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Analysis of floating distance of arc 3D display with respect to inclination angle of substrate

  • Special Section: Regular Paper
  • Laser Display and Lighting Conference (LDC’ 23), Yokohama, Japan
  • Published:
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Abstract

We derive an equation that enables to get the floating distance of floating images of an arc 3D display by the radius of the arc, the angle of the arc 3D substrate, the light source illumination angle, and the observer’s angle. Conventional theoretical expression for the positions of the light source and observer relative to the center of the arc have been used to calculate the floating distance. However, when the arc3D substrate is inclined, it becomes more difficult to determine the floating distance from the actual positions of the light source and observer. In this paper, we derive an equation to approximate the floating distance from the positions of the light source and the observer while considering the tilt of the arc3D substrate and check the accuracy of the derived equation through experiments.

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Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Yamamoto, H., Tomiyama, Y., Suyama, S.: Floating aerial LED signage based on aerial imaging by retro-reflection (AIRR). Opt. Express 22(22), 26919–26924 (2014). https://doi.org/10.1364/OE.22.026919

    Article  ADS  Google Scholar 

  2. Sakane, S., Kudo, D., Mukoujima, N., Yasugi, M., Suyama, S., Yamamoto, H.: Formation of multiple aerial LED signs in multiple lanes formed with AIRR by use for two beam splitters. Opt Rev (2023). https://doi.org/10.1007/s10043-022-00771-y

    Article  Google Scholar 

  3. Plummer, J.W.T., Gardner, Leo R.: A mechanically generated hologram? Applied Optics 31(31), 6585–6588 (1992). https://doi.org/10.1364/AO.31.006585m

    Article  ADS  Google Scholar 

  4. W. J. Beaty,: Drawing Holograms by Hand. Proc. SPIE, Vol. 5005, pp. 156-167 (2003) DOI: https://doi.org/10.1117/12.478434

  5. Sato, S., Saji, I., Suyama, S. and Yamamoto. H.: The blur width of the bright spot can be reduced by increasing the observation distance in the front projection of the arc 3D display. Proc. DHIP 2021, P. 22 (2021).

  6. Saji, I., Nakata, M., Kashihara, Y., Hayashi, A. and Yamamoto, H.: Patterned Glass Etching for Popping-Up Signage. The International Display Workshops (IDW ’20), Vol.27, p.261–264 (2020) DOI: https://doi.org/10.36463/idw.2020.0261 .

  7. Suyama, S., Mizushina, H., Yamamoto, H.: Theoretical and experimental perceived depths in arc 3D displays: On/Off switching using liquid-crystal active devices. IEEE Ind. Appl. Mag. 27(1), 69–81 (2021). https://doi.org/10.1109/MIAS.2020.3024451

    Article  Google Scholar 

  8. Yamada, N., Maeda, C., Yamamoto, H. and Suyama, S.: Theoretical and measured evaluation of lighting and observation angle dependence of perceived depth in arc 3-D display. The 19th International Display Workshops in conjunction with Asia Display 2012 (IDW/AD’12), 3Dp – 14, pp. 1219–1222 (2012).

  9. Oishi, H., Fujii, K., Yasugi, M., Suyama, S. and Yamamoto, H.: Analyses on Long-range Pop-up Distance Change Caused by Angle Changes of Light Source, Substrate, and Observation in Arc 3D Display. Proc. OPTICS & PHOTONICS International Council 2023, LDC11-05 (2023).

  10. Nagata, S.: The binocular fusion of human vision on stereoscopic displays - field of view and environment effects. Ergonomics 39(11), 1273–1284 (1996). https://doi.org/10.1080/00140139608964547

    Article  Google Scholar 

  11. Westheimer, G., Tanzman, Irving J.: Qualitative Depth Localization with Diplopic Images. Optical Society of America 46(2), 116–117 (1956). https://doi.org/10.1364/JOSA.46.000116

    Article  ADS  Google Scholar 

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Funding

Japan Society for the Promotion of Science, 20H05702, Hirotsugu Yamamoto,19H04155,Hirotsugu Yamamoto

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Authors and Affiliations

  1. Utsunomiya University, Utsunomiya, Tochigi, Japan

    Hiroto Oishi, Shiro Suyama & Hirotsugu Yamamoto

  2. Nagaoka University of Technology, Nagaoka, Niigata, Japan

    Kengo Fujii

  3. Fukui Prefectural University, Obama, Fukui, Japan

    Masaki Yasugi

Authors
  1. Hiroto Oishi
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  2. Kengo Fujii
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  3. Masaki Yasugi
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  4. Shiro Suyama
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  5. Hirotsugu Yamamoto
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Contributions

HO contributed for this paper as 1st author. He derived the equations and conducted the experiments and wrote the original draft. KF, MY and SS checked the equations and edited the manuscript. HY designed the experiments and edited the manuscript.

Corresponding author

Correspondence to Hirotsugu Yamamoto.

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Oishi, H., Fujii, K., Yasugi, M. et al. Analysis of floating distance of arc 3D display with respect to inclination angle of substrate. Opt Rev 30, 637–646 (2023). https://doi.org/10.1007/s10043-023-00841-9

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  • DOI: https://doi.org/10.1007/s10043-023-00841-9

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