High-speed 3D shape measurement for dynamic scenes using bi-frequency tripolar PWM fringe projection

High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection

Chao Zuo, Qian Chen, Guohua Gu, Shijie Feng, Fangxiaoyu Feng, Rubin Li, Guochen Shen

Jiangsu Key Laboratory of Spectral Imaging & Intelligent Sense,

Nanjing University of Science and Technology, Nanjing, Jiangsu Province 210094, China

Abstract

This paper introduces a high-speed three-dimensional (3-D) shape measurement technique for dynamic scenes by using bi-frequency tripolar pulse-width-modulation (TPWM) fringe projection. Two wrapped phase maps with different wavelengths can be obtained simultaneously by our bi-frequency phase-shifting algorithm. Then the two phase maps are unwrapped using a simple look-up-table based number-theoretical approach. To guarantee the robustness of phase unwrapping as well as the high sinusoidality of projected patterns, TPWM technique is employed to generate ideal fringe patterns with slight defocus. We detailed our technique, including its principle, pattern design, and system setup. Several experiments on dynamic scenes were performed, verifying that our method can achieve a speed of 1250 frames per second for fast, dense, and accurate 3-D measurements.

Files

            PDF          Media 1        Media 2

Citations

Zuo, C., Chen, Q., Gu, G., Feng, S., Feng, F., Li, R., & Shen, G. (2013). High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection. Optics and Lasers in Engineering, 51(8), 953-960.

Results

Fig. 1. (a)–(e) Captured scene with fringe patterns; (f) wrapped phase map 1 (fringe pitch 48 pixels); (g) wrapped phase map 2 (fringe pitch 28 pixels); (h) the segmented regions identified by the rounded (p2ϕ1−p1ϕ2)/2π for the LUT; (i) absolute phase map 1(fringe pitch 48 pixels); (g) absolute phase map 2 (fringe pitch 28 pixels); (k) one cross-section (highlighted in (h)) of the measured (p2ϕ1−p1ϕ2)/2π and its corresponding ideal values; (f) error signal between the ideal stair signal and the calculated one.

Fig. 2. Reconstructed 3-D result with color-coded depth (a) and texture (b) (Media 1).

Fig. 3. Measurement result of a rotating fan (1250Hz). (a) Photograph of the measured fan; (b) one captured fringe image of the fan; (c) the reconstructed 3-D result (Media 2).

Methods

Fig. 1. Number-theoretical phase unwrapping for two-wavelengths of 3 and 5 pixels. Using values of (3ϕ1−5ϕ2)/2π, we can determine fringe order pairs (k1, k2) without ambiguity.

The number-theoretical method can successfully cope even with sets of wavelengths which are not necessarily relative primes. More specifically, it correctly unwraps the phase up to the value in the absolute phase which equals to LCM (λ1,λ2) source. Here LCM () represents a function whose output is the least common multiple for input parameters, which is a minimal number divisible by the wavelengths used.

Fig. 2. TPWM waveform generation and harmonics distribution. (a) The sinusoidal and the two modulation triangle waveforms displaced by π ( fc = 10 f0); (b) the resultant TPWM pattern; (c) frequency spectrum of (b).

Fig. 2 shows an example of TPWM pattern with fc = 10 f0, where fc and f0 stand for the frequency of triangular carrier and the sinusoidal waveform, respectively. The TPWM waveform is generated by comparing two high-frequency triangular carrier displaced by π shift with the desired sinusoidal waveform. Fig. 2(c) shows the spectrum of the TPWM waveform. It can be observed that the spectrum of the TPWM pattern has peaks around the frequency 2fc, so they can be easily suppressed even with a nearly focused optical system, and thus an quasi-ideal sinusoidal pattern can be obtained.

Fig. 3. TPWM patterns and their decompositions. (a) Fringe pitch 48 pixels; (b) Fringe pitch 28 pixels.

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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