Abstract

This paper describes a superposition compound eye imaging system for extending the depth-of-field (DOF) and the field-of-view (FOV) using a spherical array of erect imaging optics and deconvolution processing. This imaging system had a three-dimensionally space-invariant point spread function generated by the superposition optics. A sharp image with a deep DOF and a wide FOV could be reconstructed by deconvolution processing with a single filter from a single captured image. The properties of the proposed system were confirmed by ray-trace simulations.

© 2012 OSA

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  34. D. Keum, J. Hyukjin, and J. Ki-Hun, “Planar emulation of natural compound eyes,” Small 8, 2169–2173 (2012).
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2012 (4)

L. Li and A. Y. Yi, “Design and fabrication of a freeform microlens array for a compact large-field-of-view compound-eye camera,” Appl. Opt. 51, 1843–1852 (2012).
[Crossref] [PubMed]

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref] [PubMed]

D. Dumas, M. Fendler, F. Berger, B. Cloix, C. Pornin, N. Baier, G. Druart, J. Primot, and E. le Coarer, “Infrared camera based on a curved retina,” Opt. Lett. 37, 653–655 (2012).
[Crossref] [PubMed]

D. Keum, J. Hyukjin, and J. Ki-Hun, “Planar emulation of natural compound eyes,” Small 8, 2169–2173 (2012).
[Crossref] [PubMed]

2011 (2)

R. Horisaki, T. Nakamura, and J. Tanida, “Superposition imaging for three-dimensionally space-invariant point spread functions,” Appl. Phys. Express 4, 112501 (2011).
[Crossref]

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, “Flexible depth of field photography,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 58–71 (2011).
[Crossref]

2010 (4)

2009 (3)

2008 (3)

2007 (1)

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, “Three-dimensional information acquisition using a compound imaging system,” Opt. Rev. 14, 347–350 (2007).
[Crossref]

2006 (2)

K.-H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
[Crossref] [PubMed]

J. W. Duparré and F. C. Wippermann, “Micro-optical artificial compound eyes,” Bioinspiration Biomimetics 1, R1 (2006).
[Crossref]

2005 (1)

2001 (1)

1995 (1)

1990 (1)

E. J. Warrant and P. D. McIntyre, “Limitations to resolution in superposition eyes,” J. Comp. Physiol., A 167, 785–803 (1990).
[Crossref]

1988 (1)

D. E. Nilsson, “A new type of imaging optics in compound eyes,” Nature 332, 76–78 (1988).
[Crossref]

1979 (1)

M. F. Land, F. A. Burton, and V. B. Meyer-Rochow, “The optical geometry of euphausiid eyes,” J. Comp. Physiol., A 130, 49–62 (1979).
[Crossref]

1978 (1)

S. Laughlin and S. McGinness, “The structures of dorsal and ventral regions of a dragonfly retina,” Cell Tissue Res. 188, 427–447 (1978).
[Crossref] [PubMed]

1972 (1)

G. Häusler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[Crossref]

Baier, N.

Berger, F.

Brady, D. J.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref] [PubMed]

R. Horisaki, K. Choi, J. Hahn, J. Tanida, and D. J. Brady, “Generalized sampling using a compound-eye imaging system for multi-dimensional object acquisition,” Opt. Express 18, 19367–19378 (2010).
[Crossref] [PubMed]

D. J. Brady and N. Hagen, “Multiscale lens design,” Opt. Express 17, 10659–10674 (2009).
[Crossref] [PubMed]

D. L. Marks and D. J. Brady, “Gigagon: A monocentric lens design imaging 40 gigapixels,” in “Imaging Systems,” (Optical Society of America, 2010), p. ITuC2.

Bräuer, A.

Brückner, A.

Burton, F. A.

M. F. Land, F. A. Burton, and V. B. Meyer-Rochow, “The optical geometry of euphausiid eyes,” J. Comp. Physiol., A 130, 49–62 (1979).
[Crossref]

Cathey, W. T.

Catrysse, P. B.

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92, 091114 (2008).
[Crossref]

Choi, K.

Cloix, B.

Cossairt, O.

O. Cossairt, C. Zhou, and S. K. Nayar, “Diffusion Coding Photography for Extended Depth of Field,” ACM Trans. Graph. (also Proc. of ACM SIGGRAPH) (2010).

O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in “IEEE International Conference on Computational Photography (ICCP),” (2011).

Dannberg, P.

Dinyari, R.

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92, 091114 (2008).
[Crossref]

Dowski, J. E. R.

Druart, G.

Dumas, D.

Duparré, J.

Duparré, J. W.

J. W. Duparré and F. C. Wippermann, “Micro-optical artificial compound eyes,” Bioinspiration Biomimetics 1, R1 (2006).
[Crossref]

Fallah, H. R.

Feller, S. D.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref] [PubMed]

Fendler, M.

Gehm, M. E.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref] [PubMed]

Golish, D. R.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Guérineau, N.

Hagen, N.

Hahn, J.

Haïdar, R.

Häusler, G.

G. Häusler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[Crossref]

Hiura, S.

S. Hiura, A. Mohan, and R. Raskar, “Krill-eye: Superposition compound eye for wide-angle imaging via grin lenses,” IPSJ Transactions on Computer Vision and Applications 2, 186–199 (2010).
[Crossref]

Horisaki, R.

R. Horisaki, T. Nakamura, and J. Tanida, “Superposition imaging for three-dimensionally space-invariant point spread functions,” Appl. Phys. Express 4, 112501 (2011).
[Crossref]

R. Horisaki, K. Choi, J. Hahn, J. Tanida, and D. J. Brady, “Generalized sampling using a compound-eye imaging system for multi-dimensional object acquisition,” Opt. Express 18, 19367–19378 (2010).
[Crossref] [PubMed]

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, “Three-dimensional information acquisition using a compound imaging system,” Opt. Rev. 14, 347–350 (2007).
[Crossref]

T. Nakamura, R. Horisaki, and J. Tanida, “Experimental verification of computational superposition imaging for compensating defocus and off-axis aberrated images,” in “Computational Optical Sensing and Imaging,” (Optical Society of America, 2012), p. CM2B.4.

Huang, K.

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92, 091114 (2008).
[Crossref]

Hyukjin, J.

D. Keum, J. Hyukjin, and J. Ki-Hun, “Planar emulation of natural compound eyes,” Small 8, 2169–2173 (2012).
[Crossref] [PubMed]

Ichioka, Y.

Irie, S.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, “Three-dimensional information acquisition using a compound imaging system,” Opt. Rev. 14, 347–350 (2007).
[Crossref]

Ishida, K.

Jeong, K.-H.

K.-H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
[Crossref] [PubMed]

Karimzadeh, A.

Keum, D.

D. Keum, J. Hyukjin, and J. Ki-Hun, “Planar emulation of natural compound eyes,” Small 8, 2169–2173 (2012).
[Crossref] [PubMed]

Ki-Hun, J.

D. Keum, J. Hyukjin, and J. Ki-Hun, “Planar emulation of natural compound eyes,” Small 8, 2169–2173 (2012).
[Crossref] [PubMed]

Kim, J.

K.-H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
[Crossref] [PubMed]

Kittle, D. S.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref] [PubMed]

Komatsu, S.

Kondou, N.

Kumagai, T.

Kuthirummal, S.

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, “Flexible depth of field photography,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 58–71 (2011).
[Crossref]

Land, M. F.

M. F. Land, F. A. Burton, and V. B. Meyer-Rochow, “The optical geometry of euphausiid eyes,” J. Comp. Physiol., A 130, 49–62 (1979).
[Crossref]

M. F. Land and D.-E. Nilsson, Animal Eyes (Oxford University Press, USA, 2002).

Laughlin, S.

S. Laughlin and S. McGinness, “The structures of dorsal and ventral regions of a dragonfly retina,” Cell Tissue Res. 188, 427–447 (1978).
[Crossref] [PubMed]

le Coarer, E.

Lee, L. P.

K.-H. Jeong, J. Kim, and L. P. Lee, “Biologically inspired artificial compound eyes,” Science 312, 557–561 (2006).
[Crossref] [PubMed]

Leitel, R.

Li, L.

Maekawa, S.

S. Maekawa, K. Nitta, and O. Matoba, “Transmissive optical imaging device with micromirror array,” in “Proceedings of the SPIE,” (2006), p. 63920E.
[Crossref]

Marks, D. L.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref] [PubMed]

D. L. Marks and D. J. Brady, “Gigagon: A monocentric lens design imaging 40 gigapixels,” in “Imaging Systems,” (Optical Society of America, 2010), p. ITuC2.

Matoba, O.

S. Maekawa, K. Nitta, and O. Matoba, “Transmissive optical imaging device with micromirror array,” in “Proceedings of the SPIE,” (2006), p. 63920E.
[Crossref]

McGinness, S.

S. Laughlin and S. McGinness, “The structures of dorsal and ventral regions of a dragonfly retina,” Cell Tissue Res. 188, 427–447 (1978).
[Crossref] [PubMed]

McIntyre, P. D.

E. J. Warrant and P. D. McIntyre, “Limitations to resolution in superposition eyes,” J. Comp. Physiol., A 167, 785–803 (1990).
[Crossref]

Meyer-Rochow, V. B.

M. F. Land, F. A. Burton, and V. B. Meyer-Rochow, “The optical geometry of euphausiid eyes,” J. Comp. Physiol., A 130, 49–62 (1979).
[Crossref]

Miau, D.

O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in “IEEE International Conference on Computational Photography (ICCP),” (2011).

Miyatake, S.

Miyazaki, D.

Mohan, A.

S. Hiura, A. Mohan, and R. Raskar, “Krill-eye: Superposition compound eye for wide-angle imaging via grin lenses,” IPSJ Transactions on Computer Vision and Applications 2, 186–199 (2010).
[Crossref]

Morimoto, T.

Mouroulis, P.

Nagahara, H.

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, “Flexible depth of field photography,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 58–71 (2011).
[Crossref]

Nakamura, T.

R. Horisaki, T. Nakamura, and J. Tanida, “Superposition imaging for three-dimensionally space-invariant point spread functions,” Appl. Phys. Express 4, 112501 (2011).
[Crossref]

T. Nakamura, R. Horisaki, and J. Tanida, “Experimental verification of computational superposition imaging for compensating defocus and off-axis aberrated images,” in “Computational Optical Sensing and Imaging,” (Optical Society of America, 2012), p. CM2B.4.

Nayar, S. K.

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, “Flexible depth of field photography,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 58–71 (2011).
[Crossref]

O. Cossairt, C. Zhou, and S. K. Nayar, “Diffusion Coding Photography for Extended Depth of Field,” ACM Trans. Graph. (also Proc. of ACM SIGGRAPH) (2010).

O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in “IEEE International Conference on Computational Photography (ICCP),” (2011).

Nilsson, D. E.

D. E. Nilsson, “A new type of imaging optics in compound eyes,” Nature 332, 76–78 (1988).
[Crossref]

Nilsson, D.-E.

M. F. Land and D.-E. Nilsson, Animal Eyes (Oxford University Press, USA, 2002).

Nitta, K.

S. Maekawa, K. Nitta, and O. Matoba, “Transmissive optical imaging device with micromirror array,” in “Proceedings of the SPIE,” (2006), p. 63920E.
[Crossref]

Ogura, Y.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, “Three-dimensional information acquisition using a compound imaging system,” Opt. Rev. 14, 347–350 (2007).
[Crossref]

Peumans, P.

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92, 091114 (2008).
[Crossref]

Pornin, C.

Primot, J.

Raskar, R.

S. Hiura, A. Mohan, and R. Raskar, “Krill-eye: Superposition compound eye for wide-angle imaging via grin lenses,” IPSJ Transactions on Computer Vision and Applications 2, 186–199 (2010).
[Crossref]

Rim, S.-B.

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92, 091114 (2008).
[Crossref]

Rommeluère, S.

Schreiber, P.

Stack, R. A.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref] [PubMed]

Stollberg, K.

Taboury, J.

Takahashi, Y.

Tanida, J.

R. Horisaki, T. Nakamura, and J. Tanida, “Superposition imaging for three-dimensionally space-invariant point spread functions,” Appl. Phys. Express 4, 112501 (2011).
[Crossref]

R. Horisaki, K. Choi, J. Hahn, J. Tanida, and D. J. Brady, “Generalized sampling using a compound-eye imaging system for multi-dimensional object acquisition,” Opt. Express 18, 19367–19378 (2010).
[Crossref] [PubMed]

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, “Three-dimensional information acquisition using a compound imaging system,” Opt. Rev. 14, 347–350 (2007).
[Crossref]

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, “Thin observation module by bound optics (TOMBO): Concept and experimental verification,” Appl. Opt. 40, 1806–1813 (2001).
[Crossref]

T. Nakamura, R. Horisaki, and J. Tanida, “Experimental verification of computational superposition imaging for compensating defocus and off-axis aberrated images,” in “Computational Optical Sensing and Imaging,” (Optical Society of America, 2012), p. CM2B.4.

Thétas, S.

Tünnermann, A.

Vera, E. M.

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
[Crossref] [PubMed]

Warrant, E. J.

E. J. Warrant and P. D. McIntyre, “Limitations to resolution in superposition eyes,” J. Comp. Physiol., A 167, 785–803 (1990).
[Crossref]

Wippermann, F. C.

J. W. Duparré and F. C. Wippermann, “Micro-optical artificial compound eyes,” Bioinspiration Biomimetics 1, R1 (2006).
[Crossref]

Yamada, K.

Yi, A. Y.

Zhou, C.

S. Kuthirummal, H. Nagahara, C. Zhou, and S. K. Nayar, “Flexible depth of field photography,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 58–71 (2011).
[Crossref]

O. Cossairt, C. Zhou, and S. K. Nayar, “Diffusion Coding Photography for Extended Depth of Field,” ACM Trans. Graph. (also Proc. of ACM SIGGRAPH) (2010).

Appl. Opt. (5)

Appl. Phys. Express (1)

R. Horisaki, T. Nakamura, and J. Tanida, “Superposition imaging for three-dimensionally space-invariant point spread functions,” Appl. Phys. Express 4, 112501 (2011).
[Crossref]

Appl. Phys. Lett. (1)

R. Dinyari, S.-B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92, 091114 (2008).
[Crossref]

Bioinspiration Biomimetics (1)

J. W. Duparré and F. C. Wippermann, “Micro-optical artificial compound eyes,” Bioinspiration Biomimetics 1, R1 (2006).
[Crossref]

Cell Tissue Res. (1)

S. Laughlin and S. McGinness, “The structures of dorsal and ventral regions of a dragonfly retina,” Cell Tissue Res. 188, 427–447 (1978).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of computational superposition imaging.

Fig. 2
Fig. 2

Schematic diagram of single-shot computational superposition imaging based on spherical superposition compound eyes with (a) positive and (b) negative curvatures.

Fig. 3
Fig. 3

Schematic diagram of DOF extension using a spherical array of ideal erect lenses.

Fig. 4
Fig. 4

Geometrical relationship between the pitches of the erect lenses and detectors.

Fig. 5
Fig. 5

MTFs of GRIN lens arrays with different diameters.

Fig. 6
Fig. 6

Ray-trace of a spherical GRIN lens array. (a) Overview, (b) rays passing through GRIN lenses, and (c) rays near sensor surface.

Fig. 7
Fig. 7

Misfocus MTFs. (a) MTFs of ideal single lens with a diameter of 20 mm. MTFs of ideal erect lens arrays with (b) D = 5 mm, (c) D = 10 mm, and (d) D = 20 mm. MTFs of GRIN lens arrays with (e) D = 5 mm, (f) D = 10 mm, and (g) D = 20 mm.

Fig. 8
Fig. 8

Performance verification with Lenna image. Images captured by (a) the ideal single lens and (b) the GRIN lens array without noise. Deconvolution results of images captured by the GRIN lens array (c) with and (d) without additional Gaussian noise.

Fig. 9
Fig. 9

PSNRs of the final images shown in Fig. 8. Note that the PSNR of the GRIN lens array at Ψ = 0 without noise is ∞ dB.

Tables (2)

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Table 1 System parameters in simulations.

Tables Icon

Table 2 Parameters of GRIN lenses in simulations.

Equations (11)

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

z i mar = ( z o + t ) ( R 2 2 r 2 ) 2 r 2 R 2 r 2 ( R 2 2 r 2 ) + 2 ( z o + t ) R 2 r 2 + t ,
f = R 2 ,
z i par = z o f z o + f = z o R 2 z o + R .
z i = z i par .
z o mar = ( z i t ) ( R 2 2 r 2 ) + 2 r 2 R 2 r 2 ( R 2 2 r 2 ) 2 ( z i t ) R 2 r 2 t ,
z o par = z i f z i + f = z i R 2 z i + R ,
s = z o mar z o par .
F i / # = z i D .
p 1 ( z i mar t ) p d z i z i mar .
n = n 0 + n d 2 d 2 + n d 4 d 4 + n d 6 d 6 + n z z + n z 2 z 2 + n z 3 z 3 ,
Ψ = π D 2 4 λ ( 1 f 1 z ψ 1 z i ) .

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