## Lensless zoomable holographic projection using scaled Fresnel diffraction |

Optics Express, Vol. 21, Issue 21, pp. 25285-25290 (2013)

http://dx.doi.org/10.1364/OE.21.025285

Acrobat PDF (3768 KB)

### Abstract

Projectors require a zoom function. This function is generally realized using a zoom lens module composed of many lenses and mechanical parts; however, using a zoom lens module increases the system size and cost, and requires manual operation of the module. Holographic projection is an attractive technique because it inherently requires no lenses, reconstructs images with high contrast and reconstructs color images with one spatial light modulator. In this paper, we demonstrate a lensless zoomable holographic projection. Without using a zoom lens module, this holographic projection realizes the zoom function using a numerical method, called scaled Fresnel diffraction which can calculate diffraction at different sampling rates on a projected image and hologram.

© 2013 OSA

## 1. Introduction

2. M. Freeman, M. Champion, and S. Madhavan, “Scanned Laser Pico-Projectors: Seeing the Big Picture (with a Small Device),”Optics & Photonics News **20(5)**, 28–34 (2009). [CrossRef]

4. E. Buckley, “Holographic projector using one lens,” Opt. Lett. **35**, 3399–3401 (2010). [CrossRef] [PubMed]

5. H.-C. Lin, N. Collings, M.-S. Chen, and Y.-H. Lin, “A holographic projection system with an electrically tuning and continuously adjustable optical zoom,” Opt. Express **20**, 27222–27229 (2012). [CrossRef] [PubMed]

6. Y.-H. Lin and M.-S. Chen, “A Pico Projection System With Electrically Tunable Optical Zoom Ratio Adopting Two Liquid Crystal Lenses,” J. Disp. Tech. **8**, 401–404 (2012). [CrossRef]

10. R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted Fresnel diffraction for computational holography,” Opt. Express **15**, 5631–5640 (2007). [CrossRef] [PubMed]

11. T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. **15**, 075302(5pp) (2013). [CrossRef]

12. 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**, 20840–20846 (2009). [CrossRef] [PubMed]

16. M. Makowski, I. Ducin, K. Kakarenko, M. Sypek, and A. Kolodziejczyk, “Speckle Suppression in Color Holographic Projection by Pixel Separation,” in *Digital Holography and Three-Dimensional Imaging*, OSA Technical Digest (online) (Optical Society of America, 2013), paper DTu1A.6. [CrossRef]

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

## 2. Lensless zoomable holographic projection

*μ*m) and a non-polarizing beam splitter cube. We placed the output of the fiber and a projection screen at 50 mm and

*z*from the SLM. The output of the fiber can be regarded as a point light source because the diameter is 1

*μ*m. We observe zoomable projected images on the projection screen by displaying holograms calculated by ARSS-Fresnel diffraction and speckle reduction method. The direct light from the output of the fiber is overlapped on the projected image; however, the direct light diffuses over the projection screen.

### 2.1. ARSS-Fresnel diffraction

*k*is the wave number,

*λ*is the wavelength of light,

*u*

_{1}(

*x*

_{1}) is the source plane (an image that we want to project),

*u*

_{2}(

*x*

_{2}) is the destination plane (a hologram), and

*z*is the propagation distance between the source and destination planes.

*x*

_{2}−

*sx*

_{1}+

*o*)

^{2}instead of (

*x*

_{2}−

*x*

_{1})

^{2}in Eq. (1) where

*s*is the scaling parameter and

*o*is offset from the origin. The scaling parameter is defined as the ratio of Δ

_{1}/Δ

_{2}where Δ

_{1}and Δ

_{2}are the sampling pitches on the projected image and hologram. Substituting the relation

*x*is a variable for the generation of exp(i

_{h}*ϕ*

_{h}),

*x*is the aliasing-free area and exp(

_{max}*iϕ*), exp(

_{u}*iϕ*) and

_{h}*C*are defined by

_{z}11. T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. **15**, 075302(5pp) (2013). [CrossRef]

### 2.2. Hologram generation with speckle reduction

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

*N*different initial random phase distributions and calculates

*N*holograms by GS algorithm. “Hologram 1” and “Hologram N” in Fig. 2(b) mean the generated holograms with GS algorithm and initial random phase 1 and N, respectively. We can observe speckle-reduced projected images because speckle noise suppression is realized by alternately displaying the

*N*holograms at high speed. In this experiment, we used different initial random phase distributions of

*N*= 20.

## 3. Results

*N*= 20. The projected image had reduced speckle noise, compared with those shown in Figs. 3 (a) and (b).

*z*=200 mm, a sampling pitch on the hologram of 8

*μ*m and a wavelength of 671 nm as the calculation conditions. In addition, the holograms were optimized by the multiple random phase method with five iterations and

*N*= 20. The upper images are the projected image calculated by Shifted-Fresnel diffraction, when changing the sampling pitch of the projected image from 10

*μ*m to 14

*μ*m. In the sampling pitch of the projected image of over 12

*μ*m, an aliasing noise is incurred in the projected images. The bottom images are the projected image calculated by ARSS-Fresnel diffraction. In the projected images, the aliasing noise is incurred. Moreover, the light is not wasted on the aliasing artifacts, which allows a brighter reconstruction of the main central image.

*z*= 450 mm. We can observe zoomable projected images only by changing the sampling pitch on the projected image. When the sampling pitch of the projected image is 18

*μ*m, the image size is approximately 37mm × 37mm. Note that the pixel number of the projected image is 2,048 × 2,048. When using a large sampling pitch on the projected image, the brightness of the projected image is darker because the light power is spread on a large area. We used our computational wave optics library, CWO++ [17

17. T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. **183**, 1124–1138 (2012). [CrossRef]

## 4. Conclusion

16. M. Makowski, I. Ducin, K. Kakarenko, M. Sypek, and A. Kolodziejczyk, “Speckle Suppression in Color Holographic Projection by Pixel Separation,” in *Digital Holography and Three-Dimensional Imaging*, OSA Technical Digest (online) (Optical Society of America, 2013), paper DTu1A.6. [CrossRef]

## Acknowledgments

## References and links

1. | W. O. Davis, R. Sprague, and J. Miller, “MEMS-based pico projector display,” Optical MEMs and Nanophotonics, 2008 IEEE/LEOS International Conference, 31–32 (2008). |

2. | M. Freeman, M. Champion, and S. Madhavan, “Scanned Laser Pico-Projectors: Seeing the Big Picture (with a Small Device),”Optics & Photonics News |

3. | E. Buckley, “Holographic Laser Projection,” J. Display Technol. |

4. | E. Buckley, “Holographic projector using one lens,” Opt. Lett. |

5. | H.-C. Lin, N. Collings, M.-S. Chen, and Y.-H. Lin, “A holographic projection system with an electrically tuning and continuously adjustable optical zoom,” Opt. Express |

6. | Y.-H. Lin and M.-S. Chen, “A Pico Projection System With Electrically Tunable Optical Zoom Ratio Adopting Two Liquid Crystal Lenses,” J. Disp. Tech. |

7. | T. Shimobaba, A. Gotchev, N. Masuda, and T. Ito, “Proposal of zoomable holographic projection without zoom lens,” IDW’11, |

8. | T. Shimobaba, T. Kakue, N. Masuda, and T. Ito, “Numerical investigation of zoomable holographic projection without a zoom lens,” JSID |

9. | T. Shimobaba, T. Kakue, N. Masuda, and T. Ito, “Zoomable Color Holographic Projection Method Without a Zoom Lens,” IDW/AD’ 12, |

10. | R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted Fresnel diffraction for computational holography,” Opt. Express |

11. | T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. |

12. | 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 |

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

14. | M. Makowski, I. Ducin, K. Kakarenko, A. Kolodziejczyk, A. Siemion, A. Siemion, J. Suszek, M. Sypek, and D. Wojnowski, “Efficient image projection by Fourier electroholography,” Opt. Lett. |

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

16. | M. Makowski, I. Ducin, K. Kakarenko, M. Sypek, and A. Kolodziejczyk, “Speckle Suppression in Color Holographic Projection by Pixel Separation,” in |

17. | T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun. |

**OCIS Codes**

(090.1760) Holography : Computer holography

(090.2870) Holography : Holographic display

(090.5694) Holography : Real-time holography

**ToC Category:**

Holography

**History**

Original Manuscript: June 24, 2013

Revised Manuscript: August 19, 2013

Manuscript Accepted: August 20, 2013

Published: October 15, 2013

**Citation**

Tomoyoshi Shimobaba, Michal Makowski, Takashi Kakue, Minoru Oikawa, Naohisa Okada, Yutaka Endo, Ryuji Hirayama, and Tomoyoshi Ito, "Lensless zoomable holographic projection using scaled Fresnel diffraction," Opt. Express **21**, 25285-25290 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-25285

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### References

- W. O. Davis, R. Sprague, and J. Miller, “MEMS-based pico projector display,” Optical MEMs and Nanophotonics, 2008 IEEE/LEOS International Conference, 31–32 (2008).
- M. Freeman, M. Champion, and S. Madhavan, “Scanned Laser Pico-Projectors: Seeing the Big Picture (with a Small Device),”Optics & Photonics News20(5), 28–34 (2009). [CrossRef]
- E. Buckley, “Holographic Laser Projection,” J. Display Technol.99, 1–6 (2010).
- E. Buckley, “Holographic projector using one lens,” Opt. Lett.35, 3399–3401 (2010). [CrossRef] [PubMed]
- H.-C. Lin, N. Collings, M.-S. Chen, and Y.-H. Lin, “A holographic projection system with an electrically tuning and continuously adjustable optical zoom,” Opt. Express20, 27222–27229 (2012). [CrossRef] [PubMed]
- Y.-H. Lin and M.-S. Chen, “A Pico Projection System With Electrically Tunable Optical Zoom Ratio Adopting Two Liquid Crystal Lenses,” J. Disp. Tech.8, 401–404 (2012). [CrossRef]
- T. Shimobaba, A. Gotchev, N. Masuda, and T. Ito, “Proposal of zoomable holographic projection without zoom lens,” IDW’11, PRJ3(2011).
- T. Shimobaba, T. Kakue, N. Masuda, and T. Ito, “Numerical investigation of zoomable holographic projection without a zoom lens,” JSID20, 533–538 (2012). [CrossRef]
- T. Shimobaba, T. Kakue, N. Masuda, and T. Ito, “Zoomable Color Holographic Projection Method Without a Zoom Lens,” IDW/AD’ 12, PRJp-5 (2012).
- R. P. Muffoletto, J. M. Tyler, and J. E. Tohline, “Shifted Fresnel diffraction for computational holography,” Opt. Express15, 5631–5640 (2007). [CrossRef] [PubMed]
- T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt.15, 075302(5pp) (2013). [CrossRef]
- 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, 20840–20846 (2009). [CrossRef] [PubMed]
- 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, 1227–1229 (2010). [CrossRef] [PubMed]
- M. Makowski, I. Ducin, K. Kakarenko, A. Kolodziejczyk, A. Siemion, A. Siemion, J. Suszek, M. Sypek, and D. Wojnowski, “Efficient image projection by Fourier electroholography,” Opt. Lett.36, 3018–3020 (2011). [CrossRef] [PubMed]
- M. Makowski, I. Ducin, K. Kakarenko, J. Suszek, M. Sypek, and A. Kolodziejczyki, “Simple holographic projection in color,” Opt. Express20, 25130–25136 (2012). [CrossRef] [PubMed]
- M. Makowski, I. Ducin, K. Kakarenko, M. Sypek, and A. Kolodziejczyk, “Speckle Suppression in Color Holographic Projection by Pixel Separation,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (online) (Optical Society of America, 2013), paper DTu1A.6. [CrossRef]
- T. Shimobaba, J. Weng, T. Sakurai, N. Okada, T. Nishitsuji, N. Takada, A. Shiraki, N. Masuda, and T. Ito, “Computational wave optics library for C++: CWO++ library,” Comput. Phys. Commun.183, 1124–1138 (2012). [CrossRef]

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