Abstract

A rigorous approach is proposed to improve the resolution of integral imaging (InI) by finding the appropriate form of irregularity in the arrangement of the InI lenslets. The improvement of the resolution is achieved through redistribution of the sampling points in a uniform manner. The optimization process for finding the optimum pattern of the lens-array irregularity is carried out by minimizing a cost function, whose mathematical closed-form expression is provided. The minimization of the proposed cost function ensures the uniform distribution of sampling points and thus improves the resolution within the desired depth of field (DOF) and field of view (FOV). A set of standard resolution charts is used to demonstrate the improvement of the quality of the three-dimensional (3D) images obtained by using the optimized irregular lens array. It is shown that the overall level of the lateral and depth resolutions is improved at the same time.

© 2012 Optical Society of America

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References

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2012

2011

2008

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A Compound-eye system with irregular lens-array arrangement,” Proc. SPIE 7072, 70720G (2008).
[CrossRef]

2006

J. Y. Son, B. Javidi, and K. -D. Kwack, “Methods for displaying 3D images,” Proc. IEEE 94, 502–523 (2006).
[CrossRef]

2005

2004

2003

1996

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22, 469–483 (1996).
[CrossRef]

1980

Y. A. Dudnikov, B. K. Rozhkov, and E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

1970

R. L. de Montebello, “Wide angle integral-photography: the integram technique,” Proc. SPIE 120, 73–91 (1970).

1931

1908

M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. (Paris) 7, 821–825 (1908).

Antipova, E. N.

Y. A. Dudnikov, B. K. Rozhkov, and E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Bagheri, S.

Barber, C. B.

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22, 469–483 (1996).
[CrossRef]

Choi, H.

Corral, M. M.

de Montebello, R. L.

R. L. de Montebello, “Wide angle integral-photography: the integram technique,” Proc. SPIE 120, 73–91 (1970).

Dobkin, D. P.

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22, 469–483 (1996).
[CrossRef]

Dudnikov, Y. A.

Y. A. Dudnikov, B. K. Rozhkov, and E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Hong, S.-H.

Horisaki, R.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A Compound-eye system with irregular lens-array arrangement,” Proc. SPIE 7072, 70720G (2008).
[CrossRef]

Huhdanpaa, H. T.

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22, 469–483 (1996).
[CrossRef]

Ives, H. E.

Jang, J. S.

Jang, J.-S.

Javidi, B.

Jung, S.

Kagawa, K.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A Compound-eye system with irregular lens-array arrangement,” Proc. SPIE 7072, 70720G (2008).
[CrossRef]

Kavehvash, Z.

Kim, Y.

Kwack, K. -D.

J. Y. Son, B. Javidi, and K. -D. Kwack, “Methods for displaying 3D images,” Proc. IEEE 94, 502–523 (2006).
[CrossRef]

Lee, B.

Lippmann, M. G.

M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. (Paris) 7, 821–825 (1908).

Masaki, Y.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A Compound-eye system with irregular lens-array arrangement,” Proc. SPIE 7072, 70720G (2008).
[CrossRef]

Mehrany, Kh.

Min, S. -W.

Min, S.-W.

Nakao, Y.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A Compound-eye system with irregular lens-array arrangement,” Proc. SPIE 7072, 70720G (2008).
[CrossRef]

Navarro, H.

Okoshi, T.

T. Okoshi, Three Dimensional Imaging Techniques (Academic, 1976).

Onural, L.

Park, J.-H.

Rozhkov, B. K.

Y. A. Dudnikov, B. K. Rozhkov, and E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Saavedra, G.

Son, J. Y.

J. Y. Son, B. Javidi, and K. -D. Kwack, “Methods for displaying 3D images,” Proc. IEEE 94, 502–523 (2006).
[CrossRef]

Tanida, J.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A Compound-eye system with irregular lens-array arrangement,” Proc. SPIE 7072, 70720G (2008).
[CrossRef]

Toyoda, T.

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A Compound-eye system with irregular lens-array arrangement,” Proc. SPIE 7072, 70720G (2008).
[CrossRef]

Valyus, N. A.

N. A. Valyus, Stereoscopy (Focal, 1966).

Yontem, A.

ACM Trans. Math. Softw.

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, “The Quickhull algorithm for convex hulls,” ACM Trans. Math. Softw. 22, 469–483 (1996).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. (Paris)

M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. (Paris) 7, 821–825 (1908).

Opt. Eng.

J. S. Jang and B. Javidi, “Very-large scale integral imaging (VLSII) for 3D display,” Opt. Eng. 44, 014001 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. IEEE

J. Y. Son, B. Javidi, and K. -D. Kwack, “Methods for displaying 3D images,” Proc. IEEE 94, 502–523 (2006).
[CrossRef]

Proc. SPIE

R. Horisaki, Y. Nakao, T. Toyoda, K. Kagawa, Y. Masaki, and J. Tanida, “A Compound-eye system with irregular lens-array arrangement,” Proc. SPIE 7072, 70720G (2008).
[CrossRef]

R. L. de Montebello, “Wide angle integral-photography: the integram technique,” Proc. SPIE 120, 73–91 (1970).

Sov. J. Opt. Technol.

Y. A. Dudnikov, B. K. Rozhkov, and E. N. Antipova, “Obtaining a portrait of a person by the integral photography method,” Sov. J. Opt. Technol. 47, 562–563 (1980).

Other

N. A. Valyus, Stereoscopy (Focal, 1966).

T. Okoshi, Three Dimensional Imaging Techniques (Academic, 1976).

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Figures (4)

Fig. 1.
Fig. 1.

Regular and irregular lens arrays, their typical sampling rays, and the RoI. Lenslets of the regular and irregular lens arrays and their sampling rays are depicted by dashed and solid lines, respectively in (a) front view, (b) top view, and (c) left view.

Fig. 2.
Fig. 2.

(a) Reconstructed image in the lateral resolution plane (plane A) of regular lens array, (b) its high-frequency contents enlarged to show how good the resolution is, (c) reconstructed image in the lateral resolution plane (plane A) of irregular lens array, and (d) its high-frequency contents enlarged to show how good the resolution is.

Fig. 3.
Fig. 3.

(a) Reconstructed image in the depth resolution plane (plane B) of regular lens array, (b) its high-frequency contents enlarged to show how good the resolution is, (c) reconstructed image in the depth resolution plane (plane B) of irregular lens array, and (d) its high-frequency contents enlarged to show how good the resolution is.

Fig. 4.
Fig. 4.

(a) Reconstructed image in z=408.2mm (plane C) of regular lens array, (b) its high-frequency contents enlarged to show how good the resolution is, (c) reconstructed image in plane C of irregular lens array, and (d) its high-frequency contents enlarged to show how good the resolution is.

Equations (7)

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

z+gspq+g=xxixpxi=yyjyqyj.
tan1(xpxig)θx,pqαxtan1(yqyjg)θy,pqαy.
za(zazL)cos(θx,pq)cos(θy,pq)+spq<z<za+(zRza)cos(θx,pq)cos(θy,pq)+spq,
{z=zix=(zi+g)(xpxi)spq+g+xiy=(zi+g)(yqyj)spq+g+yj,
{xxixpxi=xxixpxiyyjyqyj=yyjyqyjxpxispq+g(z+g)+xi=xpxispq+g(z+g)+xi,
f(spq,θx,pq,θy,pq)={(Ed2+σd2)+(Em2+σm2)N+ΣCn2}.
fpq=(1f+1g1g+spq)1.

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