Abstract

A retroreflector array improves the visual quality of three-dimensional (3D) image in the pinhole-type integral imaging display. Conventionally, the limited size of the apertures of the pinhole array restricts the fill factor of the pixelated 3D images. We propose a system with a retroreflector, which consists of the array of corner cubes that increases the fill factor of the pixel by the diffraction. The pixel spreading model is developed by an equivalent corner cube structure. The simulation of pixel spreading by the Fraunhofer diffraction agrees well with experimental results, and proves the effectiveness of the proposed method to improve the visual quality while not sacrificing the viewing angle and the depth perception.

© 2017 Optical Society of America

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References

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  1. G. Lippmann, “La photographic integrale,” CR Acad. Sci. 146, 446–451 (1908).
  2. J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  9. J. Arai, H. Kawai, and F. Okano, “Microlens arrays for integral imaging system,” Appl. Opt. 45(36), 9066–9078 (2006).
    [Crossref] [PubMed]
  10. S.-W. Min, J. Hong, and B. Lee, “Analysis of an optical depth converter used in a three-dimensional integral imaging system,” Appl. Opt. 43(23), 4539–4549 (2004).
    [Crossref] [PubMed]
  11. Y. Kim, J. Kim, J.-M. Kang, J.-H. Jung, H. Choi, and B. Lee, “Point light source integral imaging with improved resolution and viewing angle by the use of electrically movable pinhole array,” Opt. Express 15(26), 18253–18267 (2007).
    [Crossref] [PubMed]
  12. J.-S. Jang and B. Javidi, “Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor,” Appl. Opt. 42(11), 1996–2002 (2003).
    [Crossref] [PubMed]
  13. S. Park, B.-S. Song, and S.-W. Min, “Analysis of image visibility in projection-type integral imaging system without diffuser,” J. Opt. Soc. Korea 14(2), 121–126 (2010).
    [Crossref]
  14. S.-W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys. 44(2), L71–L74 (2005).
    [Crossref]
  15. D. A. Arnold, “Method of calculating retroreflector-array transfer functions,” SAO Special Report 382 (1979).
  16. K. Arrington and G. Geri, “Conjugate-optical retroreflector display system: Optical principles and perceptual issues,” J. Soc. Inf. Disp. 8(2), 123–128 (2000).
    [Crossref]
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    [Crossref]
  19. J. Liu and R. M. Azzam, “Polarization properties of corner-cube retroreflectors: theory and experiment,” Appl. Opt. 36(7), 1553–1559 (1997).
    [Crossref] [PubMed]

2014 (2)

2011 (1)

2010 (1)

2009 (2)

2008 (1)

2007 (1)

2006 (2)

2005 (1)

S.-W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys. 44(2), L71–L74 (2005).
[Crossref]

2004 (1)

2003 (1)

2000 (1)

K. Arrington and G. Geri, “Conjugate-optical retroreflector display system: Optical principles and perceptual issues,” J. Soc. Inf. Disp. 8(2), 123–128 (2000).
[Crossref]

1998 (1)

1997 (2)

1908 (1)

G. Lippmann, “La photographic integrale,” CR Acad. Sci. 146, 446–451 (1908).

Arai, J.

Arrington, K.

K. Arrington and G. Geri, “Conjugate-optical retroreflector display system: Optical principles and perceptual issues,” J. Soc. Inf. Disp. 8(2), 123–128 (2000).
[Crossref]

Azzam, R. M.

Chen, N.

Choi, H.

Choi, H.-J.

Choi, S.

Geri, G.

K. Arrington and G. Geri, “Conjugate-optical retroreflector display system: Optical principles and perceptual issues,” J. Soc. Inf. Disp. 8(2), 123–128 (2000).
[Crossref]

Hahn, J.

Hong, J.

Hong, K.

Hoshino, H.

Jang, J.-S.

Javidi, B.

Jung, J.-H.

Kang, J.-M.

Kawai, H.

Kim, E.-H.

Kim, H.

Kim, J.

Y. Kim, J. Kim, J.-M. Kang, J.-H. Jung, H. Choi, and B. Lee, “Point light source integral imaging with improved resolution and viewing angle by the use of electrically movable pinhole array,” Opt. Express 15(26), 18253–18267 (2007).
[Crossref] [PubMed]

S.-W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys. 44(2), L71–L74 (2005).
[Crossref]

Kim, Y.

Lee, B.

Lippmann, G.

G. Lippmann, “La photographic integrale,” CR Acad. Sci. 146, 446–451 (1908).

Liu, J.

Martinez-Corral, M.

Martinez-Cuenca, R.

Min, S.-W.

Mishina, T.

Oi, R.

Okano, F.

Okui, M.

Park, J.-H.

Park, S.

Pons, A.

Saavedra, G.

Senoh, T.

Song, B.

Song, B.-S.

Sung, H.

Suyama, S.

Tomiyama, Y.

Yamamoto, H.

Yamamoto, K.

Yuyama, I.

Appl. Opt. (8)

J.-H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009).
[Crossref] [PubMed]

J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. 50(34), H87–H115 (2011).
[Crossref] [PubMed]

F. Okano, H. Hoshino, J. Arai, and I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36(7), 1598–1603 (1997).
[Crossref] [PubMed]

J. Arai, F. Okano, H. Hoshino, and I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37(11), 2034–2045 (1998).
[Crossref] [PubMed]

J. Arai, H. Kawai, and F. Okano, “Microlens arrays for integral imaging system,” Appl. Opt. 45(36), 9066–9078 (2006).
[Crossref] [PubMed]

S.-W. Min, J. Hong, and B. Lee, “Analysis of an optical depth converter used in a three-dimensional integral imaging system,” Appl. Opt. 43(23), 4539–4549 (2004).
[Crossref] [PubMed]

J.-S. Jang and B. Javidi, “Improvement of viewing angle in integral imaging by use of moving lenslet arrays with low fill factor,” Appl. Opt. 42(11), 1996–2002 (2003).
[Crossref] [PubMed]

J. Liu and R. M. Azzam, “Polarization properties of corner-cube retroreflectors: theory and experiment,” Appl. Opt. 36(7), 1553–1559 (1997).
[Crossref] [PubMed]

CR Acad. Sci. (1)

G. Lippmann, “La photographic integrale,” CR Acad. Sci. 146, 446–451 (1908).

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Korea (2)

J. Soc. Inf. Disp. (1)

K. Arrington and G. Geri, “Conjugate-optical retroreflector display system: Optical principles and perceptual issues,” J. Soc. Inf. Disp. 8(2), 123–128 (2000).
[Crossref]

Jpn. J. Appl. Phys. (1)

S.-W. Min, J. Kim, and B. Lee, “New characteristic equation of three-dimensional integral imaging system and its applications,” Jpn. J. Appl. Phys. 44(2), L71–L74 (2005).
[Crossref]

Opt. Express (4)

Other (1)

D. A. Arnold, “Method of calculating retroreflector-array transfer functions,” SAO Special Report 382 (1979).

Supplementary Material (4)

NameDescription
» Visualization 1       Experimental result of conventional pinhole-type integral imaging system
» Visualization 2       Experimental result of proposed system
» Visualization 3       Experimental result of pinhole-type integral imaging system
» Visualization 4       Experimental result of optimazed proposed system

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram of proposed system which consists of pinhole-type integral imaging, a beam splitter and a retroreflector.
Fig. 2
Fig. 2 Geometrical analysis of retroreflector in two-dimensional.
Fig. 3
Fig. 3 (a) Geometrical analysis of retroreflector in three-dimensional (b) Effective aperture of retroreflector when incoming light is normal to incident plane.
Fig. 4
Fig. 4 (a) Three reflecting surfaces of retroreflector (b) Six regions based on reflection order.
Fig. 5
Fig. 5 Simulation results of Fraunhofer diffraction with phase shift of retroreflector. (a) Pinhole aray, (b) The distance from pinhole array to retroreflector is at 40 mm, (c) 50 mm, (d) 60 mm, (e) 70 mm, (f) 80 mm, (g) 90 mm and (h) 100 mm.
Fig. 6
Fig. 6 2D simulation results of intensity distribution of Fraunhofer diffraction depending on the distance from the pinhole array to the retroreflector. There are two pinhole which gray box is the pinhole size and black box is the one elemental image size. (a) Intensity distribution of Fraunhofer diffraction by retroreflector in two pinholes. (b) There are two pinholes used in initial simulation setup. Total and pinhole size is 1.564 mm and 0.276 mm, respectively. (c) Magnification of (a) at near 0 mm. 1st peaks are overlapped from 80 mm to 100 mm. Red box R1 and R2 are 1st peaks of intensity distribution from 80 mm to 100 mm. R3 is the overlapped region of them.
Fig. 7
Fig. 7 (a) Experimental setup, (b) Experimental result located at character image ’K’, (c) ’H’ and (d) ’U’.
Fig. 8
Fig. 8 Experimental results of Fraunhofer diffraction with phase shift of retroreflector. (a) Pinhole array, (b) The distance from pinhole array to retroreflector is at 40 mm, (c) 50 mm, (d) 60 mm, (e) 70 mm, (f) 80 mm, (g) 90 mm and (h) 100 mm.
Fig. 9
Fig. 9 Experimental results of pinhole-type integral imaging and the proposed system (a) Left view of pinhole-type integral imaging, (b) center view, (c) right view (see Visualization 1),(d) Left view of the proposed system, (e) center view, (f) right view (see Visualization 2).
Fig. 10
Fig. 10 The optimized experimental results of pinhole-type integral imaging and the proposed system (a) Left view of pinhole-type integral imaging, (b) center view, (c) right view (see Visualization 3), (d) Left view of the proposed system, (e) center view, (f) right view (see Visualization 4).

Tables (2)

Tables Icon

Table 1 Specification of experiment for image location

Tables Icon

Table 2 Specification of experiment for optimization

Equations (3)

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U m (x,y)= exp(ikz)exp(i αx+βy 2 ) iλz × , { U i (ξ,η)exp(i ϕ m (ξ,η))exp(i k 2z ( ξ 2 + η 2 )) } exp(i(αξ+βη))dξdη
I(x,y)= m=1 6 U m (x,y) U m * (x,y) .
D optimized = argmax D Z ( I 1st ( D z ) I overlapped ( D z )) ,

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