Geometric pose and optical axis error synchronous calibration method for reflective phase deflectometry system

Abstract

The present application belongs to the field of optical detection, and particularly relates to a geometric pose and optical axis error synchronous calibration method of a reflection type phase deflectometry system, which takes the pose of a plane mirror as a reference, establishes redundant geometric constraints in multiple poses through mirror reflection, and jointly solves the geometric external parameters of the system; meanwhile, a reverse ray tracing model and a normal integral model are simultaneously constructed in the calibration stage, and combined with the actual measurement surface shape data of an interferometer, the system optical axis error field is explicitly stripped out, and the decoupling separation of the system structure error and the surface shape error is realized. The method not only greatly simplifies the system building process and avoids the dependence on high-precision mechanical auxiliary devices, but also effectively improves the overall detection precision and low-frequency error control capability of the reflection type phase deflectometry system by simultaneously modeling and compensating the system optical axis error in the calibration stage, thereby providing an engineering adaptable technical foundation for high-precision freeform optical detection.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of optical detection, and particularly relates to a geometric pose and optical axis error synchronous calibration method of a reflection type phase deflectometry system. BACKGROUND

[0002] In high-end optical detection and precision machining systems, the surface accuracy of optical elements such as mirrors has a direct impact on the imaging quality, wavefront control capability and energy focusing efficiency of the system. Phase measuring deflectometry (PMD) has become a key technology for in-situ detection of mirrors and rapid evaluation of free-form surfaces due to its high resolution, non-contact, strong environmental adaptability and other advantages. In particular, monocular reflection type PMD systems are more suitable for engineering deployment due to their simple structure and ease of integration.

[0003] However, the detection accuracy of such systems is highly dependent on the geometric parameters of the system (particularly the spatial parameters between the camera and the screen) and the optical path alignment accuracy. In actual applications, due to idealized assumptions of the imaging model (such as the pinhole model approximation), non-uniform brightness distribution of the screen light source, internal and external parameter errors in Zhang Zhengyou calibration, and installation errors of system components, the system still has optical axis deviation after calibration, i.e. the actual light propagation path deviates from the designed optical axis direction. This optical axis error will significantly affect the accuracy of reverse ray tracing and accumulate in the normal vector integration reconstruction process, causing low-frequency surface distortion, ultimately leading to the mixing of the detection results and the real mirror shape, and seriously affecting the measurement accuracy and system stability.

[0004] Existing technologies mostly focus on achieving high-precision geometric pose calibration between the camera and the screen through high-precision auxiliary devices (such as laser trackers, pinhole diaphragms, mechanical pose platforms, etc.), but most of them fail to establish a system modeling and extraction mechanism for optical axis error, especially lacking an integrated method for simultaneously solving the system external parameters and optical axis error in the calibration stage. Therefore, there is an urgent need for an integrated calibration scheme that can simultaneously achieve high-precision calibration of system geometric external parameters and explicit extraction of optical axis error to improve the overall detection accuracy and engineering applicability of PMD systems. SUMMARY

[0005] Therefore, the present application aims to provide a geometric pose and optical axis error synchronous calibration method of a reflection type phase deflectometry system to solve the problems of dependence on external equipment, low system pose calibration accuracy, mixing of system optical axis error and low-frequency surface error, and inability to strip the system optical axis error in the calibration of monocular reflection type phase deflectometry systems.

[0006] To achieve the above-mentioned purposes, the technical solution of the present application is as follows:

[0007] A geometric pose and optical axis error synchronous calibration method of a reflective phase deflectometry system, comprising the following steps:

[0008] S1: a monocular reflective phase deflectometry system is built, which comprises a camera, a display screen, a plane mirror and a standard chessboard calibration board; the coded pattern emitted by the display screen is reflected to the camera through the plane mirror;

[0009] S2: the camera is calibrated for internal parameters by using the standard chessboard calibration board, and a world coordinate system is established on the surface of the plane mirror;

[0010] S3: the plane mirror is transformed into at least three different spatial poses, and the mirror surface at each pose of the plane mirror is imaged and collected; based on the collected mirror surface information, a spatial projection model of the mirror camera corresponding to each pose of the plane mirror is constructed by combining the Householder reflection transformation model, and an overdetermined equation set is established through the spatial geometric constraint between image points, and the overdetermined equation set is solved to obtain the relative position relationship between the camera and the display screen, so as to realize the calibration of the geometric external parameters of the system; wherein the mirror camera refers to a virtual camera formed by the reflection of the camera through the plane mirror, and the image point refers to a pixel point in the mirror image of the coded pattern captured by the camera after being reflected by the plane mirror;

[0011] S4: based on the calibrated camera internal parameters and the system geometric external parameters, a reverse ray tracing model is constructed, the normal vector of each sampling point on the mirror surface of the plane mirror is determined through ray tracing, and the initial surface shape of the mirror surface of the plane mirror is reconstructed through integral slope;

[0012] S5: the initial surface shape of the reconstructed mirror surface of the plane mirror is differentially compared with the real surface shape of the mirror surface of the plane mirror measured by the interferometer, the system optical axis error is extracted, and the decoupling and separation of the system optical axis error and the surface shape error are realized.

[0013] Further, in step S3, the spatial projection model of the mirror camera corresponding to each pose of the plane mirror is:

[0014] ;

[0015] In the formula, is the distance from the mirror surface of the plane mirror to the origin of the world coordinate system; is the normal vector of the plane mirror; is the Householder matrix; is the translation vector of the mirror surface of the plane mirror; is the internal parameter matrix of the camera; and are the rotation matrix and the translation vector between the camera and the display screen; is the three-dimensional coordinates of the feature points on the coded pattern in the world coordinate system; These are the pixel coordinates of the image points; Scale factor; This is the matrix transpose symbol.

[0016] Furthermore, in step S3, the construction of the overdetermined system of equations is specifically as follows:

[0017] For each pose of the plane mirror, a linear constraint equation is established based on the mapping relationship between feature points on the coded pattern and image points:

[0018] ;

[0019] In the formula, and Let the rotation matrix and translation vector be the relationship between the camera and the display screen. , The rotation matrix and translation vector of the mirror camera corresponding to the first mirror image captured by the camera; , The rotation matrix and translation vector of the mirror camera corresponding to the second mirror image captured by the camera; This is the matrix transpose symbol;

[0020] Combining the linear constraint equations for all poses, we form a system of linear equations:

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] In the formula, The coefficient matrix, It is a 3×3 identity matrix. For the first coded pattern The three-dimensional coordinates of each feature point in the world coordinate system; for The negative 3×3 submatrix; The first time the camera captured The rotation matrix of the mirror camera corresponding to the mirror image; for and The 3×3 submatrix resulting from multiplication and negation; The first time the camera captured The rotation matrix of the mirror camera corresponding to the mirror image; is the transpose of the rotation matrix . is an unknown parameter vector, the unknown parameter vector comprising a rotation matrix and a translation vector between the camera and the display screen. are the 1st column, 2nd column and 3rd column of the rotation matrix , respectively. is a constant term matrix of the linear equation set.

[0027] Further, in step S3, the solution of the overdetermined equation set is specifically:

[0028] the linear equation set is solved by singular value decomposition method , to obtain the rotation matrix and the translation vector between the camera and the display screen, so as to realize the calibration of the system geometric extrinsic parameters.

[0029] Further, after obtaining the system geometric extrinsic parameters by the singular value decomposition method, there is further an optimization step:

[0030] a re-projection error function with the minimum re-projection error as the target is constructed to optimize the initial system geometric extrinsic parameters, and the re-projection error function is:

[0031] .

[0032] In the formula, is the re-projection error; , is the number of feature points in each mirror image used to establish the constraint; , is the number of poses of the plane mirror; is the pixel coordinate of the j th feature point in the i th pose of the plane mirror captured by the camera; is the predicted value of ; is the rotation matrix between the camera and the display screen, is the translation vector between the camera and the display screen; is the normal vector of the mirror in the j th pose of the plane mirror; is the distance from the mirror to the world coordinate origin in the j th pose of the plane mirror.

[0033] Further, in step S4, the construction of the inverse ray tracing model is specifically:

[0034] The camera optical center is regarded as a point light source, and the camera coordinate system and the image plane coordinate system of the display screen are unified to a world coordinate system established by the mirror surface of the plane mirror;

[0035] For each sampling point on the mirror surface of the plane mirror, a vector from the camera optical center to the sampling point is defined as an incident light vector, and a vector from the sampling point to a pixel point on the display screen is defined as an outgoing light vector;

[0036] According to the incident light vector and the outgoing light vector, a reverse light path is reconstructed in space to obtain a reverse light ray tracing model.

[0037] Further, according to the reflection law, a mirror surface normal vector of each sampling point on the mirror surface of the plane mirror is calculated from the incident light vector and the outgoing light vector, and the calculation formula is as follows:

[0038] ;

[0039] In the formula, is a normalized incident light vector; is a normalized outgoing light vector; is a normalized mirror surface normal vector.

[0040] Further, in step S4, the reconstruction of the initial surface shape of the mirror surface of the plane mirror is specifically:

[0041] According to the mirror surface normal vector of each sampling point on the mirror surface of the plane mirror, the slope of the mirror surface of the plane mirror is calculated, and the initial surface shape of the mirror surface of the plane mirror is recovered by integrating the slope;

[0042] The slope of the mirror surface of the plane mirror includes the gradient of the mirror surface of the plane mirror in the x direction and the gradient of the mirror surface of the plane mirror in the y direction :

[0043] ;

[0044] In the formula, is a three-dimensional coordinate of a feature point on the encoding pattern in the world coordinate system; is a normalized incident light vector in the x direction; is a normalized incident light vector in the y direction.

[0045] Further, in step S5, the calculation formula of the system optical axis error is as follows:

[0046] ;

[0047] In the formula, to reconstruct the initial surface shape of the mirror surface of the plane mirror; to measure the real surface shape of the plane mirror by an interferometer.

[0048] Further, for the last pose transformation of the plane mirror, it is placed flat on the position of the mirror to be measured.

[0049] Compared with the prior art, the present application can achieve the following beneficial effects:

[0050] 1. The present application uses a mirror multi-pose geometric constraint model to calibrate the geometric external parameters of the system (the relative pose between the camera and the display screen) while explicitly extracting and quantifying the system optical axis error, solving the problem of the difficulty in separating the two and the error aliasing in the traditional method. The optical axis error is modeled and compensated in the calibration stage, effectively suppressing the low-frequency error accumulation in the subsequent surface reconstruction, and significantly improving the overall detection accuracy of the phase deflecting system.

[0051] 2. Only one plane mirror and a standard checkerboard calibration plate are needed, without relying on high-cost auxiliary equipment such as a laser tracker and a precision displacement stage, greatly reducing the system construction complexity and cost. The calibration process is simple and efficient, suitable for engineering sites, field environments and automated detection platforms, and has good engineering adaptability and promotional value.

[0052] 3. By constructing an overdetermined equation set through multi-pose mirror geometric constraints, and combining singular value decomposition and nonlinear optimization, the influence of image noise and pose disturbance on the calibration results is effectively suppressed, and the stability and repeatability of the calibration process are improved. The method has strong fault tolerance and compensation ability for non-ideal factors such as system installation error and imaging model approximation.

[0053] 4. By comparing the reconstructed surface shape of the plane mirror with the measured surface shape by the interferometer in a differential manner, the system optical axis error is explicitly separated, forming a closed-loop process of "calibration-reconstruction-compensation". The extracted system optical axis error field can be used as a system inherent error for real-time compensation in subsequent actual mirror measurement, improving the accuracy and consistency of surface reconstruction.

[0054] 5. This method not only performs excellently in plane mirror calibration, but also provides a reliable calibration basis for in-situ detection of complex optical elements such as free-form surfaces and aspheric surfaces. Through active extraction and compensation of the system optical axis error, the system performs outstandingly in low-frequency error control, and is suitable for optical systems with extremely high requirements for low-frequency surface accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0055] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of the present application and its description are used to explain the present application and are not intended to limit the present application. In the drawings:

[0056] Figure 1 A flowchart of a geometric pose and optical axis error synchronous calibration method of a reflective phase deflectometry system according to an embodiment of the present invention;

[0057] Figure 2 A schematic diagram of a principle of a monocular reflective phase deflectometry system according to an embodiment of the present invention;

[0058] Figure 3 A schematic diagram of a principle of a pinhole imaging model according to an embodiment of the present invention;

[0059] Figure 4 A schematic diagram of a principle of reflection imaging of a plane mirror according to an embodiment of the present invention;

[0060] Figure 5 A schematic diagram of a system geometric extrinsic pose calibration model according to an embodiment of the present invention;

[0061] Figure 6 A schematic diagram of a reverse ray tracing model according to an embodiment of the present invention;

[0062] Figure 7 A schematic diagram of an initial surface shape of a plane mirror area integral slope reconstruction according to an embodiment of the present invention;

[0063] Figure 8 A schematic diagram of a real surface shape of a plane mirror surface measured by an interferometer according to an embodiment of the present invention;

[0064] Figure 9 A schematic diagram of a surface shape of a system optical axis error according to an embodiment of the present invention.

[0065] Explanation of reference signs:

[0066] Display screen 1, coded pattern 11, mirror image 12, display screen image plane 13, plane mirror 2, plane mirror surface 21, camera 3, camera image plane 31, plane where camera optical center is located 32, mirror image camera 33, camera optical center 34, display screen image plane coordinate system 4, world coordinate system 5, camera coordinate system 6. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention will be further described in detail below in combination with the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and do not constitute a limitation on the present invention.

[0068] It should be noted that the embodiments in the present invention and the features in the embodiments can be combined with each other without conflict.

[0069] In the description of the present application, it should be understood that the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second" and the like are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined with "first", "second" and the like can be explicitly or implicitly included one or more. In the description of the present application, unless otherwise specified, the meaning of "a plurality of" is two or more.

[0070] In the description of the present application, it should be noted that unless otherwise specified and limited, the terms "assembly", "connection", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, and it can be connected inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0071] The present application will be described in detail below Figures 1-9 with reference to the drawings and in conjunction with the embodiments.

[0072] Optical axis error is a key factor limiting the measurement accuracy of the reflective phase deflectometry system, mainly due to the aliasing of low-frequency information caused by the system optical axis error and the imaging model approximation, resulting in the difficulty in effectively distinguishing the system optical axis error and the measured surface shape. Therefore, the present application proposes a calibration method that fuses a pinhole imaging model and mirror image multi-pose geometric constraints, which explicitly extracts the system optical axis error while calibrating the geometric external parameters between the camera and the display screen, and realizes the decoupling and separation of the error in the calibration stage.

[0073] As Figure 1 shown, the geometric pose and optical axis error synchronous calibration method of the reflective phase deflectometry system provided by the embodiments of the present application comprises the following steps:

[0074] S1: build a monocular reflective phase deflectometry system, which includes a camera, a display screen, a plane mirror and a standard chessboard calibration plate.

[0075] The built monocular reflection phase deflection system is shown in Figure 2. The display screen 1 is used to display a regularized coded pattern, such as a chessboard, a dot array, and the like. The coded pattern emitted by the display screen 1 is reflected by the plane mirror 2 to the camera 3. Under the reflection of the plane mirror 2, the coded pattern forms a virtual image, i.e. a mirror image of the coded pattern, which is captured by the camera 3 to form a mirror image image.

[0076] S2: The camera is calibrated by using a standard chessboard calibration plate, and a world coordinate system is established on the surface of the plane mirror.

[0077] Through a plurality of standard chessboard calibration plates, a plurality of groups of chessboard images in different poses are formed, and the intrinsic parameters of the camera 3 are calibrated by using Zhang Zhengyou calibration method.

[0078] The camera 3 is equivalent to a pinhole imaging model, which is one of the camera models, simple and universal, and the principle is shown in Figure 3. Figure 3 In the pinhole imaging model, three coordinate systems are defined, i.e. a camera coordinate system 31, an image coordinate system 32, and a pixel coordinate system 33. .

[0079] The conversion relationship between the image coordinate system 32 and the pixel coordinate system 33 can be expressed as homogeneous coordinates:

[0080] (1);

[0081] In formula (1), , which are the focal lengths of the camera 3 in the x and y directions, i.e. the intrinsic parameters of the camera 3, , which are obtained by using Zhang's calibration method.

[0082] Since Zhang Zhengyou calibration method is prior art, the specific calibration method of the camera 3 intrinsic parameters will not be described herein.

[0083] ​​​​S3: transform the plane mirror to at least three different spatial poses, image and collect the mirror surface under each pose of the plane mirror; based on the collected mirror surface information and a Householder reflection transformation model, construct a spatial projection model of a mirror camera corresponding to each pose of the plane mirror, and through spatial geometric constraints between image points, establish an over-determined equation set, solve the over-determined equation set, obtain the relative position relationship between the camera and the display screen, and realize calibration of system geometric external parameters; wherein the mirror camera refers to a virtual camera formed by reflection of the camera through the plane mirror, and the image point refers to a pixel point in a mirror image of the coded pattern captured by the camera after reflection of the coded pattern through the plane mirror.

[0084] The mirror surface information collected by the camera 3 is a mirror pattern of the coded pattern. In the calibration stage of system geometric external parameters, the plane mirror 2 is controlled to be transformed in space in not less than three non-coplanar poses (the last time the plane mirror 2 is placed flat at the to-be-measured mirror position), to form coded patterns in multiple poses.

[0085] The reflection imaging principle of the plane mirror 2 is as shown in Figure 4 The coded pattern 11 emitted by the display screen 1 is reflected by the plane mirror 2 to form a mirror coded pattern, and a mirror image 12 containing mirror surface pose and surface shape information is collected by the camera 3. In order to simplify geometric modeling, the equivalent concept of mirror camera 33 is introduced, the reflection process is converted into the direct projection of the mirror camera 33 to the coded pattern 11, so as to solve the system geometric external parameters (relative pose between the camera and the display screen) and the mirror error through spatial geometric constraints.

[0086] Based on the Householder transformation model, the spatial projection model of the mirror camera 33 corresponding to each pose of the plane mirror 2 is constructed:

[0087] (2);

[0088] In formula (2), is the distance from the mirror surface of the plane mirror 2 to the origin of the world coordinate system; is the normal vector of the plane mirror 2; is the Householder matrix; is the translation vector of the mirror surface of the plane mirror 2; is the intrinsic matrix of the camera 3; and are the rotation matrix and the translation vector between the camera 3 and the display screen 1; is the three-dimensional coordinate of the feature point on the coded pattern in the world coordinate system; is the pixel coordinate of the image point; is the scale factor; is the matrix transpose symbol.

[0089] Figure 4 In, That is, the world coordinate system established on the mirror surface of the plane mirror 2, the pose of the mirror camera 33 is 、 , formula (2) can be converted to:

[0090] (3);

[0091] Let , the nonlinear equation is linearized to obtain:

[0092] (4);

[0093] In formula (4), the rotation matrix and the translation vector between the camera and the display screen are unknown quantities that need to be solved, that is, 15 unknowns need to be solved. The mirror image multi-pose is constrained and the constraint relationship between multiple mirror images is established to obtain more constraint conditions. The constraint equation between any two mirror images can be established as follows:

[0094] (5);

[0095] In formula (5), and are the rotation matrix and translation vector between the camera 3 and the display screen 1; 、 are the rotation matrix and translation vector of the mirror camera 33 corresponding to the first mirror image captured by the camera 3; 、 are the rotation matrix and translation vector of the mirror camera 33 corresponding to the second mirror image captured by the camera 3; is the matrix transpose symbol.

[0096] If considering mirror images captured by different plane mirror poses, the th mirror image can obtain constraint equations as shown in formula (5):

[0097] (6);

[0098] In formula (6), the value of i is 1, 2, …, ; is equations, when , 18 equation groups can be constructed.

[0099] Use M mirror images to represent the unknown. , and The constraint situation is written in the following form:

[0100] (7).

[0101] Equation (3) is used to express the fixed relationship between the poses of the mirror camera 33 and the real camera 3 (expressed by the reflection matrix). Starting from equation (3), the geometric constraint that the camera projections before and after reflection must be consistent is written into an equation to derive a standard linear equation system, which is equation (7).

[0102] In equation (7), The coefficient matrix (constructed from known quantities) is expressed as follows:

[0103] (8);

[0104] In equation (8), It is a 3×3 identity matrix. For the first coded pattern The three-dimensional coordinates of each feature point in the world coordinate system; for The negative 3×3 submatrix; The first time the camera captured The rotation matrix of the mirror camera corresponding to the mirror image; for and The 3×3 submatrix resulting from multiplication and negation; The first time the camera captured The rotation matrix of the mirror camera corresponding to the mirror image; Rotation matrix The transpose of .

[0105] In mathematics, it is a large matrix, and each row of the large matrix corresponds to a constraint equation. These constraint equations come from the symmetry relationship of the plane mirror surface and the projection geometry of the camera. That is, the geometric constraints are encoded into an algebraic problem. It can be understood as translating all the geometric relationships reflected by the plane mirror into a coefficient matrix in linear algebra.

[0106] The unknown parameter vector includes the rotation matrix between camera 3 and display screen 1. Translation vector This refers to the system's geometric extrinsic parameters. The expression is:

[0107] (9);

[0108] In formula (9), is a 3x3 rotation matrix, , are the first column, the second column and the third column of the rotation matrix , and are a 3x1 vector.

[0109] is a constant term matrix of the linear equation group, and its expression is:

[0110] (10);

[0111] In formula (10), is the translation vector of the mirror camera corresponding to the m-th mirror image collected by the camera.

[0112] By substituting formula (8), formula (9) and formula (10) into formula (7), the linear equation group can be solved to obtain the rotation matrix and the translation matrix between the camera 3 and the display screen 1. Since the collected mirror image contains noise errors, the rotation matrix does not satisfy the orthogonality. Singular value decomposition needs to be performed on the rotation matrix , that is:

[0113] (11);

[0114] In formula (11), is the right singular matrix in singular value decomposition, and By performing singular value decomposition on the original matrix , a system geometric parameter pose calibration model suitable for an auxiliary-free positioning device of a monocular reflection phase deflection system can be established, as shown in Figure 5 After the camera internal and system geometric parameters are calibrated, the camera coordinate system 6 and the display screen image plane coordinate system 4 are mapped to the world coordinate system 5, thereby establishing a unified model basis for subsequent light tracing.

[0115] After the system geometric parameters are obtained by singular value decomposition, a re-projection error function with the minimum re-projection error as the target is constructed, and the initial system geometric parameters are nonlinearly optimized, thereby significantly improving the stability and robustness of the system geometric parameter calibration.

[0116] The re-projection error function is:

[0117] (12); ​

[0118] in formula (12), is a re-projection error; , is the number of feature points used to establish constraints in each mirror image; , is the number of poses of the plane mirror; is the pixel coordinate of the i-th feature point in the j-th pose of the plane mirror captured by the camera; j is the pixel coordinate of the i-th feature point in the j-th pose of the plane mirror captured by the camera; i is the pixel coordinate of the i-th feature point in the j-th pose of the plane mirror captured by the camera; is the predicted value of ; is the normal vector of the mirror in the j-th pose of the plane mirror; j is the normal vector of the mirror in the j-th pose of the plane mirror; is the distance from the mirror in the j-th pose of the plane mirror to the origin of the world coordinate system. j S4: based on the calibrated camera intrinsic parameters and system geometric extrinsic parameters, an inverse ray tracing model is constructed, the normal vectors of each sampling point on the mirror of the plane mirror are determined by ray tracing, and the initial surface shape of the mirror of the plane mirror is reconstructed by integrating the slope.

[0119] After completing the high-precision calibration of the camera intrinsic parameters and the system geometric extrinsic parameters, the present application further constructs an inverse ray tracing model based on a pinhole imaging model. The inverse ray tracing model takes the camera optical center as a point light source and the display screen as an imaging surface. According to the law of reflection, the normal vector of the plane mirror can be determined by the incident light vector and the reflected light vector. That is, by single ray tracing for each pixel point in the field of view and solving, the normal vector set of each sampling point on the mirror of the plane mirror can be obtained, and then the slope is calculated, and the initial surface shape of the mirror of the plane mirror is reconstructed by integrating the slope.

[0120] As shown in FIG. 4, the inverse ray tracing model takes the camera optical center 34 as an ideal point light source, combines the camera intrinsic parameters and the system geometric extrinsic parameters obtained by calibration, and unifies the camera optical center 34, the plane mirror 21 and the display screen image 13 into the world coordinate system to establish the spatial geometric mapping relationship of the light path. According to the phase-pixel correspondence relationship established by the phase unwrapping algorithm, the sampling point coordinates on the plane mirror 21 corresponding to each pixel point of the mirror image can be determined. In the world coordinate system, it is assumed that the spatial vector connecting from the camera optical center 34 (i.e. the center of pinhole imaging) to the sampling point on the plane mirror 21 is the incident light vector, and the vector from the sampling point on the plane mirror 21 to the corresponding pixel point on the display screen is defined as the outgoing light vector. By constructing the incident light vector and the outgoing light vector, the spatial reconstruction of the inverse light path is realized, and the inverse ray tracing model is obtained.

[0121] Figure 6

[0122] ​​The ray tracing model is based on the reflection law, and the linear expression of the reflection law in three-dimensional space can be expressed as:

[0123] (13);

[0124] In formula (13), is a normalized incident light vector; is a normalized outgoing light vector; is a normalized mirror normal vector, wherein can be expressed as N is a mirror normal vector, is a normalized mirror normal vector of , that is, the third number of is not -1.

[0125] (14).

[0126] According to formula (14), the normalized mirror normal vector is calculated.

[0127] The reconstruction of the initial surface shape of the plane mirror mirror is specifically:

[0128] According to the mirror normal vector of each sampling point on the plane mirror mirror, the slope of the plane mirror mirror is calculated, and the initial surface shape of the plane mirror mirror is recovered by integrating the slope.

[0129] The slope of the plane mirror mirror includes the gradient of the plane mirror mirror in the x direction and the gradient of the plane mirror mirror in the y direction:

[0130] (15);

[0131] In formula (15), is the three-dimensional coordinate of the feature point on the encoding pattern in the world coordinate system; is the x-direction component of the normalized incident light vector ; and is the y-direction component of the normalized incident light vector .

[0132] After the gradient of the plane mirror mirror in the x direction and the gradient of the plane mirror mirror in the y direction are solved, the initial surface shape of the plane mirror mirror is reconstructed by integrating the gradient and the gradient , so as to realize the reconstruction of the three-dimensional topography of the plane mirror mirror.

[0133] S5: Difference between the initial surface shape of the reconstructed plane mirror and the real surface shape of the plane mirror measured by the interferometer, extract the system optical axis error, realize the decoupling separation of the system optical axis error and the surface error.

[0134] Due to the existence of various non-ideal factors in the monocular reflective phase deflectometry system, such as pinhole assumption in pinhole imaging model, nonlinear effect of display screen brightness response, model fitting error in system pose calibration and world coordinate system construction process. Ultimately lead to the deviation of the system optical axis direction from the theoretical optical path. These errors are mixed with the real mirror shape in the reconstruction of the initial surface shape of the plane mirror, which is difficult to distinguish and seriously affects the measurement accuracy. In order to realize high-precision stripping and modeling, a systematic error separation model needs to be further constructed. The error separation model believes that the mirror shape recovered by reverse ray tracing and normal integral In fact, it is composed of two components:

[0135] (16);

[0136] In formula (16), is the initial surface shape of the reconstructed plane mirror, and the surface shape distribution is as shown in Figure 7 ; is the real surface shape of the plane mirror, which can be obtained by interferometer, with nanometer level precision, and the surface shape distribution is as shown in Figure 8 ; represents the system optical axis error, including the projection superposition of the above various error sources in the measurement results.

[0137] The real surface shape of the plane mirror is used to difference the initial surface shape of the reconstructed plane mirror , and the system optical axis error can be accurately solved:

[0138] (17).

[0139] The calculated system optical axis error is as shown in Figure 9 This step not only realizes the explicit extraction of the system optical axis error, but also provides data support for subsequent system optical axis error compensation and surface shape result correction. The extracted can be used as a unified compensation model in the detection process, and applied to the actual free-form surface mirror measurement, which significantly improves the surface shape reconstruction accuracy of the detection system.

[0140] It should be understood that the various forms of flow shown above can be re-ordered, added to, or have steps deleted, for example. The steps recited in the present disclosure can be performed in parallel, in series, or in a different order, as long as the desired results of the technology recited in the present disclosure are achieved, and are not limited herein.

[0141] The specific embodiments discussed hereinabove are illustrative of various aspects of the present application. Alterations, modifications, combinations, sub-combinations, and the like are intended to be included within the scope of the present application. Accordingly, although specific embodiments have been described herein, these are not intended to limit the scope of the present application, as claimed.

Claims

1. A method for simultaneous calibration of geometric pose and optical axis error of a reflective phase deflectrometre, characterized in that, The method comprises the following steps: S1: a monocular reflective phase deflectometry system is built, the monocular reflective phase deflectometry system comprising a camera, a display screen, a plane mirror and a standard chessboard calibration plate; an encoded pattern emitted by the display screen is reflected to the camera by the plane mirror; S2: the camera is calibrated by using the standard chessboard calibration plate, and a world coordinate system is established on the surface of the plane mirror; S3: the plane mirror is transformed into at least three different spatial poses, and the mirror surface at each pose of the plane mirror is imaged and collected; based on the collected mirror surface information and a Householder reflection transformation model, a spatial projection model of a mirror camera corresponding to each pose of the plane mirror is constructed, and an overdetermined equation set is established through spatial geometric constraints between image points, the overdetermined equation set is solved, the relative position relationship between the camera and the display screen is obtained, and the calibration of system geometric parameters is realized; wherein the mirror camera refers to a virtual camera formed by reflection of the camera through the plane mirror, and the image point refers to a pixel point in a mirror image of the camera captured, the encoded pattern reflected by the plane mirror; in step S3, the construction of the overdetermined equation set is specifically as follows: For each pose of the plane mirror, a linear constraint equation is established according to the mapping relationship between the feature points on the encoded pattern and the image points: ； In the formula, and is a rotation matrix and a translation vector between the camera and the display screen; , is a rotation matrix and a translation vector of the mirror camera corresponding to the first mirror image captured by the camera; , is a rotation matrix and a translation vector of the mirror camera corresponding to the second mirror image captured by the camera; is a matrix transpose symbol; All the linear constraint equations of different poses are combined to form a linear equation set: ； ； ； ； ； In the formula, is a coefficient matrix, is a 3x3 unit matrix, is a three-dimensional coordinate of the i-th feature point on the encoding pattern in the world coordinate system; is a 3x3 matrix; is a 3x3 matrix; is a 3x3 matrix after taking negative; is a rotation matrix of a mirror camera corresponding to the i-th mirror image collected by the camera; is a 3x3 matrix; is a 3x3 matrix; is a 3x3 matrix after multiplying and taking negative; is a rotation matrix of a mirror camera corresponding to the i-th mirror image collected by the camera; is a 3x3 matrix; is a 3x3 matrix; is a transpose of the rotation matrix ; is an unknown parameter vector, the unknown parameter vector including a rotation matrix between the camera and the display screen and a translation vector , are the 1st column, the 2nd column and the 3rd column of the rotation matrix respectively; is a constant term matrix of the linear equation group; S4: based on the calibrated camera intrinsic parameters and system geometric parameters, a reverse ray tracing model is constructed, the normal vector of each sampling point on the plane mirror surface is determined through ray tracing, and the initial surface shape of the plane mirror is reconstructed through integral slope; S5: the initial surface shape of the reconstructed plane mirror is differentially combined with the actual surface shape of the plane mirror measured by the interferometer, the system optical axis error is extracted, and the system optical axis error and the surface shape error are decoupled and separated.

2. The geometric pose and optical axis error synchronous calibration method of the reflective phase deflectrometry system according to claim 1, characterized in that, In step S3, the spatial projection model of the mirror camera corresponding to each pose of the plane mirror is as follows: ； wherein is the distance of the mirror plane to the origin of the world coordinate system; is the normal vector of the mirror plane; is the Householder matrix; is the translation vector of the mirror plane; is the intrinsic matrix of the camera; and is the rotation matrix and translation vector between the camera and the display screen; is the three-dimensional coordinate of the feature point on the coded pattern in the world coordinate system; is the pixel coordinate of the image point; is the scale factor; is the matrix transpose symbol.

3. The method of claim 1, wherein, In step S3, the solution of the overdetermined equation set is specifically as follows: Solving linear equations by singular value decomposition , obtaining the rotation matrix and translation vector between the camera and the display screen, and calibrating the system geometric parameters.

4. The geometric pose and optical axis error synchronous calibration method of the reflective phase deflectrometry system according to claim 3, characterized in that, After the system geometric parameters are obtained by the singular value decomposition method, the following optimization step is further included: A re-projection error function with the minimum re-projection error as the target is constructed, and the initial system geometric parameters are optimized, and the re-projection error function is as follows: ； In the formula, This is due to reprojection error; , The number of feature points used to establish constraints in each mirrored image; , This represents the number of orientations of the plane mirror; The first plane mirror for the camera to collect data j In the first posture, the first i The pixel coordinates of each feature point; for The predicted value; This is a rotation matrix between the camera and the display screen. This is the translation vector between the camera and the display screen; It is the first plane mirror j The normal vector of the mirror surface under each orientation; It is the first plane mirror j The distance from the mirror surface to the origin of the world coordinate system in each orientation.

5. The method of claim 1, wherein In step S4, the construction of the reverse ray tracing model is specifically as follows: The camera optical center is taken as a point light source, and the camera coordinate system and the image plane coordinate system of the display screen are unified to the world coordinate system established by the plane mirror surface; For each sampling point on the plane mirror surface, a vector from the camera optical center to the sampling point is defined as an incident light vector, and a vector from the sampling point to a pixel point on the display screen is defined as an outgoing light vector; According to the incident light vector and the outgoing light vector, the reverse ray path is reconstructed in space to obtain the reverse ray tracing model.

6. The geometric pose and optical axis error synchronous calibration method of the reflective phase deflectrometry system according to claim 5, characterized in that, According to the reflection law, the mirror normal vector of each sampling point on the plane mirror surface is calculated from the incident light vector and the outgoing light vector, and the calculation formula is as follows: ； wherein is the normalized incident light vector; is the normalized exit light vector; is the normalized mirror normal vector.

7. The method of claim 1, wherein, In step S4, the reconstruction of the initial surface shape of the plane mirror is specifically as follows: According to the mirror normal vector of each sampling point on the mirror surface of the plane mirror, the slope of the mirror surface of the plane mirror is calculated and the initial surface shape of the mirror surface of the plane mirror is recovered by integrating the slope; The slope of the mirror of the flat mirror includes a gradient of the mirror of the flat mirror in the x direction and a gradient in the y direction : ； wherein is the three-dimensional coordinate of the feature point on the coded pattern in the world coordinate system; is the normalized incident light vector is the component in the x-direction; is the normalized incident light vector is the component in the y-direction.

8. The method of claim 1, wherein, In step S5, the system optical axis error is calculated by the following formula: ； wherein is the initial surface shape of the reconstructed plane mirror surface; is the real surface shape of the plane mirror as measured by the interferometer.

9. The method of claim 1, wherein, For the last time of the pose transformation of the plane mirror, the plane mirror is placed on the position of the mirror to be measured.

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