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摘要:
在相移轮廓术中，非标准相移轮廓术结合时域相位展开算法仅需较少的条纹图案，因而具备较高的测量效率。鉴于条纹频率对测量精度有显著影响，本文分析了非标准相移轮廓术的时域相位展开中的相位误差，并进一步评估其可靠性。研究发现，相位展开的可靠性与条纹频率分配密切相关。据此，本文引入了一种最优条纹频率分配策略。基于该策略，本文对非标准相移轮廓术的不同频率组合进行了对比实验，实验结果显示，相比于3
f h 1+2f h 2+2f h 3外差法的非最优频率组合，本文提出的频率组合的平均错误率降低了62.96%；相比于2f h +2f m +3f l 分层法的非最优频率组合，本文提出的频率组合的平均错误率降低了49.23%。Abstract:In phase-shifting profilometry, the non-standard phase-shifting profilometry combined with the temporal phase unwrapping algorithm requires fewer fringe patterns, thereby achieving higher measurement efficiency. Given that fringe frequency has a significant effect on measurement accuracy, this paper analyzes phase errors in the temporal phase unwrapping of the non-standard phase-shifting profilometry and further evaluates its reliability. It is found that the reliability of phase unwrapping is closely related to the allocation of fringe frequencies. Consequently, an optimal fringe frequency allocation strategy is proposed. Based on this strategy, this paper conducts comparative experiments on different frequency combinations of non-standard phase-shifting profilometry, and the experimental results show that compared with the non-optimal frequency combinations of the 3
f h 1+2f h 2+2f h 3 heterodyne algorithm, the average error rate of the frequency combination proposed in this paper is reduced by 62.96%; compared with the non-optimal frequency combinations of the 2f h +2f m +3f l hierarchical algorithm, the average error rate of the frequency combination proposed in this paper is reduced by 49.23%. -
图 1 双频与三频TPU算法的重建结果对比。 (a) 3-step和{fh=64, fm=8, fl=1}；(b) 3-step和{fh=64, fl=1}；(c) 3fh+2fm+2fl和{fh=64, fm=8, fl=1}；(d) 3fh+2fl和{fh=64, fl=1}；
Figure 1. Comparison of reconstruction results between dual-frequency and triple-frequency TPU algorithms. (a) 3-step and {fh=64, fm=8, fl=1};(b) 3-step and {fh=64, fl=1};(c) 3fh+2fm+2fl and {fh=64, fm=8, fl=1};(d) 3fh+2fl and {fh=64, fl=1};
图 2 3fh1+2fh2+2fh3算法的包裹相位误差方差
Figure 2. Wrapped phase error variances for 3fh1+2fh2+2fh3 algorithm
图 3 仿真曲面的三维重建结果。(a) 仿真曲面(含放大图)；(b) { fh=169, fm=13, fl=1}；(c) { fh=169, fm=5, fl=1}；(d) { fh=169, fm=20, fl=1}
Figure 3. The 3D reconstruction results of the simulated surface. (a) simulated surface (with magnified view); (b) { fh=169, fm=13, fl=1}; (c) { fh=169, fm=5, fl=1}; (d) { fh=169, fm=20, fl=1}
图 4 3fh1+2fh2+2fh3外差TPU算法的重建结果比较。 (a) 3fh1+2fh2+2fh3和{fh1=153, fh2=148, fh3=144}；(b) 3fh1+2fh2+2fh3和{fh1=153, fh2=143, fh3=134}；(c) 3fh1+2fh2+2fh3和{fh1=153, fh2=133, fh3=114}；(d) 12-step和{fh1=153, fh2=148, fh3=144}；(e) 12-step和{fh1=fh1=153, fh2=143, fh3=134}；(f) 12-step和{fh1=153, fh2=133, fh3=114}；(g) 横截面对比(第600行)；(h)为(g)的放大视图
Figure 4. Comparison of reconstruction results based on 3fh1+2fh2+2fh3 heterodyne TPU. (a) 3fh1+2fh2+2fh3 and {fh1=153, fh2=148, fh3=144}; (b) 3fh1+2fh2+2fh3 and {fh1=153, fh2=143, fh3=134}; (c) 3fh1+2fh2+2fh3 and {fh1=153, fh2=133, fh3=114}; (d) 12-step and {fh1=153, fh2=148, fh3=144}; (e) 12-step and {fh1=153, fh2=143, fh3=134}; (f) 12-step and {fh1=153, fh2=133, fh3=114}; (g) cross-sectional comparison (line 600); (h) larger view of (g)
图 5 基于2fh+2fm+3fl分层TPU算法的重建结果比较。(a) 2fh+2fm+3fl和{fh=181, fm=6, fl=1}；(b) 2fh+2fm+3fl和{ fh=181, fm=16, fl=1}；(c) 2fh+2fm+3fl和{fh=181, fm=30, fl=1}；(d) 12-step和{fh=181, fm=6, fl=1}；(e) 12-step和{ fh=181, fm=16, fl=1}(f) 12-step和{fh=181, fm=30, fl=1}；(g) 横截面对比(第170行)；(h)为(g)的放大视图
Figure 5. Comparison of reconstruction results based on 2fh+2fm+3fl hierarchical TPU. (a) 2fh+2fm+3fl and {fh=181, fm=6, fl=1}; (b) 2fh+2fm+3fl and {fh=181, fm=16, fl=1}; (c) 2fh+2fm+3fl and {fh=181, fm=30, fl=1}; (d) 12-step and {fh=181, fm=6, fl=1}; (e)12-step and {fh=181, fm=16, fl=1}; (f) 12-step and {fh=181, fm=30, fl=1}; (g) cross-sectional comparison (line 170); (h) larger view of (g)
表 1 非标准三频外差TPU的最优频率组合
Table 1. Optimal frequency combinations for non-standard triple-frequency heterodyne TPU
fh1 fh2 fh3 3fh1+2fh2+2fh3 153 143 134 2fh1+2fh2+3fh3 160 149 139 
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表 2 非标准三频分层TPU的最优频率组合
Table 2. Optimal frequency combinations for non-standard triple-frequency hierarchical TPU
fh fm fl 3fh+2fm+2fl 169 13 1 2fh+2fm+3fl 181 16 1
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表 3 基于3fh1+2fh2+2fh3外差TPU算法的定量比较
Table 3. Quantitative comparison based on 3fh1+2fh2+2fh3 heterodyne TPU
{fh1, fh2, fh3} Error rate/% RMSE/rad {153, 143, 134} 11.76 10.4789 {153, 148, 144} 30.41 11.3039 {153, 133, 114} 33.18 24.6249
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表 4 基于2fh+2fm+3fl分层TPU的定量比较
Table 4. Quantitative comparison based on 2fh+2fm+3fl hierarchical TPU
{fh, fm, fl} Error rate/% RMSE/rad {181, 16, 1} 4.56 1.5398 {181, 6, 1} 15.41 3.9469 {181, 30, 1} 6.33 4.5043
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