CN113362399B - Calibration method for positions and postures of focusing mirror and screen in deflection measurement system - Google Patents
Calibration method for positions and postures of focusing mirror and screen in deflection measurement system Download PDFInfo
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Abstract
The invention discloses a method for calibrating the position and posture of a focusing mirror and a screen in a deflection measurement system, which belongs to the technical field of deflection measurement. The method comprises the steps of firstly determining the pose of a plane mirror based on visual imaging, shooting an image of a screen reflected by the plane mirror and a focusing mirror, and calibrating the pose of the focusing mirror and the pose of the screen simultaneously only by one image. The invention can realize the rapid geometric calibration of the transition imaging deflection measurement optical path, avoids complex operation steps and improves the efficiency and the reliability of the deflection measurement of the complex curved surface.
Description
Technical Field
The invention relates to the technical field of deflection measurement, in particular to a method for calibrating the pose of a focusing mirror and a screen in a deflection measurement system.
Background
With the development of optical technology, the application of the optical free-form surface in an optical system is more and more extensive. The surface shape quality of an optical free-form surface is one of core indexes for determining the performance of a system where the optical free-form surface is located, and an optical element is required to have submicron-level surface shape precision in many applications, so that the measurement precision is usually higher than the processing precision by one order of magnitude.
Deflection measurement is a reflection mirror surface measurement technique that has been rapidly developed in recent years [ Xu, x., et al. "Self-calibration of in situ monochromatic reflectance measurement in precision optical measurement." Optics Express 2019; 27:7523-7536.]. The principle is that a plurality of groups of coding stripes are displayed on a display, a camera is used for shooting a deformation stripe pattern reflected by the surface to be measured, the surface gradient distribution of the surface shape to be measured is deduced and calculated through a geometric relation, and the height of the surface shape is obtained through reconstruction by an integral method. Since the gradient/normal information of the surface of the workpiece is measured, the gradient/normal information has the characteristics of fast sampling, good anti-interference performance and strong adaptability to complex shapes, and has recently received extensive attention of researchers [ Maldonado, A.V.. High resolution optical surface measurement with the slope measuring optical system, PhD display, Gradworks,2014 ].
In the existing deflection measurement system, generally based on a pinhole camera model, the object-image correspondence between each pixel in an acquired image and a screen pixel is established according to the demodulation phase of each pixel in the acquired image through multi-step phase shifting of the screen fringe, so that the demodulation accuracy of each pixel in the image directly determines the measurement accuracy.
However, since the camera used in the actual measurement system is not a pinhole camera under ideal conditions, there is a contradiction between the accuracy of detecting the measurement position and the accuracy of demodulating the phase of the screen, and the single focusing of the camera on the surface of the workpiece or on the screen can negatively affect the measurement result [ X Zhang, Z Niu, J Ye and M xu. correction of interference-induced phase errors in phase demodulation. optics Letters 2021; 46(9):2047-2050].
Therefore, the inventor team proposes to add an auxiliary focusing mirror in the measuring light path, namely, firstly, to image the screen on the measured workpiece through the concave focusing mirror, and then to shoot the image by the camera, so as to simultaneously improve the position resolution and the angle resolution of the deflection measurement [ Yangxiang, Zhu Rui, Chen Yunuo ].
However, the concave mirror reflection imaging does not obey the PnP similarity relation of the plane mirror, so that the focusing mirror is difficult to position.
Disclosure of Invention
The invention aims to provide a method for calibrating the poses of a focusing mirror and a screen in a deflection measurement system, aiming at solving the problem that the poses of the screen and the focusing mirror in the deflection measurement system in the prior art are difficult to calibrate.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a method for calibrating the pose of a focusing mirror and a screen in a deflection measurement system, wherein the system comprises the screen, the focusing mirror, a plane mirror with a plurality of regular spots and a camera with known internal reference, comprises the following steps,
s1, placing a plane mirror in the field of view of the camera, so that the camera can shoot an image of the screen after being reflected by the focusing mirror through the plane mirror;
s2, calibrating the position of the plane mirror relative to the camera by adopting a visual PnP (pseudo-random) rule;
s3, displaying regularly distributed mark points on the screen, and shooting an image of the screen by the camera;
calibrating a first step:
s12, constructing a virtual camera image coordinate system V in which the camera coordinate system C is symmetrical with respect to the plane mirror, and under the virtual camera image coordinate system V, each light ray C emerging from the virtual camera image satisfies a coplanar constraint condition with the center of sphere M of the focusing lens, a corresponding point Q of the light ray C on the screen under the screen coordinate system, a rotation matrix R and a translational vector T from the screen coordinate system to the virtual camera image coordinate system: c. C T (O × (RQ + T)), (1), where M ═ dO, d is the distance from the origin of the camera virtual image coordinate system to the sphere center M of the focusing lens, and O is the unit vector;
s14, reconstruction matrix F ═ O]The solution of equation (1) is constrained by x R and the vector k ═ O × T, transforming equation (1) into: c. C T FQ+c T k＝0...(2)；
S16, when the camera shoots 8 or more mark points on the screen, establishing a coplanar constraint equation set based on the formula (2) simultaneously, and solving through singular value decomposition to obtain R and T, whereinT does not contain a component T in the O direction O ；
And calibrating:
s22, performing reverse ray tracing from a camera virtual image, and establishing a plane A formed by any ray c, a reflected ray of the ray passing through the focusing mirror and a normal on the focusing mirror;
s24, constructing an orthogonal base in the plane a with O and O × (O × c), obtaining a corresponding point Q 'on the screen and a reflection point P on the focusing mirror in the orthogonal base, and obtaining a reflected light ray r on the focusing mirror by a reflection law, i.e., (Q' -P) × r ═ 0. (3);
s26, respectively substituting 16 screen and camera point pairs into a structural equation set of a formula (3) to solve 16 d and T O Removing the imaginary solution and the solution that d is smaller than the radius of the focusing lens, and obtaining correct d and T by constructing a plurality of equation sets to find the intersection of the solutions O ；
S4, calibrating T obtained in the second step O Adding the T obtained in the first calibration to obtain complete T;
and S5, converting d obtained in R, S26 obtained in S16 and complete T obtained in S4 from the virtual camera image coordinate system back into the camera coordinate system, namely completing the pose calibration of the focusing lens and the screen.
Preferably, in S16 and S26, the equation of the construct is fitted to all points using a least squares method to obtain a higher accuracy.
Further, the method further comprises the step of,
the backward ray tracing from the camera to the screen is performed M, R, T, and the value of M, R, T is further optimized by the least squares method with the reprojection error on the screen as the objective function.
Preferably, the regular spots on the plane mirror are regularly distributed circular spots, and the centers of the regular spots are used for PnP calibration in S2; the regularly distributed mark points displayed on the screen are checkerboard patterns or other characteristic patterns.
Preferably, in S16, the step of solving by singular value decomposition to obtain R and T includes,
the quadrant in which the largest angle in the rotation matrix is located is determined by the difference in the pose between the screen and the camera, and the eligible R, T, O combinations are screened from the solution set accordingly.
Preferably, the camera is a pinhole camera.
By adopting the technical scheme, the pose of the plane mirror is determined based on visual imaging, one image of the screen reflected by the plane mirror and the focusing mirror is shot, and the simultaneous calibration of the pose of the focusing mirror and the screen can be realized only by one image.
Drawings
FIG. 1 is a schematic diagram of a deflection measurement system according to the present invention;
FIG. 2 is a schematic view of a flat mirror according to the present invention;
FIG. 3 is a flow chart of a method of the present invention;
FIG. 4 is a schematic diagram of a reverse ray tracing calibration method according to the present invention;
FIG. 5 is a schematic diagram of the backward ray tracing in calibration two of the method of the present invention;
FIG. 6 is a schematic diagram of the apparatus of the present invention.
In the figure, 1-screen, 2-focusing mirror, 3-plane mirror and 4-camera.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings. It should be noted that the description of the embodiments is provided to help understanding of the present invention, but the present invention is not limited thereto. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
It should be noted that in the description of the present invention, the terms "upper", "lower", "left", "right", "front", "rear", and the like indicate orientations or positional relationships based on structures shown in the drawings, and are only used for convenience in describing the present invention, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present invention.
In the technical scheme, the terms "first" and "second" are only used for referring to the same or similar structures or corresponding structures with similar functions, and are not used for ranking the importance of the structures, or comparing the sizes or other meanings.
In addition, unless expressly stated or limited otherwise, the terms "mounted" and "connected" are to be construed broadly, e.g., the connection may be a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; the two structures can be directly connected or indirectly connected through an intermediate medium, and the two structures can be communicated with each other. To those skilled in the art, the specific meanings of the above terms in the present invention can be understood in light of the present general concepts, in connection with the specific context of the scheme.
A calibration method for the positions of a focusing mirror and a screen in a deflection measurement system is disclosed, wherein the deflection measurement system comprises a screen 1, a focusing mirror 2, a plane mirror 3 and a camera 4 as shown in FIG. 1, wherein the plane mirror 3 has a plurality of regular spots, which are regularly distributed circular spots as shown in FIG. 2, and the camera 4 is configured as a known pinhole camera.
As shown in fig. 3, the method of the present invention comprises the steps of:
step S1, the plane mirror 3 is placed in the field of view of the camera 4, so that the camera 4 can capture the image of the screen 1 reflected by the focusing mirror 2 through the plane mirror 3.
And those skilled in the art perform reasonable discharges in order, which can be achieved with a limited number of attempts.
Step S2, the position of the plane mirror 3 relative to the camera 4 is calibrated by the center of the regular spot on the plane mirror 3 and the visual PnP rule.
Firstly, after the pose of the camera 4 is fixed, the pose of the plane mirror 3 can be calibrated through the PnP rule, so the poses of the screen 1 and the focusing mirror 2 in the system need to be calibrated.
In step S3, regularly distributed mark points are displayed on the screen 1, and an image of one screen is photographed by the camera 4.
In this embodiment, the regularly distributed mark points displayed on the screen 1 are set to be checkerboard patterns or circular spot patterns.
Calibrating a first step:
step S12, constructing a camera virtual image coordinate system V in which the camera coordinate system C is symmetrical with respect to the plane mirror 3, and performing reverse ray tracing from the camera 4 to the screen 1, where each ray C emerging from the camera virtual image satisfies the following coplanar constraint conditions with the sphere center M of the focusing lens 2, the corresponding point Q of the ray C on the screen 1 in the screen coordinate system, the rotation matrix R and the translation vector T from the screen coordinate system to the camera virtual image coordinate system in the camera virtual image coordinate system V:
c T (O x (RQ + T)) (1), as shown in figure 4,
where M is dO, d is the distance from the origin of the camera virtual image coordinate system to the center M of the focusing lens 2, and O is a unit vector.
In step S14, the solution of equation (1) is constrained by reconstructing the matrix F ═ O ] × R and the vector k ═ O × T, and equation (1) is transformed into the following equation:
c T FQ+c T k＝0...(2)。
step S16, when the camera 4 shoots 8 or more mark points on the screen 1, a coplanar constraint equation set can be established simultaneously based on the formula (2), and R and T are obtained by solving through singular value decomposition, wherein T does not contain a component T along the O direction O 。
In this step, after the solutions of R and T are obtained by solving through singular value decomposition, the quadrant where the maximum angle in the rotation matrix is located can be determined through the attitude difference between the screen 1 and the camera 4, and accordingly R, T, O combinations meeting the conditions are screened from the solutions of R and T in a centralized manner.
Since k is orthogonal to O, T obtained at this time does not include a component T in the O direction O ，T O Will be solved in the subsequent step of calibration two together with d.
And calibrating:
step S22, performing backward ray tracing from the camera 4 to the screen 1, and establishing a plane a formed by any ray c, the reflected ray of the ray passing through the focusing mirror 2, and the normal on the focusing mirror 2, and it can be understood that the above-mentioned O is located in the plane a;
step S24, an orthogonal basis is constructed with O and O × (O × c) in the plane a, a corresponding point Q 'on the screen 1 and a reflection point P on the focusing mirror 2 in the orthogonal basis are obtained, and a reflected light ray r on the focusing mirror 2, that is, (Q' -P) × r is 0. (3), is obtained by the law of reflection, as shown in fig. 5.
Step S26, two groups of 16 screen and camera point pairs are respectively substituted into the structural equation set of the formula (3) to solve 16 d and T O Removing the imaginary solution and the solution that d is smaller than the radius of the focusing lens, and obtaining correct d and T by constructing a plurality of equation sets to find the intersection of the solutions O 。
Where a point pair refers to a pair of 1 landmark point on the screen 1 and the corresponding point presented on the camera.
Step S4, calibrating T obtained in the second step O And adding the T obtained in the first calibration to obtain the complete T.
And step S5, converting R obtained in step S16, d obtained in step S26, and complete T obtained in step S4 from the virtual camera image coordinate system back into the camera coordinate system, that is, completing the pose calibration of the screen 1 and the focusing lens 2.
Also, it is understood that in step S16 and step S26, the equation of the configuration is fitted to all the point pairs using the least square method to obtain higher accuracy.
In another embodiment, the method further comprises the step of further optimizing M, R, T values by a least squares method using the reprojection error on the screen 4 as an objective function by performing the above obtained M, R, T back ray tracing of the camera 4 to the screen 1.
For example, a camera with a focal length of 50mm and a target surface size of 18mm is used for calibration, and a plane mirror coordinate system and a screen coordinate system are established respectively with the centers of the plane mirror 3 and the screen 1 as origins, wherein the z-axis directions of the two coordinate systems are respectively perpendicular to the plane mirror 3 and the screen 1, and the xOy surfaces thereof are respectively on the surfaces of the plane mirror 3 and the screen 1.
The basis transformation from the plane mirror coordinate system to the camera coordinate system is then:
the base transformation of the focusing mirror 2 position and screen coordinate system to camera coordinate system:
after the camera 4 performs primary imaging on the screen 1, acquiring a point pair relation between the camera and the screen by using a checkerboard pattern displayed on the screen 4, and solving the position and the screen pose of the focusing lens under a camera virtual image coordinate system according to the calibration flow as follows:
and then converting the coordinate system of the back camera to optimize the reprojection error, and finally solving the solution to be consistent with the real value, thereby completing the calibration of the focusing lens 2 and the screen 1.
Example two
An electronic device, as shown in fig. 6, includes a memory storing executable program code and a processor coupled to the memory; and the processor calls the executable program code stored in the memory to execute the method of the first embodiment.
EXAMPLE III
A computer storage medium, in which a computer program is stored, which, when executed by a processor, performs the method of the first embodiment.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. It will be apparent to those skilled in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, and the scope of protection is still within the scope of the invention.
Claims (6)
1. A calibration method for the position and posture of a focusing mirror and a screen in a deflection measurement system comprises the screen, the focusing mirror, a plane mirror with a plurality of regular spots and a camera with known internal reference, and is characterized in that: the method comprises the following steps of,
s1, placing a plane mirror in the field of view of the camera, so that the camera can shoot an image of the screen reflected by the focusing mirror through the plane mirror;
s2, calibrating the position of the plane mirror relative to the camera by adopting a visual PnP (pseudo-random) rule;
s3, displaying regularly distributed mark points on the screen, and shooting an image of the screen by the camera;
calibrating a first step:
s12, constructing a virtual camera image coordinate system V in which the camera coordinate system C is symmetrical with respect to the plane mirror, and under the virtual camera image coordinate system V, each light ray C emergent from the virtual camera image meets a coplanar constraint condition with the sphere center M of the focusing lens, the corresponding point Q of the light ray C on the screen under the screen coordinate system, the rotation matrix R and the translation vector T from the screen coordinate system to the virtual camera image coordinate system: c. C T (O × (RQ + T)), (1), where M ═ dO, d is the distance from the origin of the camera virtual image coordinate system to the sphere center M of the focusing lens, and O is the unit vector;
s14, reconstruction matrix F ═ O]The solution of equation (1) is constrained by xr and the vector k ═ O × T, transforming equation (1) into: c. C T FQ+c T k＝0...(2)；
S16, when the camera shoots 8 or more mark points on the screen, establishing a coplanar constraint equation set based on the formula (2) simultaneously, and solving through singular value decomposition to obtain R and T, wherein T does not contain a component T along the O direction O ；
And (2) calibrating:
s22, performing reverse ray tracing from a camera virtual image, and establishing a plane A formed by any ray c, a reflected ray of the ray passing through the focusing mirror and a normal on the focusing mirror;
s24, constructing an orthogonal base in the plane a with O and O × (O × c), obtaining a corresponding point Q 'on the screen and a reflection point P on the focusing mirror in the orthogonal base, and obtaining a reflected light ray r on the focusing mirror by a reflection law, i.e., (Q' -P) × r ═ 0. (3);
s26, respectively substituting 16 screen and camera point pairs into the structural equation of the formula (3)Group solution to 16 d, T O Removing the imaginary solution and the solution that d is smaller than the radius of the focusing lens, and obtaining correct d and T by constructing a plurality of equation sets to find the intersection of the solutions O ；
S4, calibrating T obtained in the second step O Adding the T obtained in the first calibration to obtain complete T;
and S5, converting d obtained in R, S26 obtained in S16 and complete T obtained in S4 from the virtual camera image coordinate system back into the camera coordinate system, namely completing the pose calibration of the focusing lens and the screen.
2. The method of claim 1, wherein: in S16 and S26, the equation for the construct is fitted to all points using a least squares method to obtain a higher accuracy.
3. The method of claim 1, wherein: the method further comprises the step of enabling the user to select the target,
the backward ray tracing from the camera to the screen is performed M, R, T, and the value of M, R, T is further optimized by the least squares method with the reprojection error on the screen as the objective function.
4. The method of claim 1, wherein: the regular spots on the plane mirror are regularly distributed circular spots, and the centers of the regular spots are used for PnP calibration in S2; the regularly distributed mark points displayed on the screen are checkerboard patterns or other characteristic patterns.
5. The method of claim 1, wherein: in S16, the step of solving by singular value decomposition to obtain R and T includes,
the quadrant in which the largest angle in the rotation matrix is located is determined by the difference in pose between the screen and the camera, and the eligible R, T, O combinations are screened from the solution set accordingly.
6. The method of claim 1, wherein: the camera is a pinhole camera.
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