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CN117146736B - A method for measuring double-surface shape of optical element - Google Patents

A method for measuring double-surface shape of optical element Download PDF

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CN117146736B
CN117146736B CN202311137381.3A CN202311137381A CN117146736B CN 117146736 B CN117146736 B CN 117146736B CN 202311137381 A CN202311137381 A CN 202311137381A CN 117146736 B CN117146736 B CN 117146736B
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optical element
surface shape
double
reflection
fringe
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CN117146736A (en
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刘磊
张效栋
李泽骁
王冬雪
李卓桐
张宏舜
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Tianjin University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/24Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/25Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
    • G01B11/254Projection of a pattern, viewing through a pattern, e.g. moiré
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/24Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/2433Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures for measuring outlines by shadow casting

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  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Length Measuring Devices By Optical Means (AREA)

Abstract

The invention relates to the field of optical element surface shape measurement, in particular to a method for measuring the surface shape of a double surface of an optical element, which comprises the following steps: establishing a basic measuring device of the surface shape of the double surfaces of the optical element; calibrating the basic measuring device to obtain a measuring device of the surface shape of the double surfaces of the optical element; obtaining reflection stripe data of an optical element to be measured by using the measuring device; and obtaining a measurement result of the surface shape of the two surfaces of the optical element according to the reflection stripe data of the optical element to be measured, and completing calculation by shooting a single image by a camera. Finally, the method is very sensitive to the surface shape of the double surfaces of the large-size optical element because the method is calculated based on the reflection law, and can reach the measurement accuracy of micron and even submicron.

Description

一种光学元件双表面面形测量方法A method for measuring double-surface shape of optical element

技术领域Technical Field

本发明涉及光学元件面形测量领域,具体涉及一种光学元件双表面面形测量方法。The invention relates to the field of optical element surface shape measurement, and in particular to a method for measuring the double-surface surface shape of an optical element.

背景技术Background Art

光学元件,被广泛应用于军事,航空航天,光学和汽车的各个领域,如透镜,谷歌眼镜,汽车挡风玻璃等。通常利用光学元件的反射、折射效果来对光路进行一定的调整,以达成光线的方向可控性。一般来说这些光学器件都需要保证一定的面形精度以避免在使用过程中出现质量问题,例如飞行员头盔和谷歌眼镜所使用的抬头显示器(HUD)若存在较大的面形偏差,容易造成显示画面和文字的扭曲和模糊。如果带HUD的汽车玻璃面形质量较差,外界景物的图像容易产生畸变,透光度下降,影响驾驶安全性。因此,为了保证光学元件的光学性能和成像质量,需要对上下表面均进行高精度三维测量。Optical components are widely used in various fields of military, aerospace, optics and automobiles, such as lenses, Google Glass, car windshields, etc. The reflection and refraction effects of optical components are usually used to adjust the light path to achieve the controllability of the direction of the light. Generally speaking, these optical devices need to ensure a certain surface accuracy to avoid quality problems during use. For example, if there is a large surface deviation in the head-up display (HUD) used by pilot helmets and Google Glasses, it is easy to cause distortion and blurring of the displayed image and text. If the surface quality of the car glass with HUD is poor, the image of the external scene is easily distorted, the transmittance decreases, and driving safety is affected. Therefore, in order to ensure the optical performance and imaging quality of optical components, high-precision three-dimensional measurement of both the upper and lower surfaces is required.

一般来说,仅仅通过制造精度无法满足光学元件表面的精度需求,因此在制造后都需要进行测量以避免不合格品投入使用。然而,光学元件属于透明件,对透明件的测量存在诸多难点。首先,对于透明件来说,传统反射式光学测量方法往往无法获取足够强度的反射光信息,如线结构光[1],光栅结构光[2]等,都无法用于进行透明件表面测量;其次,透明件表面还存在一定的反射特性,容易对于透射式光学测量方法产生强光干扰,出现过曝等情况。同时,为提高检测效率,往往需要进行快速测量,因此接触式测量方法,如三坐标测量机,轮廓仪等测量方法都无法满足速度需求。光学元件除了测量难度大外,还存在较高测量精度的需求,进一步给其轮廓测量带来了挑战。Generally speaking, manufacturing accuracy alone cannot meet the accuracy requirements of the optical component surface, so measurements are required after manufacturing to prevent defective products from being put into use. However, optical components are transparent parts, and there are many difficulties in measuring transparent parts. First, for transparent parts, traditional reflective optical measurement methods often cannot obtain reflected light information of sufficient intensity, such as line structured light[1], grating structured light[2], etc., and cannot be used for transparent surface measurement; secondly, the surface of transparent parts also has certain reflective characteristics, which can easily cause strong light interference to the transmission optical measurement method, resulting in overexposure. At the same time, in order to improve detection efficiency, fast measurement is often required, so contact measurement methods, such as three-coordinate measuring machines, profilometers and other measurement methods, cannot meet the speed requirements. In addition to the difficulty of measuring optical components, there is also a need for high measurement accuracy, which further brings challenges to their profile measurement.

中国专利申请CN201980049399.3公布了一种基于线结构光的玻璃表面测量方法,使用紫外线结构光扫描实现玻璃表面测量。但是,首先,这种方法仅能够测量光学元件的上表面,其次,这种方法由于基于线结构光扫描,所以测量精度受位移台的制约,而大行程位移台的引入必然会增加成本,同时,线结构光扫描需要一定的时间,难以满足高速测量的需求,最后,线结构光是一种基于光学三角测量原理的方法,难以实现很高的光学级测量精度。Chinese patent application CN201980049399.3 discloses a glass surface measurement method based on line structured light, which uses ultraviolet structured light scanning to achieve glass surface measurement. However, first of all, this method can only measure the upper surface of optical components. Secondly, since this method is based on line structured light scanning, the measurement accuracy is restricted by the displacement stage, and the introduction of a large-stroke displacement stage will inevitably increase the cost. At the same time, line structured light scanning takes a certain amount of time and is difficult to meet the needs of high-speed measurement. Finally, line structured light is a method based on the principle of optical triangulation, and it is difficult to achieve high optical-level measurement accuracy.

中国专利申请CN202010795714.1公布了一种基于条纹偏折的反射面三维面形测量方法,具体通过条纹显示模块显示正弦条纹,通过相机拍摄该条纹在待测镜面反射后产生的变形条纹,利用条纹相位和高度的关系进行镜面物体快速高精度三维测量。但是,这种方法只能用于反射面上表面的测量,对于透明的光学元件来说,上下表面的反射像会混合在一起,导致测量失败。Chinese patent application CN202010795714.1 discloses a method for measuring the three-dimensional shape of a reflective surface based on fringe deflection. Specifically, a fringe display module displays sinusoidal fringes, and a camera is used to capture the deformed fringes generated by the fringes after reflection on the mirror surface to be measured. The relationship between the fringe phase and the height is used to perform fast and high-precision three-dimensional measurement of the mirror object. However, this method can only be used to measure the upper and lower surfaces of the reflective surface. For transparent optical elements, the reflected images of the upper and lower surfaces will be mixed together, resulting in measurement failure.

综合以上现有公知技术,亟需一种能够应用于光学元件上下表面面形的快速高精度测量方法。In view of the above existing known technologies, there is an urgent need for a fast and high-precision measurement method that can be applied to the upper and lower surfaces of optical components.

发明内容Summary of the invention

针对现有技术的不足,本发明提供了一种光学元件双表面面形测量方法,通过标定后的图像采集装置,准确获取光学元件的面形测量结果。In view of the deficiencies in the prior art, the present invention provides a method for measuring the double-surface shape of an optical element, which accurately obtains the shape measurement result of the optical element through a calibrated image acquisition device.

为实现上述目的,本发明提供了一种光学元件双表面面形测量方法,包括:To achieve the above object, the present invention provides a method for measuring the double-surface shape of an optical element, comprising:

建立光学元件双表面面形的基础测量装置;Establish a basic measurement device for the double-surface shape of optical elements;

对所述基础测量装置进行标定处理得到光学元件双表面面形的测量装置;Calibrate the basic measuring device to obtain a measuring device for the double-surface shape of an optical element;

利用所述测量装置获取待测量光学元件的反射条纹数据;Acquiring the reflection fringe data of the optical element to be measured by using the measuring device;

根据所述待测量光学元件的反射条纹数据得到光学元件双表面面形测量结果。The double-surface shape measurement result of the optical element is obtained according to the reflection fringe data of the optical element to be measured.

优选的,所述建立光学元件双表面面形的基础测量装置包括:Preferably, the basic measuring device for establishing the double-surface profile of an optical element comprises:

在待测量光学元件的两侧分别相对设置相机;Cameras are arranged opposite to each other on both sides of the optical element to be measured;

利用离散条纹图像显示装置分别与相机连接。The discrete fringe image display devices are connected to the cameras respectively.

优选的,对所述基础测量装置进行标定处理得到光学元件双表面面形的测量装置包括:Preferably, the measuring device for calibrating the basic measuring device to obtain the double-surface shape of the optical element comprises:

在标准平面镜上设置反光标记点作为反光标记平面镜;A reflective marking point is set on a standard plane mirror as a reflective marking plane mirror;

利用所述基础测量装置采集反光标记平面镜的多角度反射条纹图像;The basic measuring device is used to collect multi-angle reflection stripe images of the reflective marking plane mirror;

利用所述多角度反射条纹图像基于双目视觉原理计算反光标记点的坐标;Utilizing the multi-angle reflection fringe image to calculate the coordinates of the reflective marking point based on the binocular vision principle;

利用所述反光标记点的坐标获取对应面形方程;Obtaining the corresponding surface equation using the coordinates of the reflective marking points;

根据所述面形方程对基础测量装置完成标定处理得到光学元件双表面面形的测量装置。The basic measuring device is calibrated according to the surface shape equation to obtain a measuring device for the double-surface surface shape of an optical element.

进一步的,利用所述多角度反射条纹图像基于双目视觉原理计算反光标记点的坐标的计算式如下:Furthermore, the coordinates of the reflective marking points are calculated using the multi-angle reflected fringe image based on the binocular vision principle as follows:

其中,Ai、Bi、Ci、Di为标准平面镜上设置反光标记点的坐标,ni为第i组标准平面镜的法向量,di为第i组标准平面镜与坐标原点之间的距离,h为反光标记点的厚度。Among them, Ai , Bi , Ci , Di are the coordinates of the reflective marking points set on the standard plane mirror, ni is the normal vector of the i-th group of standard plane mirrors, di is the distance between the i-th group of standard plane mirrors and the coordinate origin, and h is the thickness of the reflective marking point.

优选的,根据所述待测量光学元件的反射条纹数据得到光学元件双表面面形测量结果包括:Preferably, obtaining the double-surface shape measurement result of the optical element according to the reflection fringe data of the optical element to be measured includes:

利用所述待测量光学元件的反射条纹数据进行分离处理得到反射条纹分离数据;Using the reflection fringe data of the optical element to be measured to perform separation processing to obtain reflection fringe separation data;

获取所述反射条纹分离数据的拓扑关系;Acquire the topological relationship of the reflection fringe separation data;

根据所述拓扑关系进行相位解算处理得到反射条纹数据的解算结果;Performing phase resolution processing according to the topological relationship to obtain a resolution result of the reflection fringe data;

利用所述反射条纹数据的解算结果得到光学元件双表面面形测量结果。The calculation result of the reflection fringe data is used to obtain the double-surface shape measurement result of the optical element.

进一步的,获取所述反射条纹分离数据的拓扑关系包括:Furthermore, obtaining the topological relationship of the reflection fringe separation data includes:

利用所述基础测量装置的相机对应特征点作为基准点;Using the camera corresponding feature points of the basic measurement device as reference points;

基于所述基准点根据单轮廓方向进行搜索分别得到反射条纹图像的上表面与离散反射条纹的拓扑关系和反射条纹图像的下表面与离散反射条纹的拓扑关系;Based on the reference point, searching in a single contour direction respectively obtains a topological relationship between an upper surface of the reflection fringe image and discrete reflection fringe and a topological relationship between a lower surface of the reflection fringe image and discrete reflection fringe;

利用所述反射条纹图像的上表面与离散反射条纹的拓扑关系和反射条纹图像的下表面与离散反射条纹的拓扑关系作为反射条纹分离数据的拓扑关系。The topological relationship between the upper surface of the reflection fringe image and the discrete reflection fringe and the topological relationship between the lower surface of the reflection fringe image and the discrete reflection fringe are used as the topological relationship of the reflection fringe separation data.

进一步的,利用所述反射条纹数据的解算结果得到光学元件双表面面形测量结果包括:Furthermore, obtaining the double-surface shape measurement result of the optical element using the solution result of the reflection fringe data includes:

根据所述反射条纹数据的解算结果基于反射定律得到反射条纹图像的上表面与下表面法线方向向量;Obtaining the normal direction vectors of the upper surface and the lower surface of the reflection fringe image based on the reflection law according to the solution result of the reflection fringe data;

利用所述上表面与下表面法线方向向量基于数值积分进行面形重建处理得到光学元件双表面面形测量结果。The surface shape measurement results of the double surfaces of the optical element are obtained by performing surface shape reconstruction processing based on numerical integration using the normal direction vectors of the upper surface and the lower surface.

进一步的,利用所述上表面与下表面法线方向向量基于数值积分进行面形重建处理得到光学元件双表面面形测量结果的计算式如下:Furthermore, the calculation formula for obtaining the double-surface surface measurement result of the optical element by performing surface reconstruction processing based on numerical integration using the normal direction vectors of the upper surface and the lower surface is as follows:

其中,(Px,Py,Pz)为上表面与下表面法线方向向量,z为光学元件双表面面形测量结果。Wherein, ( Px , Py , Pz ) are the normal direction vectors of the upper surface and the lower surface, and z is the double-surface shape measurement result of the optical element.

与最接近的现有技术相比,本发明具有的有益效果:Compared with the closest prior art, the present invention has the following beneficial effects:

本方法基于离散条纹图作为特征,因此上下表面反射后的点可以基于图像处理实现区分,是一种有效的光学元件上下表面测量方法。其次,本方法由相机拍摄单幅图像即可完成计算,与现有所有方法相比都具备显著的检测速度优势。最后,由于本方法基于反射定律进行计算,对大尺寸光学元件双表面面形非常敏感,能够达到微米甚至亚微米级的测量精度。This method is based on discrete fringe patterns as features, so the points after reflection on the upper and lower surfaces can be distinguished based on image processing, which is an effective method for measuring the upper and lower surfaces of optical components. Secondly, this method can complete the calculation by taking a single image with a camera, which has a significant detection speed advantage over all existing methods. Finally, since this method is based on the law of reflection for calculation, it is very sensitive to the double-surface shape of large-size optical components and can achieve micron or even sub-micron measurement accuracy.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1是本发明提供的一种光学元件双表面面形测量方法的流程图;FIG1 is a flow chart of a method for measuring the double-surface shape of an optical element provided by the present invention;

图2是本发明提供的一种光学元件双表面面形测量方法的基础测量装置示意图;FIG2 is a schematic diagram of a basic measuring device of a method for measuring the double-surface shape of an optical element provided by the present invention;

图3是本发明提供的一种光学元件双表面面形测量方法的离散条纹图像的成像原理示意图;3 is a schematic diagram of the imaging principle of a discrete fringe image of a method for measuring the double-surface shape of an optical element provided by the present invention;

图4是本发明提供的一种光学元件双表面面形测量方法的针对未镀膜HUD测量时上下表面相互干扰示意图;FIG4 is a schematic diagram of the mutual interference between the upper and lower surfaces when measuring an uncoated HUD in a method for measuring the double-surface shape of an optical element provided by the present invention;

图5是本发明提供的一种光学元件双表面面形测量方法的基于图像处理分离上下表面条纹图;FIG5 is a fringe diagram of upper and lower surfaces separated based on image processing in a method for measuring the double-surface shape of an optical element provided by the present invention;

图6是本发明提供的一种光学元件双表面面形测量方法的基于路径搜索确定离散条纹行和列的原理示意图;6 is a schematic diagram showing the principle of determining rows and columns of discrete stripes based on path search in a method for measuring the double-surface shape of an optical element provided by the present invention;

图7是本发明提供的一种光学元件双表面面形测量方法的基于表面法向量恢复面形原理图;7 is a schematic diagram of a method for measuring the double-surface shape of an optical element provided by the present invention, which is based on the surface normal vector to restore the surface shape;

附图标记:Reference numerals:

1、待测HUD反射镜;2、离散条纹图像显示装置;3、双目相机组;4、条纹显示装置上的单个离散条纹;5、上表面反射的单个离散条纹镜像;6、待测HUD反射镜上表面;7、待测HUD反射镜下表面;8、下表面反射的单个离散条纹镜像;9、相机拍摄到的上表面反射的离散条纹图像;10、相机拍摄到的下表面反射的离散条纹图像;11、离散条纹发射的入射光线;12、计算的反射点;13、经过表面反射后的出射光线;14、相机光心;15、离散条纹在相机像素中的坐标;16、表面法向量;17、计算得到的待测表面轮廓。1. HUD reflector to be tested; 2. Discrete stripe image display device; 3. Binocular camera group; 4. Single discrete stripe on the stripe display device; 5. Single discrete stripe image reflected from the upper surface; 6. Upper surface of HUD reflector to be tested; 7. Lower surface of HUD reflector to be tested; 8. Single discrete stripe image reflected from the lower surface; 9. Discrete stripe image reflected from the upper surface captured by the camera; 10. Discrete stripe image reflected from the lower surface captured by the camera; 11. Incident light emitted by discrete stripes; 12. Calculated reflection point; 13. Outgoing light after surface reflection; 14. Optical center of camera; 15. Coordinates of discrete stripes in camera pixels; 16. Surface normal vector; 17. Calculated surface profile to be tested.

具体实施方式DETAILED DESCRIPTION

下面结合附图对本发明的具体实施方式作进一步的详细说明。The specific implementation modes of the present invention will be further described in detail below in conjunction with the accompanying drawings.

为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其它实施例,都属于本发明保护的范围。In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

实施例1:Embodiment 1:

本发明提供了一种光学元件双表面面形测量方法,如图1所示,包括:The present invention provides a method for measuring the double-surface shape of an optical element, as shown in FIG1 , comprising:

S1、建立光学元件双表面面形的基础测量装置;S1. Establish a basic measurement device for the double-surface shape of optical elements;

S2、对所述基础测量装置进行标定处理得到光学元件双表面面形的测量装置;S2, calibrating the basic measuring device to obtain a measuring device for the double-surface shape of an optical element;

S3、利用所述测量装置获取待测量光学元件的反射条纹数据;S3, using the measuring device to obtain reflection fringe data of the optical element to be measured;

S4、根据所述待测量光学元件的反射条纹数据得到光学元件双表面面形测量结果。S4. Obtaining a double-surface shape measurement result of the optical element according to the reflection fringe data of the optical element to be measured.

S1具体包括:S1 specifically includes:

S1-1、在待测量光学元件的两侧分别相对设置相机;S1-1, cameras are arranged opposite to each other on both sides of the optical element to be measured;

S1-2、利用离散条纹图像显示装置分别与相机连接。S1-2, using discrete fringe image display devices to connect with cameras respectively.

S2具体包括:S2 specifically includes:

S2-1、在标准平面镜上设置反光标记点作为反光标记平面镜;S2-1, setting a reflective marking point on a standard plane mirror as a reflective marking plane mirror;

S2-2、利用所述基础测量装置采集反光标记平面镜的多角度反射条纹图像;S2-2, using the basic measurement device to collect multi-angle reflection fringe images of the reflective marking plane mirror;

S2-3、利用所述多角度反射条纹图像基于双目视觉原理计算反光标记点的坐标;S2-3, using the multi-angle reflection fringe image to calculate the coordinates of the reflective marking point based on the binocular vision principle;

S2-4、利用所述反光标记点的坐标获取对应面形方程;S2-4, using the coordinates of the reflective marking points to obtain the corresponding surface equation;

S2-5、根据所述面形方程对基础测量装置完成标定处理得到光学元件双表面面形的测量装置。S2-5. According to the surface shape equation, the basic measuring device is calibrated to obtain a measuring device for the double-surface surface shape of the optical element.

S2-3的计算式如下:The calculation formula of S2-3 is as follows:

其中,Ai、Bi、Ci、Di为标准平面镜上设置反光标记点的坐标,ni为第i组标准平面镜的法向量,di为第i组标准平面镜与坐标原点之间的距离,h为反光标记点的厚度。Among them, Ai , Bi , Ci , Di are the coordinates of the reflective marking points set on the standard plane mirror, ni is the normal vector of the i-th group of standard plane mirrors, di is the distance between the i-th group of standard plane mirrors and the coordinate origin, and h is the thickness of the reflective marking point.

S4具体包括:S4 specifically includes:

S4-1、利用所述待测量光学元件的反射条纹数据进行分离处理得到反射条纹分离数据;S4-1, performing separation processing on the reflection fringe data of the optical element to be measured to obtain reflection fringe separation data;

S4-2、获取所述反射条纹分离数据的拓扑关系;S4-2, obtaining the topological relationship of the reflection fringe separation data;

S4-3、根据所述拓扑关系进行相位解算处理得到反射条纹数据的解算结果;S4-3, performing phase solution processing according to the topological relationship to obtain a solution result of the reflection fringe data;

S4-4、利用所述反射条纹数据的解算结果得到光学元件双表面面形测量结果。S4-4. Obtain the double-surface shape measurement results of the optical element using the solution results of the reflection fringe data.

S4-2具体包括:S4-2 specifically includes:

S4-2-1、利用所述基础测量装置的相机对应特征点作为基准点;S4-2-1, using the camera corresponding feature points of the basic measurement device as reference points;

S4-2-2、基于所述基准点根据单轮廓方向进行搜索分别得到反射条纹图像的上表面与离散反射条纹的拓扑关系和反射条纹图像的下表面与离散反射条纹的拓扑关系;S4-2-2, searching in a single contour direction based on the reference point to obtain a topological relationship between the upper surface of the reflection fringe image and the discrete reflection fringe and a topological relationship between the lower surface of the reflection fringe image and the discrete reflection fringe;

S4-2-3、利用所述反射条纹图像的上表面与离散反射条纹的拓扑关系和反射条纹图像的下表面与离散反射条纹的拓扑关系作为反射条纹分离数据的拓扑关系。S4-2-3. Using the topological relationship between the upper surface of the reflection fringe image and the discrete reflection fringe and the topological relationship between the lower surface of the reflection fringe image and the discrete reflection fringe as the topological relationship of the reflection fringe separation data.

S4-4具体包括:S4-4 specifically includes:

S4-4-1、根据所述反射条纹数据的解算结果基于反射定律得到反射条纹图像的上表面与下表面法线方向向量;S4-4-1. Obtaining the normal direction vectors of the upper surface and the lower surface of the reflection fringe image according to the solution result of the reflection fringe data based on the law of reflection;

S4-4-2、利用所述上表面与下表面法线方向向量基于数值积分进行面形重建处理得到光学元件双表面面形测量结果。S4-4-2. Utilize the normal direction vectors of the upper surface and the lower surface to perform surface reconstruction based on numerical integration to obtain the double-surface surface measurement results of the optical element.

S4-4-2的计算式如下:The calculation formula of S4-4-2 is as follows:

其中,(Px,Py,Pz)为上表面与下表面法线方向向量,z为光学元件双表面面形测量结果。Wherein, ( Px , Py , Pz ) are the normal direction vectors of the upper surface and the lower surface, and z is the double-surface shape measurement result of the optical element.

本实施例中,一种光学元件双表面面形测量方法,如图2所示,所述基础测量装置的设置与具体标定过程如下:In this embodiment, a method for measuring the double-surface shape of an optical element is provided, as shown in FIG2 , and the setting and specific calibration process of the basic measuring device are as follows:

包括离散条纹投射装置2,待检测HUD反射镜1,双目相机组3这三部分构成。离散条纹可以使用屏幕显示图案的形式产生,也可以使用背光光源照射印制了离散条纹特征图的玻璃投射的形式产生。双目相机组用于从两个角度拍摄待待测件反射条纹的效果,并计算反射离散条纹的待测件表面点的具体坐标。如图3所示,这一过程严格遵守几何光学反射定律。系统拍摄原理如图4所示,HUD反射镜的上下表面均具有一定的反光特性,待测HUD反射镜上表面6反射的光仅经过一次镜面反射,而待测HUD反射镜下表面7反射的光经过了两次折射和一次镜面反射。上下表面反射的离散条纹图案在等效平面镜中成上表面反射的单个离散条纹镜像5和下表面反射的单个离散条纹镜像8,相机拍摄到这些镜像。为满足高精度测量需求,系统参数按照如下步骤设定:It consists of three parts: a discrete fringe projection device 2, a HUD reflector to be tested 1, and a binocular camera group 3. Discrete stripes can be generated in the form of a screen display pattern, or in the form of a backlight source irradiating a glass projection printed with a discrete fringe feature map. The binocular camera group is used to capture the effect of the reflected stripes of the test piece from two angles, and calculate the specific coordinates of the surface points of the test piece that reflect the discrete stripes. As shown in Figure 3, this process strictly abides by the law of geometric optics reflection. The shooting principle of the system is shown in Figure 4. The upper and lower surfaces of the HUD reflector have certain reflective properties. The light reflected by the upper surface 6 of the HUD reflector to be tested undergoes only one mirror reflection, while the light reflected by the lower surface 7 of the HUD reflector to be tested undergoes two refractions and one mirror reflection. The discrete fringe patterns reflected by the upper and lower surfaces are formed into a single discrete fringe mirror image 5 reflected by the upper surface and a single discrete fringe mirror image 8 reflected by the lower surface in the equivalent plane mirror, and the camera captures these images. To meet the requirements of high-precision measurement, the system parameters are set according to the following steps:

(1)首先根据待测表面面形特点与精度要求设计光源与相机布局方式。一般要求待测表面采样点密度大于1个/mm,单个相机视野小于200mm,以保证测量精度。并且每个相机视场内,HUD反射镜表面基本被离散条纹图覆盖,然后控制相机倾斜45°拍摄。(1) First, design the light source and camera layout according to the surface characteristics and accuracy requirements of the surface to be measured. Generally, the sampling point density of the surface to be measured is required to be greater than 1/mm, and the field of view of a single camera is required to be less than 200mm to ensure measurement accuracy. In addition, within the field of view of each camera, the surface of the HUD reflector is basically covered by the discrete fringe pattern, and then the camera is controlled to tilt 45° to shoot.

(2)基于相机成像公式和待测表面理想面形方程,计算理论上入射光线与待测表面的交点和出射光线。调整离散条纹的位置和密度,使相机采集的反射条纹图中不存在条纹重叠的情况且间隔合适,基于这一密度进行离散条纹图的布局和生成。(2) Based on the camera imaging formula and the ideal surface shape equation of the surface to be measured, the intersection point of the incident light and the surface to be measured and the outgoing light are calculated in theory. The position and density of the discrete fringes are adjusted so that there is no overlapping of fringes in the reflected fringe pattern collected by the camera and the interval is appropriate. Based on this density, the layout and generation of the discrete fringe pattern are performed.

(3)采用张氏标定法标定两个相机构成双目立体视觉系统,用条纹显示装置展示一个离散条纹图,在标准平面镜上随机粘贴若干反光标记点。平面镜移动到十五到二十个不同的位置和姿态,保证每个位姿情况下,通过两个相机均能拍摄到对应的平面镜反射下的条纹图像和标记点。基于双目视觉原理即可计算出平面镜所粘贴特征点的坐标,然后以改坐标作为约束,通过最优化计算平面镜和相机之间的位姿关系以及条纹显示装置和双目视觉系统之间的位姿关系。(3) The Zhang calibration method is used to calibrate two cameras to form a binocular stereo vision system. A discrete fringe pattern is displayed using a fringe display device, and several reflective markers are randomly pasted on a standard plane mirror. The plane mirror is moved to fifteen to twenty different positions and postures to ensure that in each posture, the corresponding fringe image and markers reflected by the plane mirror can be captured by both cameras. Based on the principle of binocular vision, the coordinates of the feature points pasted on the plane mirror can be calculated, and then the changed coordinates are used as constraints to optimize the posture relationship between the plane mirror and the camera, and the posture relationship between the fringe display device and the binocular vision system.

本实施例中,一种光学元件双表面面形测量方法,所述相位解算的具体流程如下:In this embodiment, a method for measuring the double-surface shape of an optical element is provided, and the specific process of phase resolution is as follows:

(1)在具体测量过程中,首先在条纹显示装置上展示一张经过布局后的离散条纹图,然后用双目视觉系统分别拍摄待测HUD反射镜上反射的条纹图。(1) In the specific measurement process, a discrete fringe pattern after layout is first displayed on a fringe display device, and then the fringe pattern reflected on the HUD reflector to be tested is photographed by a binocular vision system.

(2)对两个相机拍摄的条纹图分别进行条纹分离,根据下表面反射的条纹总在上表面反射的条纹同侧,以及下表面反射的条纹亮度比上表面反射的条纹亮度低这两个原则,识别出两个表面的反射条纹,并且在图像上分离。如图5所示,每个相机拍摄的条纹图将分离成上下表面的两张反射条纹图。(2) The fringe images captured by the two cameras are separated. According to the two principles that the fringe reflected by the lower surface is always on the same side as the fringe reflected by the upper surface and that the brightness of the fringe reflected by the lower surface is lower than that of the fringe reflected by the upper surface, the reflected fringe on the two surfaces is identified and separated on the image. As shown in Figure 5, the fringe image captured by each camera is separated into two reflected fringe images of the upper and lower surfaces.

(3)根据分离后的离散条纹图,如图6所示,从基准条纹开始,沿特定的路径搜索,将离散的条纹识别出所处的列和行,为后续的相位解包裹做基础。(3) Based on the separated discrete fringe pattern, as shown in FIG6 , starting from the reference fringe, searching along a specific path, the discrete fringe is identified in which column and row it is located, which serves as a basis for subsequent phase unwrapping.

(4)对离散条纹的列和行进行编码,在每个离散的条纹中解包裹的相位,对不同的离散条纹根据行列计算条纹级次并解包裹,获得真实相位。(4) Encode the columns and rows of discrete stripes, unwrap the phase in each discrete stripe, calculate the stripe order according to the rows and columns of different discrete stripes, unwrap them, and obtain the real phase.

(5)根据真实相位确定待测件表面采样点和相机拍摄图案的对应关系。以条纹显示装置与双目视觉装置之间的位姿为基础,如图7所示,借助反射定律和光线追迹计算各采样点处的法向量,由法向量计算梯度并积分。上下表面均执行(3)至(5)过程,最终得到待测件上下表面各采样点处的高度,插值获得待测件的三维轮廓。(5) Determine the correspondence between the sampling points on the surface of the test piece and the pattern captured by the camera based on the real phase. Based on the position between the fringe display device and the binocular vision device, as shown in Figure 7, the normal vector at each sampling point is calculated by using the reflection law and ray tracing, and the gradient is calculated and integrated from the normal vector. The upper and lower surfaces are both executed from (3) to (5), and finally the heights at each sampling point on the upper and lower surfaces of the test piece are obtained, and the three-dimensional contour of the test piece is obtained by interpolation.

本实施例中,一种光学元件双表面面形测量方法,具体实施应用如下:In this embodiment, a method for measuring the double-surface shape of an optical element is specifically implemented and applied as follows:

(1)搭建测量装置,将离散条纹图显示装置与两个相机安装在在待测的光学元件同侧,使得两个相机均可以通过透明件上表面反射拍摄到条纹图,具体提供离散条纹图的装置可以选择屏幕,也可以选择背光光源和印制了离散条纹特征图的玻璃,具体根据待测表面尺寸决定。(1) Build a measuring device, install a discrete fringe pattern display device and two cameras on the same side of the optical element to be measured, so that both cameras can capture the fringe pattern through reflection from the upper surface of the transparent member. The device for providing the discrete fringe pattern can be a screen, or a backlight source and glass printed with a discrete fringe feature pattern, which is determined according to the size of the surface to be measured.

(2)标定测量装置,采用张氏标定法标定双目立体视觉装置,采用针孔相机成像模型计算相应参数。该模型用矩阵形式表示为:(2) Calibrate the measurement device. Use Zhang’s calibration method to calibrate the binocular stereo vision device, and use the pinhole camera imaging model to calculate the corresponding parameters. The model is expressed in matrix form as follows:

其中,in,

其中,[u,v]为像素坐标,xc,yc,zc为待拍摄点在相机坐标系下的坐标。ax,ay为镜头在x,y方向等效光心与CCD靶面的归一化距离,u0,v0为CCD主点像素坐标,s为相机镜头倾斜修正量。Where [u,v] is the pixel coordinate, xc , yc , zc are the coordinates of the point to be photographed in the camera coordinate system. ax , ay are the normalized distances between the equivalent optical center of the lens in the x and y directions and the CCD target surface, u0 , v0 are the pixel coordinates of the CCD principal point, and s is the tilt correction of the camera lens.

在具体成像过程中,屏幕首先在平面镜中成一虚像,相机等效于直接拍摄这一虚像。根据相机成像矩阵计算平面镜成像模型为:In the specific imaging process, the screen first forms a virtual image in the plane mirror, and the camera is equivalent to directly photographing this virtual image. The plane mirror imaging model calculated according to the camera imaging matrix is:

其中Ps'为屏幕虚像上特征点坐标,Pc为相机像素坐标,R和T为从屏幕虚像坐标系到相机坐标系的转换矩阵,可通过单应性矩阵分解计算得到,由于这里经过了屏幕镜镜像,因此R行列式为-1。Where Ps ' is the coordinate of the feature point on the screen virtual image, Pc is the camera pixel coordinate, R and T are the transformation matrices from the screen virtual image coordinate system to the camera coordinate system, which can be calculated by homography matrix decomposition. Since it is mirrored by the screen mirror, the determinant of R is -1.

用条纹显示装置展示一个离散条纹图,在标准平面镜上随机粘贴若干反光标记点,平面镜移动多角度,并通过相机拍摄对应的平面镜反射下的条纹图像,基于双目视觉原理即可计算出平面镜所粘贴特征点的坐标,进而可计算出对应平面镜位置下的面形方程A discrete fringe pattern is displayed using a fringe display device. Several reflective marking points are randomly pasted on a standard plane mirror. The plane mirror is moved at multiple angles, and the corresponding fringe image reflected by the plane mirror is photographed by a camera. Based on the principle of binocular vision, the coordinates of the feature points pasted on the plane mirror can be calculated, and then the surface shape equation at the corresponding plane mirror position can be calculated.

其中Ai,Bi,Ci,Di为表面粘贴特征点的坐标,ni为第i组平面镜法向量,di为第i组平面镜与坐标原点之间的距离,h为所粘贴反光标记点的厚度。结合相机成像模型与平面镜成像模型可得左右相机像素与屏幕像素的映射方程。Where A i , B i , C i , D i are the coordinates of the feature points pasted on the surface, ni is the normal vector of the i-th group of plane mirrors, di is the distance between the i-th group of plane mirrors and the origin of the coordinates, and h is the thickness of the pasted reflective marking point. Combining the camera imaging model with the plane mirror imaging model, the mapping equation between the left and right camera pixels and the screen pixels can be obtained.

(3)分离上下表面反射条纹信息,上表面反射特征亮度往往会大于下表面反射特征亮度,且位于上表面反射特征的同侧,基于灰度信息和位置信息分离上下表面反射特征。(3) Separate the upper and lower surface reflection stripe information. The brightness of the upper surface reflection feature is often greater than that of the lower surface reflection feature and is located on the same side of the upper surface reflection feature. The upper and lower surface reflection features are separated based on grayscale information and position information.

(4)分别计算上下表面反射条纹之间的拓扑关系,用条纹显示装置展示一个带特征点的条纹图。如图5所示,以两个相机拍摄到的特征点为基准,在离散条纹图中从该点沿着单轮廓走向方向搜索得到第二个特征点,然后基于这两个特征点连线更新搜索方向,基于新的搜索方向得到第三个特征点,以此类推,从而搜索得到一列点,此时相当于得到了单条轮廓数据,接下来以这一列点为基准进行横向搜索,得到相邻轮廓上若干特征点之间的拓扑关系。重复上述步骤多次,直到所有点搜索完毕,确定上表离散反射条纹之间的拓扑关系和下表面离散反射条纹之间的拓扑关系。(4) Calculate the topological relationship between the upper and lower surface reflection stripes respectively, and use the stripe display device to display a stripe diagram with feature points. As shown in FIG5, taking the feature point captured by the two cameras as the reference, search from this point in the discrete stripe diagram along the direction of the single contour to obtain the second feature point, and then update the search direction based on the connection line between the two feature points, and obtain the third feature point based on the new search direction, and so on, so as to search and obtain a column of points, which is equivalent to obtaining a single contour data. Next, use this column of points as the reference to perform a horizontal search to obtain the topological relationship between several feature points on adjacent contours. Repeat the above steps multiple times until all points are searched, and determine the topological relationship between the discrete reflection stripes in the upper table and the topological relationship between the discrete reflection stripes on the lower surface.

(5)相位解算,基于(4)计算的拓扑关系进行确定各相位峰值的大致位置和级次,以此来帮助相位解包裹的展开,获取经过光学元件上下表面反射后,相机像素和屏幕像素的对应关系。(5) Phase solution: Based on the topological relationship calculated in (4), the approximate position and order of each phase peak are determined to help the phase unwrapping process unfold and obtain the correspondence between the camera pixels and the screen pixels after reflection from the upper and lower surfaces of the optical element.

(6)计算反射镜上下表面的梯度,结合(5)得到的对应关系,根据反射定律分别计算上下表面法线方向向量,记为(Px,Py,Pz)。得到待求表面法向量后,利用数值积分运算(6) Calculate the gradient of the upper and lower surfaces of the reflector, and combine the corresponding relationship obtained in (5) to calculate the normal direction vectors of the upper and lower surfaces respectively according to the law of reflection, which are recorded as (P x ,P y ,P z ). After obtaining the surface normal vector to be calculated, use numerical integration operation

进行面形重建,完成光学元件上下表面的三维轮廓测量。Perform surface reconstruction and complete the three-dimensional profile measurement of the upper and lower surfaces of optical components.

本领域内的技术人员应明白,本发明的实施例可提供为方法、系统、或计算机程序产品。因此,本发明可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且,本发明可采用在一个或多个其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

本发明是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器,使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。The present invention is described with reference to the flowchart and/or block diagram of the method, device (system), and computer program product according to the embodiment of the present application. It should be understood that each process and/or box in the flowchart and/or block diagram, as well as the combination of the process and/or box in the flowchart and/or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for implementing the functions specified in one process or multiple processes in the flowchart and/or one box or multiple boxes in the block diagram.

这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中,使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品,该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device that implements the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.

这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上,使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理,从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。These computer program instructions may also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and/or one or more boxes in the block diagram.

最后应当说明的是:以上实施例仅用以说明本发明的技术方案而非对其限制,尽管参照上述实施例对本发明进行了详细的说明,所属领域的普通技术人员应当理解:依然可以对本发明的具体实施方式进行修改或者等同替换,而未脱离本发明精神和范围的任何修改或者等同替换,其均应涵盖在本发明的权利要求保护范围之内。Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents, and any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims (6)

1.一种光学元件双表面面形测量方法,其特征在于,包括:1. A method for measuring the double-surface shape of an optical element, comprising: S1、建立光学元件双表面面形的基础测量装置;S1. Establish a basic measurement device for the double-surface shape of optical elements; S2、对所述基础测量装置进行标定处理得到光学元件双表面面形的测量装置;S2, calibrating the basic measuring device to obtain a measuring device for the double-surface shape of an optical element; S3、利用所述测量装置获取待测量光学元件的反射条纹数据;S3, using the measuring device to obtain reflection fringe data of the optical element to be measured; S4、根据所述待测量光学元件的反射条纹数据得到光学元件双表面面形测量结果;S4, obtaining a double-surface shape measurement result of the optical element according to the reflection fringe data of the optical element to be measured; S4-1、利用所述待测量光学元件的反射条纹数据进行分离处理得到反射条纹分离数据;S4-1, performing separation processing on the reflection fringe data of the optical element to be measured to obtain reflection fringe separation data; S4-2、获取所述反射条纹分离数据的拓扑关系;S4-2, obtaining the topological relationship of the reflection fringe separation data; S4-2-1、利用所述基础测量装置的相机对应特征点作为基准点;S4-2-1, using the camera corresponding feature points of the basic measurement device as reference points; S4-2-2、基于所述基准点根据单轮廓方向进行搜索分别得到反射条纹图像的上表面与离散反射条纹的拓扑关系和反射条纹图像的下表面与离散反射条纹的拓扑关系;S4-2-2, searching in a single contour direction based on the reference point to obtain a topological relationship between the upper surface of the reflection fringe image and the discrete reflection fringe and a topological relationship between the lower surface of the reflection fringe image and the discrete reflection fringe; S4-2-3、利用所述反射条纹图像的上表面与离散反射条纹的拓扑关系和反射条纹图像的下表面与离散反射条纹的拓扑关系作为反射条纹分离数据的拓扑关系;S4-2-3, using the topological relationship between the upper surface of the reflection fringe image and the discrete reflection fringe and the topological relationship between the lower surface of the reflection fringe image and the discrete reflection fringe as the topological relationship of the reflection fringe separation data; S4-3、根据所述拓扑关系进行相位解算处理得到反射条纹数据的解算结果;S4-3, performing phase solution processing according to the topological relationship to obtain a solution result of the reflection fringe data; S4-4、利用所述反射条纹数据的解算结果得到光学元件双表面面形测量结果。S4-4. Obtain the double-surface shape measurement results of the optical element using the solution results of the reflection fringe data. 2.如权利要求1所述的一种光学元件双表面面形测量方法,其特征在于,所述建立光学元件双表面面形的基础测量装置包括:2. A method for measuring the double-surface shape of an optical element as claimed in claim 1, characterized in that the basic measuring device for establishing the double-surface shape of an optical element comprises: 在待测量光学元件的两侧分别相对设置相机;Cameras are arranged opposite to each other on both sides of the optical element to be measured; 利用离散条纹图像显示装置分别与相机连接。The discrete fringe image display devices are connected to the cameras respectively. 3.如权利要求1所述的一种光学元件双表面面形测量方法,其特征在于,对所述基础测量装置进行标定处理得到光学元件双表面面形的测量装置包括:3. The method for measuring the double-surface shape of an optical element according to claim 1, wherein the step of calibrating the basic measuring device to obtain the double-surface shape of the optical element comprises: 在标准平面镜上设置反光标记点作为反光标记平面镜;A reflective marking point is set on a standard plane mirror as a reflective marking plane mirror; 利用所述基础测量装置采集反光标记平面镜的多角度反射条纹图像;The basic measuring device is used to collect multi-angle reflection stripe images of the reflective marking plane mirror; 利用所述多角度反射条纹图像基于双目视觉原理计算反光标记点的坐标;Utilizing the multi-angle reflection fringe image to calculate the coordinates of the reflective marking point based on the binocular vision principle; 利用所述反光标记点的坐标获取对应面形方程;Obtaining the corresponding surface equation using the coordinates of the reflective marking points; 根据所述面形方程对基础测量装置完成标定处理得到光学元件双表面面形的测量装置。The basic measuring device is calibrated according to the surface shape equation to obtain a measuring device for the double-surface surface shape of an optical element. 4.如权利要求3所述的一种光学元件双表面面形测量方法,其特征在于,利用所述多角度反射条纹图像基于双目视觉原理计算反光标记点的坐标的计算式如下:4. A method for measuring the double-surface shape of an optical element as claimed in claim 3, characterized in that the coordinates of the reflective marking points are calculated using the multi-angle reflected fringe image based on the binocular vision principle as follows: 其中,Ai、Bi、Ci、Di为标准平面镜上设置反光标记点的坐标,ni为第i组标准平面镜的法向量,di为第i组标准平面镜与坐标原点之间的距离,h为反光标记点的厚度。 Among them, Ai , Bi , Ci , Di are the coordinates of the reflective marking points set on the standard plane mirror, ni is the normal vector of the i-th group of standard plane mirrors, di is the distance between the i-th group of standard plane mirrors and the coordinate origin, and h is the thickness of the reflective marking point. 5.如权利要求1所述的一种光学元件双表面面形测量方法,其特征在于,利用所述反射条纹数据的解算结果得到光学元件双表面面形测量结果包括:5. The method for measuring the double-surface shape of an optical element according to claim 1, wherein obtaining the double-surface shape measurement result of the optical element using the solution result of the reflection fringe data comprises: 根据所述反射条纹数据的解算结果基于反射定律得到反射条纹图像的上表面与下表面法线方向向量;Obtaining the normal direction vectors of the upper surface and the lower surface of the reflection fringe image based on the reflection law according to the solution result of the reflection fringe data; 利用所述上表面与下表面法线方向向量基于数值积分进行面形重建处理得到光学元件双表面面形测量结果。The surface shape measurement results of the double surfaces of the optical element are obtained by performing surface shape reconstruction processing based on numerical integration using the normal direction vectors of the upper surface and the lower surface. 6.如权利要求5所述的一种光学元件双表面面形测量方法,其特征在于,利用所述上表面与下表面法线方向向量基于数值积分进行面形重建处理得到光学元件双表面面形测量结果的计算式如下:6. A method for measuring the double-surface shape of an optical element as claimed in claim 5, characterized in that the calculation formula for obtaining the double-surface shape measurement result of the optical element by performing shape reconstruction processing based on numerical integration using the normal direction vectors of the upper surface and the lower surface is as follows: 其中,(Px,Py,Pz)为上表面与下表面法线方向向量,z为光学元件双表面面形测量结果。 Wherein, ( Px , Py , Pz ) are the normal direction vectors of the upper and lower surfaces, and z is the double-surface shape measurement result of the optical element.
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