Abstract

Monocentric multi-scale (MMS) lenses are a new approach to high-resolution wide-angle imaging, where a monocentric objective lens is shared by an array of identical rotationally symmetric secondary imagers that each acquire one overlapping segment of a mosaic. This allows gigapixel images to be computationally integrated from conventional image sensors and relatively simple optics. Here we describe the MMS design space, introducing constraints on image continuity and uniformity, and show how paraxial system analysis can provide both volume scaling and a systematic design methodology for MMS imagers. We provide the detailed design of a 120° field of viewimager (currently under construction) resolving 2 gigapixels at 41.5 μrad instantaneous field of view, and demonstrate reasonable agreement with the first-order scaling calculation.

© 2012 Optical Society of America

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2011 (4)

2009 (2)

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

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

2008 (2)

W. C. Sweatt, D. D. Gill, D. P. Adams, M. J. Vasile, and A. A. Claudet, “Diamond milling of micro-optics,” IEEE Aerosp. Electron. Syst. Mag. 23, 13–17 (2008).
[CrossRef]

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[CrossRef]

2005 (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, 763–776 (2005).
[CrossRef]

2004 (1)

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

1989 (1)

1986 (1)

B. W. Clare and D. L. Kepert, “The closest packing of equal circles on a sphere,” Proc. R. Soc. A 405, 329–344 (1986).
[CrossRef]

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, 763–776 (2005).
[CrossRef]

Adams, D. P.

W. C. Sweatt, D. D. Gill, D. P. Adams, M. J. Vasile, and A. A. Claudet, “Diamond milling of micro-optics,” IEEE Aerosp. Electron. Syst. Mag. 23, 13–17 (2008).
[CrossRef]

Ang, L. P.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Antoniades, J.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[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, 763–776 (2005).
[CrossRef]

Atchison, David A.

George Smith and David A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997), Chap. 17.

Aussel, H.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[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, 763–776 (2005).
[CrossRef]

Bartley, C.

R. Sargent, C. Bartley, P. Dille, J. Keller, I. Nourbakhsh, and R. LeGrand, “Timelapse GigaPan: Capturing, sharing, and exploring timelapse gigapixel imagery,” presented at the Fine International Conference on Gigapixel Imaging for Science, Pittsburgh, PA (2010).

Berger, R.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Brady, D. J.

D. L. Marks and D. J. Brady, “Close-up imaging using microcamera arrays for focal plane synthesis,” Opt. Eng. 50, 033205 (2011).
[CrossRef]

D. L. Marks, E. J. Tremblay, J. E. Ford, and D. J. Brady, “Microcamera aperture scale in monocentric gigapixel cameras,” Appl. Opt. 50, 5824–5833 (2011).
[CrossRef]

H. S. Son, D. L. Marks, J. Hahn, J. Kim, and D. J. Brady, “Design of a spherical focal surface using close packed relay optics,” Opt. Express 19, 16132–16138 (2011).
[CrossRef]

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

H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

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

D. Golish, E. Vera, K. Kelly, Q. Gong, D. J. Brady, and M. E. Gehm, “Image formation in multiscaleoptical systems,” in Computational Optical Sensing and Imaging (Optical Society of America, 2011), paper JTuE4.

Braun, M.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[CrossRef]

Brewer, P.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[CrossRef]

Burgett, W.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Chambers, K. C.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Chester, D.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[CrossRef]

Chun, M.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Clare, B. W.

B. W. Clare and D. L. Kepert, “The closest packing of equal circles on a sphere,” Proc. R. Soc. A 405, 329–344 (1986).
[CrossRef]

Clark, S.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Claudet, A. A.

W. C. Sweatt, D. D. Gill, D. P. Adams, M. J. Vasile, and A. A. Claudet, “Diamond milling of micro-optics,” IEEE Aerosp. Electron. Syst. Mag. 23, 13–17 (2008).
[CrossRef]

Cossairt, O.

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

Cossairt, O. S.

Dille, P.

R. Sargent, C. Bartley, P. Dille, J. Keller, I. Nourbakhsh, and R. LeGrand, “Timelapse GigaPan: Capturing, sharing, and exploring timelapse gigapixel imagery,” presented at the Fine International Conference on Gigapixel Imaging for Science, Pittsburgh, PA (2010).

Dombeck, T.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Douglas, A.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Edwards, J.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[CrossRef]

Ford, J.

H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

Ford, J. E.

D. L. Marks, E. J. Tremblay, J. E. Ford, and D. J. Brady, “Microcamera aperture scale in monocentric gigapixel cameras,” Appl. Opt. 50, 5824–5833 (2011).
[CrossRef]

J. E. Ford and E. Tremblay, “Extreme form factor imagers,” in Imaging Systems (Optical Society of America, 2010), paper IMC2.

Gehm, M. E.

D. Golish, E. Vera, K. Kelly, Q. Gong, D. J. Brady, and M. E. Gehm, “Image formation in multiscaleoptical systems,” in Computational Optical Sensing and Imaging (Optical Society of America, 2011), paper JTuE4.

Gershfield, C.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[CrossRef]

Gill, D. D.

W. C. Sweatt, D. D. Gill, D. P. Adams, M. J. Vasile, and A. A. Claudet, “Diamond milling of micro-optics,” IEEE Aerosp. Electron. Syst. Mag. 23, 13–17 (2008).
[CrossRef]

Golish, D.

D. Golish, E. Vera, K. Kelly, Q. Gong, D. J. Brady, and M. E. Gehm, “Image formation in multiscaleoptical systems,” in Computational Optical Sensing and Imaging (Optical Society of America, 2011), paper JTuE4.

Gong, Q.

D. Golish, E. Vera, K. Kelly, Q. Gong, D. J. Brady, and M. E. Gehm, “Image formation in multiscaleoptical systems,” in Computational Optical Sensing and Imaging (Optical Society of America, 2011), paper JTuE4.

Haas, D.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[CrossRef]

Hafner, D.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Hagen, N.

Hahn, J.

H. S. Son, D. L. Marks, J. Hahn, J. Kim, and D. J. Brady, “Design of a spherical focal surface using close packed relay optics,” Opt. Express 19, 16132–16138 (2011).
[CrossRef]

H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

Heasley, J.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Hoblitt, J.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Hodapp, K. W.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

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, 763–776 (2005).
[CrossRef]

Hude, C.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Isani, S.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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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, 763–776 (2005).
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K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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R. Sargent, C. Bartley, P. Dille, J. Keller, I. Nourbakhsh, and R. LeGrand, “Timelapse GigaPan: Capturing, sharing, and exploring timelapse gigapixel imagery,” presented at the Fine International Conference on Gigapixel Imaging for Science, Pittsburgh, PA (2010).

Kelly, K.

D. Golish, E. Vera, K. Kelly, Q. Gong, D. J. Brady, and M. E. Gehm, “Image formation in multiscaleoptical systems,” in Computational Optical Sensing and Imaging (Optical Society of America, 2011), paper JTuE4.

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H. Kenner, Geodesic Math and How to Use It, 2nd ed.(University of California, 2003).

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B. W. Clare and D. L. Kepert, “The closest packing of equal circles on a sphere,” Proc. R. Soc. A 405, 329–344 (1986).
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Michael Kidger, Fundamental Optical Design (SPIE, 2002), Chap. 7.

Kim, J.

H. S. Son, D. L. Marks, J. Hahn, J. Kim, and D. J. Brady, “Design of a spherical focal surface using close packed relay optics,” Opt. Express 19, 16132–16138 (2011).
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H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

Knecht, J.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

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

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K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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LeGrand, R.

R. Sargent, C. Bartley, P. Dille, J. Keller, I. Nourbakhsh, and R. LeGrand, “Timelapse GigaPan: Capturing, sharing, and exploring timelapse gigapixel imagery,” presented at the Fine International Conference on Gigapixel Imaging for Science, Pittsburgh, PA (2010).

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B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
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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, 763–776 (2005).
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Liu, E.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
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Lohmann, A. W.

Luppino, G. A.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Lupton, R.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Maberry, M.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Madden, D. G.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
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Magnier, E.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Mannery, E.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Mansoorian, B.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

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D. L. Marks, E. J. Tremblay, J. E. Ford, and D. J. Brady, “Microcamera aperture scale in monocentric gigapixel cameras,” Appl. Opt. 50, 5824–5833 (2011).
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H. S. Son, D. L. Marks, J. Hahn, J. Kim, and D. J. Brady, “Design of a spherical focal surface using close packed relay optics,” Opt. Express 19, 16132–16138 (2011).
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H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

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

McLaughlin, P.

H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

Messier, A.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Miau, D.

O. S. Cossairt, D. Miau, and S. K. Nayar, “Scaling law for computational imaging using spherical optics,” J. Opt. Soc. Am. A 28, 2540–2553 (2011).
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O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in IEEE International Conference on Computational Photography (IEEE, 2011).

Monet, D.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Morgan, J.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Nayar, S. K.

O. S. Cossairt, D. Miau, and S. K. Nayar, “Scaling law for computational imaging using spherical optics,” J. Opt. Soc. Am. A 28, 2540–2553 (2011).
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O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in IEEE International Conference on Computational Photography (IEEE, 2011).

Newcomb, K.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Nourbakhsh, I.

R. Sargent, C. Bartley, P. Dille, J. Keller, I. Nourbakhsh, and R. LeGrand, “Timelapse GigaPan: Capturing, sharing, and exploring timelapse gigapixel imagery,” presented at the Fine International Conference on Gigapixel Imaging for Science, Pittsburgh, PA (2010).

Onaka, P.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Pfeffer, Michael

Michael Pfeffer, “Optomechanics of plastic optical components,” in Handbook of Plastic Optics, S. Bäumer, ed. (Wiley-VCH, 2005).

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K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Rathman, D.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Ryan, A.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Sargent, R.

R. Sargent, C. Bartley, P. Dille, J. Keller, I. Nourbakhsh, and R. LeGrand, “Timelapse GigaPan: Capturing, sharing, and exploring timelapse gigapixel imagery,” presented at the Fine International Conference on Gigapixel Imaging for Science, Pittsburgh, PA (2010).

Shafique, K. H.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
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Shaver, D.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Shaw, J.

H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

Siegmund, W.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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Slattery, R.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Smith, George

George Smith and David A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997), Chap. 17.

Soares, A.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Son, H.

H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

Son, H. S.

Stack, R.

H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

Stevens, M.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
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Stevenson, C.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Suntharalingam, V.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

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W. C. Sweatt, D. D. Gill, D. P. Adams, M. J. Vasile, and A. A. Claudet, “Diamond milling of micro-optics,” IEEE Aerosp. Electron. Syst. Mag. 23, 13–17 (2008).
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Szapudi, I.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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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, 763–776 (2005).
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Targove, J. D.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
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Tonry, J.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
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J. E. Ford and E. Tremblay, “Extreme form factor imagers,” in Imaging Systems (Optical Society of America, 2010), paper IMC2.

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D. L. Marks, E. J. Tremblay, J. E. Ford, and D. J. Brady, “Microcamera aperture scale in monocentric gigapixel cameras,” Appl. Opt. 50, 5824–5833 (2011).
[CrossRef]

H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

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, 763–776 (2005).
[CrossRef]

Vasile, M. J.

W. C. Sweatt, D. D. Gill, D. P. Adams, M. J. Vasile, and A. A. Claudet, “Diamond milling of micro-optics,” IEEE Aerosp. Electron. Syst. Mag. 23, 13–17 (2008).
[CrossRef]

Vera, E.

D. Golish, E. Vera, K. Kelly, Q. Gong, D. J. Brady, and M. E. Gehm, “Image formation in multiscaleoptical systems,” in Computational Optical Sensing and Imaging (Optical Society of America, 2011), paper JTuE4.

Wainscoat, R.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Warner, K.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Waterson, M.

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

Wein, S.

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[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, 763–776 (2005).
[CrossRef]

Young, D.

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

Zeon, L. P.

L. P. Zeon Chemicals, Louisville, Ky. 40211, http://www.zeonchemicals.com/ .

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, 763–776 (2005).
[CrossRef]

Appl. Opt. (2)

Astron. Nachr. (1)

K. W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, and M. Waterson, “Design of the Pan-STARRS telescopes,” Astron. Nachr. 325, 636–642 (2004).
[CrossRef]

IEEE Aerosp. Electron. Syst. Mag. (1)

W. C. Sweatt, D. D. Gill, D. P. Adams, M. J. Vasile, and A. A. Claudet, “Diamond milling of micro-optics,” IEEE Aerosp. Electron. Syst. Mag. 23, 13–17 (2008).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

D. L. Marks and D. J. Brady, “Close-up imaging using microcamera arrays for focal plane synthesis,” Opt. Eng. 50, 033205 (2011).
[CrossRef]

Opt. Express (2)

Proc. R. Soc. A (1)

B. W. Clare and D. L. Kepert, “The closest packing of equal circles on a sphere,” Proc. R. Soc. A 405, 329–344 (1986).
[CrossRef]

Proc. SPIE (2)

B. Leininger, J. Edwards, J. Antoniades, D. Chester, D. Haas, E. Liu, M. Stevens, C. Gershfield, M. Braun, J. D. Targove, S. Wein, P. Brewer, D. G. Madden, and K. H. Shafique, “Autonomous real-time ground ubiquitous surveillance-imaging system (ARGUS-IS),” Proc. SPIE 6981, 69810H (2008).
[CrossRef]

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

Other (16)

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

H. Son, D. L. Marks, E. J. Tremblay, J. Ford, J. Hahn, R. Stack, A. Johnson, P. McLaughlin, J. Shaw, J. Kim, and D. J. Brady, “A multiscale, wide field, gigapixel camera,” in Imaging Systems Applications (Optical Society of America, 2011), paper JTuE2.

George Smith and David A. Atchison, The Eye and Visual Optical Instruments (Cambridge University, 1997), Chap. 17.

Michael Kidger, Fundamental Optical Design (SPIE, 2002), Chap. 7.

T. Sutton, “On the panoramic lens,” a paper read toBritish Association Report in 1861, as described in Patents for Inventions, Abridgements of the Specifications Relating to Photography (Great Britain Patent Office, 1861).

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

R. Sargent, C. Bartley, P. Dille, J. Keller, I. Nourbakhsh, and R. LeGrand, “Timelapse GigaPan: Capturing, sharing, and exploring timelapse gigapixel imagery,” presented at the Fine International Conference on Gigapixel Imaging for Science, Pittsburgh, PA (2010).

V. Suntharalingam, R. Berger, S. Clark, J. Knecht, A. Messier, K. Newcomb, D. Rathman, R. Slattery, A. Soares, C. Stevenson, K. Warner, D. Young, L. P. Ang, B. Mansoorian, and D. Shaver,” A 4-side tileable back-illuminated 3D-integrated Mpixel CMOS image sensor, “in Proceedings of IEEE International Solid State Circuits Conference Technical Digest (IEEE, 2009).

J. E. Ford and E. Tremblay, “Extreme form factor imagers,” in Imaging Systems (Optical Society of America, 2010), paper IMC2.

H. Kenner, Geodesic Math and How to Use It, 2nd ed.(University of California, 2003).

http://mathworld.wolfram.com/SphericalCap.html .

D. Golish, E. Vera, K. Kelly, Q. Gong, D. J. Brady, and M. E. Gehm, “Image formation in multiscaleoptical systems,” in Computational Optical Sensing and Imaging (Optical Society of America, 2011), paper JTuE4.

ZEMAX, Radiant ZEMAX LLC, 112th Avenue NE, Bellevue, Wash. 98004.

L. P. Zeon Chemicals, Louisville, Ky. 40211, http://www.zeonchemicals.com/ .

Aptina Imaging, San Jose, Calif. 95134, http://www.aptina.com/

Michael Pfeffer, “Optomechanics of plastic optical components,” in Handbook of Plastic Optics, S. Bäumer, ed. (Wiley-VCH, 2005).

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Figures (11)

Fig. 1.
Fig. 1.

First-order MMS lens models. (a) Keplerian-type and (b) Galilean-type.

Fig. 2.
Fig. 2.

Keplerian-type with stop in objective. (a) Layout showing three subimagers, and (b) relative illumination for a full field of ±60°.

Fig. 3.
Fig. 3.

Keplerian-type with stop at the array camera. (a) Layout showing three subimagers, and (b) relative illumination for a full field of ±60°.

Fig. 4.
Fig. 4.

Detail for calculation of vignetting with stop at the array camera. (a) Keplerian-type at the onset of vignetting, and (b) Galilean-type at the onset of vignetting.

Fig. 5.
Fig. 5.

(a) Relative illumination for (b) flat-flat field orientation with ideal hexagonal packing, and (c) vertex-edge field orientation with a 15% spacing irregularity.

Fig. 6.
Fig. 6.

Scaling of first-order model parameters for fixed sensor size (Np=2800, p=1.4μm). (a) Keplerian-type minimum required magnification versus 2D resolution, (b) Galilean-type optimal magnification vs. 2D resolution, (c) Keplerian-type optical volume vs. 2D resolution and (d) Galilean-type optical volume vs. 2D resolution. (c) and (d) both use the “optimal” value of magnification from (b) for comparison. Solid line volume curves (c and d) represent more realistic sensor packing requirements due to sensor packaging (ρ=2). Dashed line volume curve represents the extension to the curve possible when the sensor package is not included (ρ=1).

Fig. 7.
Fig. 7.

Effect of objective F/# and telescope magnification on optical volume for Keplerian-type designs at (a) 2 gigapixels and (b) 50 gigapixels aggregate resolution. Identical fixed sensor size and packaging used for both (Np=2800, p=1.4μm, ρ=2).

Fig. 8.
Fig. 8.

Area and volume as a function of 2D resolution comparing the Keplerian MMS imager architecture (blue curves) and the multicamera array architecture (red curve) for fixed sensor size (Np=2800, p=1.4μm, ρ=2). (a) 2D projected optical area, and (b) optical volume. Both system architectures are F/2.1 at the image plane.

Fig. 9.
Fig. 9.

Size comparison at 50 gigapixels aggregate resolution over 120° symmetric field of view. (Left) 50 gigapixel multicamera array: 6,360 independent 8 megapixel cameras each 84×168mm. 6.2 m diameter for full 120° concave array. (Right) 50 Gigapixel monocentric multiscale imager: 6,360 common aperture 8 megapixel imagers. 1.6 m system diameter at M=5.8, F/#o=9. Both system architectures are F/2.1 at the image plane.

Fig. 10.
Fig. 10.

Layout of the MOSAIC 2 gigapixel MMS lens design. (a) Multiscale arrangement showing monocentric objective and surrounding subimagers; (b) 4-element injection-molded subimager layout, and (c) perspective view showing hexagonal tiling and light sharing of subimagers.

Fig. 11.
Fig. 11.

Single channel performance for the MOSAIC 2 gigapixel MMS lens system. (a) Polychromatic MTF (0.47, 0.55, 0.65 μm); (b) Relative illumination over field required in vertex direction; (c) Through-focus polychromatic MTF at 90cyc/mm (¼ Nyquist), and (d) through-focus MTF at 178cyc/mm (½ Nyquist). (a), (c) and (d) show Tangential and Sagittal data for field angles of 0° (blue), 1° (green), 2° (red), 3° (light green), 4° (purple) and 4.6° (cyan).

Tables (4)

Tables Icon

Table 1. Comparison Between First-Order Model Parameters for the 2 Gigapixel MOSAIC Design

Tables Icon

Table 2. Single Path Prescription Data for 2 Gigapixel MOSAIC Camera (Sec. 4)

Tables Icon

Table 3. Single Path Prescription Data for 2 Gigapixel MOSAIC Camera (Sec. 4): Aspheric Terms

Tables Icon

Table 4. Single Path Prescription Data for 2 Gigapixel MOSAIC Camera (Sec. 4): DOEa

Equations (25)

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

fAC=XS2|M|tan(α),
DAC=0.61·Npλ|M|tan(α).
DEP=2dtan(α),
αVonset=DEPDAC2d.
lrelief,FL=dMfEP2fFL,
fFL,max=fEP2dM+DEPDAC2Mtanα.
tan(α)=DEPDAC2lrelief,
α=tan1(|M|tan(α)).
lrelief=foM2foMXS4M2F/#ACtan2(α).
lε=MDAC2tan(α),
Do=XSF/#ACtan(α)=2Dε,
Mopt=Xs4fotan2(α)1F/#AC+1.
tan(α)=(Do/2)M(DEP/2)Md.
F/#o=foDε=2foDo,
|Mmin|=12F/#otan(α)1.
Volume=2.09rf3+1.8325rb3,
rb,Keplerian=XS2tan(α)[F/#oF/#AC(11M)21M12M2F/#ACtan(α)].
rb,Galilean=XS2tan(α)F/#oF/#AC[11M+F/#ACF/#oM].
rbρXS2tan(α),
fMCA=XS2tan(α)
DMCA=0.61·Npλtan(α).
AreaMCA,opticslim=(32NADMCAsin(FOVT/2))2π
AreaMCA,sensorlim=(32NA(ρXS)sin(FOVT/2))2π
VolumeMCA,opticslim=πfMCA(NADMCA2)2
VolumeMCA,sensorlim=πfMCA(NA(ρXS)2)2

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