Abstract

In integral imaging, the quality of a reconstructed image degrades with increasing viewing angle due to the wavefront aberrations introduced by the lens-array. A wavefront aberration correction method is proposed to enhance the image quality with a pre-filtering function array (PFA). To derive the PFA for an integral imaging display, the wavefront aberration characteristic of the lens-array is analyzed and the intensity distribution of the reconstructed image is calculated based on the wave optics theory. The minimum mean square error method is applied to manipulate the elemental image array (EIA) with a PFA. The validity of the proposed method is confirmed through simulations as well as optical experiments. A 45-degree viewing angle integral imaging display with enhanced image quality is achieved.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  24. R. C. Gonzales and R. E. Wood, Digital Image Processing (Prentice Hall, 2002).

2018 (1)

2017 (2)

2016 (1)

2015 (2)

2014 (3)

2013 (3)

X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications [Invited],” Appl. Opt. 52(4), 546–560 (2013).
[Crossref] [PubMed]

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photonics 5(4), 456–535 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (1)

2010 (2)

2007 (1)

2006 (1)

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[Crossref]

2002 (1)

1978 (1)

Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys. 17(9), 1683–1684 (1978).
[Crossref]

1931 (1)

1908 (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Ai, L. Y.

Beausoleil, R. G.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Brug, J.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Chen, C. W.

C. W. Chen, M. Cho, Y. P. Huang, and B. Javidi, “Improved viewing zones for projection type integral imaging 3D display using adaptive liquid crystal prism array,” J. Disp. Technol. 10(3), 198–203 (2014).
[Crossref]

Chen, Y.

Cho, M.

C. W. Chen, M. Cho, Y. P. Huang, and B. Javidi, “Improved viewing zones for projection type integral imaging 3D display using adaptive liquid crystal prism array,” J. Disp. Technol. 10(3), 198–203 (2014).
[Crossref]

Choi, H.

Choi, S.

Dong, X. B.

Duo, C.

Fan, F. C.

Fang, F.

Fattal, D.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Fiorentino, M.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Gao, X.

Geng, J.

J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photonics 5(4), 456–535 (2013).
[Crossref] [PubMed]

Guan, Y.

Huang, Y. P.

C. W. Chen, M. Cho, Y. P. Huang, and B. Javidi, “Improved viewing zones for projection type integral imaging 3D display using adaptive liquid crystal prism array,” J. Disp. Technol. 10(3), 198–203 (2014).
[Crossref]

Igarashi, Y.

Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys. 17(9), 1683–1684 (1978).
[Crossref]

Ives, H. E.

Jang, J. S.

Jang, J. Y.

Javidi, B.

Jiang, C. C.

Jiang, L.

Jung, J. H.

Kang, H. H.

Kang, J. M.

Karimzadeh, A.

Kim, E. S.

Kim, J.

Kim, Y.

Lee, B.

Lee, J. H.

Li, D. H.

Li, Y.

Lin, C.

Lippmann, G.

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

Liu, X.

Luo, J. Y.

Martinez-Corral, M.

Martínez-Corral, M.

Martinez-Cuenca, R.

Murata, H.

Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys. 17(9), 1683–1684 (1978).
[Crossref]

Navarro, H.

Pang, B.

Peng, Z.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Pons, A.

Saavedra, G.

Sang, X.

Shin, D.

Stern, A.

X. Xiao, B. Javidi, M. Martinez-Corral, and A. Stern, “Advances in three-dimensional integral imaging: sensing, display, and applications [Invited],” Appl. Opt. 52(4), 546–560 (2013).
[Crossref] [PubMed]

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[Crossref]

Tolosa, Á.

Tran, T.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Ueda, M.

Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys. 17(9), 1683–1684 (1978).
[Crossref]

Vo, S.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Wang, A. H.

Wang, K.

Wang, Q. H.

Wang, X.

Wu, X.

Wu, Y.

Xiao, X.

Xing, S.

Xu, D.

Yan, B.

Yang, C.

Yang, S.

Yu, C.

Yu, X.

Yuan, J.

Zhang, J.

Zhang, X.

Zhao, W. X.

Zhu, L.

Adv. Opt. Photonics (1)

J. Geng, “Three-dimensional display technologies,” Adv. Opt. Photonics 5(4), 456–535 (2013).
[Crossref] [PubMed]

Appl. Opt. (4)

C. R. Acad. Sci. (1)

G. Lippmann, “La photographie integrale,” C. R. Acad. Sci. 146, 446–451 (1908).

J. Disp. Technol. (1)

C. W. Chen, M. Cho, Y. P. Huang, and B. Javidi, “Improved viewing zones for projection type integral imaging 3D display using adaptive liquid crystal prism array,” J. Disp. Technol. 10(3), 198–203 (2014).
[Crossref]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

Y. Igarashi, H. Murata, and M. Ueda, “3D display system using a computer generated integral photography,” Jpn. J. Appl. Phys. 17(9), 1683–1684 (1978).
[Crossref]

Nature (1)

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Opt. Express (9)

S. Xing, X. Sang, X. Yu, C. Duo, B. Pang, X. Gao, S. Yang, Y. Guan, B. Yan, J. Yuan, and K. Wang, “High-efficient computer-generated integral imaging based on the backward ray-tracing technique and optical reconstruction,” Opt. Express 25(1), 330–338 (2017).
[Crossref] [PubMed]

J. Zhang, X. Wang, X. Wu, C. Yang, and Y. Chen, “Wide-viewing integral imaging using fiber-coupled monocentric lens array,” Opt. Express 23(18), 23339–23347 (2015).
[Crossref] [PubMed]

J. Y. Jang, D. Shin, and E. S. Kim, “Optical three-dimensional refocusing from elemental images based on a sifting property of the periodic δ-function array in integral-imaging,” Opt. Express 22(2), 1533–1550 (2014).
[Crossref] [PubMed]

X. B. Dong, L. Y. Ai, and E. S. Kim, “Integral imaging-based large-scale full-color 3-D display of holographic data by using a commercial LCD panel,” Opt. Express 24(4), 3638–3651 (2016).
[Crossref] [PubMed]

H. H. Kang, J. H. Lee, and E. S. Kim, “Enhanced compression rate of integral images by using motion-compensated residual images in three-dimensional integral-imaging,” Opt. Express 20(5), 5440–5459 (2012).
[Crossref] [PubMed]

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]

C. Yu, J. Yuan, F. C. Fan, C. C. Jiang, S. Choi, X. Sang, C. Lin, and D. Xu, “The modulation function and realizing method of holographic functional screen,” Opt. Express 18(26), 27820–27826 (2010).
[Crossref] [PubMed]

X. Sang, X. Gao, X. Yu, S. Xing, Y. Li, and Y. Wu, “Interactive floating full-parallax digital three-dimensional light-field display based on wavefront recomposing,” Opt. Express 26(7), 8883–8889 (2018).
[Crossref] [PubMed]

Á. Tolosa, R. Martinez-Cuenca, H. Navarro, G. Saavedra, M. Martínez-Corral, B. Javidi, and A. Pons, “Enhanced field-of-view integral imaging display using multi-Köhler illumination,” Opt. Express 22(26), 31853–31863 (2014).
[Crossref] [PubMed]

Opt. Lett. (2)

Proc. IEEE (1)

A. Stern and B. Javidi, “Three-dimensional image sensing, visualization, and processing using integral imaging,” Proc. IEEE 94(3), 591–607 (2006).
[Crossref]

Other (2)

H. Gross, W. Singer, M. Totzeck, F. Blechinger, and B. Achtner, Handbook of Optical Systems (Wiley Online Library, 2005).

R. C. Gonzales and R. E. Wood, Digital Image Processing (Prentice Hall, 2002).

Supplementary Material (2)

NameDescription
» Visualization 1       the displayed 3D image with the captured EIA (without correction)
» Visualization 2       the displayed 3D image with the PEIA (with correction)

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Figures (10)

Fig. 1
Fig. 1 Block diagram of the proposed system: (a) capturing stage, (b) pre-filtering stage, (c) optical reconstruction stage.
Fig. 2
Fig. 2 (a) Reconstruction process of the volume pixel A ' . (b) Ideal wavefront map; (c) distorted wavefront map. (d) RMS wavefront aberration of the imperfect lens.
Fig. 3
Fig. 3 (a) 81 representative field sections of the E I 00 . (b) 25 field sections in the upper-right corner of Fig. 3(a) and the corresponding field positions (these field sections are plotted, for the lens is rotationally symmetric).
Fig. 4
Fig. 4 (a) Imaging process of a pixel in the integral imaging display. (b) Intensity distribution of spot A ' vs. intensity distribution of an ideal spot. (c) RMS spot of A ' (central, RMS radius = 184.8um) vs. RMS spot of an ideal spot (right top corner, RMS radius = 0).
Fig. 5
Fig. 5 Spot diagrams of the lens unit in 25 field sections (RMS spot size: “S5”: 3.18mm, “S6”: 3.42mm, “S7”: 3.68mm, “S8”: 3.88mm, “S9”: 0.97mm, “S14”: 2.34mm, “S15”: 2.59mm, “S16”: 3.04mm, “S17”: 3.68mm, “S18”: 4.55mm, “S23”: 1.70mm, “S24”: 1.94mm, “S25”: 2.41mm, “S26”: 3.04mm, “S27”: 3.88mm, “S32”: 1.22mm, “S33”: 1.47mm, “S34”: 1.94mm, “S35”: 2.59mm, “S36”: 3.42mm, “S41”: 0.97mm, “S42”: 1.22mm, “S43”: 1.69mm, “S44”: 2.34mm, “S45”: 3.18mm).
Fig. 6
Fig. 6 RMS wavefront aberrations without correction and with correction.
Fig. 7
Fig. 7 The simulation with the proposed method: (a) original images, (b) reconstructed images without correction, (c) reconstructed images with correction.
Fig. 8
Fig. 8 Optical configuration of the integral imaging display.
Fig. 9
Fig. 9 Two kinds of EIAs: (a) Captured EIA, (b) PEIA.
Fig. 10
Fig. 10 Image quality of the reconstructed 3D object is improved. The top row shows different views of the displayed 3D image with the captured EIA (see Visualization 1). The bottom row shows different views of the displayed 3D image with the PEIA (see Visualization 2).

Tables (2)

Tables Icon

Table 1 Surface Specifications of the lens unit.

Tables Icon

Table 2 Zernike coefficients of field sections S1~S81.

Equations (11)

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W 00 = W 00 ( ξ 2 + η 2 , η y 0 , y 0 2 , ξ x 0 , x 0 2 ) = a 1 ( ξ 2 + η 2 ) + a 2 η y 0 + a 2 ξ x 0 + b 1 ( ξ 2 + η 2 ) 2 + b 2 η y 0 ( ξ 2 + η 2 ) + b 2 ξ x 0 ( ξ 2 + η 2 ) + b 3 η 2 y 0 2 + b 3 ξ 2 x 0 2 + b 4 y 0 2 ( ξ 2 + η 2 ) + b 4 x 0 2 ( ξ 2 + η 2 ) + b 5 η y 0 3 + b 5 ξ x 0 3
( x 0 , y 0 ) = { ( 0.9 H m , 0.9 H m ) , ( x 0 , y 0 ) Ω S 1 ( 0.7 H m , 0.9 H m ) , ( x 0 , y 0 ) Ω S 2 ( 0.7 H m , 0.9 H m ) , ( x 0 , y 0 ) Ω S 8 ( 0.9 H m , 0.9 H m ) , ( x 0 , y 0 ) Ω S 9 , ( x 0 , y 0 ) = { ( 0.9 H m , 0.7 H m ) , ( x 0 , y 0 ) Ω S 10 ( 0.7 H m , 0.7 H m ) , ( x 0 , y 0 ) Ω S 11 ( 0.7 H m , 0.7 H m ) , ( x 0 , y 0 ) Ω S 17 ( 0.9 H m , 0.7 H m ) , ( x 0 , y 0 ) Ω S 18 ( x 0 , y 0 ) = { ( 0.9 H m , 0.7 H m ) , ( x 0 , y 0 ) Ω S 64 ( 0.7 H m , 0.7 H m ) , ( x 0 , y 0 ) Ω S 65 ( 0.7 H m , 0.7 H m ) , ( x 0 , y 0 ) Ω S 71 ( 0.9 H m , 0.7 H m ) , ( x 0 , y 0 ) Ω S 72 , ( x 0 , y 0 ) = { ( 0.9 H m , 0.9 H m ) , ( x 0 , y 0 ) Ω S 73 ( 0.7 H m , 0.9 H m ) , ( x 0 , y 0 ) Ω S 74 ( 0.7 H m , 0.9 H m ) , ( x 0 , y 0 ) Ω S 80 ( 0.9 H m , 0.9 H m ) , ( x 0 , y 0 ) Ω S 81
W 00 ( ξ , η ) = W [ x ] ( ξ , η ) = Z 0 [ x ] + Z 1 [ x ] η + Z 2 [ x ] ξ + Z 3 [ x ] [ 2 ( ξ 2 + η 2 ) 1 ] + Z 4 [ x ] ( η 2 ξ 2 ) + Z 5 [ x ] 2 ξ η + Z 6 [ x ] [ 2 η + 3 η ( ξ 2 + η 2 ) ] + Z 7 [ x ] [ 2 ξ + 3 ξ ( ξ 2 + η 2 ) ] + Z 8 [ x ] [ 1 6 ( ξ 2 + η 2 ) + 6 ( ξ 2 + η 2 ) 2 ] s u b j e c t t o ( x 0 A 00 , y 0 A 00 ) Ω x , f o r x = S 1 , S 2 S 80 , S 81
W m n ( ξ , η ) = W 00 ( ξ p m , η p n )
h ( x , y ; z ) = | 1 λ 2 l g Ω E I Ω L δ ( x 0 x 0 A m n , y 0 y 0 A m n ) × exp { i k 2 l [ ( ξ x 0 A m n ) 2 + ( η y 0 A m n ) 2 ] } × P m n ( ξ , η ) × exp { i k 2 f [ ( ξ p m ) 2 + ( η p n ) 2 ] } × exp { i k 2 g [ ( x ξ ) 2 + ( y η ) 2 ] } d x 0 d y 0 d ξ d η | 2
P m n ( ξ , η ) = { exp [ i k W m n ( ξ , η ) ] ( ξ p m ) 2 + ( η p n ) 2 ( p / 2 ) 2 0 o t h e r w i s e
h ( x , y ; z ) = | M + exp [ i k W m n ( λ g u , λ g v ) ] exp { i 2 π [ ( x M x 0 A m n ) u + ( y M y 0 A m n ) v ] } d u d v | 2
R I m n ( x , y ; z ) = I m n ( x 0 , y 0 ; z ) h ( x , y ; z )
R I ( x , y ; z ) = m = M , n = N m = M , n = N R I m n ( x , y ; z ) = m = M , n = N m = M , n = N I m n ( x 0 , y 0 ; z ) h ( x , y ; z )
R I ( x , y ; z ) = m = M , n = N m = M , n = N P I m n ( x 0 , y 0 ; z ) h ( x , y ; z ) = m = M , n = N m = M , n = N I m n ( x 0 , y 0 ; z ) h 1 ( x , y ; z ) h ( x , y ; z )
m = M , n = N m = M , n = N P I m n ( x , y ; z ) = m = M , n = N m = M , n = N 1 F T [ h ( x , y ; z ) ] | F T [ h ( x , y ; z ) ] | 2 | F T [ h ( x , y ; z ) ] | 2 + K F T [ I m n ( x , y ; z ) ]

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