一种新的非球面零朗奇检测法

提出一种新的零朗奇检测法用于测量大口径非球面镜的面形。利用光线追迹和正弦条纹的相位信息设计补偿正弦光栅。使用透射液晶显示屏显示补偿正弦光栅并作为相移装置。一个离轴点光源发出的光被镜面反射后通过补偿正弦光栅,摄像机记录携带镜面偏差信息的相移条纹图。通过对相移条纹图的分析确定被测镜面的实际横向像差以及对应的理想横向像差,然后基于朗奇检测的几何原理得到被测镜面的偏差梯度,对其积分获得被测镜面的偏差,进而重建被测镜面的三维面形。与传统的零朗奇检测法相比,这种方法可以消除补偿光栅上每个条纹带边缘的锯齿形状,而且可以获得镜面上足够多的待测点信息。计算机模拟和初步实验验证了该方法的可行性。     

An improved phase retrieval algorithm for optical aspheric surface measurement

In order to overcome the measurement and calculation difficulty for aspheric surface with phase retrieval technology, an improved phase retrieval algorithm was proposed. Due to significant departure from sphere surface, reflected light from different part of the aspheric surface under test will overlap in some areas in the collected images by CCD with general phase retrieval measurement setup, which will lead to the failure to recover the surface phase. The proposed algorithm will only use those areas without light overlapping in each image in the iteration process and employ several defocused images to recover the whole surface. This algorithm can improve the measurement range for aspheric surface with phase retrieval technology. The experimental system was established and a 180 mm diameter, f/1.6 parabolic mirror and a 180 mm effective diameter, f/1.33 hyperboloid mirror were tested by the proposed method. The experimental results show that the retrieved surface errors are in good consistent with that obtained by interferometer, which confirms the validity of the proposed algorithm.     

Shack-Hartmann波前传感器非零位在轴检测离轴非球面反射镜

在离轴非球面反射镜研磨后期和粗抛光阶段,被测反射镜面形与理想面形存在着较大的偏差,表面反射率较低,采用干涉测量会因局部区域干涉条纹过密或条纹对比度过低,造成普通干涉仪无法进行全口径测量,而普通接触式轮廓仪测量精度此时已经不能满足加工要求。鉴于Shack-Hartmann波前传感器较大的动态范围和较高的测量精度,提出了采用Shack-Hartmann波前传感器非零位在轴检测离轴非球面面形,研究了该方法的检测原理并搭建了检测系统,分析了系统误差来源,并制作了用于在轴检测离轴非球面的参考波前,对两个不同加工精度的离轴非球面反射镜进行了测量,并与干涉仪的测量结果进行了对比。对比结果表明,Shack-Hartmann波前传感器的测量结果是正确可靠的,并且可以弥补轮廓仪测量和干涉仪测量的不足,从而证明了采用Shack-Hartmann波前传感器在轴检测离轴非球面的可行性和正确性。     

Null test of aspheric surface based on digital phase-shift interferometer

In order to implement the null test of aspheric surfaces as simply as that of spherical ones in a commercial digital phase-shift interferometer, computer generated holograms (CGHs) that are composed of a main CGH, which produces the ideal aspheric wavefront, and an alignment CGH, which aids in calibration, were utilized. The principle of testing aspheric surface in an interferometer with CGHs is explained and critical aspects in designing, fabricating and calibrating CGHs are discussed in detail. Error analysis of the experimental results demonstrated that the uncertainty of the testing system is better than λ/10 (λ=0.6328 μm).     

Testing a large aspheric surface based on analysis of scanning 3D interferogram

A new method based on new reconstruction algorithm and new interferogram fringe analysis was proposed for testing a large aspheric surface. In the testing process, firstly, the interferometer or the tested aspheric surface was shifted relatively for measurement of the whole aperture of the tested aspheric surface to obtain a series of interferograms. Then these interferograms were analyzed to extract the best matching point, where the annular sub-surface was tangent with the corresponding reference sphere of the reference wavefront. Finally, the wavefront aberration of the whole aperture was figured out to describe the deformation information of the tested surface. Without any additional null optical elements, this method can perform the measurement directly. So, this method provides an effective and convenient means of testing the large-aperture aspheric surface. The mathematical model of this method is described, and the results of simulation tests are presented to verify it.     

条纹反射法测量三维面形中的积分算法

基于不同梯度数据噪声,研究讨论了几种典型的梯度积分算法,并提出了一种改进的Southwell全局积分算法.以重建面形和原始面形的相似度、均方根误差作为算法性能参数,对梯度数据进行模拟测试.搭建条纹反射实验平台,对标准凹球面反射镜进行积分重建,并将条纹反射法测量结果和实际元件参数进行对比.实验结果表明：用改进的Southwell算法重建的凹球面的半径误差为0.09%,结构相似度大于0.999,其重建速度为原算法的1.2倍.改进后的Southwell算法相较于传统的积分算法,获得了更高的重建质量和重建效率,满足镜面物体测量的非接触、精度高、稳定性强等要求.     

Lens distortion elimination for improving measurement accuracy of fringe projection profilometry

Fringe projection profilometry (FPP) is a powerful method for three-dimensional (3D) shape measurement. However, the measurement accuracy of the existing FPP is often hindered by the distortion of the lens used in FPP. In this paper, a simple and efficient method is presented to overcome this problem. First, the FPP system is calibrated as a stereovision system. Then, the camera lens distortion is eliminated by correcting the captured images. For the projector lens distortion, distorted fringe patterns are generated according to the lens distortion model. With these distorted fringe patterns, the projector can project undistorted fringe patterns, which means that the projector lens distortion is eliminated. Experimental results show that the proposed method can successfully eliminate the lens distortions of FPP and therefore improves its measurement accuracy.     

Discussions on on-machine measurement of aspheric lens-mold surface

At present, regarding to the machining of aspheric lens mold, there are two major methods to carry out the on-machine measurement (OMM) — contacting method (CM) and non-contacting method (NCM). Here such two methods are reviewed in detail. CM is mainly based on the contacting probe which is scratching aspheric surface of lens mold to achieve profile data. To be efficient, an idea with 45° tilt of probe is proposed for OMM of lens mold by Suzuki. But generally speaking, the contacting OMM is not so efficient and can only deal with axisymmetric aspheric lens mold. On the contrary, NCM mostly uses laser to achieve aspheric profile without any contact. On ultra-precision lathe, laser scanning system or laser interferometer is mounted on the frame of lathe and transfers measurement data to machining system efficiently. However, most NCMs need stable environment and low working noise except instantaneous phase-shifting shearing interferometry (IPSSI). Therefore, a new idea about IPSSI is proposed in this paper to realize OMM of lens molds. Unfortunately, it's also difficult to test the high numerical aperture aspheric or free-form lens molds. By comparison, the newly-developed fringe reflection (FR) method is becoming the promising method because it features the high efficiency and high accuracy. However, this method has not been used for OMM system yet. Much research should be conducted for FR OMM technology.     

基于条纹反射的光学表面疵病检测法

提出一种基于条纹反射的光学表面疵病检测方法,检测系统由液晶显示屏、CCD相机和计算机组成.检测时在显示屏上分别显示水平和垂直两个方向正交的正弦性条纹,用CCD相机记录经被测表面反射的正弦条纹像,通过相移技术得到两个方向正交的相位分布和对比度分布,通过对比度分布确定被测表面的疵病位置.被测面表面面形相关信息包含在相位分布中,其表面疵病细节信息包含在局部微观相位分布之中.对相位分布进行多项式拟合后相减得到疵病引起的微观相位分布,计算得到表面疵病的梯度分布,积分得其高度分布.实验验证了该方法的可行性.     

Applications of windowed Fourier fringe analysis in optical measurement: A review

The applications of windowed Fourier fringe analysis in the past decade are reviewed. Because fringe patterns from different optical measurement systems are similar, the reviewed applications are classified according to the functions of the windowed Fourier transform being used in fringe pattern analysis: denosing exponential phase fields, demodulating carrier fringe patterns, getting phase derivatives, and utilizing local properties. From these applications, the windowed Fourier transform is shown to be effective and versatile for fringe pattern analysis.     

Three-dimensional shape measurement for an underwater object based on two-dimensional grating pattern projection

In this paper, a practical method using phase tracking and ray tracing algorithms is proposed for measuring the three-dimensional (3D) shape of an underwater object. A 2D projected sinusoidal fringe goes through the water and illuminates the tested object. Firstly, the phase tracking algorithm is employed to identify homologous points in phase distributions of the deformed fringe captured by the camera and these of the fringe pattern projected by the projector. The projector is regarded as a special camera as regards the stereovision principle. In the calibrated system, both ray directions of the homologous points can be easily figured out. Secondly, the ray tracing algorithm is used to trace the propagation path of each ray and to calculate the 3D coordinates of each point on the tested object's surface. Finally, the whole shape of the tested object can be reconstructed.     

Improved intensity-optimized dithering technique for 3D shape measurement

The recently proposed optimized dithering techniques are able to improve measurement quality obviously. However, those phase-based optimization methods are sensitive to the amount of defocusing while intensity-based optimization methods cannot reduce the phase error efficiently. This paper presents a novel method, minimizing a proposed objective function named intensity residual error (IRE), as well as a novel framework, optimizing pixels group by group, to construct binary patterns for high-quality 3D shape measurement. Both the simulation and experimental results show that this proposed algorithm can achieve phase quality improvements over other recently optimized dithering techniques with various amounts of defocusing.     

Three-dimensional shape measurement technique for shiny surfaces by adaptive pixel-wise projection intensity adjustment

Conventional methods based on analyses of the absolute gray levels of pixels in fringe pattern images are affected by the problems of image saturation, interreflection, and high sensitivity to noise when obtaining three-dimensional (3D) shape measurements of shiny surfaces. This study presents a robust, adaptive, and fast 3D shape measurement technique, which adaptively adjusts the pixel-wise intensity of the projected patterns, thus it avoids image saturation and has a high signal to noise ratio (SNR) during 3D shape measurement for shiny surfaces. Compared with previous time-consuming methods using multiple exposures and the projection of fringe patterns with multiple intensities, where a large number of fringe pattern images need to be captured, the proposed technique needs to capture far fewer pattern images for measurement. In addition, it can greatly reduce the time costs to obtain the optimal projection intensities by the fusion of uniform gray level patterns and coordinates mapping. Our experimental results demonstrate that the proposed technique can achieve highly accurate and efficient 3D shape measurement for shiny surfaces.     

子孔径拼接检测大口径非球面技术的研究

为了无需其他辅助光学元件就能够实现对大口径非球面的测量,提出了子孔径拼接干涉检测方法。并基于齐次坐标变换、最小二乘法以及Zernike多项式拟合建立了综合优化和误差均化的拼接数学模型;开发了子孔径拼接检测非球面算法软件,进行了计算机模拟和仿真实验;设计和搭建了子孔径拼接干涉检测装置,并利用子孔径拼接实现了对口径为350mm的双曲面的检测;为了分析和对比,对待测非球面进行零位补偿检测实验,子孔径拼接所得的面形分布和零位补偿检测所得的全口径面形分布都是一致的,其面形误差PV值和RMS值的偏差分别为0.032λ和0.004λ(λ=632.8nm)。从而提供了除零位补偿检测外另一种定量测试非球面尤其是大口径非球面的手段。     

Simple real-time 3-D displacement measurement by fringe analysis using a photorefractive interferometer

A simple 3-D displacement measurement method using a photorefractive interferometer is proposed and experimentally demonstrated. A photorefractive crystal attached to the sample under test is used to record an original spherical wave that provides a shifted reconstructed wave after displacement. The shifted wave interferes with direct wave to form an interferogram. By analyzing the fringe pattern the in-place and out-of-place displacements can be determined at the same time. This method works in real-time and is easy to operate with adequate accuracy comparable with or even better than that of other techniques.     

大型双曲面次镜面形检测技术现状及发展趋势

随着以双曲面为次镜的两镜光学系统在天文和空间光学等领域的应用日趋广泛,双曲面次镜的口径和相对口径越来越大,由此对双曲面次镜的面形检测技术提出了很高的要求。本文基于国外有代表性的双曲面次镜参数分析了其基本特征和发展趋势,重点介绍了国外大型双曲面次镜的面形检测技术,并对其中的关键技术进行了分析。同时,概述了国内双曲面次镜检测技术现状。最后,总结和展望了大型双曲面次镜面形检测技术发展趋势。提出今后一段时间内,高均匀性的光学透射材料,高精度、大口径的辅助元件以及基于子孔径拼接的检测方法和数据处理方法是该领域的研究重点。     

BP neural network applied to 3D object measurement based on fringe pattern projection

In the fringe projection profilometry, the traditional triangle method, such as Fourier-transform profilometry (FTP), is difficult to recover the stepped shape object from the deformed fringe pattern. In order to solve this problem, the neural network is introduced to deal with this kind of fringe patterns and gain the three-dimensional (3D) information of the measured object. By training the network, the relationship between the deformed fringe pattern and the height of the object can be obtained, and thereby the height of the object can be obtained. Furthermore, the object can be reconstructed perfectly without knowing the optical parameters of the experiment system. An obvious merit of this network method is that it can recover the 3D object in a short time and only need one deformed fringe pattern. Computer simulations and experiment validate the feasibility of the method.     

Selection and optimization of mirror structure of off-axis two-mirror afocal system北大核心CSCD

According to the structural characteristics of aspheric off-axis two-mirror optical system, the imaging characteristics of the system were analyzed by using primary aberration theory. Based on the characteristics of different aspheric surfaces, the vector expression of system aberrations was derived. Using the Seidel coefficients, the primary wave aberration of systems were expanded and values of system aberration for different aspheric surface shapes were specifically calculated. After the evaluation index of the off-axis structure was determined, the imaging qualities of different surface shape combinations were compared. Then the optimal surface shape selection method was analyzed by quantitative comparison results. The results show that compared with other reflector combination methods, the spherical aberration, coma and astigmatism of the off-axis double paraboloid system are all 0, the wavefront RMS is much better than λ/14 (λ=0.587 6 μm), and the Strehl ratio is greater than 0.8. According to the calculation results, it not only has a stronger ability to suppress multiple primary aberrations, but also can effectively compress the volume of the system. Copyright ©2022 Journal of Applied Optics. All rights reserved.     

利用计算机辅助装调检测矩形大口径离轴非球面的方法研究

通过非球面的零位补偿法,完成了对矩形大口径离轴非球面镜的检测。先用光学设计软件Zemax从理论上分析了在检测中会出现的现象,并结合计算机辅助装调技术,确定在检测过程中相对敏感的自由度,然后控制这些量,使补偿器和非球面的相对关系与理论设计相吻合,在Zygo相位干涉仪上测得最终结果。在λ=632.8nm时,中心圆口径与两个边缘圆口径面形误差RMS分别为0.022λ,0.037λ,0.032λ。检测结果,达到预期目的。