Abstract

Wide-viewing angle integral imaging by means of a negative refractive index planoconcave lens array is theoretically investigated. The optical properties of a negative refractive index lens are analyzed from the point of view of integral imaging. The effective focal length of a positive index planoconvex lens and a negative index planoconcave lens with the same surface spherical curvature R are approximated as f P,eff=2R and f N,eff=R, respectively. This short effective focal length of the negative index lens is advantageous for extending the viewing angle of the integral imaging. In addition, some other optical properties of a negative index lens are analyzed and compared for a positive index lens. Three-dimensional ray-tracing observation simulations of integral imaging systems with a negative index lens array and a positive index lens array are then performed, in a comparative study of the wide-viewing angle mode for integral imaging. A three-dimensional ray-tracing simulator for an integral imaging system is then developed. Some interesting issues that appear in the wide-viewing mode of integral imaging are discussed. The negative refractive index planoconcave lens was found to give a wider viewing angle of -60(deg.) ~+60(deg.) and reduces aberration with only a single spherical planoconcave lens.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
    [CrossRef]
  21. K.-Y. Kim, "Photon tunneling in composite layers of negative- and positive-index media," Phys. Rev. E 70, 047603 (2004).
    [CrossRef]
  22. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, (Wiley, New York, 2001).
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    [CrossRef]
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    [CrossRef]
  25. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
    [CrossRef] [PubMed]

2008 (2)

2007 (2)

2006 (2)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

D. Schurig and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

2005 (1)

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

2004 (7)

2003 (2)

2002 (2)

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[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]

2000 (1)

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Arai, J.

Choi, H.

Dohi, T.

Dolling, G.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, and M. H. Tanielian, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Haino, Y.

Hua, H.

Iwahara, M.

Jang, J.

Javidi, B.

Jung, S.

Kawakita, M.

Kim, J.

Kim, K.-Y.

K.-Y. Kim, "Photon tunneling in composite layers of negative- and positive-index media," Phys. Rev. E 70, 047603 (2004).
[CrossRef]

Kim, Y.

Lee, B.

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, and M. H. Tanielian, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Liao, H.

Linden, S.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Lu, W. T.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Min, S.

Min, S. -W.

Min, S.-W.

Nemat-Nasser, S. C.

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Nielsen, J. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, and M. H. Tanielian, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Nobuhiko, H.

Okano, F.

Padilla, W.

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, and M. H. Tanielian, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Parimi, P. V.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Park, J.

Park, J.-H.

Sasaki, H.

Sato, M.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. Schurig and D. R. Smith, "Negative index lens aberrations," Phys. Rev. E 70, 065601 (2004).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

D. Schurig and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

D. Schurig and D. R. Smith, "Negative index lens aberrations," Phys. Rev. E 70, 065601 (2004).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Sridhar, S.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Suehiro, K.

Tanielian, M. H.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, and M. H. Tanielian, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Thompson, M. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, and M. H. Tanielian, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, and M. H. Tanielian, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

Vier, D. C.

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Vodo, P.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Wang, X.

Wegener, M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780nm wavelength," Opt. Lett. 32, 53-55 (2007).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Yoshimura, M.

Appl. Opt. (2)

Appl. Phys. Lett. (3)

D. Schurig and D. R. Smith, "Free-space microwave focusing by a negative-index gradient lens," Appl. Phys. Lett. 88, 081101 (2006).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, and M. H. Tanielian, "Performance of a negative index of refraction lens," Appl. Phys. Lett. 84, 3232-3234 (2004).
[CrossRef]

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, "Focusing by planoconcave lens using negative refraction," Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Opt. Express (4)

Opt. Lett. (7)

Phys. Rev. E (2)

D. Schurig and D. R. Smith, "Negative index lens aberrations," Phys. Rev. E 70, 065601 (2004).
[CrossRef]

K.-Y. Kim, "Photon tunneling in composite layers of negative- and positive-index media," Phys. Rev. E 70, 047603 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

D. R. Smith, W. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "A composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Science (2)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Other (4)

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing, (Wiley, New York, 2001).

H. Choi, J.-H. Park, J. Hong, and B. Lee, "Depth-enhanced integral imaging with a stepped lens array or a composite lens array for three-dimensional display," The 16th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2003), Tucson, AZ, 2, 730-731, Oct. 2003.
[CrossRef]

B. Javidi and F. Okano, eds., Three Dimensional Television, Video, and Display Technologies (Springer, 2002).

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, 2006), pp. 333-378.
[CrossRef]

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Figures (13)

Fig. 1.
Fig. 1.

Structures and ray traces of (a) negative index planocancave lens (NIL) and (b) positive index planoconvex lens (PIL).

Fig. 2.
Fig. 2.

Ray tracing profiles of NIL at normal incidence: (a) perspective view, (b) meridional cross-section, ray tracing profiles of PIL at normal incidence: (c) perspective view, (d) meridional cross-section.

Fig. 3.
Fig. 3.

Ray tracing profiles of NIL and PIL at oblique incidence of 70(deg.): (a) perspective view, (b) meridional cross-section of NIL and (c) perspective view, (d) meridional cross-section of PIL.

Fig. 4.
Fig. 4.

Crossing point distribution, x(xi), for (a) normal incidence and (b) oblique incidence 70(deg.).

Fig. 5.
Fig. 5.

Fourier transform properties of NIL and PIL: (a) focus position µ(θi ), (b) effective window w(θi ) for NIL, and (c) focus position µ(θi ), (d) effective window w(θi ) for PIL.

Fig. 6.
Fig. 6.

(a) pick-up setup and (b) display setup of InIm system.

Fig. 7.
Fig. 7.

Elemental images (a) for NIL InIm with a lens focal length of f N,eff =0.2cm and (b) for PIL InIm with a lens focal length of f P,eff =1cm.

Fig. 8.
Fig. 8.

Images of the 3D target object observed at various viewing angle position.

Fig. 9.
Fig. 9.

Images of the InIm with paraxial perfect lens of focal length f N,eff =0.2cm.

Fig. 10.
Fig. 10.

Images of the InIm with an NIL array of effective focal length f N,eff =0.2cm.

Fig. 11.
Fig. 11.

Images of the InIm with a perfect paraxial lens array of focal length f P,eff =1cm.

Fig. 12.
Fig. 12.

Images of the InIm with a PIL array of effective focal length f P,eff =1cm.

Fig. 13.
Fig. 13.

Comparison of InIm images with (a) PIL array and (b)NIL array.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

n n sin θ = sin θ i ,
n n sin ( ϕ θ ) = sin ψ ,
x = R sin ϕ + ( z R cos ϕ ) tan ( ψ + ϕ ) .
n p sin θ = sin θ i ,
n p sin ( ϕ + θ ) = sin ψ ,
x = R sin ϕ + ( z + R cos ϕ ) tan ( ψ ϕ ) .
( z i , x i ) = ( R cos ϕ , R sin ϕ ) , for NIL ,
( z i , x i ) = ( R cos ϕ , R sin ϕ ) , for PIL .
x ( x i ) = R sin ϕ + ( z f R cos ϕ ) tan ( ψ + ϕ ) , for NIL ,
x ( x i ) = R sin ϕ + ( z f R cos ϕ ) tan ( ψ ϕ ) , for PIL ,
flatness ( x ( x i ) ; R x i R , z = z f ) = max ( x ( x i ) ) min ( x ( x i ) ) max ( x ( x i ) ) + min ( x ( x i ) ) .
ρ = max ( x ( x i ) ) min ( x ( x i ) ) for x i ( x i , 1 , x i , 2 ) ,
μ = [ max ( x ( x i ) ) + min ( x ( x i ) ) ] 2 .
μ ( θ i ) = f eff sin θ i .
f N , eff = 0.4 R ,
f P , eff = 2 R .
( 1 l 2 f 0 λ ( l 1 + l 2 ) λ l 1 l 2 f 0 0 1 l 2 f 0 λ ( l 1 + l 2 ) λ l 1 l 2 f 1 ( λ f ) 0 1 l 1 f 0 0 1 ( λ f ) 0 1 l 1 f ) ( u v ρ u ρ v ) = ( x y ρ x ρ y ) ,

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