Abstract

Monocentric lenses have recently changed from primarily a historic curiosity to a potential solution for panoramic high-resolution imagers, where the spherical image surface is directly detected by curved image sensors or optically transferred onto multiple conventional flat focal planes. We compare imaging and waveguide-based transfer of the spherical image surface formed by the monocentric lens onto planar image sensors, showing that both approaches can make the system input aperture and resolution substantially independent of the input angle. We present aberration analysis that demonstrates that wide-field monocentric lenses can be focused by purely axial translation and describe a systematic design process to identify the best designs for two-glass symmetric monocentric lenses. Finally, we use this approach to design an F/1.7, 12 mm focal length imager with an up to 160° field of view and show that it compares favorably in size and performance to conventional wide-angle imagers.

© 2012 Optical Society of America

Full Article  |  PDF Article

Errata

Igor Stamenov, Ilya P. Agurok, and Joseph E. Ford, "Optimization of two-glass monocentric lenses for compact panoramic imagers: general aberration analysis and specific designs: erratum," Appl. Opt. 52, 5348-5349 (2013)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-52-22-5348

References

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  2. T. Yamashita, R. Funatsu, T. Yanagi, K. Mitani, Y. Nojiri, and T. Yoshida, “A camera system using three 33-megapixel CMOS image sensors for UHDTV2,” SMPTE J. 120, 24–31 (2011).
    [CrossRef]
  3. R. Kingslake, A History of the Photographic Lens (Academic, 1989), pp. 49–67.
  4. G. Krishnan and S. K. Nayar, “Towards a true spherical camera,” Proc. SPIE 7240, 724002 (2009).
    [CrossRef]
  5. J. E. Ford, and E. Tremblay, “Extreme form factor imagers,” in Imaging Systems, OSA Technical Digest (CD) (2010), paper IMC2.
  6. D. J. Brady and N. Hagen, “Multiscale lens design,” Opt. Express 17, 10659–10674 (2009).
    [CrossRef]
  7. O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in IEEE International Conference on Computational Photography (IEEE, 2011), pp. 1–8.
  8. 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, OSA Technical Digest (2011), paper JTuE2.
  9. D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
    [CrossRef]
  10. E. J. Tremblay, D. L. Marks, D. J. Brady, and J. E. Ford, “Design and scaling of monocentric multiscale imagers,” Appl. Opt. 51, 4691–4702 (2012).
    [CrossRef]
  11. P. Milojkovic and J. Mait, “Space-bandwidth scaling for wide field-of-view imaging,” Appl. Opt. 51, A36–A47 (2012).
    [CrossRef]
  12. J. A. Waidelich, “Spherical lens imaging device,” U.S. patent 3,166,623 (19January1965).
  13. J. J. Hancock, The design, fabrication, and calibration of a fiber filter spectrometer, Ph.D. Thesis (University of Arizona, 2012); see also product datasheets posted on Schott Fiber Optics website, “Schott Fiber Optic Faceplates” (faceplates_us_march_2011.pdf) and “Schott Fused Imaging Fiber Tapers” (Tapers-US-October_2011.pdf).
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  18. J. M. Cobb, D. Kessler, and J. E. Roddy, “Autostereoscopic optical apparatus,” U.S. Patent 6,871,956 (29March2005).
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    [CrossRef]
  21. M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University, 1999).
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    [CrossRef]
  24. R. Kingslake and R. B. Johnson, Lens Design Fundamentals, 2nd ed. (SPIE, 2010).
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    [CrossRef]
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  36. http://psilab.ucsd.edu/PhysicalApertureStopFamily3.zip .
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    [CrossRef]
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2012 (3)

2011 (2)

T. Yamashita, R. Funatsu, T. Yanagi, K. Mitani, Y. Nojiri, and T. Yoshida, “A camera system using three 33-megapixel CMOS image sensors for UHDTV2,” SMPTE J. 120, 24–31 (2011).
[CrossRef]

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

2010 (2)

2009 (2)

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

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

2002 (1)

J. M. Cobb, D. Kessler, and J. Agostinelli, “Optical design of a monocentric autostereoscopic immersive display,” Proc. SPIE 4832, 80–90 (2002).
[CrossRef]

2001 (1)

2000 (1)

J. Kulmer and M. Bauer, “Fish-eye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

1999 (1)

I. Agurok, “Method of ‘truss’ approximation in wavefront testing,” Proc. SPIE 3782, 337–348 (1999).
[CrossRef]

1985 (1)

1964 (1)

Achtner, B.

H. Gross, F. Blechinger, and B. Achtner, Survey of Optical Instruments, Vol. 4 of Handbook of Optical Systems (Wiley, 2008).

Agostinelli, J.

J. M. Cobb, D. Kessler, and J. Agostinelli, “Optical design of a monocentric autostereoscopic immersive display,” Proc. SPIE 4832, 80–90 (2002).
[CrossRef]

Agurok, I.

I. Agurok, “Method of ‘truss’ approximation in wavefront testing,” Proc. SPIE 3782, 337–348 (1999).
[CrossRef]

Bauer, M.

J. Kulmer and M. Bauer, “Fish-eye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

Blechinger, F.

H. Gross, F. Blechinger, and B. Achtner, Survey of Optical Instruments, Vol. 4 of Handbook of Optical Systems (Wiley, 2008).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University, 1999).

Brady, D.

Brady, D. J.

E. J. Tremblay, D. L. Marks, D. J. Brady, and J. E. Ford, “Design and scaling of monocentric multiscale imagers,” Appl. Opt. 51, 4691–4702 (2012).
[CrossRef]

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

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, OSA Technical Digest (2011), paper JTuE2.

Buchdahl, H. A.

H. A. Buchdahl, Optical Aberrations Coefficients (Dover, 1968).

Churilovskiy, V.

V. Churilovskiy, The Theory of Chromatism and Third Order Aberrations (Mashinostroenie, 1968).

Cobb, J. M.

J. M. Cobb, D. Kessler, and J. Agostinelli, “Optical design of a monocentric autostereoscopic immersive display,” Proc. SPIE 4832, 80–90 (2002).
[CrossRef]

J. M. Cobb, D. Kessler, and J. E. Roddy, “Autostereoscopic optical apparatus,” U.S. Patent 6,871,956 (29March2005).

Cossairt, O.

O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in IEEE International Conference on Computational Photography (IEEE, 2011), pp. 1–8.

Drougard, R.

Feller, S. D.

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

Ford, J.

D. Marks, E. Tremblay, J. Ford, and D. Brady, “Multicamera 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, OSA Technical Digest (2011), paper JTuE2.

Ford, J. E.

E. J. Tremblay, D. L. Marks, D. J. Brady, and J. E. Ford, “Design and scaling of monocentric multiscale imagers,” Appl. Opt. 51, 4691–4702 (2012).
[CrossRef]

J. E. Ford, and E. Tremblay, “Extreme form factor imagers,” in Imaging Systems, OSA Technical Digest (CD) (2010), paper IMC2.

Funatsu, R.

T. Yamashita, R. Funatsu, T. Yanagi, K. Mitani, Y. Nojiri, and T. Yoshida, “A camera system using three 33-megapixel CMOS image sensors for UHDTV2,” SMPTE J. 120, 24–31 (2011).
[CrossRef]

Gardner, I.

I. Gardner, “Application of algebraic aberration equations to optical design,” Scientific Papers of the Bureau of Standards No. 550 (1927).

Gehm, M. E.

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

Golish, D. R.

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

Gross, H.

H. Gross, F. Blechinger, and B. Achtner, Survey of Optical Instruments, Vol. 4 of Handbook of Optical Systems (Wiley, 2008).

Hagen, N.

Hahn, 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, OSA Technical Digest (2011), paper JTuE2.

Han, J.-H.

Hancock, J. J.

J. J. Hancock, The design, fabrication, and calibration of a fiber filter spectrometer, Ph.D. Thesis (University of Arizona, 2012); see also product datasheets posted on Schott Fiber Optics website, “Schott Fiber Optic Faceplates” (faceplates_us_march_2011.pdf) and “Schott Fused Imaging Fiber Tapers” (Tapers-US-October_2011.pdf).

Horimoto, M.

M. Horimoto, “Fish eye lens system,” U.S. Patent 4,412,726(1November1983).

Johnson, A.

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, OSA Technical Digest (2011), paper JTuE2.

Johnson, R. B.

R. Kingslake and R. B. Johnson, Lens Design Fundamentals, 2nd ed. (SPIE, 2010).

Kang, J. U.

Kessler, D.

J. M. Cobb, D. Kessler, and J. Agostinelli, “Optical design of a monocentric autostereoscopic immersive display,” Proc. SPIE 4832, 80–90 (2002).
[CrossRef]

J. M. Cobb, D. Kessler, and J. E. Roddy, “Autostereoscopic optical apparatus,” U.S. Patent 6,871,956 (29March2005).

Kim, 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, OSA Technical Digest (2011), paper JTuE2.

Kingslake, R.

R. Kingslake, A History of the Photographic Lens (Academic, 1989), pp. 49–67.

R. Kingslake and R. B. Johnson, Lens Design Fundamentals, 2nd ed. (SPIE, 2010).

Kittle, D. S.

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

Krishnan, G.

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

Kulmer, J.

J. Kulmer and M. Bauer, “Fish-eye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

Lee, J.

Li, Y. F.

Lit, J. W. Y.

Mait, J.

Marks, D.

Marks, D. L.

E. J. Tremblay, D. L. Marks, D. J. Brady, and J. E. Ford, “Design and scaling of monocentric multiscale imagers,” Appl. Opt. 51, 4691–4702 (2012).
[CrossRef]

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

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, OSA Technical Digest (2011), paper JTuE2.

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, OSA Technical Digest (2011), paper JTuE2.

Miau, D.

O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in IEEE International Conference on Computational Photography (IEEE, 2011), pp. 1–8.

Milojkovic, P.

Mitani, K.

T. Yamashita, R. Funatsu, T. Yanagi, K. Mitani, Y. Nojiri, and T. Yoshida, “A camera system using three 33-megapixel CMOS image sensors for UHDTV2,” SMPTE J. 120, 24–31 (2011).
[CrossRef]

Nayar, S. K.

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

O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in IEEE International Conference on Computational Photography (IEEE, 2011), pp. 1–8.

Nojiri, Y.

T. Yamashita, R. Funatsu, T. Yanagi, K. Mitani, Y. Nojiri, and T. Yoshida, “A camera system using three 33-megapixel CMOS image sensors for UHDTV2,” SMPTE J. 120, 24–31 (2011).
[CrossRef]

Rayces, J. L.

Roddy, J. E.

J. M. Cobb, D. Kessler, and J. E. Roddy, “Autostereoscopic optical apparatus,” U.S. Patent 6,871,956 (29March2005).

Rosete-Aguilar, M.

Rusinov, M. M.

M. M. Rusinov, Handbook of Computational Optics(Mashinostroenie, 1984), Chap. 23.

Sasian, J.

Schott,

Schott glass catalog, http://www.us.schott.com/advanced_optics/english/download/schott_optical_glass_catalogue_excel_june_2012.xls .Schott.

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, OSA Technical Digest (2011), paper JTuE2.

Slyusarev, G. G.

G. G. Slyusarev, Aberrations and Optical Design Theory, 2nd ed. (Adam Hilger, 1984).

Smith, W.

W. Smith, Modern Lens Design, 2nd ed. (McGraw Hill, 2005).

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, OSA Technical Digest (2011), paper JTuE2.

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, OSA Technical Digest (2011), paper JTuE2.

Stack, R. A.

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

Tremblay, E.

D. Marks, E. Tremblay, J. Ford, and D. Brady, “Multicamera 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, OSA Technical Digest (CD) (2010), paper IMC2.

Tremblay, E. J.

E. J. Tremblay, D. L. Marks, D. J. Brady, and J. E. Ford, “Design and scaling of monocentric multiscale imagers,” Appl. Opt. 51, 4691–4702 (2012).
[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, OSA Technical Digest (2011), paper JTuE2.

Vera, E. M.

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

Waidelich, J. A.

J. A. Waidelich, “Spherical lens imaging device,” U.S. patent 3,166,623 (19January1965).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University, 1999).

Yamashita, T.

T. Yamashita, R. Funatsu, T. Yanagi, K. Mitani, Y. Nojiri, and T. Yoshida, “A camera system using three 33-megapixel CMOS image sensors for UHDTV2,” SMPTE J. 120, 24–31 (2011).
[CrossRef]

Yanagi, T.

T. Yamashita, R. Funatsu, T. Yanagi, K. Mitani, Y. Nojiri, and T. Yoshida, “A camera system using three 33-megapixel CMOS image sensors for UHDTV2,” SMPTE J. 120, 24–31 (2011).
[CrossRef]

Yoshida, T.

T. Yamashita, R. Funatsu, T. Yanagi, K. Mitani, Y. Nojiri, and T. Yoshida, “A camera system using three 33-megapixel CMOS image sensors for UHDTV2,” SMPTE J. 120, 24–31 (2011).
[CrossRef]

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

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

Nature (1)

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

Opt. Express (2)

Proc. SPIE (4)

I. Agurok, “Method of ‘truss’ approximation in wavefront testing,” Proc. SPIE 3782, 337–348 (1999).
[CrossRef]

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

J. M. Cobb, D. Kessler, and J. Agostinelli, “Optical design of a monocentric autostereoscopic immersive display,” Proc. SPIE 4832, 80–90 (2002).
[CrossRef]

J. Kulmer and M. Bauer, “Fish-eye lens designs and their relative performance,” Proc. SPIE 4093, 360–369 (2000).
[CrossRef]

SMPTE J. (1)

T. Yamashita, R. Funatsu, T. Yanagi, K. Mitani, Y. Nojiri, and T. Yoshida, “A camera system using three 33-megapixel CMOS image sensors for UHDTV2,” SMPTE J. 120, 24–31 (2011).
[CrossRef]

Other (24)

R. Kingslake, A History of the Photographic Lens (Academic, 1989), pp. 49–67.

J. E. Ford, and E. Tremblay, “Extreme form factor imagers,” in Imaging Systems, OSA Technical Digest (CD) (2010), paper IMC2.

O. Cossairt, D. Miau, and S. K. Nayar, “Gigapixel computational imaging,” in IEEE International Conference on Computational Photography (IEEE, 2011), pp. 1–8.

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, OSA Technical Digest (2011), paper JTuE2.

W. Smith, Modern Lens Design, 2nd ed. (McGraw Hill, 2005).

J. M. Cobb, D. Kessler, and J. E. Roddy, “Autostereoscopic optical apparatus,” U.S. Patent 6,871,956 (29March2005).

Hoya glass catalog, http://www.hoya-opticalworld.com/english/ (20June2012).

J. A. Waidelich, “Spherical lens imaging device,” U.S. patent 3,166,623 (19January1965).

J. J. Hancock, The design, fabrication, and calibration of a fiber filter spectrometer, Ph.D. Thesis (University of Arizona, 2012); see also product datasheets posted on Schott Fiber Optics website, “Schott Fiber Optic Faceplates” (faceplates_us_march_2011.pdf) and “Schott Fused Imaging Fiber Tapers” (Tapers-US-October_2011.pdf).

http://psilab.ucsd.edu/VirtualStopFamily1.zip .

http://psilab.ucsd.edu/PhysicalApertureStopFamily3.zip .

R. Kingslake and R. B. Johnson, Lens Design Fundamentals, 2nd ed. (SPIE, 2010).

G. G. Slyusarev, Aberrations and Optical Design Theory, 2nd ed. (Adam Hilger, 1984).

M. Born and E. Wolf, Principles of Optics, 7th expanded ed. (Cambridge University, 1999).

V. Churilovskiy, The Theory of Chromatism and Third Order Aberrations (Mashinostroenie, 1968).

I. Gardner, “Application of algebraic aberration equations to optical design,” Scientific Papers of the Bureau of Standards No. 550 (1927).

H. A. Buchdahl, Optical Aberrations Coefficients (Dover, 1968).

Schott glass catalog, http://www.us.schott.com/advanced_optics/english/download/schott_optical_glass_catalogue_excel_june_2012.xls .Schott.

Ohara glass catalog, http://www.oharacorp.com/xls/glass-data-2012.xls .

Sumita glass catalog, http://www.sumita-opt.co.jp/ja/goods/data/glassdata.xls .

Hoya glass catalog, http://www.hoyaoptics.com/pdf/MasterOpticalGlass.xls .

M. M. Rusinov, Handbook of Computational Optics(Mashinostroenie, 1984), Chap. 23.

M. Horimoto, “Fish eye lens system,” U.S. Patent 4,412,726(1November1983).

H. Gross, F. Blechinger, and B. Achtner, Survey of Optical Instruments, Vol. 4 of Handbook of Optical Systems (Wiley, 2008).

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Figures (15)

Fig. 1.
Fig. 1.

(a) Optical layout of a 2.4 gigapixel monocentric multiscale lens and (b) the same image field transferred by tapered fiber bundles instead of multiple relay optics.

Fig. 2.
Fig. 2.

Monocentric lens imaging with (a) a physical aperture stop at the center of the objective lens and (b) a “virtual stop” accomplished by limiting the NA of the image transfer, which, as drawn, are fiber bundles made from nonimaging low-NA optical fibers.

Fig. 3.
Fig. 3.

First- and third-order consideration of monocentric lens refocus.

Fig. 4.
Fig. 4.

Third-order aberration theory applied to monocentric lens design.

Fig. 5.
Fig. 5.

Monocentric lens real ray trace variables.

Fig. 6.
Fig. 6.

Example of dependence of criterion Q on the radius r1.

Fig. 7.
Fig. 7.

Image formation in the monocentric lens.

Fig. 8.
Fig. 8.

AWARE2 lens and global optimum solution.

Fig. 9.
Fig. 9.

MTF and ray aberration performance comparison of the (a) fabricated AWARE2 prototype and (b) new AWARE2 design candidate.

Fig. 10.
Fig. 10.

Correlation between polychromatic mean square wavefront deformation and MTF at 200lp/mm for candidates.

Fig. 11.
Fig. 11.

Highest ranked design solution (high-index center glass).

Fig. 12.
Fig. 12.

MTF performance of monocentric lens (a) focused at infinity (design) and (b) refocused at a flat object at 0.5 m.

Fig. 13.
Fig. 13.

Top member of the third family (lower center glass index) operating in (a) the physical aperture stop, including a 73° field angle to illustrate the effect of aperture vignetting and (b) “virtual” aperture stop mode, with uniform response up to 80°.

Fig. 14.
Fig. 14.

Comparison of two conventional wide-field lenses with a monocentric-waveguide lens. All have a 12 mm focal length, 120° field of view, and similar light collection, but the monocentric lens provides higher resolution in a compact volume.

Fig. 15.
Fig. 15.

Systematic diagram of photographic lens setup families, including monocentric multiscale and waveguide imagers. Figure adapted from [39].

Tables (4)

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Table 1. Optical Prescription of the Fabricated AWARE2 Lens

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Table 2. Optical Prescription of the Top Design Solution for the AWARE2 Lens

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Table 3. Top Solutions for a f/1.7 f=12mm Monocentric Lens

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Table 4. Optical Prescription for Refocusing of the Monocentric Lens, Showing Multiple Configurations for Three Object Distances

Equations (38)

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Δx=f2dff2d.
Δx(β1)=f2cos(β1)d=Δxcos(β1)BinfQ¯=Δx(β1)cos(β1)=Δx=AinfA¯,
C=12s=1mhs(βs+1βs1ns+11ns)2(αs+1ns+1αsns),
D=12s=1m(1ns1ns+1)rs+C,
C=14nim(1Rt1Rs)andD=12nim1Rs,
ri=hini+1nini+1αi+1niαi,
αi+1=nini+1αi+hini+1nini+iri,
hi+1=hiαi+1di,
1f=2r1(11n2)+2r2(1n21n3).
B=12s=14hs(αs+1αs1ns+11ns)2(αs+1ns+1αsns).
W040=14Bρ4=ρ=118s=14hs(αs+1αs1ns+11ns)2(αs+1ns+1αsns),
r1=h1n21n2α2orα2=h1n21n2r1.
W040=h14((n223n2n3+n32)32f3(n2n3)2(n21)(n22n3)(n31)4n22(n2n3)2r13+(n21)2(n22+n2n3+n32)8fn22(n2n3)2r12(n21)(n22+n2n3+n32)16f2n2(n2n3)2r1).
L0=2W020=h12((n31)(2f(1n2)+n2r1)f(n2n3)r1n3v3(n21)(2f(1n3)+n3r1)f(n2n3)r1n2v2).
sin(ϕ1)=hr1.
sin(ϕ1)=hr1n2.
sin(ϕ2)=r1r2sin(ϕ1)=r1r2hr1n2=hr2n2.
sin(ϕ2)=n2n3sin(ϕ2)=n2n3hr2n2=hr2n3.
sin(ϕ3)=n3n2sin(ϕ3)=n3n2hr2n3=hr2n2.
sin(ϕ4)=r2r1sin(ϕ3)=hr1n2.
sin(ϕ4)=n2sin(ϕ4)=hr1.
ϕ4ϕ1.
S=r1sin(ϕ4)sin[180°(180°ϕ4)(180°ϕ1ϕ22ϕ33ϕ44)]
S=r1sin(ϕ4)sin(180°+2ϕ1+ϕ22+ϕ33+ϕ44).
ϕ1=arcsin(hr1).
ϕ22=ϕ2ϕ1=arcsin(hr2n2)arcsin(hr1n2),
ϕ33=180°2ϕ2=180°2arcsin(hr2n3),
ϕ44=ϕ3ϕ4=arcsin(hr2n2)arcsin(hr1n2).
S=hsin{2[arcsin(hr1)arcsin(hr1n2)+arcsin(hr2n2)arcsin(hr2n3)]}.
ΔS(hi)=S(hi)f.
Q=i=13Abs(ΔS(hi,λ))+j=13kjAbs[ΔS(hj,λ)ΔS(hk,λ)],
ΔY=WρλA,
ΔS(ρ)=ΔYAρ=WρλA2ρ,
ΔS(ρ,λi)A2λi=4C20+C40(24ρ212)+C60(120ρ4120ρ2+24)+C80(560ρ6840ρ4+360ρ240).
j=19[ΔS(ρ,λi)A2λi4C20(λi)C40(λi)(24ρ212)C60(λi)(120ρ4120ρ2+24)C80(λi)(560ρ6840ρ4+360ρ240)]2=min.
dS=4C20(λ2)λ2A2.
C20new(λi)=C20(λi)dSA24λi.
(ΔΦ)2=Φ¯2(Φ¯)2=12i=13{[C20new(λi)]23+[C40(λi)]25+[C60(λi)]27+[C80(λi)]29},

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