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Three-dimensional shape measurement of composite surface based on defocused binary display and fringe projection
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摘要:
由于复合表面物体中漫反射部分和镜面部分反射性质不同，受到相机景深的限制，镜面成像的正弦条纹发生离焦，从而引起相位误差。为了实现复合表面物体的高效、高精度测量，本文提出了一种离焦二值结合正弦条纹的复合表面三维形貌测量方法。首先，本文基于刃边法与二次模糊法对系统离焦程度进行分区标定，解决了由于相机倾斜放置导致参考面离焦程度不同的问题。然后，建立二值条纹相位误差模型，确定最佳条纹宽度和离焦量范围。最后，对轻微离焦区域的二值条纹进行离焦补偿，确保相机采集的条纹均在最佳离焦范围内。在此基础上进行三维形貌测量。实验结果表明，所提方法使镜面部分误差从原来的0.033 mm降至0.019 mm，提高了复合表面测量精度。
Abstract:Due to the different reflective properties of the diffuse and specular components in composite surface objects and the limitations imposed by the camera depth of field, defocusing of sinusoidal fringes occurs in specular imaging, leading to phase errors. To achieve the efficient and high-precision measurement of composite surface objects, this paper proposes a method for three-dimensional surface topography measurement by combining defocused binary patterns with sinusoidal fringes. Firstly, the paper partitions and calibrates the defocus level of the system based on the edge and second-order blur methods, addressing the issue of varying defocus levels of the reference surface due to the tilted placement of the camera. Then, a binary fringe phase error model is established to determine the optimal fringe width and the defocus range. Finally, defocus compensation is applied to the binary fringes in the slightly defocused region, ensuring that the captured fringes are within the optimal defocus range. Three-dimensional surface topography measurement is conducted based on this approach. Experimental results show that the proposed method reduces the error in the specular component from 0.033 mm to 0.019 mm, thereby improving the accuracy of composite surface measurement.
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Overview: In the field of smart manufacturing, there is a growing need for the precise measurement of composite surface components exhibiting both specular and diffuse reflection characteristics. The construction of a measurement system based on fringe projection and phase-shifting deflectometry allows for the non-destructive and rapid acquisition of three-dimensional information for composite surface objects. However, the structured light by reflecting from the measured surface, exhibits different imaging positions, significantly increasing the difficulty in camera focusing and leading to defocusing blur issues, causing phase errors.
To expand the system measurement range and achieve the efficient and high-precision measurement of composite surface objects, this paper proposes a method for three-dimensional surface topography measurement by combining defocused binary patterns with sinusoidal fringes. Firstly, considering the varying defocus levels on the same plane due to the angle between the camera and the reference plane, the paper introduces a method combining the edge and second-order blur methods. It utilizes a chessboard pattern to accurately partition and quantify the defocus level, completing system defocus calibration. Secondly, based on the established model of optimal defocus, period, and phase error for binary fringes, and considering the actual blur level within the system measurement range, the paper selects the optimal width of binary fringes and the range of defocus, determining smooth regions with minimal phase error. Then, considering that the tilted placement of the camera may cause some regions of the fringes to deviate from sinusoidal behavior, slightly defocused fringes outside the smooth regions are pre-compensated with a Gaussian filter. This is done by calculating the parameters of the Gaussian function and convolving it with the fringes, ensuring that the deformed fringe patterns captured by the camera are within the optimal defocus range. This operation effectively suppresses high-order harmonics of binary fringes, expanding their applicability. Finally, appropriate binary fringes are displayed on two screens, and sinusoidal projection is displayed on the project, allowing the camera to capture clear sinusoidal and quasi-sinusoidal fringes. This method completes three-dimensional surface topography measurement for the composite surface.
The method employs the combination of the edge method and the second-order blur method for defocus assessment, achieving a measurement accuracy of 0.1 pixel or more and ensuring accurate measurement of full-field defocus in the dual-screen system. Experimental results show that the combination of binary and sinusoidal fringes proposed in this paper reduces errors in the specular part and the transition region between specular and diffuse components from 0.033 mm to 0.019 mm, enhancing the accuracy of composite surface measurement.
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图 1 复合表面测量系统中相机景深示意图
Figure 1. Schematic diagram of camera depth of field in composite surface measurement system
图 5 基于条纹投影和直接相位偏折的复合表面测量系统模型
Figure 5. Composite surface measurement system model based on fringe projection and direct phase measure deflectometry
图 7 离焦量化方法仿真。(a)仿真刃边法结果分析；(b)同一位置实际高斯核估计
Figure 7. Defocus quantification method simulation. (a) Analysis of results of simulated edge method; (b) Estimation of defocus amount
图 8 离焦标定。(a)边缘离焦值；(b)多个位置平面拟合离焦值
Figure 8. Defocus calibration. (a) Edge defocus value; (b) Defocus values fitted to multiple positions using plane fitting
图 9 相位误差模型分析。(a)相位误差仿真；(b)实验误差对比
Figure 9. Analysis of phase error model. (a) Simulation of the phase error; (b) Experimental and simulation error comparison
图 10 LCD-参考面的最佳离焦分析。(a)最佳离焦量选择；(b) LCD离焦范围
Figure 10. Optimal defocus analysis of the LCD-reference surface. (a) Optimal defocusing selection; (b) Defocusing range of LCD
图 11 参考平面频谱分析。(a)前端二值；(b)后端二值；(c)前端调制二值
Figure 11. Reference plane spectrum analysis. (a) Binary at the front end; (b) Binary at the back end; (c) Modulated binary at the front end
图 12 复合表面物体。(a)电脑标识；(b)环形台阶
Figure 12. Composite surfaces object. (a) Computer identification; (b) Ring step
图 13 LCD-被测台阶的最佳离焦分析。(a)最佳离焦量选择；(b) LCD部分范围离焦量
Figure 13. Optimal defocus analysis of the LCD-measured step. (a) Optimal defocusing selection; (b) Defocusing amount for LCD component
图 14 台阶相位展开及对比。(a)未调制的二值条纹图；(b)传统正弦条纹图；(c)调制后的二值条纹图；(d)正弦条纹图；(e)图(a)的绝对相位；(f)图(b)的绝对相位；(g)图(c)的绝对相位；(h)图(d)的绝对相位
Figure 14. Phase unwrapping and comparison of step. (a) Uncompensated binary fringes; (b) Sinusoidal fringes; (c) Compensated binary fringes; (d) Sinusoidal fringes; (e) Absolute phase of (a) ; (f) Absolute phase of (b) ; (g) Absolute phase of (c) ; (h) Absolute phase of (d)
图 15 镜面部分三维形貌对比。(a)未调制的二值条纹；(b)正弦条纹；(c)调制后的二值条纹
Figure 15. Comparison of three-dimensional topography for specular components. (a) Uncompensated binary fringes; (b) Sinusoidal fringes; (c) Compensated binary fringes
图 16 复合表面物体三维形貌恢复。(a)电脑标识表面形貌；(b)台阶重建深度
Figure 16. Results of three-dimensional surface topography reconstruction for composite objects. (a) Surface topography of computer identification; (b) Reconstructed depth of step
表 1 三维结果对比
Table 1. Comparison of three-dimensional results
Step
planeMeasured by
CMM /mmMeasured by
proposed value /mmAbsolute
error /mmBinary-sin
fringeSin fringe Binary-sin
fringeSin fringe 1-2 3.000 2.978 2.970 0.022 0.030 2-3 4.000 4.019 4.033 0.019 0.033 3-4 5.000 5.039 5.051 0.039 0.051 4-5 5.500 5.523 5.521 0.023 0.021 5-6 6.500 6.478 6.477 0.022 0.023 
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