Abstract

The seemingly inherent deficiencies of integral imaging systems—in particular, the depth of field limitation—are, in this Letter, partly resolved by using an irregular lens array, where each lens is either rotated or displaced from its original position in the conventional flat lens array. It is shown that having an array of lenses in the integral imaging system has some sort of redundancy that could be exploited to improve the quality of the image formation. The needed rotation or displacement of constituent lenses in the array is found by using a meticulous optimization algorithm, which tries to evenly distribute the optical rays emanating from each of the lenses to form the final image.

© 2011 Optical Society of America

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References

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  1. A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
    [CrossRef]
  2. S. F. Ray, Applied Photographic Optics (Focal Press, 2002).
  3. M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 22, 597 (2005).
    [CrossRef]
  4. M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 43, 5806 (2004).
    [CrossRef] [PubMed]
  5. Y. Kim, J.-H. Park, H. Choi, S. Jung, S.-W. Min, and B. Lee, Opt. Express 12, 421 (2004).
    [CrossRef] [PubMed]
  6. J.-S. Jang and B. Javidi, Opt. Express 12, 3778 (2004).
    [CrossRef] [PubMed]
  7. R. Horisaki, K. Kagawa, Y. Nakao, T. Toyoda, Y. Masaki, and J. Tanida, Appl. Phys. Express 3, 022501 (2010).
    [CrossRef]
  8. C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, ACM Trans. Math. Softw. 22, 469 (1996).
    [CrossRef]
  9. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

2010 (1)

R. Horisaki, K. Kagawa, Y. Nakao, T. Toyoda, Y. Masaki, and J. Tanida, Appl. Phys. Express 3, 022501 (2010).
[CrossRef]

2006 (1)

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

2005 (1)

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 22, 597 (2005).
[CrossRef]

2004 (3)

1996 (1)

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, ACM Trans. Math. Softw. 22, 469 (1996).
[CrossRef]

Barber, C. B.

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, ACM Trans. Math. Softw. 22, 469 (1996).
[CrossRef]

Choi, H.

Cuenca, R. M.

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 22, 597 (2005).
[CrossRef]

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 43, 5806 (2004).
[CrossRef] [PubMed]

Dobkin, D. P.

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, ACM Trans. Math. Softw. 22, 469 (1996).
[CrossRef]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

Horisaki, R.

R. Horisaki, K. Kagawa, Y. Nakao, T. Toyoda, Y. Masaki, and J. Tanida, Appl. Phys. Express 3, 022501 (2010).
[CrossRef]

Huhdanpaa, H. T.

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, ACM Trans. Math. Softw. 22, 469 (1996).
[CrossRef]

Jang, J.-S.

Javidi, B.

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 22, 597 (2005).
[CrossRef]

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 43, 5806 (2004).
[CrossRef] [PubMed]

J.-S. Jang and B. Javidi, Opt. Express 12, 3778 (2004).
[CrossRef] [PubMed]

Jung, S.

Kagawa, K.

R. Horisaki, K. Kagawa, Y. Nakao, T. Toyoda, Y. Masaki, and J. Tanida, Appl. Phys. Express 3, 022501 (2010).
[CrossRef]

Kim, Y.

Lee, B.

Martinez-Corral, M.

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 22, 597 (2005).
[CrossRef]

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 43, 5806 (2004).
[CrossRef] [PubMed]

Masaki, Y.

R. Horisaki, K. Kagawa, Y. Nakao, T. Toyoda, Y. Masaki, and J. Tanida, Appl. Phys. Express 3, 022501 (2010).
[CrossRef]

Min, S.-W.

Nakao, Y.

R. Horisaki, K. Kagawa, Y. Nakao, T. Toyoda, Y. Masaki, and J. Tanida, Appl. Phys. Express 3, 022501 (2010).
[CrossRef]

Park, J.-H.

Ray, S. F.

S. F. Ray, Applied Photographic Optics (Focal Press, 2002).

Saavedra, G.

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 22, 597 (2005).
[CrossRef]

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 43, 5806 (2004).
[CrossRef] [PubMed]

Stern, A.

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

Tanida, J.

R. Horisaki, K. Kagawa, Y. Nakao, T. Toyoda, Y. Masaki, and J. Tanida, Appl. Phys. Express 3, 022501 (2010).
[CrossRef]

Toyoda, T.

R. Horisaki, K. Kagawa, Y. Nakao, T. Toyoda, Y. Masaki, and J. Tanida, Appl. Phys. Express 3, 022501 (2010).
[CrossRef]

ACM Trans. Math. Softw. (1)

C. B. Barber, D. P. Dobkin, and H. T. Huhdanpaa, ACM Trans. Math. Softw. 22, 469 (1996).
[CrossRef]

Appl. Opt. (2)

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 22, 597 (2005).
[CrossRef]

M. Martinez-Corral, B. Javidi, R. M. Cuenca, and G. Saavedra, Appl. Opt. 43, 5806 (2004).
[CrossRef] [PubMed]

Appl. Phys. Express (1)

R. Horisaki, K. Kagawa, Y. Nakao, T. Toyoda, Y. Masaki, and J. Tanida, Appl. Phys. Express 3, 022501 (2010).
[CrossRef]

Opt. Express (2)

Proc. IEEE (1)

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

Other (2)

S. F. Ray, Applied Photographic Optics (Focal Press, 2002).

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

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Figures (4)

Fig. 1
Fig. 1

Linear lens array and its principal rays (dashed line), the information-carrying segment of the principal rays (solid line), and the RoI.

Fig. 2
Fig. 2

Histogram of the distances between sampling points for (a) conventional regular lens array (b) optimized irregular lens array.

Fig. 3
Fig. 3

(a) Original rectangular object. (b) Reconstructed image obtained by using the conventional regular lens array, (c) the optimized irregular lens array with the appropriate RoI, and (d) an inappropriate RoI.

Fig. 4
Fig. 4

(a) Original objects. (b) Reconstructed image obtained by using the conventional regular lens array and (c) the optimized irregular lens array.

Tables (1)

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Table 1 Optimized s x i , s z i , and θ i for the Test 4 × 1 Lens Array

Equations (2)

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1 / g + 1 / z 0 = 1 / f
f { s x i , s z i , θ i } = { w 1 [ E d 2 + σ d 2 ] + w 2 [ E d f 2 + σ d f 2 ] P + P f } ,

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