Three-Dimensional Measurement of Specular Surfaces Using Phase Measuring Deflectometry

Fig. 4. Absolute phase distribution for effective measuring area of concave mirror. (a) Three-dimensional figure (transverse fringe); (b) vertical view (transverse fringe); (c) three-dimensional figure (vertical fringe); (d) vertical view (vertical fringe)

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Fig. 5. Unit normal vector distribution of concave mirror. (a) Three-dimensional figure (component along x axis); (b) vertical view (component along x axis); (c) three-dimensional figure (component along y axis); (d) vertical view (component along y axis); (e) three-dimensional figure(component along z axis); (f) vertical view (component along z axis)

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Fig. 6. Measuring results of concave mirror. (a) Three-dimensional figure; (b) vertical view

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Table 1. Parameters for camera model
View table
Table 1. Parameters for camera model
Parameter Expression Degree of freedom
Perspective collineation A= $\begin{matrix} [\begin{matrix} α_{x} & g & u_{0} \\ 0 & α_{y} & v_{0} \\ 0 & 0 & 1 \end{matrix}] \end{matrix}$ 5
Radial distortion, tangential distortion k₁,k₂,p₁,p₂ 4
External parameters R= $\begin{matrix} [\begin{matrix} r_{1} & r_{2} & r_{3} \\ r_{4} & r_{5} & r_{6} \\ r_{7} & r_{8} & r_{9} \end{matrix}] \end{matrix}$ ,t= $\begin{matrix} [\begin{matrix} t_{x} \\ t_{y} \\ t_{z} \end{matrix}] \end{matrix}$ 6

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Beiting Lü. Three-Dimensional Measurement of Specular Surfaces Using Phase Measuring Deflectometry[J]. Laser & Optoelectronics Progress, 2019, 56(3): 031201

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