Abstract

The resolution of a camera system determines the fidelity of visual features in captured images. Higher resolution implies greater fidelity and, thus, greater accuracy when performing automated vision tasks, such as object detection, recognition, and tracking. However, the resolution of any camera is fundamentally limited by geometric aberrations. In the past, it has generally been accepted that the resolution of lenses with geometric aberrations cannot be increased beyond a certain threshold. We derive an analytic scaling law showing that, for lenses with spherical aberrations, resolution can be increased beyond the aberration limit by applying a postcapture deblurring step. We then show that resolution can be further increased when image priors are introduced. Based on our analysis, we advocate for computational camera designs consisting of a spherical lens shared by several small planar sensors. We show example images captured with a proof-of-concept gigapixel camera, demonstrating that high resolution can be achieved with a compact form factor and low complexity. We conclude with an analysis on the trade-off between performance and complexity for computational imaging systems with spherical lenses.

© 2011 Optical Society of America

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  1. “DARPA at 50” (2010), http://www.darpa.mil/WorkArea/DownloadAsset.aspx?id=2685.
  2. K. Fife, A. El Gamal, and H. Wong, “A 3 Mpixel multi-aperture image sensor with 0.7 um pixels in 0.11 um CMOS,” in IEEE International Solid State Circuits Conference (IEEE, 2008), p. 48.
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  4. M. Robinson, G. Feng, and D. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 74290M (2009).
    [CrossRef]
  5. M. D. Robinson and V. Bhakta, “Experimental validation of extended depth-of-field imaging via spherical coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB4.
  6. F. Guichard, H.-P. Nguyen, R. Tessières, M. Pyanet, I. Tarchouna, and F. Cao, “Extended depth-of-field using sharpness transport across color channels,” Proc. SPIE 7250, 72500N(2009).
    [CrossRef]
  7. O. Cossairt and S. Nayar, “Spectral focal sweep: extended depth of field from chromatic aberrations,” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.
  8. M. Ben-Ezra, “High resolution large format tile-scan—camera design, calibration, and extended depth of field,” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.
  9. S. Wang and W. Heidrich, “The design of an inexpensive very high resolution scan camera system,” Comput. Graph. Forum 23, 441–450 (2004).
    [CrossRef]
  10. “The Gigapixl Project,” http://www.gigapixl.org/ (2007).
  11. B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
    [CrossRef]
  12. Y. Nomura, L. Zhang, and S. Nayar, “Scene collages and flexible camera arrays,” in Proceedings of the Eurographics Symposium on Rendering Techniques, Grenoble, France, 2007 (Eurographics Association, 2007), pp. 127–138.
  13. D. J. Brady and N. Hagen, “Multiscale lens design,” Opt. Express 17, 10659–10674 (2009).
    [CrossRef]
  14. R. Kingslake, A History of the Photographic Lens (Academic, 1989).
  15. R. Luneburg, Mathematical Theory of Optics (University of California, 1964).
  16. S. Rim, P. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” in Proc. SPIE 5678, 48–58 (2005).
    [CrossRef]
  17. G. Krishnan and S. Nayar, “Towards a true spherical camera,” Proc. SPIE 7240, 724002 (2009).
    [CrossRef]
  18. R. Dinyari, S. Rim, K. Huang, P. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92, 091114 (2008).
    [CrossRef]
  19. H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
    [CrossRef]
  20. L. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310, 1148–1150 (2005).
    [CrossRef]
  21. D. Marks and D. Brady, “Gigagon: a monocentric lens design imaging 40 gigapixels,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuC2.
  22. Similar camera designs are also being pursued by the DARPA MOSAIC project, led by D. J. Brady. See “Terrapixel imaging,” presented at ICCP ’10, Invited Talk, MIT Media Lab, Cambridge, Mass., 29 March 2010.
  23. E. Dowski and J. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995).
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  24. E. Dowski, Jr., R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000) .
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  25. D. Robinson and D. G. Stork, “Extending depth-of-field: spherical coding versus asymmetric wavefront coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB3.
  26. A. W. Lohmann, “Scaling laws for lens systems,” Appl. Opt. 28, 4996–4998 (1989).
    [CrossRef]
  27. J. Geary, Introduction to Lens Design: With Practical ZEMAX Examples (Willmann-Bell, 2002).
  28. A. Levin, W. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” in European Conference on Computer Vision (2008), pp. 88–101.
  29. A. Levin, S. Hasinoff, P. Green, F. Durand, and W. Freeman, “4d frequency analysis of computational cameras for depth of field extension,” in ACM SIGGRAPH 2009 papers (SIGGRAPH ’09) (Association for Computing Machinery, 2009), pp. 1–14.
  30. O. Cossairt, C. Zhou, and S. Nayar, “Diffusion coded photography for extended depth of field,” in ACM SIGGRAPH 2010 papers (SIGGRAPH ’10) (Association for Computing Machinery, 2010), pp. 1–10.
  31. L. J. Slater, Generalized Hypergeometric Functions (Cambridge University, 1966).
  32. ZEMAX Optical Design Software (2010), http://www.zemax.com/.
  33. A. Chakrabarti, K. Hirakawa, and T. Zickler, “Computational color constancy with spatial correlations,” Harvard Technical Report TR-09-10 (2010).
  34. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).
  35. C. Zhou and S. Nayar, “What are good apertures for defocus deblurring?” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.
  36. Lumenera Corporation (2010), http://www.lumenera.com/.
  37. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” in Proc. SPIE 6064, 354–365 (2006).
    [CrossRef]
  38. Microsoft Image Composite Editor (ICE) website (2010), http://research.microsoft.com/en-us/um/redmond/groups/ivm/ICE/.

2010 (10)

“DARPA at 50” (2010), http://www.darpa.mil/WorkArea/DownloadAsset.aspx?id=2685.

O. Cossairt and S. Nayar, “Spectral focal sweep: extended depth of field from chromatic aberrations,” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

M. Ben-Ezra, “High resolution large format tile-scan—camera design, calibration, and extended depth of field,” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

D. Marks and D. Brady, “Gigagon: a monocentric lens design imaging 40 gigapixels,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuC2.

O. Cossairt, C. Zhou, and S. Nayar, “Diffusion coded photography for extended depth of field,” in ACM SIGGRAPH 2010 papers (SIGGRAPH ’10) (Association for Computing Machinery, 2010), pp. 1–10.

ZEMAX Optical Design Software (2010), http://www.zemax.com/.

A. Chakrabarti, K. Hirakawa, and T. Zickler, “Computational color constancy with spatial correlations,” Harvard Technical Report TR-09-10 (2010).

C. Zhou and S. Nayar, “What are good apertures for defocus deblurring?” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

Lumenera Corporation (2010), http://www.lumenera.com/.

Microsoft Image Composite Editor (ICE) website (2010), http://research.microsoft.com/en-us/um/redmond/groups/ivm/ICE/.

2009 (7)

D. Robinson and D. G. Stork, “Extending depth-of-field: spherical coding versus asymmetric wavefront coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB3.

A. Levin, S. Hasinoff, P. Green, F. Durand, and W. Freeman, “4d frequency analysis of computational cameras for depth of field extension,” in ACM SIGGRAPH 2009 papers (SIGGRAPH ’09) (Association for Computing Machinery, 2009), pp. 1–14.

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

G. Krishnan and S. Nayar, “Towards a true spherical camera,” Proc. SPIE 7240, 724002 (2009).
[CrossRef]

M. Robinson, G. Feng, and D. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 74290M (2009).
[CrossRef]

M. D. Robinson and V. Bhakta, “Experimental validation of extended depth-of-field imaging via spherical coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB4.

F. Guichard, H.-P. Nguyen, R. Tessières, M. Pyanet, I. Tarchouna, and F. Cao, “Extended depth-of-field using sharpness transport across color channels,” Proc. SPIE 7250, 72500N(2009).
[CrossRef]

2008 (4)

K. Fife, A. El Gamal, and H. Wong, “A 3 Mpixel multi-aperture image sensor with 0.7 um pixels in 0.11 um CMOS,” in IEEE International Solid State Circuits Conference (IEEE, 2008), p. 48.

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

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

A. Levin, W. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” in European Conference on Computer Vision (2008), pp. 88–101.

2007 (2)

Y. Nomura, L. Zhang, and S. Nayar, “Scene collages and flexible camera arrays,” in Proceedings of the Eurographics Symposium on Rendering Techniques, Grenoble, France, 2007 (Eurographics Association, 2007), pp. 127–138.

“The Gigapixl Project,” http://www.gigapixl.org/ (2007).

2006 (1)

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” in Proc. SPIE 6064, 354–365 (2006).
[CrossRef]

2005 (4)

S. Rim, P. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” in Proc. SPIE 5678, 48–58 (2005).
[CrossRef]

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

J. Goodman, Introduction to Fourier Optics (Roberts, 2005).

L. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310, 1148–1150 (2005).
[CrossRef]

2004 (1)

S. Wang and W. Heidrich, “The design of an inexpensive very high resolution scan camera system,” Comput. Graph. Forum 23, 441–450 (2004).
[CrossRef]

2002 (1)

J. Geary, Introduction to Lens Design: With Practical ZEMAX Examples (Willmann-Bell, 2002).

2000 (1)

E. Dowski, Jr., R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000) .
[CrossRef]

1998 (1)

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).

1995 (1)

1989 (2)

A. W. Lohmann, “Scaling laws for lens systems,” Appl. Opt. 28, 4996–4998 (1989).
[CrossRef]

R. Kingslake, A History of the Photographic Lens (Academic, 1989).

1966 (1)

L. J. Slater, Generalized Hypergeometric Functions (Cambridge University, 1966).

1964 (1)

R. Luneburg, Mathematical Theory of Optics (University of California, 1964).

Adams, A.

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Antunez, E.

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Barth, A.

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Ben-Ezra, M.

M. Ben-Ezra, “High resolution large format tile-scan—camera design, calibration, and extended depth of field,” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

Bertero, M.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).

Bhakta, V.

M. D. Robinson and V. Bhakta, “Experimental validation of extended depth-of-field imaging via spherical coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB4.

Boccacci, P.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).

Brady, D.

D. Marks and D. Brady, “Gigagon: a monocentric lens design imaging 40 gigapixels,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuC2.

Brady, D. J.

Cao, F.

F. Guichard, H.-P. Nguyen, R. Tessières, M. Pyanet, I. Tarchouna, and F. Cao, “Extended depth-of-field using sharpness transport across color channels,” Proc. SPIE 7250, 72500N(2009).
[CrossRef]

Cathey, J.

Catrysse, P.

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

S. Rim, P. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” in Proc. SPIE 5678, 48–58 (2005).
[CrossRef]

Chakrabarti, A.

A. Chakrabarti, K. Hirakawa, and T. Zickler, “Computational color constancy with spatial correlations,” Harvard Technical Report TR-09-10 (2010).

Choi, W.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Cormack, R.

E. Dowski, Jr., R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000) .
[CrossRef]

Cossairt, O.

O. Cossairt and S. Nayar, “Spectral focal sweep: extended depth of field from chromatic aberrations,” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

O. Cossairt, C. Zhou, and S. Nayar, “Diffusion coded photography for extended depth of field,” in ACM SIGGRAPH 2010 papers (SIGGRAPH ’10) (Association for Computing Machinery, 2010), pp. 1–10.

Dabov, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” in Proc. SPIE 6064, 354–365 (2006).
[CrossRef]

Dinyari, R.

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

S. Rim, P. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” in Proc. SPIE 5678, 48–58 (2005).
[CrossRef]

Dowski, E.

E. Dowski, Jr., R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000) .
[CrossRef]

E. Dowski and J. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995).
[CrossRef]

Durand, F.

A. Levin, S. Hasinoff, P. Green, F. Durand, and W. Freeman, “4d frequency analysis of computational cameras for depth of field extension,” in ACM SIGGRAPH 2009 papers (SIGGRAPH ’09) (Association for Computing Machinery, 2009), pp. 1–14.

A. Levin, W. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” in European Conference on Computer Vision (2008), pp. 88–101.

Egiazarian, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” in Proc. SPIE 6064, 354–365 (2006).
[CrossRef]

El Gamal, A.

K. Fife, A. El Gamal, and H. Wong, “A 3 Mpixel multi-aperture image sensor with 0.7 um pixels in 0.11 um CMOS,” in IEEE International Solid State Circuits Conference (IEEE, 2008), p. 48.

Feng, G.

M. Robinson, G. Feng, and D. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 74290M (2009).
[CrossRef]

Fife, K.

K. Fife, A. El Gamal, and H. Wong, “A 3 Mpixel multi-aperture image sensor with 0.7 um pixels in 0.11 um CMOS,” in IEEE International Solid State Circuits Conference (IEEE, 2008), p. 48.

Foi, A.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” in Proc. SPIE 6064, 354–365 (2006).
[CrossRef]

Freeman, W.

A. Levin, S. Hasinoff, P. Green, F. Durand, and W. Freeman, “4d frequency analysis of computational cameras for depth of field extension,” in ACM SIGGRAPH 2009 papers (SIGGRAPH ’09) (Association for Computing Machinery, 2009), pp. 1–14.

A. Levin, W. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” in European Conference on Computer Vision (2008), pp. 88–101.

Geary, J.

J. Geary, Introduction to Lens Design: With Practical ZEMAX Examples (Willmann-Bell, 2002).

Geddes, J.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Green, P.

A. Levin, S. Hasinoff, P. Green, F. Durand, and W. Freeman, “4d frequency analysis of computational cameras for depth of field extension,” in ACM SIGGRAPH 2009 papers (SIGGRAPH ’09) (Association for Computing Machinery, 2009), pp. 1–14.

Guichard, F.

F. Guichard, H.-P. Nguyen, R. Tessières, M. Pyanet, I. Tarchouna, and F. Cao, “Extended depth-of-field using sharpness transport across color channels,” Proc. SPIE 7250, 72500N(2009).
[CrossRef]

Hagen, N.

Hasinoff, S.

A. Levin, S. Hasinoff, P. Green, F. Durand, and W. Freeman, “4d frequency analysis of computational cameras for depth of field extension,” in ACM SIGGRAPH 2009 papers (SIGGRAPH ’09) (Association for Computing Machinery, 2009), pp. 1–14.

Heidrich, W.

S. Wang and W. Heidrich, “The design of an inexpensive very high resolution scan camera system,” Comput. Graph. Forum 23, 441–450 (2004).
[CrossRef]

Hirakawa, K.

A. Chakrabarti, K. Hirakawa, and T. Zickler, “Computational color constancy with spatial correlations,” Harvard Technical Report TR-09-10 (2010).

Horowitz, M.

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Huang, K.

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

S. Rim, P. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” in Proc. SPIE 5678, 48–58 (2005).
[CrossRef]

Huang, Y.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Joshi, N.

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Katkovnik, V.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” in Proc. SPIE 6064, 354–365 (2006).
[CrossRef]

Kingslake, R.

R. Kingslake, A History of the Photographic Lens (Academic, 1989).

Ko, H.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Krishnan, G.

G. Krishnan and S. Nayar, “Towards a true spherical camera,” Proc. SPIE 7240, 724002 (2009).
[CrossRef]

Lee, L.

L. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310, 1148–1150 (2005).
[CrossRef]

Levin, A.

A. Levin, S. Hasinoff, P. Green, F. Durand, and W. Freeman, “4d frequency analysis of computational cameras for depth of field extension,” in ACM SIGGRAPH 2009 papers (SIGGRAPH ’09) (Association for Computing Machinery, 2009), pp. 1–14.

A. Levin, W. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” in European Conference on Computer Vision (2008), pp. 88–101.

Levoy, M.

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Lohmann, A. W.

Luneburg, R.

R. Luneburg, Mathematical Theory of Optics (University of California, 1964).

Malyarchuk, V.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Marks, D.

D. Marks and D. Brady, “Gigagon: a monocentric lens design imaging 40 gigapixels,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuC2.

Nayar, S.

O. Cossairt and S. Nayar, “Spectral focal sweep: extended depth of field from chromatic aberrations,” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

O. Cossairt, C. Zhou, and S. Nayar, “Diffusion coded photography for extended depth of field,” in ACM SIGGRAPH 2010 papers (SIGGRAPH ’10) (Association for Computing Machinery, 2010), pp. 1–10.

C. Zhou and S. Nayar, “What are good apertures for defocus deblurring?” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

G. Krishnan and S. Nayar, “Towards a true spherical camera,” Proc. SPIE 7240, 724002 (2009).
[CrossRef]

Y. Nomura, L. Zhang, and S. Nayar, “Scene collages and flexible camera arrays,” in Proceedings of the Eurographics Symposium on Rendering Techniques, Grenoble, France, 2007 (Eurographics Association, 2007), pp. 127–138.

Nguyen, H.-P.

F. Guichard, H.-P. Nguyen, R. Tessières, M. Pyanet, I. Tarchouna, and F. Cao, “Extended depth-of-field using sharpness transport across color channels,” Proc. SPIE 7250, 72500N(2009).
[CrossRef]

Nomura, Y.

Y. Nomura, L. Zhang, and S. Nayar, “Scene collages and flexible camera arrays,” in Proceedings of the Eurographics Symposium on Rendering Techniques, Grenoble, France, 2007 (Eurographics Association, 2007), pp. 127–138.

Peumans, P.

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

S. Rim, P. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” in Proc. SPIE 5678, 48–58 (2005).
[CrossRef]

Pyanet, M.

F. Guichard, H.-P. Nguyen, R. Tessières, M. Pyanet, I. Tarchouna, and F. Cao, “Extended depth-of-field using sharpness transport across color channels,” Proc. SPIE 7250, 72500N(2009).
[CrossRef]

Rim, S.

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

S. Rim, P. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” in Proc. SPIE 5678, 48–58 (2005).
[CrossRef]

Robinson, D.

D. Robinson and D. G. Stork, “Extending depth-of-field: spherical coding versus asymmetric wavefront coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB3.

Robinson, M.

M. Robinson, G. Feng, and D. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 74290M (2009).
[CrossRef]

Robinson, M. D.

M. D. Robinson and V. Bhakta, “Experimental validation of extended depth-of-field imaging via spherical coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB4.

Rogers, J. A.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Sarama, S.

E. Dowski, Jr., R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000) .
[CrossRef]

Slater, L. J.

L. J. Slater, Generalized Hypergeometric Functions (Cambridge University, 1966).

Song, J.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Stork, D.

M. Robinson, G. Feng, and D. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 74290M (2009).
[CrossRef]

Stork, D. G.

D. Robinson and D. G. Stork, “Extending depth-of-field: spherical coding versus asymmetric wavefront coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB3.

Stoykovich, M.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Szema, R.

L. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310, 1148–1150 (2005).
[CrossRef]

Talvala, E.

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Tarchouna, I.

F. Guichard, H.-P. Nguyen, R. Tessières, M. Pyanet, I. Tarchouna, and F. Cao, “Extended depth-of-field using sharpness transport across color channels,” Proc. SPIE 7250, 72500N(2009).
[CrossRef]

Tessières, R.

F. Guichard, H.-P. Nguyen, R. Tessières, M. Pyanet, I. Tarchouna, and F. Cao, “Extended depth-of-field using sharpness transport across color channels,” Proc. SPIE 7250, 72500N(2009).
[CrossRef]

Vaish, V.

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Wang, S.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

S. Wang and W. Heidrich, “The design of an inexpensive very high resolution scan camera system,” Comput. Graph. Forum 23, 441–450 (2004).
[CrossRef]

Wilburn, B.

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Wong, H.

K. Fife, A. El Gamal, and H. Wong, “A 3 Mpixel multi-aperture image sensor with 0.7 um pixels in 0.11 um CMOS,” in IEEE International Solid State Circuits Conference (IEEE, 2008), p. 48.

Xiao, J.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Yu, C.

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Zhang, L.

Y. Nomura, L. Zhang, and S. Nayar, “Scene collages and flexible camera arrays,” in Proceedings of the Eurographics Symposium on Rendering Techniques, Grenoble, France, 2007 (Eurographics Association, 2007), pp. 127–138.

Zhou, C.

C. Zhou and S. Nayar, “What are good apertures for defocus deblurring?” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

O. Cossairt, C. Zhou, and S. Nayar, “Diffusion coded photography for extended depth of field,” in ACM SIGGRAPH 2010 papers (SIGGRAPH ’10) (Association for Computing Machinery, 2010), pp. 1–10.

Zickler, T.

A. Chakrabarti, K. Hirakawa, and T. Zickler, “Computational color constancy with spatial correlations,” Harvard Technical Report TR-09-10 (2010).

ACM Trans. Graph. (1)

B. Wilburn, N. Joshi, V. Vaish, E. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776(2005).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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

Comput. Graph. Forum (1)

S. Wang and W. Heidrich, “The design of an inexpensive very high resolution scan camera system,” Comput. Graph. Forum 23, 441–450 (2004).
[CrossRef]

Nature (1)

H. Ko, M. Stoykovich, J. Song, V. Malyarchuk, W. Choi, C. Yu, J. Geddes III, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Opt. Express (1)

Proc. SPIE (6)

E. Dowski, Jr., R. Cormack, and S. Sarama, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000) .
[CrossRef]

S. Rim, P. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” in Proc. SPIE 5678, 48–58 (2005).
[CrossRef]

G. Krishnan and S. Nayar, “Towards a true spherical camera,” Proc. SPIE 7240, 724002 (2009).
[CrossRef]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising with block-matching and 3D filtering,” in Proc. SPIE 6064, 354–365 (2006).
[CrossRef]

F. Guichard, H.-P. Nguyen, R. Tessières, M. Pyanet, I. Tarchouna, and F. Cao, “Extended depth-of-field using sharpness transport across color channels,” Proc. SPIE 7250, 72500N(2009).
[CrossRef]

M. Robinson, G. Feng, and D. Stork, “Spherical coded imagers: improving lens speed, depth-of-field, and manufacturing yield through enhanced spherical aberration and compensating image processing,” Proc. SPIE 7429, 74290M (2009).
[CrossRef]

Science (1)

L. Lee and R. Szema, “Inspirations from biological optics for advanced photonic systems,” Science 310, 1148–1150 (2005).
[CrossRef]

Other (24)

D. Marks and D. Brady, “Gigagon: a monocentric lens design imaging 40 gigapixels,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuC2.

Similar camera designs are also being pursued by the DARPA MOSAIC project, led by D. J. Brady. See “Terrapixel imaging,” presented at ICCP ’10, Invited Talk, MIT Media Lab, Cambridge, Mass., 29 March 2010.

J. Geary, Introduction to Lens Design: With Practical ZEMAX Examples (Willmann-Bell, 2002).

A. Levin, W. Freeman, and F. Durand, “Understanding camera trade-offs through a Bayesian analysis of light field projections,” in European Conference on Computer Vision (2008), pp. 88–101.

A. Levin, S. Hasinoff, P. Green, F. Durand, and W. Freeman, “4d frequency analysis of computational cameras for depth of field extension,” in ACM SIGGRAPH 2009 papers (SIGGRAPH ’09) (Association for Computing Machinery, 2009), pp. 1–14.

O. Cossairt, C. Zhou, and S. Nayar, “Diffusion coded photography for extended depth of field,” in ACM SIGGRAPH 2010 papers (SIGGRAPH ’10) (Association for Computing Machinery, 2010), pp. 1–10.

L. J. Slater, Generalized Hypergeometric Functions (Cambridge University, 1966).

ZEMAX Optical Design Software (2010), http://www.zemax.com/.

A. Chakrabarti, K. Hirakawa, and T. Zickler, “Computational color constancy with spatial correlations,” Harvard Technical Report TR-09-10 (2010).

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).

C. Zhou and S. Nayar, “What are good apertures for defocus deblurring?” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

Lumenera Corporation (2010), http://www.lumenera.com/.

M. D. Robinson and V. Bhakta, “Experimental validation of extended depth-of-field imaging via spherical coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB4.

“DARPA at 50” (2010), http://www.darpa.mil/WorkArea/DownloadAsset.aspx?id=2685.

K. Fife, A. El Gamal, and H. Wong, “A 3 Mpixel multi-aperture image sensor with 0.7 um pixels in 0.11 um CMOS,” in IEEE International Solid State Circuits Conference (IEEE, 2008), p. 48.

J. Goodman, Introduction to Fourier Optics (Roberts, 2005).

O. Cossairt and S. Nayar, “Spectral focal sweep: extended depth of field from chromatic aberrations,” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

M. Ben-Ezra, “High resolution large format tile-scan—camera design, calibration, and extended depth of field,” in 2010 IEEE International Conference on Computational Photography (ICCP) (IEEE, 2010), pp. 1–8.

“The Gigapixl Project,” http://www.gigapixl.org/ (2007).

Microsoft Image Composite Editor (ICE) website (2010), http://research.microsoft.com/en-us/um/redmond/groups/ivm/ICE/.

Y. Nomura, L. Zhang, and S. Nayar, “Scene collages and flexible camera arrays,” in Proceedings of the Eurographics Symposium on Rendering Techniques, Grenoble, France, 2007 (Eurographics Association, 2007), pp. 127–138.

R. Kingslake, A History of the Photographic Lens (Academic, 1989).

R. Luneburg, Mathematical Theory of Optics (University of California, 1964).

D. Robinson and D. G. Stork, “Extending depth-of-field: spherical coding versus asymmetric wavefront coding,” in Computational Optical Sensing and Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB3.

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