## Viewing region maximization of an integral floating display through location adjustment of viewing window

Optics Express, Vol. 15, Issue 20, pp. 13023-13034 (2007)

http://dx.doi.org/10.1364/OE.15.013023

Acrobat PDF (301 KB)

### Abstract

Integral floating display is a recently proposed three-dimensional (3D) display method which provides a dynamic 3D image in the vicinity to an observer. It has a viewing window only through which correct 3D images can be observed. However, the positional difference between the viewing window and the floating image causes limited viewing zone in integral floating system. In this paper, we provide the principle and experimental results of the location adjustment of the viewing window of the integral floating display system by modifying the elemental image region for integral imaging. We explain the characteristics of the viewing window and propose how to move the viewing window to maximize the viewing zone.

© 2007 Optical Society of America

## 1. Introduction

1. S.-W. Min, M. Hahn, J. Kim, and B. Lee, “Three-dimensional electro-floating display system using an integral imaging method,” Opt. Express **13**, 4358–4369 (2005). [CrossRef] [PubMed]

11. J. Hong, J.-H. Park, J. Kim, and B. Lee, “Analysis of image depth in integral imaging and its enhancement by correction to elemental images,” Novel Optical Systems Design and Optimization VII, SPIE Annual Meeting, Proc. SPIE **5524**, Denver, Colorado, USA, 387–395, Aug. 2004. [CrossRef]

12. J.-H. Park, S.-W. Min, S. Jung, and B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. **40**, 5217–5232 (2001). [CrossRef]

1. S.-W. Min, M. Hahn, J. Kim, and B. Lee, “Three-dimensional electro-floating display system using an integral imaging method,” Opt. Express **13**, 4358–4369 (2005). [CrossRef] [PubMed]

1. S.-W. Min, M. Hahn, J. Kim, and B. Lee, “Three-dimensional electro-floating display system using an integral imaging method,” Opt. Express **13**, 4358–4369 (2005). [CrossRef] [PubMed]

## 2. Location change of the viewing window in the integral floating system

### 2.1. The viewing angle of an integral imaging system

*f*is the focal length of the elemental lens,

_{i}*g*is the gap between the display device and the lens array,

*φ*is the pitch of the elemental lens and

*s*is the elemental image region for one elemental lens. In conventional design,

*s*and

*φ*are the same. We want to find out the viewing angle

*θ*for the middle elemental lens. The viewing angle is defined as the angular range inside which the observer can watch a correct 3D image. For correct view of the 3D image, each elemental image area should be observed through the corresponding elemental lens. In Fig. 2, the middle area indicated by black stripes of the display device should be observed through the middle elemental lens.

*θ*. The lowest ray in real mode and the highest ray in virtual mode, indicated by thick arrows, start at the boundary of the striped region. If the angle of parallel rays after the refraction is smaller than

*θ*, then all the rays will start from the black striped region. If the angle of parallel rays after the refraction is larger than

*θ*, then some portion or all of rays will not start from the black striped region. Therefore, we conclude that

*θ*is the viewing angle. The light rays indicated with thick arrows in Fig. 2 have a special meaning. Among the light rays which do not start from the black striped region, the light rays with thick arrows have the smallest angle to the normal of the elemental lens after the refraction. In fact, the thick arrow lines come from the boundaries between the striped region and its neighbor region. We will refer to them as ‘critical rays’ throughout this paper. The viewing angle of the real mode and the virtual mode integral imaging is acquired through simple geometrical calculation;

### 2.2. The viewing window of a conventional integral floating system

*w*can be calculated by multiplying the focal length of the floating lens by two times (full width) of the tangent of the viewing angle given in Eq. (1);

_{f}*f*is the focal length of the floating lens. It is an interesting fact that

_{f}*w*is independent of

_{f}*g*, the gap between the lens array and the display device, when the virtual mode of integral imaging system is used. It is because the viewing angle of integral imaging is also independent of

*g*as in Eq. (1) for the virtual mode. By expanding our discussion three-dimensionally, we can find the area of the viewing window.

### 2.3. Location change of the viewing window

*s*, the size of each elemental image area, to be different from

*φ*, the pitch of the elemental lens. Precisely, we let

*s*to be

*d*distant from the lens array. The role of the viewing window of integral imaging is just like that of the viewing window of integral floating; correct 3D images can only be observed through the viewing window.

*d*takes positive sign when the viewing window is behind the lens array and negative sign when the viewing window is in front of the lens array.

*s*is smaller than

*φ*when the viewing window is behind the lens array but bigger than

*φ*when the viewing window is in front of the lens array. The relationship among

*φ*,

*s*and

*d*are illustrated in Fig. 4.

*w*, the size of the viewing window of the integral imaging, can be derived as

_{i}*w*, is independent of

_{i}*g*for virtual mode.

*b*is the distance between the floating lens and the viewing window of integral floating display. We can find

*b*by applying lens law to

*a*+

*d*and

*f*. With

_{f}*b*and

*w*, known, the size of the viewing window of integral floating system

_{i}*w*can be described as

_{f}*w*of the proposed design is independent of

_{f}*g*for the integral floating display using virtual mode of integral imaging. The validation of Eq. (5) is verified through an experiment in which the location and the size of the window are measured.

*b*=350mm). Since

*b*and

*a*+

*d*satisfy the lens law

*f*is 175mm,

_{f}*a*+

*d*should be 350mm to make

*b*350mm. Virtual mode of integral imaging is used for the experiment and

*a*is changed to 250mm, 225mm and 200mm. A diffuser is placed at 350mm away from the floating lens, the desired location of the viewing window for the integral floating system. The size of the viewing window appeared on the diffuser is measured for each case as shown in Fig. 6.

## 3. Viewing region maximization of an integral floating display

### 3.1. Viewing region in integral floating display

*d*distant from the viewing window and the center of the 3D volume is Δ distant from the viewing window. The longitudinal size of the 3D volume is

_{o}*l*and the transversal size of the 3D volume is

*h*. Here,

*l*and

*h*are constant values for design process. Our goal is to maximize

*u*for given

*d*,

_{o}*l*and

*h*. In the discussion of the viewing region maximization process, only location (with respect to the 3D volume) and size of the viewing window are considered. Surely, too small integral imaging system with a few numbers of elemental lenses can restrict the viewing region so that the 3D image is unobservable even through the viewing window. But this problem can easily be overcome by expanding the integral imaging system to a proper size. Here we assume that an integral imaging system with enough size and resolution is provided and the only obstacle for enlarging

*u*is the location and size adjustment between the viewing window and the 3D volume. Also, the viewing angle of the integral imaging system need not be considered here because its effect is included in the position and the size of the viewing window of integral floating display.

*u*can be described as

*u*. Again, with some algebra, we get

### 3.2. Viewing region maximization in conventional integral floating display

*u*when other conditions are fixed. But Δ cannot be reduced less than

*l*/2. If Δ is less than

*l*/2, then some part of the 3D volume will be less than focal length distant from the floating lens and impossible to display (recall that the 3D image is a real image formed by the floating lens, a convex lens, and real images are more than focal length distant from the convex lens). In this design, a virtual mode of integral imaging system is preferred because we want to put the 3D volume as close as possible to the viewing window and the image sources should be very far from the floating lens. If we use real mode integral imaging, then the 3D image source will be produced between the lens array of integral imaging system and the floating lens. It usually leads to very large Δ and small viewing region. Therefore, we used virtual mode integral imaging system to construct an integral floating display. However, the analysis and the discussion throughout this paper cover both the real mode and the virtual mode integral imaging systems.

*l*and

*h*are assumed to be 80mm and 50mm, respectively. The observer is assumed to be 1m distant from the floating lens. This set of parameter values will be maintained in the rest of the paper and also in the experiment. The calculated size of the viewing region

*u*versus Δ varying from 40mm to 120mm is illustrated in Fig. 9. The viewing region is clearly maximized when Δ is 40mm, which is the value of

*l*/2.

### 3.3. Viewing region maximization through location adjustment of the viewing window

*w*will be smaller as

_{f}*a*gets bigger because (

*b*-

*f*) will have a positive value. Therefore,

_{f}*a*should be as small as possible. But too small

*a*is bad for delivering feel of depth. In our case, proper

*a*for good image quality was around 200mm. With

*a*set to 200mm,

*u*can be calculated using Eqs. (6) and (7) and the result is illustrated in Fig. 10.

## 4. Experimental results

*f*is 175mm,

_{f}*f*is 22mm,

_{i}*φ*is 10mm,

*a*is 200mm,

*h*is 50mm and

*l*is 80mm. The experimental setup is shown in Fig. 11.

## 5. Conclusion

## Acknowledgment

## References and links

1. | S.-W. Min, M. Hahn, J. Kim, and B. Lee, “Three-dimensional electro-floating display system using an integral imaging method,” Opt. Express |

2. | B. Lee, J. Kim, and S.-W. Min, “Integral floating 3D display system: principle and analysis,” Three-Dimensional TV, Video, and Display V, Optics East, Boston, MA, USA, Proc. SPIE. |

3. | J. Kim, Y. Kim, S.-W. Cho, S.-W. Min, and B. Lee, “Viewing angle enhancement of an integral imaging system.” Society for Information Display 2006 International Symposium Digest of Technical Paper, San Francisco, CA, USA, vol. |

4. | G. Lippmann, “La photographic intergrale,” C. R. Acad. Sci. |

5. | F. Okano, J. Arai, H. Hoshino, and I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. |

6. | A. Stern and B. Javidi, “Three-Dimensional Image Sensing and Reconstruction with Time-Division Multiplexed Computational Integral Imaging,” Appl. Opt. |

7. | B. Lee, J.-H. Park, and S.-W. Min, “Three-dimensional display and information processing based on integral imaging,” in Digital Holography and Three-Dimensional Display (edited by T.-C. Poon), Springer, New York, USA, 2006, Chapter 12. |

8. | J. S. Jang, F. Jin, and B. Javidi, “Three-dimensional integral imaging with large depth of focus using real and virtual image fields,” Opt. Lett. |

9. | M. Okui, J. Arai, Y. Nojiri, and F. Okano, “Optical screen for direct projection of integral imaging,” Appl. Opt. |

10. | H. Choi, Y. Kim, J.-H. Park, S. Jung, and B. Lee, “Improved analysis on the viewing angle of integral imaging,” Appl. Opt. |

11. | J. Hong, J.-H. Park, J. Kim, and B. Lee, “Analysis of image depth in integral imaging and its enhancement by correction to elemental images,” Novel Optical Systems Design and Optimization VII, SPIE Annual Meeting, Proc. SPIE |

12. | J.-H. Park, S.-W. Min, S. Jung, and B. Lee, “Analysis of viewing parameters for two display methods based on integral photography,” Appl. Opt. |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(110.2990) Imaging systems : Image formation theory

**ToC Category:**

Image Processing

**History**

Original Manuscript: June 11, 2007

Revised Manuscript: August 13, 2007

Manuscript Accepted: September 21, 2007

Published: September 25, 2007

**Citation**

Joowhan Kim, Sung-Wook Min, and Byoungho Lee, "Viewing region maximization of an integral floating display through location adjustment of viewing window," Opt. Express **15**, 13023-13034 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-20-13023

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### References

- S.-W. Min, M. Hahn, J. Kim, and B. Lee, "Three-dimensional electro-floating display system using an integral imaging method," Opt. Express 13, 4358-4369 (2005). [CrossRef] [PubMed]
- B. Lee, J. Kim, and S.-W. Min, "Integral floating 3D display system: principle and analysis," Three-Dimensional TV, Video, and Display V, Optics East, Boston, MA, USA, Proc. SPIE. 6392, paper 6392-18, Oct. 2006.
- J. Kim, Y. Kim, S.-W. Cho, S.-W. Min and B. Lee, "Viewing angle enhancement of an integral imaging system." Society for Information Display 2006 International Symposium Digest of Technical Paper, San Francisco, CA, USA, Vol. 37, book I, 186-189, June 2006.
- G. Lippmann, "La photographic intergrale," C. R. Acad. Sci. 146, 446-451 (1908).
- F. Okano, J. Arai, H. Hoshino, and I. Yuyama, "Three-dimensional video system based on integral photography," Opt. Eng. 38, 1072-1077 (1999). [CrossRef]
- A. Stern and B. Javidi, "Three-Dimensional Image Sensing and Reconstruction with Time-Division Multiplexed Computational Integral Imaging," Appl. Opt. 42, 7036-7042 (2003). [CrossRef] [PubMed]
- B. Lee, J.-H. Park, and S.-W. Min, "Three-dimensional display and information processing based on integral imaging," in Digital Holography and Three-Dimensional Display, T.-C. Poon, ed., (Springer, New York, USA, 2006), Chap. 12.
- J. S. Jang, F. Jin, and B. Javidi, "Three-dimensional integral imaging with large depth of focus using real and virtual image fields," Opt. Lett. 28, 1421-1423 (2003). [CrossRef] [PubMed]
- M. Okui, J. Arai, Y. Nojiri, and F. Okano, "Optical screen for direct projection of integral imaging," Appl. Opt. 45, 9132-9139 (2006). [CrossRef] [PubMed]
- H. Choi, Y. Kim, J.-H. Park, S. Jung, and B. Lee, "Improved analysis on the viewing angle of integral imaging," Appl. Opt. 44, 2311-2317 (2005). [CrossRef] [PubMed]
- J. Hong, J.-H. Park, J. Kim, and B. Lee, "Analysis of image depth in integral imaging and its enhancement by correction to elemental images," Novel Optical Systems Design and Optimization VII, SPIE Annual Meeting, Proc. SPIE 5524, Denver, Colorado, USA, 387-395, Aug. 2004. [CrossRef]
- J.-H. Park, S.-W. Min, S. Jung, and B. Lee, "Analysis of viewing parameters for two display methods based on integral photography," Appl. Opt. 40, 5217-5232 (2001). [CrossRef]

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