Optimized pulse width modulation pattern strategy for threedimensional profilometry156
发表时间：20190710 00:00 Optimized pulse width modulation pattern strategy for threedimensional profilometry with projector defocusing Chao Zuo, Qian Chen, Shijie Feng, Fangxiaoyu Feng, Guohua Gu, and Xiubao Sui Jiangsu Key Laboratory of Spectral Imaging & Intelligent Sense, Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, China
Abstract Threedimensional profilometry by sinusoidal fringe projection using phaseshifting algorithms is usually distorted by the nonlinear intensity response of commercial video projectors. To overcome this problem, several methods including sinusoidal pulse width modulation (SPWM) were proposed to generate sinusoidal fringe patterns with binary ones by defocusing the project to some certain extent. However, the residual errors are usually nonnegligible for highly accurate measurement fields, especially when the defocusing level is insufficient. In this work, we propose two novel methods to further improve the defocusing technique. We find that by properly optimizing SPWM patterns according to some criteria, and combining SPWM technique with fourstep phaseshifting algorithm, the dominant undesired harmonics will have no impact on the phase obtained. We also propose a new sinusoidal fringe generation technique called tripolar SPWM, which can generate ideal sinusoidal fringe patterns with a very small degree of defocusing. Simulations and experiments are presented to verify the performance of these two proposed techniques. Files Citations Chao Zuo, Qian Chen, Shijie Feng, Fangxiaoyu Feng, Guohua Gu, and Xiubao Sui, "Optimized pulse width modulation pattern strategy for threedimensional profilometry with projector defocusing," Appl. Opt. 51, 44774490 (2012).
Results Fig. 1. 3D measurement results of a plaster geometric model using different patterns (fringe pitch 60 pixels) with different phaseshifting algorithms when the projector is slightly defocused. The first row shows the tested object with SBM pattern (a), the 3D results of three, four, and fivestep phaseshifting algorithms using SBM patterns (b)–(d). The second row shows the tested object with SPWM pattern (f c= 8f 0) (e), the 3D results of three, four, and fivesteps phaseshifting algorithms using SPWM patterns (f c= 8f 0) (f–h). The third row shows the tested object with SPWM pattern (f c = 9f 0) (i), the 3D results of three, four, and fivesteps phaseshifting algorithms using SPWM patterns (f c = 9f 0) (j)–(l). The forth row shows the tested object with tripolar SPWM pattern ( f c = 8f 0) (m), and the 3D results of three, four, and fivestep phaseshifting algorithms using tripolar patterns ( f c = 8f 0) (np). Fig. 2. 3D shape measurement of a complex sculpture using the proposed techniques (fringe pitch 48 pixels). (a) One of SPWM pattern with f c = 6f 0; (b) the measured object with the slightly defocused SPWM pattern; (c) 3D result with the SPWM plus four step phaseshifting method; (d) one of tripolar SPWM pattern with f c = 7f 0; (e) the measured object with the slightly defocused tripolar SPWM pattern; (f) 3D result with the tripolar SPWM plus threestep phaseshifting method. Methods Table 1. Sensitivity of Different PhaseShifting Algorithms to Harmonics. To analyze how each harmonic frequency component affects the calculated phase for different phaseshifting algorithms, we just added one specific harmonic component to the ideal sinusoid wave signals one time. Then we compared the calculated phase with the correct one, and we would know whether we can get a distortionfree phase even when the particular harmonic component exists. Table 1 summarizes the results. Fig. 1. Simulation results of SPWM (f c = 8f 0) using three to fivestep phaseshifting algorithms. (a) The original SPWM pattern; (b) the Gaussian smoothed version of (a); (c) frequency spectrum of (a); (d) frequency spectrum of (b); (e) the phase error of threestep algorithm (RMS: 0.2319 rad); (f) the phase error of fourstep algorithm (RMS: 0.0436 rad); (g) the phase error of fivestep algorithm(RMS: 0.1396 rad).
Fig.2 shows how the tripolar SPWM pattern is generated (f c = 10f 0). First, two highfrequency triangular carriers displaced by π shift in phase are compared with desired a sinusoidal pattern to get two bipolar SPWM patterns. Note the second bipolar SPWM pattern corresponding to the π shifted triangular carrier (shown in red) should be inversed; i.e., when the intensity value of the sinusoidal wave form is less than the triangular waveform, the value of SPWM pattern is “1”; otherwise, the intensity value is “0.” Then the resultant tripolar SPWM waveform is the difference of the two bipolar SPWM patterns.
Fig. 3. Simulation results of tripolar SPWM(f c = 8f 0) using three to fivestep phaseshifting algorithms. (a) The originaltripolar SPWM pattern; (b) the Gaussian smoothed version of (a) (filter size 8 pixels, standard deviation 1.5 pixels); (c) frequency spectrumof (a); (d) frequency spectrum of (b); (e) the phase error of threestep algorithm (RMS: 0.0488 rad); (f) the phase error of fourstep algorithm(RMS: 0.0468 rad); (g) the phase error of fivestep algorithm (RMS: 0.0389 rad).
 Contact Chao Zuo Associate professor at the school of Electronic and Optical Engineering Email: surpasszuo@163.com Nanjing University of Science and Technology, Jiangsu Province (210094), P.R.China
Qian Chen Dean of the school of Electronic and Optical Engineering Email: chenqian@njust.edu.cn Nanjing University of Science and Technology, Jiangsu Province (210094), P.R.China
Shijie Feng Ph.D. Candidate of NJUST Email:geniusshijie@163.com ( or 311040574@njust.edu.cn) Nanjing University of Science and Technology, Jiangsu Province (210094), P.R.China
