CN105403173B - A kind of light field deviation art measuring system calibration mirror and its application process - Google Patents
A kind of light field deviation art measuring system calibration mirror and its application process Download PDFInfo
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Abstract
本发明属于光学测量领域,涉及一种光场偏折术测量系统标定镜及其应用方法。本标定镜用于标定光场偏折术系统的位姿关系,用于标定相机5和双层光平面调制器间3和4的关系以及双层光平面调制器3和4间的关系,包括一个标定镜其镜面由标准棋盘格镜面和反射镜面并联组成;即将棋盘格刻画在一个平面反射镜的一部分上,使其具有标定棋盘格和反射功能;所述标定方法分为普通相机标定法和光场相机标定法。所述标定方法只需一次拍摄即可完成所有位姿关系的标定,具有操作简单容易操作,精度高等优点。所述光场相机标定法填补了国内外关于光场偏折术测量系统光场相机模式下标定的空白,为光场偏折术测量系统测量高反射物体提供了基础。
The invention belongs to the field of optical measurement, and relates to a calibration mirror of an optical field deflection measurement system and an application method thereof. This calibration mirror is used to calibrate the pose relationship of the light field deflectometry system, and is used to calibrate the relationship between the camera 5 and the double-layer optical plane modulator 3 and 4 and the relationship between the double-layer optical plane modulator 3 and 4, including The mirror surface of a calibration mirror is composed of a standard checkerboard mirror and a reflection mirror in parallel; the checkerboard is described on a part of a plane mirror, so that it has the calibration checkerboard and reflection functions; the calibration method is divided into ordinary camera calibration and optical Field camera calibration method. The calibration method can complete the calibration of all pose relationships with only one shot, and has the advantages of simple and easy operation, high precision, and the like. The light field camera calibration method fills in the domestic and foreign gaps in the calibration of the light field camera mode of the light field deflection measurement system, and provides a basis for the light field deflection measurement system to measure highly reflective objects.
Description
技术领域technical field
本发明设计光学测量领域,涉及一种光场偏折术测量系统标定镜及其应用方法。The invention relates to the field of optical measurement, and relates to a calibration mirror of an optical field deflection measurement system and an application method thereof.
背景技术Background technique
光学三维形貌测量技术以其非接触、精度高、速度快等的优点在航空航天、汽车制造业、反向工程、计算机辅助设计、计算机辅助制造等领域得到了广泛的应用。结构光投影获取物体三维面形具有快速全场测量,测量精度较高等优点,已被广泛地应用于漫反射表面的三维测量。现在制造领域,针对镜面,近镜面等高反射表面的测量需求也很多,如光学制造领域的光学元件表面,镜面以及抛光磨具等,对这些高反射表面,常采用相位偏折术法进行测量。Optical three-dimensional shape measurement technology has been widely used in aerospace, automobile manufacturing, reverse engineering, computer-aided design, computer-aided manufacturing and other fields due to its advantages of non-contact, high precision and fast speed. The three-dimensional surface shape obtained by structured light projection has the advantages of fast full-field measurement and high measurement accuracy, and has been widely used in the three-dimensional measurement of diffuse reflective surfaces. Now in the field of manufacturing, there are many measurement requirements for highly reflective surfaces such as mirrors and near mirrors, such as the surface of optical components, mirrors, and polishing abrasives in the field of optical manufacturing. For these highly reflective surfaces, phase deflection is often used for measurement. .
由单投影设备和CCD摄像机组成的相位偏折术测量系统,具有求解法线不唯一的特点,测量系统有较大误差。目前国内外基于相位偏折术提出了多种实现对高反射物体表面的形貌测量的解决方案,但是都存在着一定的不足。在提出的光场偏折术测量系统中,解决了求解法线‘不唯一问题’,并且该系统在光场相机模式下对物体表面高度变化,以及由此引起的反射光线变化具有更高的响应特性,因此能获得关于待测物体表面更高的测量精度。在光场偏折术测量系统中,需要对双层平面调制器和相机的位姿关系以及双层平面调制器间的位姿关系进行标定,由于双层平面调制器不在相机的视野范围内,给标定带来了困难,目前国内外关于标定方法存在着明显不足。比如,Petz采用在标定镜上面贴控制点的方法,这些控制点需要通过摄影测量方法测得,很明显利用摄影测量测得控制点的坐标会增加测量时间和测量成本。而且目前来说,国内外针对光场偏折术测量系统的光场相机模式下的标定还没有出现。The phase deflection measurement system composed of a single projection device and a CCD camera has the characteristic that the normal line is not unique, and the measurement system has a large error. At present, various solutions based on phase deflection technique have been proposed to realize the topography measurement of the surface of highly reflective objects, but there are certain deficiencies in all of them. In the proposed light field deflectometry measurement system, the 'non-unique problem' of solving the normal is solved, and the system has a higher sensitivity to the change of the surface height of the object and the change of the reflected light caused by it in the light field camera mode. Response characteristics, so higher measurement accuracy can be obtained with respect to the surface of the object to be measured. In the deflectometry measurement system, it is necessary to calibrate the pose relationship between the double-layer planar modulator and the camera, and the pose relationship between the double-layer planar modulators. Since the double-layer planar modulator is not within the field of view of the camera, It brings difficulties to the calibration. At present, there are obvious deficiencies in the calibration methods at home and abroad. For example, Petz uses the method of sticking control points on the calibration mirror. These control points need to be measured by photogrammetry. Obviously, using photogrammetry to measure the coordinates of the control points will increase the measurement time and cost. And at present, the calibration of the light field camera mode for the light field deflectometry measurement system at home and abroad has not yet appeared.
发明内容Contents of the invention
针对上述问题,本发明的目的是提供一种光场偏折术测量系统标定镜及其应用方法,给出该标定镜的形状结构,以及应用该标定镜进行的标定方法,使得光场偏折术的感知系统和投射系统的位姿关系可通过一次拍摄来实现,为光场偏折术系统进行高精度测量高反射物体提供了基础。In view of the above problems, the object of the present invention is to provide a calibration mirror of light field deflection measurement system and its application method, provide the shape structure of the calibration mirror, and the calibration method using the calibration mirror, so that the light field deflection The pose relationship between the sensing system and the projection system of the technique can be realized by one shot, which provides a basis for the high-precision measurement of highly reflective objects by the deflectometry system.
为了实现上述目的,本发明采用如下技术方案:In order to achieve the above object, the present invention adopts the following technical solutions:
一种光场偏折术测量系统标定镜,用于标定光场偏折术系统的位姿关系,适用于相机和双层光平面调制器间的关系以及双层光平面调制器间的关系,它包括一个反射组由棋盘格镜面和平面反射镜镜面两部分并联组成;所述标准棋盘格刻画在一个平面反射镜镜面的一部分上,使其同时具有标定棋盘格和反射功能。A deflectometry measurement system calibration mirror, used to calibrate the pose relationship of the deflectometry system, suitable for the relationship between cameras and double-layer optical plane modulators and the relationship between double-layer optical plane modulators, It includes a reflective group consisting of a checkerboard mirror and a plane reflector in parallel; the standard checkerboard is carved on a part of the plane reflector, so that it has the functions of calibrating the checkerboard and reflection.
所述标定相机和双层光平面调制器的位姿关系,本发明针对相机和双层平面调制器位姿关系有两种情况,普通相机模式和光场相机模式,相应的标定算法分为普通相机标定算法和光场相机标定算法。The pose relationship between the calibration camera and the double-layer light plane modulator, the present invention has two situations for the pose relationship between the camera and the double-layer plane modulator, the normal camera mode and the light field camera mode, and the corresponding calibration algorithm is divided into common camera Calibration algorithm and light field camera calibration algorithm.
所述普通相机标定算法通过在双层平面调制器上分时显示与标定镜刻画棋盘格同尺寸的标准棋盘格,并由相机拍摄得到同时具有标定镜棋盘格和标定镜反射双层平面调制器显示的棋盘格图案,然后通过二维平面棋盘格标定法完成标定。标定后,经过参数转换,可以得到标定镜棋盘格和标定镜内棋盘格在相机坐标系下的位置姿态关系。由镜面镜像理论可知,实际双层平面调制器棋盘格和标定镜内反射棋盘格关于标定镜镜面对称,因此对标定镜内棋盘格关于标定镜进行镜像计算就可以得到相机和双层平面调制器和的位姿关系,当两层调制器相对相机的位姿关系计算完成后,经过参数变换就可以得到双层平面调制器间的位姿关系。由上述可知一次拍摄就可以得到相机和双层平面调制器的位姿关系以及双层平面调制器间的位姿关系。The common camera calibration algorithm displays a standard checkerboard of the same size as the checkerboard drawn by the calibration mirror on the double-layer planar modulator in time-sharing, and is captured by the camera to obtain a double-layer planar modulator with both the checkerboard grid of the calibration mirror and the reflection of the calibration mirror. The displayed checkerboard pattern is then calibrated by a two-dimensional planar checkerboard calibration method. After calibration, after parameter conversion, the position and attitude relationship of the checkerboard in the calibration mirror and the checkerboard in the calibration mirror under the camera coordinate system can be obtained. According to the theory of mirror mirroring, the actual double-layer planar modulator checkerboard and the internal reflection checkerboard of the calibration mirror are mirror-symmetrical with respect to the calibration mirror, so the camera and the double-layer planar modulator can be obtained by performing mirror calculation on the checkerboard in the calibration mirror with respect to the calibration mirror After the calculation of the pose relationship between the two-layer modulators relative to the camera is completed, the pose relationship between the two-layer planar modulators can be obtained through parameter transformation. From the above, it can be known that the pose relationship between the camera and the double-layer planar modulator and the pose relationship between the two-layer planar modulators can be obtained in one shot.
所述光场相机标定算法,首先需要对光场相机参数进行标定。这里的光场相机参数标定主要是指标定微透镜的中心位置,在之后的标定实验中主要用到提取光场微透镜中心像素组成的子孔径图像。根据光场成像模型,当三维空间物体经光场相机主透镜在微透镜阵列面上清晰成像,即微透镜阵列上每个位置仅仅来源于物面上同一点的光线。经微透镜的空间复用,CCD或CMOS传感器上像素是来自于此点不同方向的光线信息。确定像素与微透镜的对应关系转化为确定像素与空间物面点的对应关系。采用多频相移的方法确定物面点和像素的关系,通过光场相机拍摄多频相移条纹图像,计算其平均相移条纹图像亮度,由于微透镜的渐晕效应导致微透镜中心位置亮度较高,而边缘处较弱,因此可以通过峰值检测算法确定微透镜的中心像素。由于光场相机制造完成后其物理参数是确定的,因此对微透镜中心参数标定一次即可。标定光场相机和双层平面调制器的位姿关系采用光场相机拍摄标定镜和标定镜内反射调制器上显示的具有与标定镜同尺寸的棋盘格图案,提取每幅光场图像的子孔径图像,子孔径图像的像素坐标用其微透镜中心下的像素坐标代替,最后采用二维平面棋盘格标定法进行标定。相机与双层平面调制器的位姿关系通过棋标定镜内棋盘格关于标定镜面镜像获得,通过参数转换进而可以得到双层平面调制器间的位姿关系。The light field camera calibration algorithm first needs to calibrate the parameters of the light field camera. The light field camera parameter calibration here mainly refers to the center position of the microlens. In the subsequent calibration experiments, it is mainly used to extract the sub-aperture image composed of the central pixels of the light field microlens. According to the light field imaging model, when a three-dimensional object is clearly imaged on the surface of the microlens array through the main lens of the light field camera, that is, each position on the microlens array only comes from the same point of light on the object surface. Through the spatial multiplexing of the microlens, the pixels on the CCD or CMOS sensor are light information from different directions at this point. Determining the corresponding relationship between pixels and microlenses is transformed into determining the corresponding relationship between pixels and spatial object plane points. The method of multi-frequency phase shift is used to determine the relationship between the object surface point and the pixel, and the multi-frequency phase-shifted fringe image is taken by the light field camera, and the average brightness of the phase-shifted fringe image is calculated. Due to the vignetting effect of the micro-lens, the brightness of the center of the micro-lens is caused. Higher, and weaker at the edges, so the central pixel of the microlens can be determined by a peak detection algorithm. Since the physical parameters of the light field camera are determined after the manufacture is completed, it is only necessary to calibrate the central parameters of the microlens once. Calibrate the pose relationship between the light field camera and the double-layer planar modulator Use the light field camera to shoot the calibration mirror and the checkerboard pattern displayed on the internal reflection modulator of the calibration mirror with the same size as the calibration mirror, and extract the subset of each light field image For the aperture image, the pixel coordinates of the sub-aperture image are replaced by the pixel coordinates under the center of the microlens, and finally the two-dimensional plane checkerboard calibration method is used for calibration. The pose relationship between the camera and the double-layer planar modulator is obtained by mirroring the checkerboard in the calibration mirror with respect to the calibration mirror, and the pose relationship between the double-layer planar modulators can be obtained through parameter conversion.
本发明由于采取以上技术方案,相较上文提到的标定方法具有以下优点:Compared with the calibration method mentioned above, the present invention has the following advantages due to the adoption of the above technical scheme:
本发明操作简单,用户只需将标定镜放在相机视场内,且相机能从标定镜镜面反射处捕捉到双层光平面调制器投射的棋盘格图像,经过一次拍摄利用二维棋盘格标定法就可完成标定。The invention is easy to operate, the user only needs to place the calibration mirror in the field of view of the camera, and the camera can capture the checkerboard image projected by the double-layer optical plane modulator from the mirror reflection of the calibration mirror, and use the two-dimensional checkerboard calibration after one shot Calibration can be completed.
本发明更容易集成到测量环境中,提高了标定效率,并能同时适用于光场偏折术系统的两种测量模式。填补了国内外标定光场偏折术系统光场相机模式下的位姿关系的空白,给光场偏折术测量系统测量高反射物体提供了基础。The invention is easier to integrate into the measurement environment, improves the calibration efficiency, and can be applicable to two measurement modes of the deflectometry system at the same time. It fills the blank of the pose relationship in the light field camera mode of the calibration light field deflectometry system at home and abroad, and provides a basis for the light field deflection measurement system to measure highly reflective objects.
附图说明Description of drawings
下面结合说明书附图以及实施方式对本发明作进一步详细的说明:The present invention will be described in further detail below in conjunction with the accompanying drawings and embodiments:
图1为本发明的标定镜示意图Fig. 1 is the calibration mirror schematic diagram of the present invention
图2为本发明的相机(普通相机和光场相机)标定示意图Fig. 2 is a schematic diagram of calibration of cameras (common camera and light field camera) of the present invention
图3为本发明的普通相机标定算法流程图Fig. 3 is the flow chart of common camera calibration algorithm of the present invention
图4为本发明的标定光场相机微透镜中心示意图Fig. 4 is a schematic diagram of the microlens center of the calibration light field camera of the present invention
图5为本发明的光场相机标定算法流程图Fig. 5 is a flow chart of the light field camera calibration algorithm of the present invention
具体实施方式Detailed ways
以下优选实施例结合附图对本发明作进一步的说明。The following preferred embodiments will further illustrate the present invention in conjunction with the accompanying drawings.
实施例一:Embodiment one:
参见图1,一种光场偏折术测量系统标定镜,用于标定光场偏折术系统的位姿关系,包括一个反射镜,其特征在于:所述反射镜的镜面由棋盘格镜面1和反射镜面2两部分相并联组成,即将棋盘格刻画在一个平面反射镜镜面的一部分上,使其具有标定棋盘格和反射功能;适用于标定相机和双层光平面调制器间的关系以及双层光平面调制器间的关系。Referring to Fig. 1, a kind of deflectometry measuring system calibration mirror is used for calibrating the pose relationship of the deflectometry system, including a reflector, and it is characterized in that: the mirror surface of the reflector is composed of checkerboard mirror surface 1 It is composed of two parts in parallel with the mirror surface 2, that is, the checkerboard is depicted on a part of the mirror surface of a plane mirror, so that it has the function of calibrating the chessboard and reflection; it is suitable for calibrating the relationship between the camera and the double-layer optical plane modulator and the double-layer optical plane modulator. The relationship between layer light planar modulators.
实施例二:本实施例与实施例一相同,特别之处是:参见图2~图5。Embodiment 2: This embodiment is the same as Embodiment 1, and the special feature is: refer to Fig. 2 to Fig. 5 .
参见图2,所述标定相机和双层光平面调制器的位姿关系,本发明针对相机5和双层平面调制器(3,4) 的位姿关系有两种情况,普通相机模式和光场相机模式,相应的标定算法分为普通相机标定算法和光场相机标定算法。相机5可同时表示普通相机和光场相机。Referring to Fig. 2, the pose relationship between the calibration camera and the double-layer planar modulator, the present invention has two situations for the pose relation between the camera 5 and the double-layer planar modulator (3, 4), ordinary camera mode and light field Camera mode, the corresponding calibration algorithm is divided into common camera calibration algorithm and light field camera calibration algorithm. Camera 5 may represent both a normal camera and a light field camera.
参见图3,所述普通相机标定算法通过在双层平面调制器(3,4)上分时显示与棋盘格镜面1刻画棋盘格同尺寸的标准棋盘格,并由相机拍摄得到同时具有棋盘格镜面1和反射镜面2反射双层平面调制器显示的棋盘格图案,然后通过二维平面棋盘格标定法完成标定。标定后,经过参数转换,可以得到棋盘格镜面1和棋盘格镜面内棋盘格在相机坐标系下的位置姿态关系;由镜面镜像理论可知,实际双层平面调制器 (3,4)棋盘格和反射镜面2关于棋盘格镜面1对称,因此对反射镜面2内棋盘格关于棋盘格镜面1进行镜像计算就可以得到相机5和双层平面调制器(3,4)的位姿关系;当双层光平面调制器(3,4)相对相机 5的位姿关系计算完成后,经过参数变换就可以得到双层平面调制器(3,4)间的位姿关系。由上述可知一次拍摄就可以得到相机和双层平面调制器的位姿关系以及双层平面调制器间的位姿关系。Referring to Fig. 3, the common camera calibration algorithm displays a standard checkerboard with the same size as the checkerboard mirror 1 on the double-layer planar modulator (3, 4) in time-sharing, and is photographed by the camera and has a checkerboard at the same time. Mirror 1 and reflecting mirror 2 reflect the checkerboard pattern displayed by the double-layer planar modulator, and then the calibration is completed by a two-dimensional planar checkerboard calibration method. After calibration, after parameter conversion, the position and attitude relationship of the checkerboard mirror 1 and the checkerboard in the checkerboard mirror under the camera coordinate system can be obtained; from the mirror image theory, the actual two-layer planar modulator (3,4) checkerboard and Reflecting mirror 2 is symmetrical with respect to checkerboard mirror 1, so the pose relationship between camera 5 and double-layer planar modulator (3, 4) can be obtained by mirroring the checkerboard in mirror 2 with respect to checkerboard mirror 1; when the double-layer After the calculation of the pose relationship between the optical planar modulators (3, 4) and the camera 5 is completed, the pose relation between the two-layer planar modulators (3, 4) can be obtained through parameter transformation. From the above, it can be known that the pose relationship between the camera and the double-layer planar modulator and the pose relationship between the two-layer planar modulators can be obtained in one shot.
参见图4和5,所述光场相机标定算法,首先需要对光场相机参数进行标定。这里的光场相机参数标定主要是指标定微透镜的中心位置,在之后的标定实验中主要用到提取光场微透镜中心像素组成的子孔径图像。通过光场相机拍摄显示器7显示的多频相移条纹图像,计算其平均相移条纹图像亮度,通过峰值检测算法确定微透镜的中心像素。标定光场相机和双层平面调制器(3,4)的位姿关系采用光场相机拍摄棋盘格镜面1和反射镜面2内反射调制器上显示的具有与标定镜同尺寸的棋盘格图案,提取每幅光场图像的子孔径图像,子孔径图像的像素坐标用其微透镜中心下的像素坐标代替,最后采用二维平面棋盘格标定法进行标定。相机与双层平面调制器的位姿关系通过棋盘格镜面1内棋盘格关于反射镜面2镜像获得,进而可以得到双层平面调制器间的位姿关系。Referring to FIGS. 4 and 5 , the light field camera calibration algorithm first needs to calibrate the parameters of the light field camera. The light field camera parameter calibration here mainly refers to the center position of the microlens. In the subsequent calibration experiments, it is mainly used to extract the sub-aperture image composed of the central pixels of the light field microlens. The multi-frequency phase-shift fringe image displayed on the display 7 is captured by a light field camera, the average brightness of the phase-shift fringe image is calculated, and the central pixel of the microlens is determined by a peak detection algorithm. Calibrate the pose relationship between the light field camera and the double-layer planar modulator (3, 4) Use the light field camera to shoot the checkerboard pattern with the same size as the calibration mirror displayed on the internal reflection modulator of the checkerboard mirror surface 1 and mirror surface 2, The sub-aperture image of each light field image is extracted, and the pixel coordinates of the sub-aperture image are replaced by the pixel coordinates under the center of the microlens. Finally, the two-dimensional plane checkerboard calibration method is used for calibration. The pose relationship between the camera and the double-layer planar modulator is obtained by mirroring the checkerboard in the checkerboard mirror surface 1 with respect to the mirror surface 2, and then the pose relationship between the double-layer planar modulators can be obtained.
工作过程和原理如下:The working process and principle are as follows:
参见图3,普通相机标定时,分为:拍摄图片、标定、镜像、参数转换。需要拍摄多幅不同姿态下的标定镜6棋盘格图片,棋盘格镜面1以及反射镜面2图片必须在相机的视场内,根据二维棋盘格标定方法,获取相机5内外参数。根据得到的相机内外参数,可以计算出棋盘格在相机坐标系下的位置姿态关系,并且由反射镜面2内棋盘格关于棋盘格镜面1做镜像,可以确定双层平面调制器(3,4)在相机坐标系下的位置姿态关系。根据中求解得到的双层光平面调制器在相机坐标系下的位置姿态关系,根据参数转换,就可以确定双层光平面调制器间的位置关系。Referring to Figure 3, when calibrating an ordinary camera, it is divided into: taking pictures, calibrating, mirroring, and parameter conversion. It is necessary to take multiple checkerboard pictures of the calibration mirror 6 in different postures. The pictures of the checkerboard mirror surface 1 and the reflection mirror surface 2 must be within the field of view of the camera. According to the two-dimensional checkerboard calibration method, the internal and external parameters of the camera 5 are obtained. According to the obtained internal and external parameters of the camera, the position and attitude relationship of the checkerboard in the camera coordinate system can be calculated, and the mirror image of the checkerboard in mirror 2 with respect to checkerboard mirror 1 can be determined to determine the double-layer planar modulator (3,4) The position and attitude relationship in the camera coordinate system. According to the position and attitude relationship of the double-layer optical plane modulator in the camera coordinate system obtained by solving in , and according to the parameter conversion, the positional relationship between the double-layer optical plane modulators can be determined.
参见图4,标定光场相机微透镜中心,显示器上显示多频相移条纹图像,光场相机进行拍摄,计算拍摄图像的平均亮度,然后根据峰值检测方法进行检测,峰值点就是微透镜中心点。Refer to Figure 4, calibrate the center of the microlens of the light field camera, and display a multi-frequency phase shift fringe image on the display. The light field camera shoots, calculates the average brightness of the captured image, and then detects it according to the peak detection method. The peak point is the center point of the microlens .
参见图5,光场相机标定时,分为:拍摄图片、提取子孔径图片、标定、镜像、参数转换。需要拍摄多幅不同姿态下的标定镜6棋盘格图片,棋盘格镜面1以及反射镜面2内棋盘格图片必须在相机的视场内,提取微透镜中心点的像素组成标定镜子孔径图像,保留子孔径图像不同像素点所对应的微透镜中心的像素坐标,根据二维棋盘格标定法确定光场相机内外参数,并且计算出棋盘格镜面1内棋盘格和反射镜面2内棋盘格在相机坐标系下的坐标信息,由反射镜面2内棋盘格关于棋盘格镜面1做镜像,可以确定双层平面调制器(3,4)在相机坐标系下的位置姿态关系。根据中求解得到的双层光平面调制器(3,4)在相机5坐标系下的位置姿态关系,根据参数转换,就可以确定双层光平面调制器(3,4)间的位置关系。Referring to Figure 5, when calibrating a light field camera, it is divided into: taking pictures, extracting sub-aperture pictures, calibrating, mirroring, and parameter conversion. It is necessary to take multiple checkerboard pictures of the calibration mirror 6 in different postures. The checkerboard pictures in the checkerboard mirror surface 1 and the mirror surface 2 must be within the field of view of the camera. The pixels at the center point of the microlens are extracted to form the calibration mirror aperture image, and the The pixel coordinates of the center of the microlens corresponding to the different pixels of the aperture image, determine the internal and external parameters of the light field camera according to the two-dimensional checkerboard calibration method, and calculate the checkerboard in the checkerboard mirror surface 1 and the mirror surface 2 in the camera coordinate system The following coordinate information is mirrored by the checkerboard in mirror surface 2 with respect to checkerboard mirror surface 1, and the position and posture relationship of the double-layer planar modulator (3, 4) in the camera coordinate system can be determined. According to the position and attitude relationship of the double-layer optical plane modulators (3, 4) in the camera 5 coordinate system obtained from the solution in , and according to the parameter conversion, the positional relationship between the double-layer optical plane modulators (3, 4) can be determined.
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