Abstract

The design of optical systems for digital cameras is complicated by the requirement that the image surface be planar, which results in complex and expensive optics. We analyze a compact optical system with a curved image surface and compare its performance to systems with planar image surfaces via optics analysis and image system simulation. Our analysis shows that a curved image surface provides a way to lower the number of optical elements, reduce aberrations including astigmatism and coma, and increase off-axis brightness and sharpness. A method to fabricate curved image focal plane arrays using monolithic silicon is demonstrated.

© 2008 Optical Society of America

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  1. P. Gregory, "Digital photography," Opt. Laser Techn. 38,306-314 (2006).
    [CrossRef]
  2. A. El Gamal and H. Eltoukhy, "CMOS image sensors," IEEE Circuits and Devices Magazine 21,6-20 (2005).
    [CrossRef]
  3. E. Hecht, Optics (Addison Wesley, 2002), p. 226.
  4. H. Jin, J. R. Abelson, M. K. Erhardt, and R. G. Nuzzo, "Soft lithographic fabrication of an image sensor array on a curved substrate," J. Vac. Sci. Technol. B 22,2548-2551 (2004).
    [CrossRef]
  5. P. J. Hung, K. Jeong, G. L. Liu, and L. P. Lee, "Microfabricated suspensions for electrical connections on the tunable elastomer membrane," Appl. Phys. Lett. 85,6051-6053 (2004).
    [CrossRef]
  6. L. Lee and R. Szema, "Inspirations from biological optics for advanced photonic systems," Science 310,1148-1150 (2005).
    [CrossRef] [PubMed]
  7. P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
    [CrossRef]
  8. P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, "Curved CCDs and their application with astronomical telescopes and stereo panoramic cameras," Proc. SPIE 5301, 109-129 (2004).
    [CrossRef]
  9. T. J. Jones and S. Nikzad, "Curved focal plane arrays using conformed thinned detector membrane," Nanotech Brief 28,No. 3 (2004).
  10. M. R. Ackermann, J. T. McGraw, and P. C. Zimmer, "Are curved focal planes necessary for wide-field survey telescopes?" Proc. SPIE 6267, 626740-626749 (2006).
    [CrossRef]
  11. P. Swain and D. Mark, "Curved CCD detector devices and arrays for multispectral astrophysical applications and terrestrial stereo panoramic cameras," Proc. SPIE 5499, 281-301 (2004).
    [CrossRef]
  12. R. Dinyari, S.-B. Rim, K. Huang, and P. Peumans, "Curving monolithic silicon for non-planar focal plane array applications," Appl. Phys. Lett. 92, 091114 (2008).
    [CrossRef]
  13. P. B. Catrysse and B. A. Wandell, "Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld," Proc. SPIE 5678,1-13 (2005).
    [CrossRef]
  14. P. Y. Maeda, P. B. Catrysse, and B. A. Wandell, "Integrating lens design with digital camera simulation," Proc. SPIE 5678, 48-58 (2005).
    [CrossRef]
  15. J. M. Rodgers, "Curved Focal Surfaces: Design Optimization Through Symmetry, Not Complexity," Photonics Tech Briefs Online, April (2003), http://www.ptbmagazine.com/content/040103_ora.html.
  16. H. Lowenthal, "Photographic objective of the triplet type," U.S. Patent 2,645,157 (1953).
  17. E. Hecht, Optics (Addison Wesley, 2002), p. 219.
  18. ISET digital camera simulator 2.0, ImageEval Consulting, Palo Alto, CA 94031.. P. B. Catrysse, X. Liu, and A. El Gamal, "QE reduction due to pixel vignetting in CMOS image sensors," Proc. SPIE 3965, 420-430 (2000).
  19. CODE V 9.5, Optical Research Associates, East Foothill Boulevard, Pasadena, CA 91107.
    [CrossRef]

2008

R. Dinyari, S.-B. Rim, K. Huang, and P. Peumans, "Curving monolithic silicon for non-planar focal plane array applications," Appl. Phys. Lett. 92, 091114 (2008).
[CrossRef]

2006

M. R. Ackermann, J. T. McGraw, and P. C. Zimmer, "Are curved focal planes necessary for wide-field survey telescopes?" Proc. SPIE 6267, 626740-626749 (2006).
[CrossRef]

P. Gregory, "Digital photography," Opt. Laser Techn. 38,306-314 (2006).
[CrossRef]

2005

A. El Gamal and H. Eltoukhy, "CMOS image sensors," IEEE Circuits and Devices Magazine 21,6-20 (2005).
[CrossRef]

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

P. B. Catrysse and B. A. Wandell, "Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld," Proc. SPIE 5678,1-13 (2005).
[CrossRef]

P. Y. Maeda, P. B. Catrysse, and B. A. Wandell, "Integrating lens design with digital camera simulation," Proc. SPIE 5678, 48-58 (2005).
[CrossRef]

2004

P. Swain and D. Mark, "Curved CCD detector devices and arrays for multispectral astrophysical applications and terrestrial stereo panoramic cameras," Proc. SPIE 5499, 281-301 (2004).
[CrossRef]

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, "Curved CCDs and their application with astronomical telescopes and stereo panoramic cameras," Proc. SPIE 5301, 109-129 (2004).
[CrossRef]

T. J. Jones and S. Nikzad, "Curved focal plane arrays using conformed thinned detector membrane," Nanotech Brief 28,No. 3 (2004).

H. Jin, J. R. Abelson, M. K. Erhardt, and R. G. Nuzzo, "Soft lithographic fabrication of an image sensor array on a curved substrate," J. Vac. Sci. Technol. B 22,2548-2551 (2004).
[CrossRef]

P. J. Hung, K. Jeong, G. L. Liu, and L. P. Lee, "Microfabricated suspensions for electrical connections on the tunable elastomer membrane," Appl. Phys. Lett. 85,6051-6053 (2004).
[CrossRef]

2000

ISET digital camera simulator 2.0, ImageEval Consulting, Palo Alto, CA 94031.. P. B. Catrysse, X. Liu, and A. El Gamal, "QE reduction due to pixel vignetting in CMOS image sensors," Proc. SPIE 3965, 420-430 (2000).

1999

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Abelson, J. R.

H. Jin, J. R. Abelson, M. K. Erhardt, and R. G. Nuzzo, "Soft lithographic fabrication of an image sensor array on a curved substrate," J. Vac. Sci. Technol. B 22,2548-2551 (2004).
[CrossRef]

Ackermann, M. R.

M. R. Ackermann, J. T. McGraw, and P. C. Zimmer, "Are curved focal planes necessary for wide-field survey telescopes?" Proc. SPIE 6267, 626740-626749 (2006).
[CrossRef]

Bailey, T.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Catrysse, P. B.

P. Y. Maeda, P. B. Catrysse, and B. A. Wandell, "Integrating lens design with digital camera simulation," Proc. SPIE 5678, 48-58 (2005).
[CrossRef]

P. B. Catrysse and B. A. Wandell, "Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld," Proc. SPIE 5678,1-13 (2005).
[CrossRef]

ISET digital camera simulator 2.0, ImageEval Consulting, Palo Alto, CA 94031.. P. B. Catrysse, X. Liu, and A. El Gamal, "QE reduction due to pixel vignetting in CMOS image sensors," Proc. SPIE 3965, 420-430 (2000).

Channin, D. J.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, "Curved CCDs and their application with astronomical telescopes and stereo panoramic cameras," Proc. SPIE 5301, 109-129 (2004).
[CrossRef]

Choi, B.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Colburn, M.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Damle, S.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Dinyari, R.

R. Dinyari, S.-B. Rim, K. Huang, and P. Peumans, "Curving monolithic silicon for non-planar focal plane array applications," Appl. Phys. Lett. 92, 091114 (2008).
[CrossRef]

Ekerdt, J.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

El Gamal, A.

A. El Gamal and H. Eltoukhy, "CMOS image sensors," IEEE Circuits and Devices Magazine 21,6-20 (2005).
[CrossRef]

ISET digital camera simulator 2.0, ImageEval Consulting, Palo Alto, CA 94031.. P. B. Catrysse, X. Liu, and A. El Gamal, "QE reduction due to pixel vignetting in CMOS image sensors," Proc. SPIE 3965, 420-430 (2000).

Eltoukhy, H.

A. El Gamal and H. Eltoukhy, "CMOS image sensors," IEEE Circuits and Devices Magazine 21,6-20 (2005).
[CrossRef]

Erhardt, M. K.

H. Jin, J. R. Abelson, M. K. Erhardt, and R. G. Nuzzo, "Soft lithographic fabrication of an image sensor array on a curved substrate," J. Vac. Sci. Technol. B 22,2548-2551 (2004).
[CrossRef]

Gregory, P.

P. Gregory, "Digital photography," Opt. Laser Techn. 38,306-314 (2006).
[CrossRef]

Huang, K.

R. Dinyari, S.-B. Rim, K. Huang, and P. Peumans, "Curving monolithic silicon for non-planar focal plane array applications," Appl. Phys. Lett. 92, 091114 (2008).
[CrossRef]

Hung, P. J.

P. J. Hung, K. Jeong, G. L. Liu, and L. P. Lee, "Microfabricated suspensions for electrical connections on the tunable elastomer membrane," Appl. Phys. Lett. 85,6051-6053 (2004).
[CrossRef]

Jeong, K.

P. J. Hung, K. Jeong, G. L. Liu, and L. P. Lee, "Microfabricated suspensions for electrical connections on the tunable elastomer membrane," Appl. Phys. Lett. 85,6051-6053 (2004).
[CrossRef]

Jin, H.

H. Jin, J. R. Abelson, M. K. Erhardt, and R. G. Nuzzo, "Soft lithographic fabrication of an image sensor array on a curved substrate," J. Vac. Sci. Technol. B 22,2548-2551 (2004).
[CrossRef]

Johnson, S.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Jones, T. J.

T. J. Jones and S. Nikzad, "Curved focal plane arrays using conformed thinned detector membrane," Nanotech Brief 28,No. 3 (2004).

Lee, L.

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

Lee, L. P.

P. J. Hung, K. Jeong, G. L. Liu, and L. P. Lee, "Microfabricated suspensions for electrical connections on the tunable elastomer membrane," Appl. Phys. Lett. 85,6051-6053 (2004).
[CrossRef]

Lipp, S. A.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, "Curved CCDs and their application with astronomical telescopes and stereo panoramic cameras," Proc. SPIE 5301, 109-129 (2004).
[CrossRef]

Liu, G. L.

P. J. Hung, K. Jeong, G. L. Liu, and L. P. Lee, "Microfabricated suspensions for electrical connections on the tunable elastomer membrane," Appl. Phys. Lett. 85,6051-6053 (2004).
[CrossRef]

Liu, X.

ISET digital camera simulator 2.0, ImageEval Consulting, Palo Alto, CA 94031.. P. B. Catrysse, X. Liu, and A. El Gamal, "QE reduction due to pixel vignetting in CMOS image sensors," Proc. SPIE 3965, 420-430 (2000).

Maeda, P. Y.

P. Y. Maeda, P. B. Catrysse, and B. A. Wandell, "Integrating lens design with digital camera simulation," Proc. SPIE 5678, 48-58 (2005).
[CrossRef]

Mark, D.

P. Swain and D. Mark, "Curved CCD detector devices and arrays for multispectral astrophysical applications and terrestrial stereo panoramic cameras," Proc. SPIE 5499, 281-301 (2004).
[CrossRef]

Mark, D. S.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, "Curved CCDs and their application with astronomical telescopes and stereo panoramic cameras," Proc. SPIE 5301, 109-129 (2004).
[CrossRef]

McGraw, J. T.

M. R. Ackermann, J. T. McGraw, and P. C. Zimmer, "Are curved focal planes necessary for wide-field survey telescopes?" Proc. SPIE 6267, 626740-626749 (2006).
[CrossRef]

Nikzad, S.

T. J. Jones and S. Nikzad, "Curved focal plane arrays using conformed thinned detector membrane," Nanotech Brief 28,No. 3 (2004).

Nounu, H.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Nuzzo, R. G.

H. Jin, J. R. Abelson, M. K. Erhardt, and R. G. Nuzzo, "Soft lithographic fabrication of an image sensor array on a curved substrate," J. Vac. Sci. Technol. B 22,2548-2551 (2004).
[CrossRef]

Peumans, P.

R. Dinyari, S.-B. Rim, K. Huang, and P. Peumans, "Curving monolithic silicon for non-planar focal plane array applications," Appl. Phys. Lett. 92, 091114 (2008).
[CrossRef]

Rim, S.-B.

R. Dinyari, S.-B. Rim, K. Huang, and P. Peumans, "Curving monolithic silicon for non-planar focal plane array applications," Appl. Phys. Lett. 92, 091114 (2008).
[CrossRef]

Ruchhoeft, P.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Sreenivasan, S. V.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Stewart, M.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Swain, P.

P. Swain and D. Mark, "Curved CCD detector devices and arrays for multispectral astrophysical applications and terrestrial stereo panoramic cameras," Proc. SPIE 5499, 281-301 (2004).
[CrossRef]

Swain, P. K.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, "Curved CCDs and their application with astronomical telescopes and stereo panoramic cameras," Proc. SPIE 5301, 109-129 (2004).
[CrossRef]

Szema, R.

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

Taylor, G. C.

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, "Curved CCDs and their application with astronomical telescopes and stereo panoramic cameras," Proc. SPIE 5301, 109-129 (2004).
[CrossRef]

Wandell, B. A.

P. B. Catrysse and B. A. Wandell, "Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld," Proc. SPIE 5678,1-13 (2005).
[CrossRef]

P. Y. Maeda, P. B. Catrysse, and B. A. Wandell, "Integrating lens design with digital camera simulation," Proc. SPIE 5678, 48-58 (2005).
[CrossRef]

Willson, C. G.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Wolfe, J. C.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Zimmer, P. C.

M. R. Ackermann, J. T. McGraw, and P. C. Zimmer, "Are curved focal planes necessary for wide-field survey telescopes?" Proc. SPIE 6267, 626740-626749 (2006).
[CrossRef]

Appl. Phys. Lett.

P. J. Hung, K. Jeong, G. L. Liu, and L. P. Lee, "Microfabricated suspensions for electrical connections on the tunable elastomer membrane," Appl. Phys. Lett. 85,6051-6053 (2004).
[CrossRef]

R. Dinyari, S.-B. Rim, K. Huang, and P. Peumans, "Curving monolithic silicon for non-planar focal plane array applications," Appl. Phys. Lett. 92, 091114 (2008).
[CrossRef]

IEEE Circuits and Devices Magazine

A. El Gamal and H. Eltoukhy, "CMOS image sensors," IEEE Circuits and Devices Magazine 21,6-20 (2005).
[CrossRef]

J. Vac. Sci. Technol. B

H. Jin, J. R. Abelson, M. K. Erhardt, and R. G. Nuzzo, "Soft lithographic fabrication of an image sensor array on a curved substrate," J. Vac. Sci. Technol. B 22,2548-2551 (2004).
[CrossRef]

J. Vac. Sci. Technol. B.

P. Ruchhoeft, M. Colburn, B. Choi, H. Nounu, S. Johnson, T. Bailey, S. Damle, M. Stewart, J. Ekerdt, S. V. Sreenivasan, J. C. Wolfe, and C. G. Willson, "Patterning curved surfaces: Template generation by ion beam proximity lithography and relief transfer by step and flash imprint lithography," J. Vac. Sci. Technol. B. 172965-2969 (1999).
[CrossRef]

Nanotech Brief

T. J. Jones and S. Nikzad, "Curved focal plane arrays using conformed thinned detector membrane," Nanotech Brief 28,No. 3 (2004).

Opt. Laser Techn.

P. Gregory, "Digital photography," Opt. Laser Techn. 38,306-314 (2006).
[CrossRef]

Proc. SPIE

P. K. Swain, D. J. Channin, G. C. Taylor, S. A. Lipp, and D. S. Mark, "Curved CCDs and their application with astronomical telescopes and stereo panoramic cameras," Proc. SPIE 5301, 109-129 (2004).
[CrossRef]

M. R. Ackermann, J. T. McGraw, and P. C. Zimmer, "Are curved focal planes necessary for wide-field survey telescopes?" Proc. SPIE 6267, 626740-626749 (2006).
[CrossRef]

P. Swain and D. Mark, "Curved CCD detector devices and arrays for multispectral astrophysical applications and terrestrial stereo panoramic cameras," Proc. SPIE 5499, 281-301 (2004).
[CrossRef]

ISET digital camera simulator 2.0, ImageEval Consulting, Palo Alto, CA 94031.. P. B. Catrysse, X. Liu, and A. El Gamal, "QE reduction due to pixel vignetting in CMOS image sensors," Proc. SPIE 3965, 420-430 (2000).

P. B. Catrysse and B. A. Wandell, "Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld," Proc. SPIE 5678,1-13 (2005).
[CrossRef]

P. Y. Maeda, P. B. Catrysse, and B. A. Wandell, "Integrating lens design with digital camera simulation," Proc. SPIE 5678, 48-58 (2005).
[CrossRef]

Science

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

Other

E. Hecht, Optics (Addison Wesley, 2002), p. 226.

J. M. Rodgers, "Curved Focal Surfaces: Design Optimization Through Symmetry, Not Complexity," Photonics Tech Briefs Online, April (2003), http://www.ptbmagazine.com/content/040103_ora.html.

H. Lowenthal, "Photographic objective of the triplet type," U.S. Patent 2,645,157 (1953).

E. Hecht, Optics (Addison Wesley, 2002), p. 219.

CODE V 9.5, Optical Research Associates, East Foothill Boulevard, Pasadena, CA 91107.
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Modulation transfer functions (MTFs) of (a) a simple plano-convex lens with a planar image plane (System I), (b) Cooke triplet lens camera system with a planar image plane (System II) and (c) a simple ball lens with a spherical curved image plane (System III). (a–c) MTFs of diffraction limited systems (black dotted lines), image points on axis (red), tangential image points (solid) at 0.4 field (green) and 0.7 field (blue) and sagittal image points (dashed dots) at both fields are shown. Inset: schematics of the three systems.

Fig. 2.
Fig. 2.

Point spread functions for (a-c,g-i,m-o) on-axis and (d-f,j-l,p-r) off-axis (2mm image height) points. (a-f) show PSFs for System I, (g-l) for System II and (m-r) for System III.

Fig. 3.
Fig. 3.

Ray curves of astigmatism field curvature of (a) System I, (b) System II and (c) System III. Tangential field curvature (dotted lines) and sagittal field curvature (solid lines) are shown together.

Fig. 4.
Fig. 4.

(a) Mapping of image points on a curved image plane to points on a 2-D image plane in system III. (b–d) Image height distortion of (b) System I (c) System II and (d) System III

Fig. 5.
Fig. 5.

Relative illumination fall-off of (a) System I, (b) System II and (c) System III.

Fig. 6.
Fig. 6.

(a) Object image and simulated radiometric images by (b) System I (c) System II and (d) System III.

Fig. 7.
Fig. 7.

(a,b) Optical micrographs of a fabricated curved silicon die. (a) Curved die on a spherical surface with radius of cuvature of 1cm. (b) Detail of the curved die at an off-axis location. (c) Scanning electron microscopy (SEM) picture of an undeformed die.

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