﻿ 结合线结构光立体视觉和条纹反射法的三维轮廓检测系统
 光学仪器  2019, Vol. 41 Issue (5): 85-90 PDF

3D shape measurement system based on line structure light stereo vision and fringe reflection
BIN Boyi, WAN Xinjun, XIE Shuping, LÜ Song, SONG Ke
School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: With the increasing commercial application of free-form surfaces, the profile measurement capability of related molds and optical components has become a key bottleneck in the development and application of free-form optics, and the demand for free-form optics inspection tools is also increasing. In this paper, we developed an integrated free-form optics profile measurement system based on the fringe reflection principle, and the system is also combined with a laser stripe stereo vision measurement capability. The developed system is capable of measuring both rough surfaces and smooth optical surfaces. The measurement experiments prove that the current developed system can measure free-form optics with a diagonal size of approximately 300 mm, and the measurement uncertainty within ±1 μm.
Key words: fringe reflection    stereo vision    free-form optics

1 基本原理 1.1 线结构光双目立体视觉数学模型

 图 1 立体空间下线结构光双目成像的原理 Figure 1 Principle of laser line binocular imaging in the stereo space

 $\left\{ \begin{split}&{s_{\rm L}}\left[ {\begin{array}{*{20}{c}} {{X_{\rm L}}}\\ {{Y_{\rm L}}}\\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{f_{\rm L}}}&0&0\\ 0&{{f_{\rm L}}}&0\\ 0&0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_{\rm R}}}\\ {{y_{\rm R}}}\\ {{z_{\rm R}}} \end{array}} \right] \\ &{s_{\rm R}}\left[ {\begin{array}{*{20}{c}} {{X_{\rm R}}}\\ {{Y_{\rm R}}}\\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{f_{\rm R}}}&0&0\\ 0&{{f_{\rm R}}}&0\\ 0&0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_{\rm L}}}\\ {{y_{\rm L}}}\\ {{z_{\rm L}}} \end{array}} \right] \end{split} \right.$ (1)

 $\left[ \begin{array}{c}{x_{\rm R}} \\ {y_{\rm R}} \\ {z_{\rm R}}\end{array}\right]={ M} \left[ \begin{array}{c}{x_{\rm L}} \\ {y_{\rm L}} \\ {z_{\rm L}} \\ {1}\end{array}\right] \\$ (2)

 $k\left[ \!{\begin{array}{*{20}{c}} {{X_R}}\\ {{Y_R}}\\ 1 \end{array}}\! \right] = \left[ \!{\begin{array}{*{20}{c}} {{f_R}{r_1}}&{{f_R}{r_2}}&{{f_R}{r_3}}&{{f_R}{t_1}}\\ {{f_R}{r_4}}&{{f_R}{r_5}}&{{f_R}{r_6}}&{{f_R}{t_2}}\\ {{r_7}}&{{r_8}}&{{r_9}}&{{t_3}} \end{array}}\! \right]\left[\!\! {\begin{array}{*{20}{c}} {z\dfrac{{{X_L}}}{{{f_L}}}}\\ {z\dfrac{{{Y_L}}}{{{f_L}}}}\\ z\\ 1 \end{array}}\!\! \right]$ (3)

 $\left\{\!\!\begin{array}{l}{x\!=\!z \dfrac{X_{\rm L}}{f_{\rm L}}} \\ {y\!=\!z \dfrac{Y_{\rm L}}{f_{\rm L}}} \\ {z\!=\!\dfrac{f_{\rm L}\left(f_{\rm L} t_{1}-X_{\rm L} t_{3}\right)}{X_{\rm R}\left(r_{7} X_{\rm L}\!+\!r_{8} Y_{\rm L}\!+\!r_{9} f_{\rm L}\right)\!-\!f_{\rm R}\left(r_{1} X_{\rm L}\!+\!r_{2} Y_{\rm L}+r_{3} f_{\rm L}\right)}}\!\!\!\!\!\!\!\!\!\!\!\!\! \\ \;\;\;{\!=\!\dfrac{f_{\rm L}\left(f_{\rm L} t_{2}-X_{\rm L} t_{3}\right)}{X_{\rm R}\left(r_{7} X_{\rm L}\!+\!r_{8} Y_{\rm L}\!+\!r_{9} f_{\rm L}\right)\!-\!f_{\rm R}\left(r_{4} X_{\rm L}\!+\!r_{5} Y_{\rm L}\!+\!r_{6} f_{\rm L}\right)}}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\end{array}\right. \!\!\!\!\!\!$ (4)

1.2 PMD测量方法基本原理

 图 2 相位测量偏折测量法的原理 Figure 2 General scheme for phase measuring deflectometry

 ${{n}} = \frac{{{{r}} - {{i}}}}{ \left\|{{{r}} - {{i}}}\right\|} = \left[ {{{\left( {\frac{{{{r}} - {{i}}}}{ \left\|{{{r}} - {{i}}}\right\|}} \right)}_{{x}}}, {{\left( {\frac{{{{r}} - {{i}}}}{ \left\|{{{r}} - {{i}}}\right\|}} \right)}_{{y}}}, {{\left( {\frac{{{{r}} - {{i}}}}{ \left\|{{{r}} - {{i}}}\right\|}} \right)}_{{z}}}} \right]$ (5)

 ${{n}} = \left( { - \frac{p}{N}, - \frac{q}{N}, \frac{1}{N}} \right)$ (6)

 $\left\{ \begin{split} &\dfrac{{\partial x}}{{\partial z}} = - \dfrac{{{{\left( {\dfrac{{{{r}} - {{i}}}}{\left\|{{{r}} - {{i}}}\right\|}} \right)}_{{x}}}}}{{{{\left( {\dfrac{{{{r}} - {{i}}}}{\left\|{{{r}} - {{i}}}\right\|}} \right)}_{{z}}}}} \\ & \dfrac{{\partial y}}{{\partial z}} = - \dfrac{{{{\left( {\dfrac{{{{r}} - {{i}}}}{\left\|{{{r}} - {{i}}}\right\|}} \right)}_{{y}}}}}{{{{\left( {\dfrac{{{{r}} - {{i}}}}{\left\|{{{r}} - {{i}}}\right\|}} \right)}_{{z}}}}} \end{split} \right.$ (7)

 $I\left( {x, y} \right) = a\left( {x, y} \right) + b\left( {x, y} \right)\cos \left[ {\varphi \left( {x, y} \right)} \right]$ (8)

 $\varphi \left( {x, y} \right) = {\arctan }\frac{{{I_4} - {I_2}}}{{{I_1} - {I_3}}}$ (9)

2 系统组成

 图 3 本文搭建的系统示意图 Figure 3 Schematic diagram of the system
3 实验结果及分析

 图 4 待测件和采集过程中拍摄到的线激光图片和反射条纹图片 Figure 4 Subject under test （SUT） and images captured by the cameras during the measurement

 图 5 线激光扫描的结果和PMD测量结果 Figure 5 Line laser scanning result and PMD measurement result

 图 6 CAD模型和PMD测量的点云数据三维对比结果 Figure 6 Comparison of CAD model and PMD measured point cloud data

 图 7 对光学平晶的测量结果 Figure 7 Measurement result of an optic flat
4 结　论

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