Study on phase error of binary fringe from defocusing projection
doi: 10.37188/CO.EN-2025-0046
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摘要:
由于实际的离焦投影系统产生非线性效应，影响了相位测量精度，为此对二值条纹离焦投影的相位误差展开研究。基于该领域研究现状分析，给出了非线性系统中变形条纹图信号光强的分布表达式，分析了频谱中出现了高级频谱成份并与基频成份混在一起产生混叠现象的原因。采用了对投影仪进行离焦处理的方法滤除频谱中的高级频谱成份，过滤出其中的一个基频成份并进行逆傅里叶变换，得到空间域中的条纹光强表达式；采用相移算法与相位展开得到包含连续信号的连续相位，推导出了在实际测量中进行相位展开后的误差表达式。用仿真与实验验证了基本原理的正确分析，仿真结果表明，采用本文方法所得误差值分别为二值条纹离焦法的34.51%、参考文献[1]的44.83%、参考文献[10]的67.83%；实验结果表明，采用本文方法具有良好的相位恢复效果，且相对应的相位误差也比较小。
Abstract:Due to the nonlinear effects produced by the actual defocusing projection system, which affect the accuracy of phase measurement, the phase error of binary fringe defocusing projection was studied. Based on the analysis of the current study status in the field, an expression for the intensity distribution of deformed fringe pattern signal in nonlinear systems is given, and the reasons for both high-order spectra components occurrence and their mixing with the fundamental frequency components, resulting in spectra overlapping, are analyzed. The method of defocusing the projector was employed to remove the higher-order harmonic components in the spectra domain and filter out one of the fundamental frequency components. An inverse Fourier transform was then performed on the spectra to obtain the expression of fringe intensity in the spatial domain. The continuous phase containing continuous signals was obtained using the phase-shift algorithm and phase unwrapping, and the expression for phase error after unwrapping in actual measurement systems was derived. The correct analysis of the basic principles has been verified through simulation and experiments. The simulation results indicate that the errors value obtained by the method mentioned in this paper are 34.51% for the binary fringe defocusing method, 44.83% for method of reference [1], and 67.83% for method of reference [10], respectively. The experiment results indicate that the phase recovered by using our method has good effects, and the corresponding phase error is relatively small.
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Key words:
- phase measurement /
- defocusing projection /
- system nonlinear /
- phase-shifting /
- phase error
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