Abstract

The relation between the viewing characteristics and the system parameters of the integral floating system, which is a brand new three-dimensional display technique, is analyzed. The system parameters considered include the focal length and the pitch of the lens array, the focal length of the floating lens, the image resolution of the integrated image, and the distance from the integral imaging system to the floating lens. The viewing characteristics of the integral floating are defined and described in terms of viewing window, floating image resolution, and floating image thickness. The ray-optical analysis is performed for the explanation of the viewing window and the floating image resolution, while the wave-optical methods are used to analyze the image thickness.

© 2008 Optical Society of America

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  1. S.-W. Min, M. Hahn, J. Kim, and B. Lee, “Three-dimensional electro-floating display system using an integral imaging method,” Opt. Exp. 13, 4358-4369 (2005).
    [CrossRef]
  2. G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 46, 446-451 (1908).
  3. 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]
  4. 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]
  5. 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,” Proc. SPIE 5524, 387-395 (2004).
    [CrossRef]
  6. 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]
  7. S. Jung, J.-H. Park, H. Choi, and B. Lee, “Viewing-angle-enhanced integral three-dimensional imaging along all directions without mechanical movement,” Opt. Exp. 11, 1346-1356 (2003).
    [CrossRef]
  8. S.-W. Min, J. Kim, and B. Lee, “Wide-viewing projection-type integral imaging system with an embossed screen,” Opt. Lett. 29, 2420-2422 (2004).
    [CrossRef] [PubMed]
  9. B. Lee, J. Kim, and S.-W. Min, “Integral floating 3D display system: principle and analysis,” Proc. SPIE 6392, 6392-18 (2006).
  10. J. Kim, S.-W. Min, and B. Lee, “Viewing region maximization of an integral floating display through location adjustment of viewing window,” Opt. Exp. 15, 13023-13034 (2007).
    [CrossRef]

2007 (1)

J. Kim, S.-W. Min, and B. Lee, “Viewing region maximization of an integral floating display through location adjustment of viewing window,” Opt. Exp. 15, 13023-13034 (2007).
[CrossRef]

2006 (1)

B. Lee, J. Kim, and S.-W. Min, “Integral floating 3D display system: principle and analysis,” Proc. SPIE 6392, 6392-18 (2006).

2005 (3)

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

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]

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 (2)

S.-W. Min, J. Kim, and B. Lee, “Wide-viewing projection-type integral imaging system with an embossed screen,” Opt. Lett. 29, 2420-2422 (2004).
[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,” Proc. SPIE 5524, 387-395 (2004).
[CrossRef]

2003 (1)

S. Jung, J.-H. Park, H. Choi, and B. Lee, “Viewing-angle-enhanced integral three-dimensional imaging along all directions without mechanical movement,” Opt. Exp. 11, 1346-1356 (2003).
[CrossRef]

2001 (1)

1908 (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 46, 446-451 (1908).

Choi, H.

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]

S. Jung, J.-H. Park, H. Choi, and B. Lee, “Viewing-angle-enhanced integral three-dimensional imaging along all directions without mechanical movement,” Opt. Exp. 11, 1346-1356 (2003).
[CrossRef]

Hahn, M.

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

Hong, J.

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,” Proc. SPIE 5524, 387-395 (2004).
[CrossRef]

Jung, S.

Kim, J.

J. Kim, S.-W. Min, and B. Lee, “Viewing region maximization of an integral floating display through location adjustment of viewing window,” Opt. Exp. 15, 13023-13034 (2007).
[CrossRef]

B. Lee, J. Kim, and S.-W. Min, “Integral floating 3D display system: principle and analysis,” Proc. SPIE 6392, 6392-18 (2006).

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]

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

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,” Proc. SPIE 5524, 387-395 (2004).
[CrossRef]

S.-W. Min, J. Kim, and B. Lee, “Wide-viewing projection-type integral imaging system with an embossed screen,” Opt. Lett. 29, 2420-2422 (2004).
[CrossRef] [PubMed]

Kim, Y.

Lee, B.

J. Kim, S.-W. Min, and B. Lee, “Viewing region maximization of an integral floating display through location adjustment of viewing window,” Opt. Exp. 15, 13023-13034 (2007).
[CrossRef]

B. Lee, J. Kim, and S.-W. Min, “Integral floating 3D display system: principle and analysis,” Proc. SPIE 6392, 6392-18 (2006).

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]

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

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]

S.-W. Min, J. Kim, and B. Lee, “Wide-viewing projection-type integral imaging system with an embossed screen,” Opt. Lett. 29, 2420-2422 (2004).
[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,” Proc. SPIE 5524, 387-395 (2004).
[CrossRef]

S. Jung, J.-H. Park, H. Choi, and B. Lee, “Viewing-angle-enhanced integral three-dimensional imaging along all directions without mechanical movement,” Opt. Exp. 11, 1346-1356 (2003).
[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]

Lippmann, G.

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 46, 446-451 (1908).

Min, S.-W.

J. Kim, S.-W. Min, and B. Lee, “Viewing region maximization of an integral floating display through location adjustment of viewing window,” Opt. Exp. 15, 13023-13034 (2007).
[CrossRef]

B. Lee, J. Kim, and S.-W. Min, “Integral floating 3D display system: principle and analysis,” Proc. SPIE 6392, 6392-18 (2006).

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]

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

S.-W. Min, J. Kim, and B. Lee, “Wide-viewing projection-type integral imaging system with an embossed screen,” Opt. Lett. 29, 2420-2422 (2004).
[CrossRef] [PubMed]

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]

Park, J.-H.

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,” Proc. SPIE 5524, 387-395 (2004).
[CrossRef]

S. Jung, J.-H. Park, H. Choi, and B. Lee, “Viewing-angle-enhanced integral three-dimensional imaging along all directions without mechanical movement,” Opt. Exp. 11, 1346-1356 (2003).
[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]

Appl. Opt. (2)

C. R. Acad. Sci. (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 46, 446-451 (1908).

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. Exp. (3)

S. Jung, J.-H. Park, H. Choi, and B. Lee, “Viewing-angle-enhanced integral three-dimensional imaging along all directions without mechanical movement,” Opt. Exp. 11, 1346-1356 (2003).
[CrossRef]

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

J. Kim, S.-W. Min, and B. Lee, “Viewing region maximization of an integral floating display through location adjustment of viewing window,” Opt. Exp. 15, 13023-13034 (2007).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

B. Lee, J. Kim, and S.-W. Min, “Integral floating 3D display system: principle and analysis,” Proc. SPIE 6392, 6392-18 (2006).

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,” Proc. SPIE 5524, 387-395 (2004).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

(Color online) Illustration of an integral floating display.

Fig. 2
Fig. 2

Calculation of the size of the viewing window.

Fig. 3
Fig. 3

(Color online) Integral imaging system designed to provide the maximum viewing region for an integral floating display.

Fig. 4
Fig. 4

Calculation of the spatial density of pixels of the 3D image.

Fig. 5
Fig. 5

Calculation of the total number of the pixels in the 3D image.

Fig. 6
Fig. 6

(Color online) Coordinates for the wave optical simulation of the integral floating system.

Fig. 7
Fig. 7

Intensity profiles of the impulse responses.

Fig. 8
Fig. 8

Spot sizes of the impulse responses for various observed distances.

Fig. 9
Fig. 9

Experimental results for the spot sizes varying the position of the diffuser.

Fig. 10
Fig. 10

(Color online) Three-dimensional images constructed by the integral floating display system. The locations of K, H, and U are 400 m m , 350 m m , and 300 m m in front of the floating lens: (a) a 3D floating image and (b) a set of diffusing images.

Tables (1)

Tables Icon

Table 1 Predetermined Experimental Parameters

Equations (14)

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w f = φ f i b f f a ( b f f ) f f ,
s = φ d g d .
s = φ b f f a ( b f f ) b f f ( a f i ) ( b f f ) .
N i = R e s ,
R f = R e f i f f b f f ( a f i ) ( b f f ) .
N f = R f w f .
w f = φ b f f a ( b f f ) f i f f ,
N f = R e φ b f f a ( b f f ) b f f ( a f i ) ( b f f ) .
U L A ( x 1 , y 1 ; ξ , η ) = e j k g j λ g e j k 2 g ( x 1 2 + y 1 2 ) { U ( ξ , η ) × e j k 2 g ( ξ 2 + η 2 ) } e j 2 π λ g ( x 1 ξ + y 1 η ) d ξ d η ,
U L A ( x 1 , y 1 ) = U L A ( x 1 , y 1 ) exp { j k 2 f i [ ( x 1 X 1 q ) 2 + ( y 1 Y 1 q ) 2 ] } ,
U F L ( x 2 , y 2 ; x 1 , y 1 ) = e j k a j λ a e j k 2 a ( x 2 2 + y 2 2 ) { U L A ( x 1 , y 1 ) × e j k 2 a ( x 1 2 + y 1 2 ) } e j 2 π λ a ( x 2 x 1 + y 2 y 1 ) d x 1 d y 1 .
U FL ( x 2 , y 2 ) = U FL ( x 2 , y 2 ) exp { j k 2 f f [ ( x 2 X 2 ) 2 + ( y 2 Y 2 ) 2 ] } ,
U o u t ( u , v ; ξ , η ) = e j k d j λ d e j k 2 d ( u 2 + v 2 ) { U F L ( x 2 , y 2 ) × e j k 2 d ( x 2 2 + y 2 2 ) } e j 2 π λ d ( u x 2 + v y 2 ) d x 2 d y 2 .
I ( u , v ; ξ , η ) = | h ( u , v ; ξ , η ) | 2 .

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