Laser & Optoelectronics Progress, Volume. 58, Issue 11, 1112008(2021)
A Random Two-Step Phase Shift Algorithm Based on Polynomial Fitting Background Light
Figures & Tables(13)
Fig. 2. Initial setting values. (a) Initial wave surface to be measured; (b) background light; (c) modulation
Fig. 3. Background light with different K values. (a) Estimated values; (b) relative residual error
Fig. 4. Background light at K = 5. (a) Estimated values; (b) relative residual error
Fig. 5. Results of the surface shape at K=5. (a) Fitting surface shape; (b) surface shape residual error
Fig. 6. Surface shape results with different methods. (a) PV values of surface shape residual error; (b) RMS values of surface shape residual error
Fig. 7. Phase shift interferograms. (a) b=0.01, δ=0; (b) b=0.01, δ=π/4; (c) b=0.15, δ=0; (d) b=0.15, δ=π/4
Fig. 8. Relationship between illumination nonuniformity coefficient b and surface shape residual error
Fig. 9. Surface shape residual error of the analog interferogram after phase recovery under different noise intensities with different methods. (a) PV values; (b) RMS values
Table 1. Standard deviation of background light relative residual error
View tableTable 1. Standard deviation of background light relative residual error
K 0 1 2 3 4 5 6 7 Standard deviation 0.394 0.324 0.049 0.048 0.043 0.025 0.039 0.052
Table 2. Results of the algorithm
View tableTable 2. Results of the algorithm
K 0 1 2 3 4 5 6 7 0.1679 0.1658 0.2480 0.2493 0.2497 0.2507 0.2503 0.2496 0.0821 0.0842 0.0020 0.0007 0.0003 0.0007 0.0003 0.0004 Fitting surface shape PV/λ 1.7911 1.7949 2.0450 2.0464 2.0343 2.0376 2.0379 2.0351 Fitting surface shape RMS/λ 0.3080 0.3486 0.4161 0.4161 0.4159 0.4159 0.4161 0.4159 Surface shape residual error PV/λ 1.8446 1.4164 0.0144 0.0140 0.0135 0.0094 0.0124 0.0171 Surface shape residual error RMS/λ 0.3151 0.2090 0.0014 0.0015 0.0018 0.0013 0.0018 0.0023 Time/min 0.006 0.048 0.191 0.524 1.295 2.629 4.943 9.702
Table 3. Comparsion of the operation time of phase recovery and surface shape residual error of analog interferograms with different pixel number
View tableTable 3. Comparsion of the operation time of phase recovery and surface shape residual error of analog interferograms with different pixel number
Image size /(pixel×pixel） Time /min Surface shape residual error PV/λ Surface shape residual error RMS/λ 200200 0.631 0.0110 0.0016 500500 5.027 0.0081 0.0011 800×800 24.677 0.0118 0.0014
Table 4. Results of PFBL and GS algorithms under different phase shifts
View tableTable 4. Results of PFBL and GS algorithms under different phase shifts
Theoretical value of phase shift/π 0.1 0.2 0.3 0.4 0.5 0.6 0.7 PFBL Estimated value of phase shift/π 0.1003 0.2005 0.3008 0.4008 0.5006 0.5991 0.6993 Residual error of phase shift/π 0.0003 0.0005 0.0008 0.0008 0.0006 0.0009 0.0007 Time/min 2.77 2.66 2.75 2.76 2.73 2.71 2.63 GS Estimated value of phase shift/π 0.1226 0.2197 0.2902 0.3858 0.4825 0.5869 0.6845 Residual error of phase shift/π 0.0226 0.0197 0.0098 0.0142 0.0175 0.0131 0.0155 Time/min 5.43 5.33 5.47 5.38 5.45 5.42 5.36
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Jing Li, Ailing Tian, Dasen Wang, Bingcai Liu, Xueliang Zhu, Hongjun Wang. A Random Two-Step Phase Shift Algorithm Based on Polynomial Fitting Background Light[J]. Laser & Optoelectronics Progress, 2021, 58(11): 1112008
Paper Information
Category: Instrumentation, Measurement and Metrology
Received: Nov. 5, 2020
Accepted: Dec. 14, 2020
Published Online: Jun. 7, 2021
The Author Email: Ailing Tian (ailintian@xatu.edu.cn)
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