【作者】 刘鑫；

【导师】 李大海；

【作者基本信息】 四川大学 ， 光学工程， 2022， 硕士

【摘要】 近年来,随着光学事业的发展,光学元件的微型化已经成为一种发展趋势。例如在现代光通信的连接器件、手机镜头以及各种微透镜阵列等场景中对小口径和小曲率半径元件的需求日益增加。加工离不开检测,所以对这些元件参数的测量就显得尤其重要。对于光学元件的检测,传统的曲率半径测量方法主要有接触式测量和非接触式测量。以上两类测量方法对于曲率半径的测量均存在一定的限制,例如接触式测量因为需要探针或者标准样板与待测元件接触时可能对待测元件造成损伤,并且测量的结果与样板的精度有关,待测元件的大小受到样板的选择限制。非接触式测量也存在测量采样点有限以及干涉测量的成本高且受环境等噪声的影响较大,不容易实现元件的在位测量。相位测量偏折术是一种非接触高精度元件面形检测方法,主要利用了待测元件的反射性质来实现测量,其具有结构简单、成本低、检测动态范围很大等特点,已经受到了广泛的关注。当利用相位测量偏折术与干涉测量法测量曲面光学元件时,曲面元件存在反射率低和边缘条纹过密等问题,使得相机拍摄的条纹图对比度较低和边缘模糊,这是由于光线在在待测元件边缘处反射的光路变长以及条纹调制传递函数下降而造成的。因此,本文在传统相位测量偏折术的基础上,探究了一种基于逆光线追迹的预畸变条纹投影与微分几何方法相结合来测量光学元件上的每点平均曲率半径的方法,并且该方法还能够解决由于光学元件的口径和曲率半径较小而陡度过大造成的反射条纹边缘模糊的问题。最后通过非线性最小二乘拟合来优化出待测元件的二次曲面系数和顶点曲率半径。本文的主要内容和创新点如下:1、首先介绍了光学元件在光学系统中的重要作用以及对光学元件检测的研究意义,并且分析对比了目前的光学元件的曲率半径测量方法的原理和限制,最后对相位测量偏折术的结构和测量元件表面面形时涉及到的相机标定、编码条纹投影以及面形重建等方法进行了介绍。2、在传统相位测量偏折术的结构光投影的基础上,提出了一种基于逆光线追迹的预畸变条纹投影并结合微分几何算法来测量曲面光学元件上的每点平均曲率半径的方法,该方法不仅可以测量光学元件上的每点平均曲率半径,而且能够克服相位测量偏折术测量口径和曲率半径较小而陡度过大的光学元件时因为光线在待测元件边缘处反射的光路变长以及条纹调制传递函数下降而造成的边缘模糊问题。并且利用迭代算法获取待测元件上各点的坐标和矢高数据,再结合微分几何算法从而获得待测元件上的每点平均曲率半径。除此之外,利用非线性最小二乘算法将测量的坐标和矢高数据进行拟合获得待测元件的二次曲面系数以及顶点曲率半径,便于获得待测元件的曲面类型。3、利用本文提出的方法分别对球面和非球面进行了模拟验证,并且利用插值的方法来模拟相机拍摄过程。为了进一步验证所提方法的可行性,详细介绍了测量待测元件所搭建的实验光路组成以及测量流程,实验对曲率半径为8.26mm的球面和一个二次曲面系数为-1.332且顶点曲率半径为7.769mm的非球面进行了测量,并且利用非线性最小二乘拟合测量的待测元件的二次曲面系数和顶点曲率半径。更多还原

【Abstract】 In recent years,with the development of optics,the miniaturization of optical elements have become a trend.For example,there is an increasing demand for small-diameter and small curvature radius elements in scenarios such as connection devices for modern optical communications,cell phone lenses,and various microlens arrays.Processing is inseparable from detection,so it is particularly important to measure the parameters of these elements.For the detection of optical elements,the traditional radius of curvature measurement methods are mainly contact measurement and non-contact measurement.Both of the above two measurement methods have certain limitations on the measurement of the radius of curvature.For example,contact measurement may cause damage to the measuring elements when probe or standard sample plate is in contact with the elements to be measured,and the measurement result is related to the accuracy of the sample plate,so the size of the elements to be measured are limited by the selection of sample plate.Non-contact measurement also has some problems,such as limited sampling points,high cost,easy to be affected by environmental noise,and difficult to achieve online measurement of elements.Phase measuring deflectometry is a non-contact high-precision elements surface shape detection method,which mainly uses the reflection properties of the elements to be measured to achieve measurement.It has the characteristics of simple structure,low cost,large dynamic detection range and so on,and has been widely concerned.When using phase measuring deflectometry and interferometry to measure the surface,curved elements have problems such as low reflectivity and dense edge fringes,which make the fringes taken by the camera have low contrast and blurred edges.This is caused by a longer light path reflected at the edge of the elements to be measured and the decline of the fringe modulation transfer function.Therefore,based on the traditional phase measuring deflectometry,a method of measuring the mean radius of curvature of each point on optical elements based on the reverse ray tracing pre-distortion fringes projection combined with a differential geometry method is investigated.And this method can also solve the problem that the edge of reflection fringes blurred because the aperture and radius of curvature of optical elements are small and steepness is too large.Finally,the quadratic surface coefficients and vertex curvature radius of the elements to be measured are optimized by nonlinear least-squares fitting.The main contents and innovations of this paper are as follows:1.This paper first introduces the important role of optical elements in optical systems and the significance of the research on optical element detection.We also analyze and compare the principles and limitations of current methods for measuring the radius of curvature of optical elements.Finally,the device of phase measuring deflectometry and the methods of camera calibration,coded fringes projection and surface reconstruction are introduced.2.Based on the structured light projection of the conventional phase measuring deflectometry,a method is proposed to measure the mean radius of curvature of each point on curved optical elements based on reverse ray tracing pre-distortion fringes projection combined with differential geometry algorithms.This method can not only measure the mean radius of curvature at each point on an optical element,but also can overcome the edge blurring problem caused by a longer optical path of light reflected at the edge of the element to be measured and a decrease in the fringes modulation transfer function when measuring optical elements with small apertures and radius of curvature but large steepness using phase measuring deflectometry.The iterative algorithm is used to obtain the coordinates and vector height data of the points on the elements to be measured with small radius of curvature,and then combined with the differential geometry algorithm to obtain the average radius of curvature of each point on the elements to be measured.In addition,a nonlinear least squares algorithm is used to fit the measured coordinates and vector height data to obtain the quadratic surface coefficients and the vertex radius of curvature of the elements to be measured,which facilitates the acquisition of the surface type of the elements to be measured.3.The proposed is simulated and verified separately for spherical and aspherical surfaces,and the interpolation method is used to simulate the camera shooting process.The proposed is simulated and verified for spherical and aspherical surfaces with small radius of curvature,respectively,and the method of using interpolation to simulate the camera shooting process is introduced.To prove the feasibility of the proposed method,the composition of the experimental optical path built to measure the elements to be measured and the measurement procedure are described in detail.Experiments were performed on a spherical surface with a radius of curvature of 8.26 mm and an aspherical surface with a quadratic surface coefficient of-1.332 and a vertex radius of curvature of 7.769 mm.And the quadratic surface coefficients and vertex curvature radius of the measured elements to be measured are fitted using nonlinear least squares.更多还原