反射镜作为光学与机械系统的重要组成部分，在激光、空间观测、太阳能热发电、航空航天等领域的应用逐渐广泛，对反射镜面体的加工制造与检测提出了更为严峻的挑战，也进一步推动了光学元件加工技术向高精度高效率方向的发展，而衡量加工过程好坏的一个重要指标为光学面形的精度。相位测量偏折术作为一种非接触式面形检测技术，以其测量范围大、检测精度高以及适用于工业现场测量等优势得到了深入研究。本文以相位检测偏折技术为基础，从预知面形模型入手，针对该模型中相位提取与图像预处理等关键问题阐述了常见的解决方案，并对测量系统进行了整体设计和选型分析，采用基于平面镜反射的灵活标定手段，并结合模式法与区域法提出了新的三维面形重建技术，实现了反射物体表面快速高精度的形貌检测，为工业生产中评价反射物体加工质量提供了一种低成本高可靠性的有效手段。由于相位偏折检测最终只能得到被测物表面离散的梯度信息，需要一种方法能够将梯度测量数据恢复为物体表面三维形貌，然而常见的三维重建方法在测量精度、检测时间与鲁棒性等方面存在不足，因此研究一种旨在快速高精度地恢复大尺寸复杂物体面形的重构技术对工业镜面检测具有重要的实际意义。融合模式重构法与区域波前重构法这两种常用技术的优势，本文提出了一种新的三维重构方法，该方法将模式法计算得到的物体表面高度分布作为迭代初始值，代入区域波前重构法中的超松弛迭代过程，从而使重建结果更加有效地逼近被测物体的真实面形。通过计算机仿真和初步实验对其收敛速度快、测量精度高以及抗噪能力强等特点进行了有效验证。为了进一步提高测量精度，提出了一种基于LCD液晶屏和参考平面镜自由移动的系统标定方法，该方法仅需要将放置于摄像机视场范围内并投影双频正弦光栅的屏幕移动两次，即可完成摄像机与反射光线的标定，然后将其结果与全局优化相结合，应用到由参考平面镜标定获取的虚拟屏位姿评估上，最后利用光束法平差优化得到高精度的几何标定结果。仿真和实验均证明该标定方法操作简单灵活，能够有效提高重构面形精度并降低测量成本、加强抗噪声能力。将这种标定技术与改进的三维重建方法相结合，以相位测量偏折术对镜面反射物体进行检测，可满足工业检测对实时高效、高精度和强抗噪能力的需求。
Specular surfaces are becoming one of the leading parts in optical and mechanical system due to the increasing development of modern industry and high technology field. High performance requirements on specular objects in laser optics, space observation, concentrating solar power, aerospace and other research areas have challenged currently-available manufacturing and fabrication. Therefore, it is of practical significance to study precise surface metrology serving as the quality testing standard for fabrication process. As one kind of the non-contact profilometry for measuring specular elements, Phase Measuring Deflectometry (PMD) has been widely applied in optical testing since it is advantageous in large dynamic range, high measurement accuracy and fast detection speed.On the basis of the principal of PMD, the pre-knowledge model has been put forward as the foundation of optical measurement. The solutions of key points in PMD including phase extracting and unwrapping, image processing has been discussed in details. With the novel system calibration method by using reflections from a plane mirror and the improved 3D surface reconstruction technique combining model and zonal approaches, the measurement speed for specular objects is fast and the accuracy is high, providing an efficient, economical and flexible approach for PMD system in practical situations.In a PMD test, only the surface slope of test objects can be determined and there is a need to search a proper 3D shape recovery method to obtain the test surface from the measurements. Incorporating the modal estimation and zonal reconstruction approaches into a unifying scheme, the thesis introduces am improved 3D shape reconstruction version of specular surfaces. The modal estimation is firstly implemented to derive the coarse height information of the measured surface as initial iteration values. Then the real shape can be recovered utilizing a modified zonal wave-front reconstruction algorithm to simultaneously achieve consistently high accuracy and dramatically rapid convergence. Moreover, the iterative process based on an advanced successive over-relaxation technique shows a consistent rejection of measurement errors, guaranteeing the stability and robustness in practical applications. The reconstruction results of numerical example as well as experimentally measured sphere mirror demonstrate the validity and efficiency of the proposed improved method.System calibration is another fundamental factor influencing the precision of PMD. In order to advance PMD to higher accuracy, the thesis describes a flexible and simple system calibration method for specular surface metrology based on the combination of reflection rays determined by the varied points on a screen and reflection images of a plane mirror without fiducials placed at three different locations. The novel calibration method can make the measurement achieve high accuracy and robustness at low cost and with simple setup, which is verified by simulation and experiment. With the application of the improved reconstruction method and the calibration technique, PMD provides an efficient, economical and flexible approach for specular surface metrology in practical situations.
