## Time efficient color fringe projection system for 3D shape and color using optimum 3-frequency Selection

Optics Express, Vol. 14, Issue 14, pp. 6444-6455 (2006)

http://dx.doi.org/10.1364/OE.14.006444

Acrobat PDF (599 KB)

### Abstract

We present a novel color fringe projection system to obtain absolute 3D shape and color of objects simultaneously. Optimum 3-frequency interferometry is used to produce time efficient analysis of the projected fringes by encoding three fringe sets of different pitch into the primary colors of a digital light projector and recording the information on a 3-chip color CCD camera. Phase shifting analysis is used to retrieve sub-wavelength phase information. Absolute phase across the field is calculated using the 3-frequency method independently at each pixel. Concurrent color data is also captured via the RGB channels of the CCD. Thus full-field absolute shape (XYZ) and color (RGB) can be obtained. In this paper we present the basis of the technique and preliminary results having addressed the issue of crosstalk between the color channels.

© 2006 Optical Society of America

## 1. Introduction

15. G. Hausler and D. Ritter, “Parallel three-dimensional sensing by color-coded triangulation,” Appl. Opt. **32**, 7164–7169 (1993). [CrossRef] [PubMed]

*π*/3 between neighboring channels. The 3D surface contour information can be retrieved from a single image snapshot of the object surface [16

16. P. S. Huang, Q. Y. Hu, F. Jin, and F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. **38**, 1065–1071 (1999). [CrossRef]

17. O. A. Skydan, M. J. Lalor, and D. R. Burton, “Technique for phase measurement and surface reconstruction by use colored structured light,” Appl. Opt. **41**, 6104–6117 (2002). [CrossRef] [PubMed]

*et al*. and Skydan et al only produce wrapped phase maps, so spatial phase unwrapping methods are required to generate the 3D shape of an object and hence these methods cannot be applied to objects with large slope or discontinuity.

*et al*. introduced a method to project two gratings simultaneously with different color and fringe pitch [18

18. S. Kakunai, T. Sakamoto, and K. Iwata, “Profile measurement taken with liquid-crystal gratings,” Appl. Opt. **38**, 2824–2828 (1999). [CrossRef]

19. A. Pfortner and J. Schwider, “Red-green-blue interferometer for the metrology of discontinuous structures,” Appl. Opt. **42**, 667–673 (2003). [CrossRef] [PubMed]

^{th}of a fringe [14

14. C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multi-frequency selection in full-field porfilometry,” Opt. Lasers Eng. **43**, 788–800 (2005). [CrossRef]

## 2. Principle

20. J. M. Younse, “Mirrors on a chip,” IEEE Spectrum **30**, 27–31 (1993). [CrossRef]

*π*/2 and the wrapped phase map calculated for each channel. Using the wrapped phase maps from the three channels, the absolute phase distribution is calculated via the fringe order and the optimum 3-frequency selection method.

### 2.1 Optimum three-frequency selection

*N*

_{f0}and

*N*

_{fi}are the maximum number of fringes and the number of fringes in the ith fringe set, respectively, and

*n*is the number of fringe sets used. When the maximum number of fringes is 100 and

*n*=3,

*N*

_{f1}=99 and

*N*

_{f2}=90. This approach resolves fringe order ambiguity as the beat obtained between

*N*

_{f0}and

*N*

_{f1}is a single fringe over the full field of view.

### 2.2 Fringe projection

*c=r, g, b*corresponds to the red, green, and blue channels, respectively,

*I*

_{c}is the gray value,

*DC*

_{c}is the average intensity,

*M*

_{c}is the fringe amplitude,

*p*

_{c}is the fringe pitch in pixels, (

*x, y*) are the horizontal and vertical pixel indices of the DLP, and

*φ*is the phase shift. The three image components combine together in a color image comprising the red, green, and blue channels, as shown in Fig. 2. The 3-CCD camera captures the composite fringe pattern into three channels as:

*m,n*are the pixel indices of the CCD,

### 2.3 Color separation

16. P. S. Huang, Q. Y. Hu, F. Jin, and F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. **38**, 1065–1071 (1999). [CrossRef]

16. P. S. Huang, Q. Y. Hu, F. Jin, and F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. **38**, 1065–1071 (1999). [CrossRef]

*π*/2 phase shift are generated and projected onto a flat white surface. Four full-color images are captured and separated into their RGB components, giving twelve grayscale images. The intensity modulations

*m, n*),

*c*=

*r, g,b*from the three channels are calculated and the ratios of the spatially averaged values of

*m, n*) between channels indicate the magnitude of the coupling effects, defined for the red channel as:

*C*

_{ij}=100×

*R*

_{ij}

*, i, j=r, g,b*and the first suffix denotes illumination from the projector and the second suffix the color plane in the detected image. The elements along the main diagonal in Eq. (5) are 100.0, that is

*C*

_{rr}

*=C*

_{gg}

*=C*

_{bb}=100.0.

## 3. Experiments and results

### 3.1 Experimental System

### 3.2 Evaluation of Crosstalk

*π*/2,

*π*, and 3

*π*/2) were generated and projected on the white surface. We evaluated the coupling effects for the red, green, and blue channels under 3 conditions: the standard DLP and camera, using additional filters and using additional filters without the DLP built-in color filter wheel.

### 3.3 Phase noise evaluation

**38**, 1065–1071 (1999). [CrossRef]

*π/σϕ*where

*σϕ*is the standard deviation of the phase noise) in these situations. The phase resolutions for the standard DLP and camera with separate color projection are 153, 156, 120 for the R, G, B channels, respectively. With composite color projection crosstalk affects are present and the phase resolutions reduce to 44, 93, 121. The phase resolution in the red channel is reduced considerably as it can be seen that this channel contains the greatest amount of crosstalk (from the green channel, see the first column of the matrix in Eq. (6)). When Huang’s method was used to compensate for the coupling effects, the phase resolution for the red channel improved (75 versus 44) while it was almost the same for the green and blue channels. Therefore, we can compensate for the crosstalk in the red channel with composite fringe projection using Huang’s method.

### 3.4 Composite fringe pattern

*σ*reliability in fringe order calculation [14

14. C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multi-frequency selection in full-field porfilometry,” Opt. Lasers Eng. **43**, 788–800 (2005). [CrossRef]

*N*

_{f0}=200 giving a dynamic range up to 24000.

*N*

_{f0}=78 giving an overall dynamic range up to 5850. Therefore, using optimum 3-frequency analysis, three fringe patterns were generated with 81, 80, and 72 fringes. With the optics used, it was found that the red channel contained a significant level of chromatic distortion compared to the blue and green channels. It is found that the generation of a single beat fringe is critical for successful fringe order calculation, in this case by forming a beat between 81 and 80 projected fringes. Therefore, to reduce the overall effects of chromatic distortion on the fringe order calculation the projected numbers of fringes were set to 81, 80 and 72 for the blue, green and red channels, respectively. The phase stepped composite RGB fringe patterns were generated and projected in sequence such that the phase and color information were captured in 4 frames.

21. P. S. Huang, C. P. Zhang, and F. P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. **42**, 163–168 (2003). [CrossRef]

## 4. Conclusions

## Acknowledgments

## References and links

1. | F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. |

2. | M. Petrov, A. Talapov, T. Robertson, A. Lebedev, A. Zhilyaev, and L. Polonskiy, “Optical 3D digitizers: bringing life to the virtual world,” IEEE Comput. Graph. Appl. |

3. | F. Blais, “Review of 20 years of range sensor development,” J. Electron Imaging |

4. | K. Creath
E.
Wolf, “ |

5. | M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3D object shapes,” Appl. Opt. |

6. | X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. |

7. | J. M. Huntley and H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. |

8. | H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. |

9. | J. M. Huntley and H. O. Saldner, “Error-reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. A |

10. | H. O. Saldner and J. M. Huntley, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. |

11. | C. E. Towers, D. P. Towers, and J. D. C. Jones, “Optimum frequency selection in multifrequency interferometry,” Opt. Lett. |

12. | D. P. Towers, C. E. Towers, and J. D. C. Jones, “Phase Measuring Method and Apparatus for Multi-Frequency Interferometry,” International Patent Application Number PCT/GB2003/003744. |

13. | C. E. Towers, D. P. Towers, and J. D.C. Jones, “Generalized frequency selection in multifrequency interferometry,” Opt. Lett. |

14. | C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimised multi-frequency selection in full-field porfilometry,” Opt. Lasers Eng. |

15. | G. Hausler and D. Ritter, “Parallel three-dimensional sensing by color-coded triangulation,” Appl. Opt. |

16. | P. S. Huang, Q. Y. Hu, F. Jin, and F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. |

17. | O. A. Skydan, M. J. Lalor, and D. R. Burton, “Technique for phase measurement and surface reconstruction by use colored structured light,” Appl. Opt. |

18. | S. Kakunai, T. Sakamoto, and K. Iwata, “Profile measurement taken with liquid-crystal gratings,” Appl. Opt. |

19. | A. Pfortner and J. Schwider, “Red-green-blue interferometer for the metrology of discontinuous structures,” Appl. Opt. |

20. | J. M. Younse, “Mirrors on a chip,” IEEE Spectrum |

21. | P. S. Huang, C. P. Zhang, and F. P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. |

**OCIS Codes**

(110.6880) Imaging systems : Three-dimensional image acquisition

(120.2650) Instrumentation, measurement, and metrology : Fringe analysis

(120.3940) Instrumentation, measurement, and metrology : Metrology

(120.5050) Instrumentation, measurement, and metrology : Phase measurement

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: February 17, 2006

Revised Manuscript: June 9, 2006

Manuscript Accepted: June 14, 2006

Published: July 10, 2006

**Citation**

Zonghua Zhang, Catherine E. Towers, and David P. Towers, "Time efficient color fringe projection system for 3D shape and color using optimum 3-frequency Selection," Opt. Express **14**, 6444-6455 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-14-6444

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### References

- F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000). [CrossRef]
- M. Petrov, A. Talapov, T. Robertson, A. Lebedev, A. Zhilyaev, and L. Polonskiy, "Optical 3D digitizers: bringing life to the virtual world," IEEE Comput. Graph. Appl. 18, 28-37 (1998). [CrossRef]
- F. Blais, "Review of 20 years of range sensor development," J. Electron Imaging 13, 231-240 (2004). [CrossRef]
- K. Creath, "Phase measurement interferometry techniques," in Progress in Optics XXVI, E. Wolf, Ed. (North Holland Publ., Amsterdam, 1988).
- M. Takeda and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3D object shapes," Appl. Opt. 22, 3977-3982 (1983). [CrossRef] [PubMed]
- X. Y. Su and W. J. Chen, "Reliability-guided phase unwrapping algorithm: a review," Opt. Lasers Eng. 42, 245-261 (2004). [CrossRef]
- J. M. Huntley and H. O. Saldner, "Temporal phase-unwrapping algorithm for automated interferogram analysis," Appl. Opt. 32, 3047-3052 (1993). [CrossRef] [PubMed]
- H. O. Saldner and J. M. Huntley, "Temporal phase unwrapping: application to surface profiling of discontinuous objects," Appl. Opt. 36, 2770-2775 (1997). [CrossRef] [PubMed]
- J. M. Huntley and H. O. Saldner, "Error-reduction methods for shape measurement by temporal phase unwrapping," J. Opt. Soc. Am. A 14, 3188-3196 (1997). [CrossRef]
- H. O. Saldner and J. M. Huntley, "Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms," Meas. Sci. Technol. 8, 986-992 (1997). [CrossRef]
- C. E. Towers, D. P. Towers, and J. D. C. Jones, "Optimum frequency selection in multifrequency interferometry," Opt. Lett. 28, 887-889 (2003). [CrossRef] [PubMed]
- D. P. Towers, C. E. Towers, and J. D. C. Jones, "Phase Measuring Method and Apparatus for Multi-Frequency Interferometry," International Patent Application Number PCT/GB2003/003744.
- C. E. Towers, D. P. Towers, and J. D.C. Jones, "Generalized frequency selection in multifrequency interferometry," Opt. Lett. 29, 1348-1450 (2004). [CrossRef] [PubMed]
- C. E. Towers, D. P. Towers, and J. D. C. Jones, "Absolute fringe order calculation using optimised multi-frequency selection in full-field porfilometry," Opt. Lasers Eng. 43, 788-800 (2005). [CrossRef]
- G. Hausler and D. Ritter, "Parallel three-dimensional sensing by color-coded triangulation," Appl. Opt. 32, 7164-7169 (1993). [CrossRef] [PubMed]
- P. S. Huang, Q. Y. Hu, F. Jin, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Opt. Eng. 38, 1065-1071 (1999). [CrossRef]
- O. A. Skydan, M. J. Lalor, and D. R. Burton, "Technique for phase measurement and surface reconstruction by use colored structured light," Appl. Opt. 41, 6104-6117 (2002). [CrossRef] [PubMed]
- S. Kakunai, T. Sakamoto, and K. Iwata, "Profile measurement taken with liquid-crystal gratings," Appl. Opt. 38, 2824-2828 (1999). [CrossRef]
- A. Pfortner and J. Schwider, "Red-green-blue interferometer for the metrology of discontinuous structures," Appl. Opt. 42, 667-673 (2003). [CrossRef] [PubMed]
- J. M. Younse, "Mirrors on a chip," IEEE Spectrum 30, 27-31 (1993). [CrossRef]
- P. S. Huang, C. P. Zhang, and F. P. Chiang, "High-speed 3-D shape measurement based on digital fringe projection," Opt. Eng. 42, 163-168 (2003). [CrossRef]

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