lowest point of the preset surface shape in the world coordinate system is obtained by finding the intersection of the pixel plane center and the optical center. The concave surface is then reconstructed based on this point. Step 3.4: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system using intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display.

[0064] In this embodiment, the specific implementation method of the nonlinear optimization unit is as follows: Step 4.1: The surface to be tested is a plane mirror, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The preset plane is simulated by the normal direction. Step 4.2: The surface to be tested is a concave reflector, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The x and y coordinates remain unchanged to obtain the preset concave surface. Step 4.3: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system through intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display. Step 4.4: Set the initial height h, tilt direction az and tilt angle alpha, and set the upper and lower limits. Obtain the gradients in the x and y directions through the reconstructed optical path, and reconstruct the surface shape based on the gradient data using Zernike polynomials.

[0065] in, It is the height value. It is the first The Zernike polynomial is represented in rectangular coordinates. and These are the coefficients of the 0th and i-th Zenic polynomials, respectively; Step 4.5: Compare the fitted surface shape with the standard surface shape; use the difference between the maximum and minimum residual values ​​as PV, take PV as the target value, and optimize it through nonlinear least squares method to obtain the optimal h, az and alpha, thereby obtaining the reconstructed surface shape and the corresponding PV and RMS.

[0066] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the scope of the invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0067] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be appropriately combined to form other embodiments that can be understood by those skilled in the art. The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for multi-angle rotational iterative reconstruction of a known surface shape for monocular phase deflection, characterized in that, Includes the following steps: Step 1: Use a checkerboard calibration board and a monitor to display a black and white checkerboard calibration display, and obtain the positional relationship between the camera and the world coordinate system and the camera intrinsic parameters; Step 2: Based on the positional relationship between the camera and the world coordinate system and the camera's intrinsic parameters, a coordinate correspondence mechanism between the display screen and the camera is established by writing a sinusoidal structured light pattern. Through the dual processes of light field modulation and image decoding, sub-pixel-level matching between the display screen pixel array and the camera imaging pixels is achieved. Step 3: Based on the sub-pixel matching of the display pixel array and the camera imaging pixels, combined with the known surface shape, simulate the known surface shape equation, preset the height, and use ray tracing to reconstruct the optical path; Step 4: Based on the known surface shape equation, preset height, and tracing reconstruction optical path, add tilt direction and angle as variables, and use PV as the target value to perform nonlinear optimization to obtain the optimal height, tilt direction, and angle, thereby obtaining the surface shape to be measured.

2. The method for multi-angle rotation and iterative reconstruction of a known surface shape for monocular phase deflection according to claim 1, characterized in that, The specific implementation method for step 1) is as follows: Step 1.1: Construct a monocular phase deflection measurement system consisting of a monocular camera and a monitor; Step 1.2: Obtain camera intrinsic parameters using checkerboard calibration; Step 1.3: The monitor displays a black and white checkerboard pattern. The calibrated positional relationship between the monitor and the camera is obtained by continuously adjusting the standard plane mirror.

3. The method for multi-angle rotation and iterative reconstruction of a known surface shape for monocular phase deflection according to claim 1, characterized in that, The specific implementation method for step 2) is as follows: Step 2.1: The monitor screen displays four sinusoidal fringe patterns with different phase differences. The folded phase is obtained using the four-step phase shift method, as shown in the following formula: in, Here, represents the grayscale value of the fringe pattern, and N is the set total number of phase-shift steps. The backlight intensity of the monitor; Modulation intensity; The desired wrapping phase; This indicates the current phase shift step number; Taking n = 4, we get the following expression: Step 2.2: Since the range of the arctangent function can only be restricted to an interval, the phase is wrapped within a period. The dual-frequency method is used to unwrap the phase and obtain the expanded phase, so as to achieve sub-pixel matching between the display pixel array and the camera imaging pixels.

4. The method for multi-angle rotation and iterative reconstruction of a known surface shape for monocular phase deflection according to claim 1, characterized in that, The specific implementation method for step 3) is as follows: Step 3.1: Simulate the predicted surface equation based on the surface shape to be measured; Step 3.2: The surface to be measured is a plane mirror, that is, the plane is reconstructed in the world coordinate system according to the preset height h to obtain the preset surface shape; Step 3.3: The surface to be measured is a concave reflector. Based on the preset height h, the lowest point of the preset surface shape in the world coordinate system is obtained by finding the intersection of the pixel plane center and the optical center. The concave surface is then reconstructed based on this point. Step 3.4: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system using intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display.

5. The method for multi-angle rotation and iterative reconstruction of a known surface shape for monocular phase deflection according to claim 1, characterized in that, The specific implementation method for step 4) is as follows: Step 4.1: The surface to be tested is a plane mirror, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The preset plane is simulated by the normal direction. Step 4.2: The surface to be tested is a concave reflector, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The x and y coordinates remain unchanged to obtain the preset concave surface. Step 4.3: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system through intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display. Step 4.4: Set the initial height h, tilt direction az and tilt angle alpha, and set the upper and lower limits. Obtain the gradients in the x and y directions through the reconstructed optical path, and reconstruct the surface shape based on the gradient data using Zernike polynomials. in, It is the height value. It is the first The Zernike polynomial is represented in rectangular coordinates. and These are the coefficients of the 0th and i-th Zenic polynomials, respectively; Step 4.5: Compare the fitted surface shape with the standard surface shape; use the difference between the maximum and minimum residual values ​​as PV, take PV as the target value, and optimize it through nonlinear least squares method to obtain the optimal h, az and alpha, thereby obtaining the reconstructed surface shape and the corresponding PV and RMS.

6. A device for multi-angle rotational iterative reconstruction of a known surface shape using monocular phase deflection, characterized in that, include: The display unit is calibrated using a checkerboard calibration plate and a display showing a black and white checkerboard calibration display, to obtain the positional relationship between the camera and the world coordinate system and the camera intrinsic parameters. The subpixel-level matching unit, based on the positional relationship between the camera and the world coordinate system and the camera's intrinsic parameters, establishes a coordinate correspondence mechanism between the display screen and the camera by writing sinusoidal structured light patterns. Through the dual processes of light field modulation and image decoding, it achieves subpixel-level matching between the display screen pixel array and the camera imaging pixels. The simulation unit, based on the sub-pixel matching of the display pixel array and the camera imaging pixels, combined with the known surface shape, simulates the known surface shape equation, presets the height, and reconstructs the optical path using ray tracing; The nonlinear optimization unit, based on the known surface shape equation, preset height, and tracing reconstruction optical path, adds tilt direction and angle as variables, and uses PV as the target value to perform nonlinear optimization to obtain the optimal height, tilt direction, and angle, thereby obtaining the surface shape to be measured.

7. The device for multi-angle rotational iterative reconstruction of a known surface shape for monocular phase deflection according to claim 6, characterized in that, The specific implementation method for calibrating the display unit is as follows: Step 1.1: Construct a monocular phase deflection measurement system consisting of a monocular camera and a monitor; Step 1.2: Obtain camera intrinsic parameters using checkerboard calibration; Step 1.3: The monitor displays a black and white checkerboard pattern. The calibrated positional relationship between the monitor and the camera is obtained by continuously adjusting the standard plane mirror.

8. The device for multi-angle rotational iterative reconstruction of a known surface shape for monocular phase deflection according to claim 6, characterized in that, The specific implementation method of the sub-pixel level matching unit is as follows: Step 2.1: The monitor screen displays four sinusoidal fringe patterns with different phase differences. The folded phase is obtained using the four-step phase shift method, as shown in the following formula: in, Here, represents the grayscale value of the fringe pattern, and N is the set total number of phase-shift steps. The backlight intensity of the monitor; Modulation intensity; The desired wrapping phase; This indicates the current phase shift step number; Taking n = 4, we get the following expression: Step 2.2: Since the range of the arctangent function can only be restricted to an interval, the phase is wrapped within a period. The dual-frequency method is used to unwrap the phase and obtain the expanded phase, so as to achieve sub-pixel matching between the display pixel array and the camera imaging pixels.

9. The device for multi-angle rotational iterative reconstruction of a known surface shape for monocular phase deflection according to claim 6, characterized in that, The specific implementation method of the simulation unit is as follows: Step 3.1: Simulate the predicted surface equation based on the surface shape to be measured; Step 3.2: The surface to be measured is a plane mirror, that is, the plane is reconstructed in the world coordinate system according to the preset height h to obtain the preset surface shape; Step 3.3: The surface to be measured is a concave reflector. Based on the preset height h, the lowest point of the preset surface shape in the world coordinate system is obtained by finding the intersection of the pixel plane center and the optical center. The concave surface is then reconstructed based on this point. Step 3.4: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system using intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display.

10. The device for multi-angle rotational iterative reconstruction of a known surface shape for monocular phase deflection according to claim 6, characterized in that, The specific implementation method of the nonlinear optimization unit is as follows: Step 4.1: The surface to be tested is a plane mirror, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The preset plane is simulated by the normal direction. Step 4.2: The surface to be tested is a concave reflector, that is, the normal line is drawn from the center of the pixel through the optical center to the preset intersection point. The changed normal direction is obtained according to the tilt direction az and the tilt angle alpha. The x and y coordinates remain unchanged to obtain the preset concave surface. Step 4.3: Convert the pixel coordinates in the pixel coordinate system to coordinates in the camera coordinate system through intrinsic parameters. The direction of the light rays from the camera to the surface under test can be obtained through the optical center position. The simulated light path is established by mapping the intersection of the simulated surface shape with these light rays and the corresponding pixel coordinates on the display. Step 4.4: Set the initial height h, tilt direction az and tilt angle alpha, and set the upper and lower limits. Obtain the gradients in the x and y directions through the reconstructed optical path, and reconstruct the surface shape based on the gradient data using Zernike polynomials. in, It is the height value. It is the first The Zernike polynomial is represented in rectangular coordinates. and These are the coefficients of the 0th and i-th Zenic polynomials, respectively; Step 4.5: Compare the fitted surface shape with the standard surface shape; use the difference between the maximum and minimum residual values ​​as PV, take PV as the target value, and optimize it through nonlinear least squares method to obtain the optimal h, az and alpha, thereby obtaining the reconstructed surface shape and the corresponding PV and RMS.

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