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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 21 — Oct. 11, 2010
  • pp: 21628–21635
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High-speed and dense three-dimensional surface acquisition using defocused binary patterns for spatially isolated objects

Yong Li, Cuifang Zhao, Yixian Qian, Hui Wang, and Hongzhen Jin  »View Author Affiliations


Optics Express, Vol. 18, Issue 21, pp. 21628-21635 (2010)
http://dx.doi.org/10.1364/OE.18.021628


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Abstract

The three-dimensional (3-D) shape measurement using defocused Ronchi grating is advantageous for the high contrast of fringe. This paper presents a method for measuring spatially isolated objects using defocused binary patterns. Two Ronchi grating with horizontal position difference of one-third of a period and an encoded pattern are adopted. The phase distribution of fringe pattern is obtained by Fourier analysis method. The measurement depth and range is enlarged because the third harmonic component and background illumination is eliminated with proposed method. The fringe order is identified by the encoded pattern. Three gray levels are used and the pattern is converted to binary image with error diffusion algorithm. The tolerance of encoded pattern is large. It is suited for defocused optical system. We also present a measurement system with a modified DLP projector and a high-speed camera. The 3-D surface acquisition speed of 60 frames per second (fps), with resolution of 640 × 480 points and that of 120 fps, with resolution of 320 × 240 points are archived. If the control logic of DMD was modified and a camera with higher speed was employed, the measurement speed would reach thousands fps. This makes it possible to analyze dynamic objects.

© 2010 OSA

1. Introduction

Optical 3-D shape measurement becomes increasingly important, with applications in industrial inspection, quality control, machine vision, entertainment and biomedicine etc.. The 3-D profilometery based on sinusoidal fringe pattern projection is one of the important methods to acquire 3-D surface of object [1

1. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000). [CrossRef]

3

3. J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010). [CrossRef]

]. It is advantageous for the non-scanning nature and full-field performance. But it is difficult to retrieve the absolute phases for spatially isolated surfaces. In phase unwrapping [4

4. T. R. Judge and P. J. Bryanston-Cross, “Review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994). [CrossRef]

,5

5. X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004). [CrossRef]

], fringe order will be ambiguous. The depth difference between spatially isolated surfaces is then indiscernible.

Several projection algorithms have been proposed to unwrap the phases [6

6. H. Zhao, W. Chen, and Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33(20), 4497–4500 (1994). [CrossRef] [PubMed]

10

10. E. B. Li, X. Peng, J. Xi, J. F. Chicharo, J. Q. Yao, and D. W. Zhang, “Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry,” Opt. Express 13(5), 1561–1569 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-5-1561. [CrossRef] [PubMed]

]. But they may slow measurement because too many patterns are employed. An alternate approach for spatially isolated objects is to use a structured encoded pattern [11

11. P. Vuylsteke and A. Oosterlinck, “Range image acquisition with a single binary-encoded light pattern,” IEEE Trans. Pattern Anal. Mach. Intell. 12(2), 148–164 (1990). [CrossRef]

13

13. S. Y. Chen and Y. F. Li, “Self-recalibration of a colour-encoded light system for automated three-dimensional measurements,” Meas. Sci. Technol. 14(1), 33–40 (2003). [CrossRef]

] instead of a fringe pattern. The structured pattern can be either a set of square patches or a set of parallel grids. These patterns are spatially encoded with gray scales or colors. Each patch or grid is then distinguishable by the encoded scheme. However, systematic accuracy is limited by the size of the patches or width of the grids. To enhance the accuracy, we propose methods which combine encoded patterns with sinusoidal fringe patterns.

2. Principles

2.1 Improved FTP algorithm

The intensity of Ronchi grating is written as
g(x)=rect(xP/2)comb(xP),
(1)
where P is the period of grating. The asterisk denotes the operation of convolution. The Fourier series expansion of Eq. (1) is
g(x)=12+2πn=1(1)n12n1cos[2π(2n1)f0x],
(2)
where f 0 = 1/P is the fundamental frequency of Ronchi grating. The defocused optical system acts as a low-pass filter [23

23. X. Y. Su, W. S. Zhou, G. Vonbally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi Grating,” Opt. Commun. 94(6), 561–573 (1992). [CrossRef]

,24

24. S. Lei and S. Zhang, “Digital Sinusoidal Fringe Pattern Generation: Defocusing Binary Patterns VS Focusing Sinusoidal Patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010). [CrossRef]

]. The higher harmonic components can be filtered out. By comparison, a sine-wave grating would have g(x) = 1/2 + 1/2cos(2πf 0 x), so the fundamental of the Ronchi grating is larger by (2/π)/(1/2) = 4/π . It means that the contrast of fringe is higher than that of focused sinusoidal fringe pattern. So, it is possible to achieve higher measurement accuracy and higher light usage efficiency. This is important for high-speed 3-D measurement.

2.2 Codification strategy of encoded pattern

In order to obtain the absolute phase distribution of spatially isolated objects, we propose an encoded pattern to identify the order of sinusoidal fringe. Figure 1
Fig. 1 Example of encoded pattern.
shows an example. The pattern consists of numbers of vertical slits. The width of slits is equal to the period of sinusoidal fringe. Three gray levels (0 denotes black,1 denotes gray and 2 denotes white) are used to form the slits. Every slit is filled with one or two gray levels. For the slits filled with two gray levels, they are filled periodically in the vertical direction. For example, the gray level of the slit is “020202…” in vertical direction. So, there are six kinds of slits. They are three kinds of slits with one gray level (0, 1 or 2) and three kinds of slits with two gray levels (0 and 1, 0 and 2 or 1 and 2). Six symbols (from ‘A’ to ‘F’) are assigned to these six kinds of slits. These slits are arranged to form the encoded pattern according to a pseudo random sequence. The sequence has following property. (1) Any subsequence with a given length (window size) should appear only once in the whole sequence. (2) There are no repeated symbols in every subsequence. For example, any subsequence with length of four characters appears only once in character sequence “ABDECFADBEFDBECDABFECB DEFBDCEABCDAECFBDE”, and there are no repeated characters in these subsequences. We obtain the pseudo random sequence by searching a Hamilton Circuit over a directed graph [26

26. Y. Li, H. Z. Jin, and H. Wang, “Three-dimensional shape measurement using binary spatio-temporal encoded illumination,” J. Opt. A, Pure Appl. Opt. 11(7), 075502 (2009). [CrossRef]

]. According to the theory of permutation, the number of permutations L generated by selecting M elements from K elements can be expressed with
L=PkM=K!(KM)!.
(8)
So, the length of pseudo random sequence is L + M-1.

The fringe order k is identified by the position of subsequence in the whole sequence. Figure 2
Fig. 2 Relationship of fringe intensity, wrapped phase, fringe order and absolute phase.
illustrates the relationship of fringe intensity I, wrapped phase φw, fringe order k and absolute phase φa. In the figure, k′ is the global position of symbol in subsequence. For example, the position of subsequence “DECF” in above pseudo random sequence is 2. The global position of ‘D’ is 2, that of ‘E’ is 3 and that of ‘F’ is 5. It is also found in Fig. 2 that the phase is wrapped in the slits. So, the fringe order of areas at left side of points where the phase jump from π to –π (jump point) is equal to k′. And that of areas at right side of jump point is equal to k′ + 1. The advantage of this encoding method is that the fringe order will not be error even if the edge of slits drifts. The edge drift is natural in defocused optical system, especially in measurement of dynamic objects. When the fringe order k is determined, the absolute phase ϕa(x, y) of fringe can be expressed as
φa(x,y)=φw(x,y)+2kπ,
(9)
where ϕw(x, y) is wrapped phase.

There are three gray levels in the encoded pattern. It should be converted to binary image because only two gray levels are used in our method. The error diffusion algorithm is the general approach to convert a multi-level image into a binary image. The quantization error of image is moved to high-frequency section in frequency domain and is represented as high frequency noise. Most amount of the high frequency noise is filtered out in the defocused optical system. High quality multi-level image is obtained even though represented with two gray levels. So, we convert the encoded pattern to binary image with this algorithm.

2.3 Decoding algorithm

In the captured image, the sum of ambient and projector illumination multiplies the object reflectivity. It should be preprocessed to eliminate this effect before recovering symbol. The intensity of the captured encoded pattern can be expressed as
I3(x,y)=Ia(x,y)+Ip(x,y),
(10)
where Ip(x, y) is relative to intensity of encoded pattern. From Eq. (3), (6), (7) and (10), we can obtain the normalized intensity
Ic(x,y)=3[I3(x,y)I0(x,y)]+2|I^0(x,y)|cos[ϕw(x,y)]2|I^0(x,y)|.
(11)
The ambient illumination and object reflectivity are eliminated. Ic(x, y) is relative to the intensity of encoded pattern and the third harmonic component. Then, it is quantified with three gray levels (0, 1 and 2). The third harmonic component will not affect the result of quantization due to the large tolerance of encoded pattern. The fringe order is identified with the method proposed in Ref [22

22. Y. Li, K. Y. Jin, H. Z. Jin, and H. Wang, “High-resolution, High-speed 3D Measurement Based on Absolute Phase Measurement,” in Proceeding of International Conference on Advanced Phase Measurement Methods in Optics and Imaging, 2010, pp.389–394.

].

We can also get the 2-D texture of objects. From Eq. (3) and (6), we get
T(x,y)=3[I3(x,y)I0(x,y)]+2|I^0(x,y)|cos[ϕw(x,y)].
(12)
Then, perform band stop filter to Eq. (12). The third harmonic component is filtered out and the texture of objects is obtained.

3 Experimental results

3.1 Experimental setup

We modified a development kit of DLP projector. It can project images up to 360 fps with resolution of 1024 × 768 pixels. The projector can also provide pulse signal according to the time when a new image is projected. The white light LED with power of 10 watts was selected as its light source. A high-speed camera (Model RM6740GE) which was synchronized with projector was used to capture the deformed image. Figure 3
Fig. 3 Measurement system
shows a photograph of measurement system. The pseudo random sequence which we adopted is “ABDECFACDCEFBEADFEBC AEDAFDBFCBADEFCABEDCFBA”. Its window size is three symbols. The 3-D reconstruction procedure is described in detail as following.

  • (1) Calculate the wrapped phase with improved phase-shifting FTP.
  • (2) Find out the curve where phase jump greater than π (jump curve) in wrapped phase map.
  • (3) Normalize and quantify the intensity of corresponding curve in captured encoded pattern.
  • (4) Recover the symbol of jump curve and obtain the fringe order by subsequence matching.
  • (5) Reconstruct 3-D coordinates of object.

3.2. Experimental results

Two experimental results are demonstrated. Firstly, we recorded a scene which consists of spatially isolated and dynamic objects. The 3-D shape was recorded at 120 fps with resolution of 320 × 240 points. Figure 4
Fig. 4 Experimental result of spatially isolated dynamic objects. (a) One selected photograph of scene with fringe. (b) Movie of reconstructed 3-D image (Media 1).
shows a selected photograph of a scene with fringes and the movie of a reconstructed 3-D image. The toy on the right side of board vibrates left and right periodically. Depth is represented with color. This video shows that the shape and position of spatially isolated and dynamic objects can be captured with proposed approach if only enough fringes are projected.

Secondly, we recorded the change of facial expressions of human. A woman was asked to speak and smile. The 3-D shape was recorded at 60 fps with resolution of 640 × 480 points. Figure 5
Fig. 5 Measurement result of facial expressions (Media 2).
shows six selected frames. The 3-D shape is represented with 3-D mesh and grayscale texture. A movie is also included. This video shows that the detail of facial expression change can be recorded well with proposed system.

4. Conclusions

A method for measuring spatially isolated objects with high-speed even superfast speed and high-resolution is proposed. Three binary patterns are employed. They are projected with a high-speed defocused projector and high quality grayscale images are obtained. The method is suited for high-speed projector which can only project binary image. The 2-D texture of objects is captured simultaneously with proposed method. A system which consists of a high-speed camera and a specially designed DLP projector is also presented. The 3-D measurement speed of 60 fps with resolution of 640 × 480 points and that of 120 fps with resolution of 320 × 240 points is achieved. We successfully demonstrate that the 3-D shape and 2-D texture of low-speed dynamic and/or spatially isolated objects can be recorded.

Acknowledgments

This work is supported by the National Natural Science Foundation of China under grants No. 60702078.

References and links

1.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000). [CrossRef]

2.

F. Blais, “Review of 20 Years of Range Sensor Development,” J. Elect. Imag. 13(1), 231–240 (2004). [CrossRef]

3.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010). [CrossRef]

4.

T. R. Judge and P. J. Bryanston-Cross, “Review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994). [CrossRef]

5.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004). [CrossRef]

6.

H. Zhao, W. Chen, and Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33(20), 4497–4500 (1994). [CrossRef] [PubMed]

7.

W. Nadeborn, P. Andrä, and W. Osten, “A robust procedure for absolute phase measurement,” Opt. Lasers Eng. 24(2-3), 245–260 (1996). [CrossRef]

8.

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997). [CrossRef] [PubMed]

9.

Y. Hao, Y. Zhao, and D. Li, “Multifrequency grating projection profilometry based on the nonlinear excess fraction method,” Appl. Opt. 38(19), 4106–4110 (1999). [CrossRef]

10.

E. B. Li, X. Peng, J. Xi, J. F. Chicharo, J. Q. Yao, and D. W. Zhang, “Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry,” Opt. Express 13(5), 1561–1569 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-5-1561. [CrossRef] [PubMed]

11.

P. Vuylsteke and A. Oosterlinck, “Range image acquisition with a single binary-encoded light pattern,” IEEE Trans. Pattern Anal. Mach. Intell. 12(2), 148–164 (1990). [CrossRef]

12.

W. Liu, Z. Wang, G. Mu, and Z. Fang, “Color-coded projection grating method for shape measurement with a single exposure,” Appl. Opt. 39(20), 3504–3508 (2000). [CrossRef]

13.

S. Y. Chen and Y. F. Li, “Self-recalibration of a colour-encoded light system for automated three-dimensional measurements,” Meas. Sci. Technol. 14(1), 33–40 (2003). [CrossRef]

14.

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983). [CrossRef] [PubMed]

15.

P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, “Color-Encoded Digital Fringe Projection Technique for High-Speed Three-Dimensional Surface Contouring,” Opt. Eng. 38(6), 1065–1071 (1999). [CrossRef]

16.

C. Guan, L. G. Hassebrook, and D. L. Lau, “Composite structured light pattern for three-dimensional video,” Opt. Express 11(5), 406–417 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-5-406. [CrossRef] [PubMed]

17.

Q. C. Zhang and X. Y. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-8-3110. [CrossRef] [PubMed]

18.

W. H. Su, “Projected fringe profilometry using the area encoded algorithm for spatially isolated and dynamic objects,” Opt. Express 16, 2590–2596 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-4-2590.

19.

P. S. Huang, C. Zhang, and F. P. Chiang, “High-Speed 3D Shape Measurement Based on Digital Fringe Projection,” Opt. Eng. 42(1), 163–168 (2003). [CrossRef]

20.

S. Zhang and S.-T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14(7), 2644–2649 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-7-2644. [CrossRef] [PubMed]

21.

S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-9-9684. [CrossRef] [PubMed]

22.

Y. Li, K. Y. Jin, H. Z. Jin, and H. Wang, “High-resolution, High-speed 3D Measurement Based on Absolute Phase Measurement,” in Proceeding of International Conference on Advanced Phase Measurement Methods in Optics and Imaging, 2010, pp.389–394.

23.

X. Y. Su, W. S. Zhou, G. Vonbally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi Grating,” Opt. Commun. 94(6), 561–573 (1992). [CrossRef]

24.

S. Lei and S. Zhang, “Digital Sinusoidal Fringe Pattern Generation: Defocusing Binary Patterns VS Focusing Sinusoidal Patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010). [CrossRef]

25.

J. Li, X. Y. Su, and L. R. Guo, “Improved Fourier transform profilometry for the automatic measurement of 3D object shapes,” Opt. Eng. 29(12), 1439 (1990). [CrossRef]

26.

Y. Li, H. Z. Jin, and H. Wang, “Three-dimensional shape measurement using binary spatio-temporal encoded illumination,” J. Opt. A, Pure Appl. Opt. 11(7), 075502 (2009). [CrossRef]

OCIS Codes
(110.6880) Imaging systems : Three-dimensional image acquisition
(120.4630) Instrumentation, measurement, and metrology : Optical inspection
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: June 24, 2010
Revised Manuscript: September 22, 2010
Manuscript Accepted: September 26, 2010
Published: September 28, 2010

Citation
Yong Li, Cuifang Zhao, Yixian Qian, Hui Wang, and Hongzhen Jin, "High-speed and dense three-dimensional surface acquisition using defocused binary patterns for spatially isolated objects," Opt. Express 18, 21628-21635 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-21-21628


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References

  1. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39(1), 10–22 (2000). [CrossRef]
  2. F. Blais, “Review of 20 Years of Range Sensor Development,” J. Elect. Imag. 13(1), 231–240 (2004). [CrossRef]
  3. J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recognit. 43(8), 2666–2680 (2010). [CrossRef]
  4. T. R. Judge and P. J. Bryanston-Cross, “Review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994). [CrossRef]
  5. X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004). [CrossRef]
  6. H. Zhao, W. Chen, and Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33(20), 4497–4500 (1994). [CrossRef] [PubMed]
  7. W. Nadeborn, P. Andrä, and W. Osten, “A robust procedure for absolute phase measurement,” Opt. Lasers Eng. 24(2-3), 245–260 (1996). [CrossRef]
  8. H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997). [CrossRef] [PubMed]
  9. Y. Hao, Y. Zhao, and D. Li, “Multifrequency grating projection profilometry based on the nonlinear excess fraction method,” Appl. Opt. 38(19), 4106–4110 (1999). [CrossRef]
  10. E. B. Li, X. Peng, J. Xi, J. F. Chicharo, J. Q. Yao, and D. W. Zhang, “Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry,” Opt. Express 13(5), 1561–1569 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-5-1561 . [CrossRef] [PubMed]
  11. P. Vuylsteke and A. Oosterlinck, “Range image acquisition with a single binary-encoded light pattern,” IEEE Trans. Pattern Anal. Mach. Intell. 12(2), 148–164 (1990). [CrossRef]
  12. W. Liu, Z. Wang, G. Mu, and Z. Fang, “Color-coded projection grating method for shape measurement with a single exposure,” Appl. Opt. 39(20), 3504–3508 (2000). [CrossRef]
  13. S. Y. Chen and Y. F. Li, “Self-recalibration of a colour-encoded light system for automated three-dimensional measurements,” Meas. Sci. Technol. 14(1), 33–40 (2003). [CrossRef]
  14. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983). [CrossRef] [PubMed]
  15. P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, “Color-Encoded Digital Fringe Projection Technique for High-Speed Three-Dimensional Surface Contouring,” Opt. Eng. 38(6), 1065–1071 (1999). [CrossRef]
  16. C. Guan, L. G. Hassebrook, and D. L. Lau, “Composite structured light pattern for three-dimensional video,” Opt. Express 11(5), 406–417 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-5-406 . [CrossRef] [PubMed]
  17. Q. C. Zhang and X. Y. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-8-3110 . [CrossRef] [PubMed]
  18. W. H. Su, “Projected fringe profilometry using the area encoded algorithm for spatially isolated and dynamic objects,” Opt. Express 16, 2590–2596 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-4-2590 .
  19. P. S. Huang, C. Zhang, and F. P. Chiang, “High-Speed 3D Shape Measurement Based on Digital Fringe Projection,” Opt. Eng. 42(1), 163–168 (2003). [CrossRef]
  20. S. Zhang and S.-T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14(7), 2644–2649 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-7-2644 . [CrossRef] [PubMed]
  21. S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010), http://www.opticsinfobase.org/abstract.cfm?uri=oe-18-9-9684 . [CrossRef] [PubMed]
  22. Y. Li, K. Y. Jin, H. Z. Jin, and H. Wang, “High-resolution, High-speed 3D Measurement Based on Absolute Phase Measurement,” in Proceeding of International Conference on Advanced Phase Measurement Methods in Optics and Imaging, 2010, pp.389–394.
  23. X. Y. Su, W. S. Zhou, G. Vonbally, and D. Vukicevic, “Automated phase-measuring profilometry using defocused projection of a Ronchi Grating,” Opt. Commun. 94(6), 561–573 (1992). [CrossRef]
  24. S. Lei and S. Zhang, “Digital Sinusoidal Fringe Pattern Generation: Defocusing Binary Patterns VS Focusing Sinusoidal Patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010). [CrossRef]
  25. J. Li, X. Y. Su, and L. R. Guo, “Improved Fourier transform profilometry for the automatic measurement of 3D object shapes,” Opt. Eng. 29(12), 1439 (1990). [CrossRef]
  26. Y. Li, H. Z. Jin, and H. Wang, “Three-dimensional shape measurement using binary spatio-temporal encoded illumination,” J. Opt. A, Pure Appl. Opt. 11(7), 075502 (2009). [CrossRef]

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