## Multiplexing encoding method for full-color dynamic 3D holographic display |

Optics Express, Vol. 22, Issue 15, pp. 18473-18482 (2014)

http://dx.doi.org/10.1364/OE.22.018473

Acrobat PDF (1901 KB)

### Abstract

The multiplexing encoding method is proposed and demonstrated for reconstructing colorful images accurately by using single phase-only spatial light modulator (SLM). It will encode the light waves at different wavelengths into one pure-phase hologram at the same time based on the analytic formulas. The three-dimensional (3D) images can be reconstructed clearly when the light waves at different wavelengths are incident into the encoding hologram. Numerical simulations and optical experiments for 2D and 3D colorful images are performed. The results show that the colorful reconstructed images with high quality are achieved successfully. The proposed multiplexing method is a simple and fast encoding approach and the size of the system is small and compact. It is expected to be used for realizing full-color 3D holographic display in future.

© 2014 Optical Society of America

## 1. Introduction

1. M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, “Simple holographic projection in color,” Opt. Express **20**(22), 25130–25136 (2012). [CrossRef] [PubMed]

1. M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, “Simple holographic projection in color,” Opt. Express **20**(22), 25130–25136 (2012). [CrossRef] [PubMed]

2. M. Hacker, G. Stobrawa, and T. Feurer, “Iterative Fourier transform algorithm for phase-only pulse shaping,” Opt. Express **9**(4), 191–199 (2001). [CrossRef] [PubMed]

3. M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express **16**(15), 11618–11623 (2008). [PubMed]

4. M. Makowski, M. Sypek, I. Ducin, A. Fajst, A. Siemion, J. Suszek, and A. Kolodziejczyk, “Experimental evaluation of a full-color compact lensless holographic display,” Opt. Express **17**(23), 20840–20846 (2009). [CrossRef] [PubMed]

5. N. Yoshikawa and T. Yatagai, “Phase optimization of a kinoform by simulated annealing,” Appl. Opt. **33**(5), 863–868 (1994). [CrossRef] [PubMed]

6. H. Zheng, T. Tao, L. Dai, and Y. Yu, “Holographic imaging of full-color real-existing three-dimensional objects with computer-generated sequential kinoforms,” Chin. Opt. Lett. **9**(4), 040901 (2011). [CrossRef]

7. A. Shiraki, N. Takada, M. Niwa, Y. Ichihashi, T. Shimobaba, N. Masuda, and T. Ito, “Simplified electroholographic color reconstruction system using graphics processing unit and liquid crystal display projector,” Opt. Express **17**(18), 16038–16045 (2009). [CrossRef] [PubMed]

8. J. Jia, Y. Wang, J. Liu, X. Li, Y. Pan, Z. Sun, B. Zhang, Q. Zhao, and W. Jiang, “Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display,” Appl. Opt. **52**(7), 1404–1412 (2013). [CrossRef] [PubMed]

3. M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express **16**(15), 11618–11623 (2008). [PubMed]

4. M. Makowski, M. Sypek, I. Ducin, A. Fajst, A. Siemion, J. Suszek, and A. Kolodziejczyk, “Experimental evaluation of a full-color compact lensless holographic display,” Opt. Express **17**(23), 20840–20846 (2009). [CrossRef] [PubMed]

9. X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” presented at the 10th International Symposium on Display Holography, Hawaii, USA, 25–29 April 2013. [CrossRef]

10. M. Oikawa, T. Shimobaba, T. Yoda, H. Nakayama, A. Shiraki, N. Masuda, and T. Ito, “Time-division color electroholography using one-chip RGB LED and synchronizing controller,” Opt. Express **19**(13), 12008–12013 (2011). [CrossRef] [PubMed]

11. T. Shimobaba, T. Takahashi, N. Masuda, and T. Ito, “Numerical study of color holographic projection using space-division method,” Opt. Express **19**(11), 10287–10292 (2011). [CrossRef] [PubMed]

12. T. Ito and K. Okano, “Color electroholography by three colored reference lights simultaneously incident upon one hologram panel,” Opt. Express **12**(18), 4320–4325 (2004). [CrossRef] [PubMed]

1. M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, “Simple holographic projection in color,” Opt. Express **20**(22), 25130–25136 (2012). [CrossRef] [PubMed]

13. M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, A. Kolodziejczyk, and M. Sypek, “Extremely simple holographic projection of color images,” Proc. SPIE **8280**, 1–6 (2012). [CrossRef]

14. M. Makowski, I. Ducin, M. Sypek, A. Siemion, A. Siemion, J. Suszek, and A. Kolodziejczyk, “Color image projection based on Fourier holograms,” Opt. Lett. **35**(8), 1227–1229 (2010). [CrossRef] [PubMed]

## 2. The multiplexing encoding method

*i*= 1, 2 or 3, corresponds to red, green or blue channel,

*u*and

*v*represent the spatial frequency. The reference plane light waves for RGB channels on the hologram plane can be written as

*x, y*) denote coordinates of the space domain, the formula in the brace represents the complex amplitude of each color component of the 3D object after the propagation process of spectrum,

16. H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. **48**(30), 5834–5841 (2009). [CrossRef] [PubMed]

17. I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. **34**, 6423–6432 (1995). [CrossRef]

18. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding Amplitude Information onto Phase-Only Filters,” Appl. Opt. **38**(23), 5004–5013 (1999). [CrossRef] [PubMed]

## 3. Numerical and optical experimental results

_{1}. In the 4f system the band-pass filter is placed on the back focus plane of L

_{1}, which is also the front focus plane L

_{2}. In the reconstructed process, the desired first orders will be picked up by the designed hole on the filter. The distance between the hole and the optic axis of the hole is determined by

_{1}. The reconstructed color image is obtained on the output plane after the back focal plane of L

_{2}. The CCD (Lumenera’s INFINITY 4-11C) is used to record the experimental results. In addition, the scaling of the reconstructed image is determined by

_{2}. In our experiment, the focal lengths of L

_{1}and L

_{2}are both 543mm and their apertures are both 120mm.

*θ*of the red and the blue reference lights are both 1.57°; the tilted angle

11. T. Shimobaba, T. Takahashi, N. Masuda, and T. Ito, “Numerical study of color holographic projection using space-division method,” Opt. Express **19**(11), 10287–10292 (2011). [CrossRef] [PubMed]

6. H. Zheng, T. Tao, L. Dai, and Y. Yu, “Holographic imaging of full-color real-existing three-dimensional objects with computer-generated sequential kinoforms,” Chin. Opt. Lett. **9**(4), 040901 (2011). [CrossRef]

19. R. Shi, J. Liu, H. Zhao, Z. Wu, Y. Liu, Y. Hu, Y. Chen, J. Xie, and Y. Wang, “Chromatic dispersion correction in planar waveguide using one-layer volume holograms based on three-step exposure,” Appl. Opt. **51**(20), 4703–4708 (2012). [CrossRef] [PubMed]

*z*

_{1}= 650 mm, and

*z*

_{2}= 500 mm. The hologram synthetized by the encoding method is then loaded into the SLM. The numerical and optical reconstructed full-color 3D images at different distances are displayed in Figs. 6(a)-6(d). When the CCD (INFINITY 4-11C) focus at 650 mm, the ‘RMB’ image is clear and ‘YGC’ image is blur as shown in Figs. 6(a) and 6(c), and vice versa. It is easily seen that the 3D colorful image is reconstructed properly and the high image quality is achieved. Note that the blue images in Figs. 6(c) and 6(d) are not aligned to the rest of the images whereas the numerical results are fine. There are two reasons that can cause the shift of the blue in Figs. 6(c) and 6(d). The first one is the mis-alignment of the system or the reference beams which can be corrected by adjusting the optical setup. The second one is that the blue laser beam (shorter wavelength) may have more dispersion in our optical system and the standard blue plane wave could be distorted. This problem can be solved by employing the achromatic optical elements in the optical system and shaping the blue laser beam to be a standard plane wave.

6. H. Zheng, T. Tao, L. Dai, and Y. Yu, “Holographic imaging of full-color real-existing three-dimensional objects with computer-generated sequential kinoforms,” Chin. Opt. Lett. **9**(4), 040901 (2011). [CrossRef]

20. K. Wakunami, H. Yamashita, and M. Yamaguchi, “Occlusion culling for computer generated hologram based on ray-wavefront conversion,” Opt. Express **21**(19), 21811–21822 (2013). [CrossRef] [PubMed]

## 4. Discussion

^{2}[21]. In our system, the diffraction efficiency of the SLM is 60%. The equation for the calculation of the required total luminous flux is defined as

^{2}) is the luminance, S (m

^{2}) is the area of the reconstructed image,

*r*is the distance of distinct vision (normally 0.25m). Assuming that the luminance of the reconstructed image is 3 cd/m

^{2}, the size of the reconstructed 2D image is 5cm × 5cm, and the efficiency of energy is 5.05%, then the obtained total luminous flux is 0.0099 lumen. According to the spectral luminous efficiency in photopic vision [21], one lumen corresponds to 45.75 milliwatts (mW) for the red light with wavelength of 671 nm, 1.66 mW for the green light with wavelength of 532 nm, and 97.48 mW for the blue light with wavelength of 473 nm. So the minimal power for the RGB lasers are 0.453 mW, 0.016 mW and 0.965 mW respectively. In the calculation, the energy loss of the laser beams in propagation is neglected.

## 5. Conclusion

## Acknowledgment

## References and links

1. | M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, “Simple holographic projection in color,” Opt. Express |

2. | M. Hacker, G. Stobrawa, and T. Feurer, “Iterative Fourier transform algorithm for phase-only pulse shaping,” Opt. Express |

3. | M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express |

4. | M. Makowski, M. Sypek, I. Ducin, A. Fajst, A. Siemion, J. Suszek, and A. Kolodziejczyk, “Experimental evaluation of a full-color compact lensless holographic display,” Opt. Express |

5. | N. Yoshikawa and T. Yatagai, “Phase optimization of a kinoform by simulated annealing,” Appl. Opt. |

6. | H. Zheng, T. Tao, L. Dai, and Y. Yu, “Holographic imaging of full-color real-existing three-dimensional objects with computer-generated sequential kinoforms,” Chin. Opt. Lett. |

7. | A. Shiraki, N. Takada, M. Niwa, Y. Ichihashi, T. Shimobaba, N. Masuda, and T. Ito, “Simplified electroholographic color reconstruction system using graphics processing unit and liquid crystal display projector,” Opt. Express |

8. | J. Jia, Y. Wang, J. Liu, X. Li, Y. Pan, Z. Sun, B. Zhang, Q. Zhao, and W. Jiang, “Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display,” Appl. Opt. |

9. | X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” presented at the 10th International Symposium on Display Holography, Hawaii, USA, 25–29 April 2013. [CrossRef] |

10. | M. Oikawa, T. Shimobaba, T. Yoda, H. Nakayama, A. Shiraki, N. Masuda, and T. Ito, “Time-division color electroholography using one-chip RGB LED and synchronizing controller,” Opt. Express |

11. | T. Shimobaba, T. Takahashi, N. Masuda, and T. Ito, “Numerical study of color holographic projection using space-division method,” Opt. Express |

12. | T. Ito and K. Okano, “Color electroholography by three colored reference lights simultaneously incident upon one hologram panel,” Opt. Express |

13. | M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, A. Kolodziejczyk, and M. Sypek, “Extremely simple holographic projection of color images,” Proc. SPIE |

14. | M. Makowski, I. Ducin, M. Sypek, A. Siemion, A. Siemion, J. Suszek, and A. Kolodziejczyk, “Color image projection based on Fourier holograms,” Opt. Lett. |

15. | J. W. Goodman, |

16. | H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt. |

17. | I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys. |

18. | J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding Amplitude Information onto Phase-Only Filters,” Appl. Opt. |

19. | R. Shi, J. Liu, H. Zhao, Z. Wu, Y. Liu, Y. Hu, Y. Chen, J. Xie, and Y. Wang, “Chromatic dispersion correction in planar waveguide using one-layer volume holograms based on three-step exposure,” Appl. Opt. |

20. | K. Wakunami, H. Yamashita, and M. Yamaguchi, “Occlusion culling for computer generated hologram based on ray-wavefront conversion,” Opt. Express |

21. | N. Ohta and A. R. Robertson, |

**OCIS Codes**

(090.1760) Holography : Computer holography

(090.2870) Holography : Holographic display

(090.1705) Holography : Color holography

(090.5694) Holography : Real-time holography

**ToC Category:**

Holography

**History**

Original Manuscript: May 23, 2014

Revised Manuscript: July 8, 2014

Manuscript Accepted: July 8, 2014

Published: July 23, 2014

**Citation**

Gaolei Xue, Juan Liu, Xin Li, Jia Jia, Zhao Zhang, Bin Hu, and Yongtian Wang, "Multiplexing encoding method for full-color dynamic 3D holographic display," Opt. Express **22**, 18473-18482 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18473

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### References

- M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyk, “Simple holographic projection in color,” Opt. Express20(22), 25130–25136 (2012). [CrossRef] [PubMed]
- M. Hacker, G. Stobrawa, and T. Feurer, “Iterative Fourier transform algorithm for phase-only pulse shaping,” Opt. Express9(4), 191–199 (2001). [CrossRef] [PubMed]
- M. Makowski, M. Sypek, and A. Kolodziejczyk, “Colorful reconstructions from a thin multi-plane phase hologram,” Opt. Express16(15), 11618–11623 (2008). [PubMed]
- M. Makowski, M. Sypek, I. Ducin, A. Fajst, A. Siemion, J. Suszek, and A. Kolodziejczyk, “Experimental evaluation of a full-color compact lensless holographic display,” Opt. Express17(23), 20840–20846 (2009). [CrossRef] [PubMed]
- N. Yoshikawa and T. Yatagai, “Phase optimization of a kinoform by simulated annealing,” Appl. Opt.33(5), 863–868 (1994). [CrossRef] [PubMed]
- H. Zheng, T. Tao, L. Dai, and Y. Yu, “Holographic imaging of full-color real-existing three-dimensional objects with computer-generated sequential kinoforms,” Chin. Opt. Lett.9(4), 040901 (2011). [CrossRef]
- A. Shiraki, N. Takada, M. Niwa, Y. Ichihashi, T. Shimobaba, N. Masuda, and T. Ito, “Simplified electroholographic color reconstruction system using graphics processing unit and liquid crystal display projector,” Opt. Express17(18), 16038–16045 (2009). [CrossRef] [PubMed]
- J. Jia, Y. Wang, J. Liu, X. Li, Y. Pan, Z. Sun, B. Zhang, Q. Zhao, and W. Jiang, “Reducing the memory usage for effective computer-generated hologram calculation using compressed look-up table in full-color holographic display,” Appl. Opt.52(7), 1404–1412 (2013). [CrossRef] [PubMed]
- X. Li, Y. Wang, J. Liu, J. Jia, Y. Pan, and J. Xie, “Color holographic display using a phase-only spatial light modulator,” presented at the 10th International Symposium on Display Holography, Hawaii, USA, 25–29 April 2013. [CrossRef]
- M. Oikawa, T. Shimobaba, T. Yoda, H. Nakayama, A. Shiraki, N. Masuda, and T. Ito, “Time-division color electroholography using one-chip RGB LED and synchronizing controller,” Opt. Express19(13), 12008–12013 (2011). [CrossRef] [PubMed]
- T. Shimobaba, T. Takahashi, N. Masuda, and T. Ito, “Numerical study of color holographic projection using space-division method,” Opt. Express19(11), 10287–10292 (2011). [CrossRef] [PubMed]
- T. Ito and K. Okano, “Color electroholography by three colored reference lights simultaneously incident upon one hologram panel,” Opt. Express12(18), 4320–4325 (2004). [CrossRef] [PubMed]
- M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, A. Kolodziejczyk, and M. Sypek, “Extremely simple holographic projection of color images,” Proc. SPIE8280, 1–6 (2012). [CrossRef]
- M. Makowski, I. Ducin, M. Sypek, A. Siemion, A. Siemion, J. Suszek, and A. Kolodziejczyk, “Color image projection based on Fourier holograms,” Opt. Lett.35(8), 1227–1229 (2010). [CrossRef] [PubMed]
- J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), chap. 2.2.
- H. Zhang, J. Xie, J. Liu, and Y. Wang, “Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection,” Appl. Opt.48(30), 5834–5841 (2009). [CrossRef] [PubMed]
- I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, “Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,” Jpn. J. Appl. Phys.34, 6423–6432 (1995). [CrossRef]
- J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding Amplitude Information onto Phase-Only Filters,” Appl. Opt.38(23), 5004–5013 (1999). [CrossRef] [PubMed]
- R. Shi, J. Liu, H. Zhao, Z. Wu, Y. Liu, Y. Hu, Y. Chen, J. Xie, and Y. Wang, “Chromatic dispersion correction in planar waveguide using one-layer volume holograms based on three-step exposure,” Appl. Opt.51(20), 4703–4708 (2012). [CrossRef] [PubMed]
- K. Wakunami, H. Yamashita, and M. Yamaguchi, “Occlusion culling for computer generated hologram based on ray-wavefront conversion,” Opt. Express21(19), 21811–21822 (2013). [CrossRef] [PubMed]
- N. Ohta and A. R. Robertson, Colorimetry: Fundamentals and Applications (John Wiley & Sons, 2005).

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