CN114279360B - Method and device for measuring multi-order phase deflection based on telecentric imaging system - Google Patents
Method and device for measuring multi-order phase deflection based on telecentric imaging system Download PDFInfo
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Abstract
The invention relates to a method and a device for measuring multi-order phase deflection based on a telecentric imaging system, wherein a phase object displays phase coding information, the phase coding information is reflected to the imaging system through a surface to be measured, absolute phase information is obtained through calculation by a computing device, and the geometrical relationship among the sagittal height and the normal vector of the imaging system, the phase object and the object to be measured is utilized to reconstruct the surface shape of a curved surface to be measured. The method overcomes the defect that a telecentric imaging system needs to use a displacement mechanism to additionally move a target or a telecentric system to eliminate ambiguity resolution of a rotation matrix.
Description
Technical Field
The invention belongs to the field of precision vision measurement, and particularly relates to a method and a device for measuring multi-order phase deflection based on a telecentric imaging system.
Background
Phase measurement deflection is a mirror surface shape method which has a large dynamic range and can realize non-contact measurement on a free-form surface without a compensation mirror. The principle is that structured light coding information containing phase information is projected to a measured surface through a phase object, the coding information is modulated and reflected by the measured surface, the deformed structured light coding pattern is shot by a camera through an imaging system, absolute phase information is recovered according to a corresponding decoding algorithm, and the corresponding relation between camera pixels and phase object coordinates is obtained. Finally, the surface shape of the surface to be measured is finally obtained by the geometric relationship and constraint among the camera pixels, the phase object, the sagittal height of the surface to be measured and the normal vector.
Phase measurement deflection is classified into monocular phase measurement deflection and monocular phase measurement deflection. Huang Lei et al (Xue, j., gao, b., mcPherson, c., beverage, j., & Idir, m. (2016) Modal phase measuring reflectometry, optics express,24 (21), 24649-24664.) achieve monocular measurement of the measured surface type by means of polynomial equations. However, the method needs prior knowledge of the measured surface shape, and the surface shape iteration process is not easy to converge. Zhang Zonghua et al (Huang, s., gao, n., gao, f., & Jiang, x. (2017, june). Full-field 3D shape measurement of specular object having discontinuous surfaces.In Fifth International Conference on Optical and Photonics Engineering (vol. 10449, p. 104490t). International Society for Optics and photonics.) use a single aperture camera to effect surface shape measurements with two screens. However, the measurement accuracy is affected by the distortion and calibration of the small hole model. To improve measurement accuracy, niu Zhenqi et al (Gao, n., zhang, z., gao, f., & Jiang, x. (2018). 3-D shape measurement of discontinuous specular objects based on advanced PMD with bi-telelectricics express,26 (2), 1615-1632.) introduce a single telecentric lens to complete the measurement of specular surface type. However, this method still requires a plurality of screens, resulting in a linear increase in the phase-code image capturing time with an increase in the number of screens during measurement.
In the multi-order phase deviation operation, only one phase object is needed to provide phase encoding. However, there is no current literature showing a multi-order phase deviation measurement system constructed using multiple telecentric systems. One key problem in a multi-order phase deflection system is that in the calibration process, the telecentric imaging system has ambiguity solutions for the rotation matrix in the external parameters due to constant amplification level. Chen Zhong et al (Liao, h., & Zhang, x. (2014) & Telecentric stereo micro-vision systems: calibration method and experimenters. Optics and Lasers in Engineering,57,82-92.) introduced two telecentric imaging systems in another binocular vision measurement field that resolved ambiguity of the rotational torque matrix in the telecentric imaging system calibration process by a micropositioning stage.
Document retrieval shows that no method and device for measuring multi-order phase deflection based on a telecentric imaging system do not need to be calibrated by a displacement table at present.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a multi-order phase deflection measuring method based on a telecentric imaging system, which can carry out high-precision measurement on a surface to be measured, and the calibration process is simple without a displacement table.
The technical scheme for realizing the purpose of the invention comprises the following steps:
a multi-order phase deflection measuring method based on a telecentric imaging system includes that a phase object displays phase coding information, the phase object reflects to the imaging system through a surface to be measured, absolute phase information is obtained through calculation of a calculating device, and the surface shape of the surface to be measured is reconstructed through the geometric relation among the imaging system, the phase object, the sagittal height and the normal vector of the object to be measured.
The innovation point of the invention is that: the imaging system is more than two telecentric imaging systems, the ambiguity solution of the rotation matrix in the spatial relative position relation between the telecentric imaging system and the phase object is eliminated by a visual auxiliary mode, the correct calibration of the spatial relative position relation between the telecentric imaging system and the phase object is further completed,
the vision assisting mode is as follows: and respectively drawing the spatial relative position relations of a plurality of telecentric imaging systems containing the rotation matrix ambiguity solutions and the phase object, and visually comparing the position relation of the calibration result with the placement position relation of the actual equipment to remove the ambiguity solutions.
Further, the number of the plurality of telecentric imaging systems may be equal to or greater than two.
Further, the number of phase objects may be equal to or greater than one.
Further, the phase information provided by the phase object may be sine phase information, square wave phase information, or triangular wave phase information.
Further, the method for resolving the phase information may be a time phase unwrapping algorithm, a space phase unwrapping algorithm, a fourier phase unwrapping algorithm, or a least square phase unwrapping algorithm.
Further, the visual auxiliary mode for eliminating the ambiguity of the rotation matrix in the external parameter calibration of the telecentric system can be manual visual auxiliary or computer visual auxiliary. A method for eliminating the ambiguity of the rotation matrix without a displacement mechanism to additionally move the target or telecentric system.
Further, the correct calibration method for the spatial relative position relationship between the telecentric imaging system and the phase object comprises the following steps:
setting the coordinates in the phase object coordinate system { L } as L p＝[X L ,Y L ,Z L ] T ；
Normal vector of plane mirror under phase object coordinate system C n＝[ C n x , C n y , C n z ] T ；
The coordinates of the phase object with respect to the plane mirror virtual image coordinate system { L' } under the telecentric lens coordinate system { C } are C p'＝[X C '，Y C '] T ，
C p 'and p' are as follows L Relation between rotation matrix a and translation vector b of p
wherein ,I 2 is a unit matrix of order 2, C n 2×1 ＝[ C n x , C n y ] T l is the distance from the telecentric lens to the plane mirror, < >>For a rotation matrix of the phase object coordinate system to the telecentric lens coordinate system,>a translation vector from the phase object coordinate system to the telecentric lens coordinate system;
computing multiple setsSolution re-projection error
The two re-projection errors are equivalent and the smallest isBy means of the two sets of residual ambiguous solutions ∈>The spatial relative position relation between a plurality of telecentric imaging systems and a phase object under two groups of solutions is respectively carried outAnd drawing, namely visually comparing the position relation of the calibration result with the placement position relation of the actual equipment, and eliminating the ambiguity solution.
The invention also provides a multi-order phase deviation measurement based on a telecentric imaging system, comprising:
1) A phase object for projecting phase information;
2) The camera is used for collecting phase information displayed by the phase object;
3) The telecentric imaging system is used for providing constant magnification for imaging and realizing high-precision measurement;
4) The surface to be measured has the capability of reflecting phase information projected by a phase object to a telecentric imaging system;
5) The computer is respectively connected with the phase object and the camera, the computer controls the phase object and the camera,
and performing calculation to obtain a measurement result of the surface to be measured.
Further, the phase object may be a planar phase object, or a curved phase object with a surface shape.
Further, the code information projected by the phase object can be visible light information, infrared light information and ultraviolet light information.
From the above scheme of the invention, the invention has the remarkable advantages that:
1. the invention eliminates the ambiguity solution of the rotation matrix in the external parameter calibration of the telecentric system by a vision auxiliary mode. The method overcomes the defect that a telecentric imaging system needs to use a displacement mechanism to additionally move a target or a telecentric system to eliminate ambiguity resolution of a rotation matrix. Therefore, the calibration and construction efficiency of the method and the device is higher and flexible.
2. Compared with a monocular phase deflection measuring system, the invention adopts a monocular telecentric imaging system, and does not need prior knowledge of the surface shape to be measured; and the measurement can be completed under the condition of a single phase object, so that the time for taking pictures by the camera is saved. Compared with the existing non-telecentric imaging system, the low distortion and constant magnification characteristics of the telecentric imaging system can provide more accurate phase deviation measurement results.
Drawings
FIG. 1 is a schematic diagram of a principle of measuring multi-order phase deviation based on a telecentric imaging system;
FIG. 2 is a diagram of monocular geometry in a multi-ocular phase deflection measurement based on a telecentric imaging system according to the present invention;
FIG. 3 is a schematic diagram of an ambiguity resolution of a parametric rotation matrix of a telecentric imaging system according to the present invention;
FIG. 4 is a schematic diagram of a system for calibrating geometrical relationships using three phase object virtual image poses according to an embodiment of the present invention;
FIG. 5 is a graph showing the results of the geometric relationship between the liquid crystal display and the telecentric imaging system in case 1 of Table 1 according to the present invention;
FIG. 6 is a graph showing the results of the geometric relationship between the liquid crystal display and the telecentric imaging system in case 8 of Table 1 according to the present invention;
FIG. 7 is a schematic diagram of the geometrical relationship between a liquid crystal display and a telecentric imaging system according to an embodiment of the invention;
fig. 8 is a schematic diagram of a measurement result of a spherical surface shape error with a radius of curvature of 300mm to be measured according to an embodiment of the present invention.
In the figure: 1 is a first camera; 2 is a second camera; 3 is a first telecentric lens; 4 is a second telecentric lens; 5 is a liquid crystal display, 6 is a computer, and 7 is a surface to be measured.
Detailed Description
A multi-order phase deflection measuring device based on a telecentric imaging system is shown in fig. 1, and comprises a first camera 1, a second camera 2 and a computer 6 of a 24-inch white light plane liquid crystal display 5, wherein a first telecentric lens 3 and a second telecentric lens 4 are respectively fastened on the first camera 1 and the second camera 2 through standard C interfaces. After calibration, phase-shifting sinusoidal stripes are projected on the liquid crystal display 5, so that the first camera 1 and the second camera 2 are controlled to acquire the phase information of the sinusoidal stripes projected by the liquid crystal display 5, the phase information of the stripes is modulated by reflection of the surface 7 to be measured, and finally, the measurement result of the surface 7 to be measured is calculated. The surface 7 to be measured is a spherical surface with a curvature radius of 300 mm.
The method for measuring the multi-order phase deflection based on the telecentric imaging system comprises the following specific steps:
(1) Building a measuring device:
the computer 6 is connected to the first camera 1, the second camera 2, and the liquid crystal display 5. The first telecentric lens 3 and the second telecentric lens 4 are fastened on the first camera 1 and the second camera 2 through standard C interfaces to form a first telecentric imaging system and a second telecentric imaging system.
(2) Calibrating the built measuring device:
in a multi-order phase deviation measuring system based on a telecentric imaging system, the relationship between a single telecentric lens and a liquid crystal display is shown in fig. 2. Defining the coordinates in the liquid crystal display coordinate system { L }, as L p＝[X L ,Y L ,Z L ] T The method comprises the steps of carrying out a first treatment on the surface of the Normal vector of plane mirror under liquid crystal display coordinate system C n＝[ C n x , C n y , C n z ] T The method comprises the steps of carrying out a first treatment on the surface of the The coordinates of the liquid crystal display with respect to the plane mirror virtual image coordinate system { L' } under the telecentric lens coordinate system { C } are C p'＝[X C '，Y C '] T Because the depth information cannot be obtained due to the characteristic of constant magnification of the telecentric lens, attention is paid to C p' does not contain the ordinate Z C '. Then C p 'and p' are as follows L The relation between the rotation matrix A of p and the translation vector b is shown as formula (1)
wherein ,
in the formula (2), I 2 Is a unit matrix of order 2, C n 2×1 ＝[ C n x , C n y ] T l is the distance from the telecentric lens to the plane mirror,is a liquid crystal coordinate systemRotation matrix to telecentric lens coordinate system, +.>Is a translation vector from the liquid crystal coordinate system to the telecentric lens coordinate system.
The presence of the ambiguous solution of rotation matrix a in the telecentric imaging system as shown in fig. 3 results in a final calibration resultThere may also be ambiguous solutions. To resolve the ambiguity, the pose of the plane mirror is adjusted as shown in fig. 4, so that the liquid crystal display generates virtual images of multiple poses. In the embodiment, the pose of the plane mirror is adjusted three times, so that the Reprojection error of the Reprojection Err of the formula (3) is adopted to eliminate +.>Is a disambiguation of (a).
Table 1 shows the calibration parameter results in the rotation matrix calibration of the telecentric imaging system
As can be seen from table 1, there are still two cases of sequence number 1 and sequence number 8. In order to eliminate ambiguity between the two cases of the sequence number 1 and the sequence number 8, the geometric relationship between the liquid crystal display 5 and the first telecentric imaging system and the second telecentric imaging system under the two cases is drawn. The geometrical relationship between the liquid crystal display 5 and the first telecentric imaging system and the second telecentric imaging system in the actual binocular phase deviation measuring system based on the telecentric imaging system is shown in fig. 7. By observing, the situation that the serial number is 1 accords with the actual situation, so that the ambiguity corresponding to the serial number 8 can be eliminated.
Meanwhile, the surface shape of the screen is not taken into consideration.The screen surface of the liquid crystal display 5 is formed as S (x, y), where x, y represents the screen element position. S (x, y) may be represented by, but is not limited to, spline surfaces, polynomial surfaces, zernike surfaces. The present example uses spline surfaces to represent the screen surface shape. Screen_x, screen_y represents the dot spacing in the horizontal and vertical directions that optimizes the resulting Screen element. The camera can observe the coding information on the screen through the reflection of the standard plane mirror under a plurality of different poses, and can image two telecentric imaging systems (corresponding superscripts are C respectively) according to a formula (4) according to a beam adjustment method 1 ，C 2 ) In the horizontal and vertical directions x 、m y Radial distortion parameter k 1 、k 2 、k 3 And tangential distortion parameter p 1 、p 2 The rotation matrix and translation vector of the liquid crystal coordinate system to the two telecentric imaging systems are further optimized.
wherein C x represents the coordinate corresponding to the pixel i of the camera, and the position of the pixel corresponding to the photographed liquid crystal screen is
(3) Reconstructing the surface shape of the curved surface to be measured:
the liquid crystal display 5 displays phase-shift sine stripes, and the phase-shift sine stripes are reflected by the surface of the surface 7 to be detected and are incident to the first telecentric imaging system and the second telecentric imaging system. The phase-shifted sinusoidal fringes are shown in reference to Huntley J M, salidner h.temporal phase-unwrapping algorithm for automated interferogram analysis J Applied Optics 1993,32 (17): 3047-3052, and the absolute phase information of the two telecentric imaging systems is obtained using a time-phase unwrapping algorithm in the literature, to obtain the correspondence between the target surface pixels of both the first camera 1 and the second camera 2 and the liquid crystal display 5 pixels.
Curved surface reconstruction process to obtain pixel x in the first camera 1 in fig. 1 1 The corresponding height of the curved surface to be measured is taken as an example. By the aforementioned first telecentricity formationThe pixel x can be obtained as a result of calibration of the image system 1 Corresponding rays. Obtaining pixel x by absolute phase 1 Screen point S of ultraviolet light liquid crystal display 5 1 . At a certain height Z of the ray, according to the law of reflection, the first camera 1 pixel x 1 Height Z, corresponding screen point S 1 A curved first normal vector may be calculated. In addition, at this height, the corresponding pixel x can be obtained from the internal reference calibration result of the second telecentric imaging system 2 Obtaining a second camera 2 pixels x by absolute phase 2 Corresponding screen point S 2 . And then, according to the law of reflection, the second camera 2 pixels x 2 Height Z, corresponding screen point S 2 A curved second normal vector may be calculated. Judging whether the first normal vector of the curved surface and the second normal vector of the curved surface are coincident, if so, the point is the pixel x 1 The corresponding height of the surface 7 to be measured belongs to the surface shape of the surface 7 to be measured; if not, continuing to make the first camera 1 pixel x 1 The corresponding ray is calculated at other heights until a coincidence point of the two normals is found. And traversing all pixel points in all the first cameras 1 to finally obtain the surface shape of the surface 7 to be measured.
In the example of fig. 1, pixel x is known 1 Pixel x 1 Corresponding rays and pixels x 1 Corresponding screen point S 1 Searching rays for different heights Z i ,Z i+1 ,Z i+2 ... According to the internal reference calibration result of the second camera 2, different pixels x corresponding to the second camera 2 at different heights are obtained 2i ,x 2i+1 ,x 2i+2 .... Pixel x 2i Corresponding screen point S 2i Pixel x 2i+1 Corresponding screen point S 2i+1 Pixel x 2i+2 Corresponding screen point S 2i+2 ...... Can see the height Z i ,Z i+1 ,Z i+3 The curved surface first normal vector represented by the solid arrows of two colors is inconsistent with the curved surface second normal vector represented by the broken arrows, so that the two points are not pixels x 1 The corresponding height of the surface 7 to be measured; at a height Z i+2 The first normal vector of the curved surface is consistent with the second normal vector of the curved surface, namely the point is the pixel x 1 Corresponding meter to be measuredThe face 7 is high.
According to the above procedure, a measurement result of the surface 7 to be measured having a radius of curvature of 300mm was finally obtained, and the surface shape error thereof is shown in fig. 8.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that it will be apparent to those skilled in the art that variations and modifications can be made without departing from the scope of the invention.
Claims (9)
1. A multi-order phase deflection measuring method based on a telecentric imaging system, a phase object displays phase coding information, the phase object reflects to the imaging system through a surface to be measured, absolute phase information is obtained through calculation by a computing device, and the surface shape of the surface to be measured is reconstructed by utilizing the geometric relation among the imaging system, the phase object, the sagittal height and the normal vector of the object to be measured, and the method is characterized in that: the imaging system is more than two telecentric imaging systems, ambiguous solutions of a rotation matrix in the spatial relative position relation between the telecentric imaging systems and the phase object are eliminated through a vision auxiliary mode, and further correct calibration of the spatial relative position relation between the telecentric imaging systems and the phase object is completed, and the vision auxiliary mode is as follows: and respectively drawing the spatial relative position relations of a plurality of telecentric imaging systems containing the rotation matrix ambiguity solutions and the phase object, and visually comparing the position relation of the calibration result with the placement position relation of the actual equipment to remove the ambiguity solutions.
2. The telecentric imaging system-based multi-order phase deviation measurement method of claim 1, wherein: the number of the phase objects is more than or equal to one.
3. The telecentric imaging system-based multi-order phase deviation measurement method of claim 1, wherein: the phase information of the phase object comprises sine phase information, square wave phase information and triangular wave phase information.
4. The telecentric imaging system-based multi-order phase deviation measurement method of claim 1, wherein: the method for obtaining absolute phase information through resolving comprises a time phase unwrapping algorithm, a space phase unwrapping algorithm, a Fourier phase unwrapping algorithm and a least square phase unwrapping algorithm.
5. The telecentric imaging system-based multi-order phase deviation measurement method of claim 1, wherein: the visual assistance is artificial visual assistance or computer visual assistance.
6. The telecentric imaging system-based multi-order phase deviation measurement method of claim 1, wherein: the phase object is a plane phase object or a curved phase object with a surface shape.
7. The telecentric imaging system-based multi-order phase deviation measurement method of claim 1, wherein: the coded information projected by the phase object is visible light information or infrared light information or ultraviolet light information.
8. The telecentric imaging system-based multi-order phase deviation measurement method of claim 1, wherein: the correct calibration method of the space relative position relation between the telecentric imaging system and the phase object comprises the following steps:
setting the coordinates in the phase object coordinate system { L } as L p＝[X L ,Y L ,Z L ] T ；
Normal vector of plane mirror under phase object coordinate system C n＝[ C n x , C n y , C n z ] T ；
The coordinates of the phase object with respect to the plane mirror virtual image coordinate system { L' } under the telecentric lens coordinate system { C } are C p'＝[X C '，Y C '] T ，
C p 'and p' are as follows L Relation between rotation matrix a and translation vector b of p
wherein ,I 2 is a unit matrix of order 2, C n 2×1 ＝[ C n x , C n y ] T l is the distance from the telecentric lens to the plane mirror, < >>For a rotation matrix of the phase object coordinate system to the telecentric lens coordinate system,>a translation vector from the phase object coordinate system to the telecentric lens coordinate system;
computing multiple setsSolution re-projection error
The two re-projection errors are equivalent and the smallest isBy means of the two sets of residual ambiguous solutions ∈>And (3) drawing spatial relative position relations of the plurality of telecentric imaging systems and the phase object under the two groups of solutions respectively, and visually comparing the position relation of the calibration result with the placement position relation of the actual equipment to remove ambiguous solutions.
9. The telecentric imaging system-based multi-order phase deviation measurement device of claim 1, wherein: comprising the following steps:
a phase object for projecting phase information;
the camera is used for collecting phase information displayed by the phase object;
the multi-eye telecentric imaging system is used for providing constant magnification for imaging and realizing high-precision measurement;
the surface to be measured has the capability of reflecting phase information projected by a phase object to a telecentric imaging system;
the computer is connected with the phase object and the camera respectively, and the computer controls the phase object and the camera and calculates to obtain a measurement result of the surface to be measured.
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