Abstract

The recent application of monocentric lenses for panoramic high-resolution digital imagers raises the question of the achievable performance limits of this lens structure and of techniques for design optimization to approach these limits. This paper defines the important regions of the design space of moderate complexity monocentric lenses and describes systematic and global optimization algorithms for the design of monocentric objective lenses of various focal lengths, apertures, and spectral bandwidths. We demonstrate the trade-off between spectral band, F-number and lens complexity, and provide design examples of monocentric lenses for specific applications.

© 2013 Optical Society of America

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2012

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]

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]

I. Stamenov, I. Agurok, and J. Ford, “Optimization of two-glass monocentric lenses for compact panoramic imagers: general aberration analysis and specific designs,” Appl. Opt. 51, 7648–7661 (2012).
[CrossRef]

D. L. Marks, H. S. Son, J. Kim, and D. Brady, “Engineering a gigapixel monocentric multiscale camera,” Opt. Eng. 51, 083202 (2012).
[CrossRef]

N. Zheng, S. C. Schmidler, D. Marks, and D. Brady, “Computer experiment and global optimization of layered monocentric lens systems,” Optik 123, 1249–1259 (2012).
[CrossRef]

2009

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

2007

2002

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

1995

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

1963

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. Stamenov, I. Agurok, and J. Ford, “Optimization of two-glass monocentric lenses for compact panoramic imagers: general aberration analysis and specific designs,” Appl. Opt. 51, 7648–7661 (2012).
[CrossRef]

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

I. Stamenov, I. Agurok, and J. Ford, “Capabilities of monocentric objective lenses,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper ITu3E.4.

Akerlof, C.

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

Arnauld, C.

D. Dayton, J. Gonglewsky, C. Arnauld, I. Mons, and D. Burns, SWIR Sky Glow Cloud Correlation with NIR and Visible Clouds: An Urban and Rural Comparison (AFRL, 2009).

Axelrod, T. S.

T. S. Axelrod, N. J. Colella, and A. G. Ledebuhr, “The wide-field-of-view camera,” in Energy and Technology Review, (Lawrence Livermore National Laboratory, 1988).

Barthelmy, S.

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

Bionta, R.

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

Born, M.

M. Born and E. Wolf, Principles of Optics7th ed. (Cambridge University, 1999).

Brady, D.

D. L. Marks, H. S. Son, J. Kim, and D. Brady, “Engineering a gigapixel monocentric multiscale camera,” Opt. Eng. 51, 083202 (2012).
[CrossRef]

N. Zheng, S. C. Schmidler, D. Marks, and D. Brady, “Computer experiment and global optimization of layered monocentric lens systems,” Optik 123, 1249–1259 (2012).
[CrossRef]

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

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]

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 (Optical Society of America, 2011), paper JTuE2.

Burns, D.

D. Dayton, J. Gonglewsky, C. Arnauld, I. Mons, and D. Burns, SWIR Sky Glow Cloud Correlation with NIR and Visible Clouds: An Urban and Rural Comparison (AFRL, 2009).

Cline, T.

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

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]

Colella, N. J.

T. S. Axelrod, N. J. Colella, and A. G. Ledebuhr, “The wide-field-of-view camera,” in Energy and Technology Review, (Lawrence Livermore National Laboratory, 1988).

Cossairt, O.

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

Dayton, D.

D. Dayton, J. Gonglewsky, C. Arnauld, I. Mons, and D. Burns, SWIR Sky Glow Cloud Correlation with NIR and Visible Clouds: An Urban and Rural Comparison (AFRL, 2009).

Fatuzzo, M.

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

Feder, D.

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.

I. Stamenov, I. Agurok, and J. Ford, “Optimization of two-glass monocentric lenses for compact panoramic imagers: general aberration analysis and specific designs,” Appl. Opt. 51, 7648–7661 (2012).
[CrossRef]

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

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 (Optical Society of America, 2011), paper JTuE2.

I. Stamenov, I. Agurok, and J. Ford, “Capabilities of monocentric objective lenses,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper ITu3E.4.

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) (Optical Society of America, 2010), paper IMC2.

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]

Gehrels, N.

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

Gill, P.

P. Gill, W. Murray, and M. Wright, Practical Optimization (Academic, 1981).

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]

Golub, G.

G. Golub and C. Van Loan, Matrix Computations (John Hopkins, 1989).

Gonglewsky, J.

D. Dayton, J. Gonglewsky, C. Arnauld, I. Mons, and D. Burns, SWIR Sky Glow Cloud Correlation with NIR and Visible Clouds: An Urban and Rural Comparison (AFRL, 2009).

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 (Optical Society of America, 2011), paper JTuE2.

Hills, R.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

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 (Optical Society of America, 2011), paper JTuE2.

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

Johnson, R. B.

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

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]

Kim, J.

D. L. Marks, H. S. Son, J. Kim, and D. Brady, “Engineering a gigapixel monocentric multiscale camera,” Opt. Eng. 51, 083202 (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 (Optical Society of America, 2011), paper JTuE2.

Kingslake, R.

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

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

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]

Kordas, J. F.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

Krishnan, G.

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

Kruger, M.

M. Kruger, B. Panov, B. Kulagin, G. Pogarev, Y. Kruger, and A. Levinson, “Handbook of opto-mechanics,” Moscow, 1963.

Kruger, Y.

M. Kruger, B. Panov, B. Kulagin, G. Pogarev, Y. Kruger, and A. Levinson, “Handbook of opto-mechanics,” Moscow, 1963.

Kulagin, B.

M. Kruger, B. Panov, B. Kulagin, G. Pogarev, Y. Kruger, and A. Levinson, “Handbook of opto-mechanics,” Moscow, 1963.

Ledebuhr, A.

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

Ledebuhr, A. G.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

T. S. Axelrod, N. J. Colella, and A. G. Ledebuhr, “The wide-field-of-view camera,” in Energy and Technology Review, (Lawrence Livermore National Laboratory, 1988).

Lee, B.

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

Levinson, A.

M. Kruger, B. Panov, B. Kulagin, G. Pogarev, Y. Kruger, and A. Levinson, “Handbook of opto-mechanics,” Moscow, 1963.

Lewis, I. T.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

Marks, D.

N. Zheng, S. C. Schmidler, D. Marks, and D. Brady, “Computer experiment and global optimization of layered monocentric lens systems,” Optik 123, 1249–1259 (2012).
[CrossRef]

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

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]

D. L. Marks, H. S. Son, J. Kim, and D. Brady, “Engineering a gigapixel monocentric multiscale camera,” Opt. Eng. 51, 083202 (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 (Optical Society of America, 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 (Optical Society of America, 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).

Mons, I.

D. Dayton, J. Gonglewsky, C. Arnauld, I. Mons, and D. Burns, SWIR Sky Glow Cloud Correlation with NIR and Visible Clouds: An Urban and Rural Comparison (AFRL, 2009).

Morrison, R.

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

Motamedi, N.

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

Murray, W.

P. Gill, W. Murray, and M. Wright, Practical Optimization (Academic, 1981).

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).

Nielsen, D. P.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

Oakley, J.

Olivas, S.

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

Panov, B.

M. Kruger, B. Panov, B. Kulagin, G. Pogarev, Y. Kruger, and A. Levinson, “Handbook of opto-mechanics,” Moscow, 1963.

Park, H.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

Pleasance, L. D.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

Pogarev, G.

M. Kruger, B. Panov, B. Kulagin, G. Pogarev, Y. Kruger, and A. Levinson, “Handbook of opto-mechanics,” Moscow, 1963.

Priest, R. E.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

Rodionov, S. A.

S. A. Rodionov, Computer Lens Design (Mashinostroenie, 1982).

Rusinov, M.

M. Rusinov, Composition of Optical Systems (Mashinostroenie, 1989).

Rusinov, M. M.

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

Schmidler, S. C.

N. Zheng, S. C. Schmidler, D. Marks, and D. Brady, “Computer experiment and global optimization of layered monocentric lens systems,” Optik 123, 1249–1259 (2012).
[CrossRef]

Schuster, G.

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

Shannon, M. J.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

Shannon, R.

R. Shannon, The Art and Science of Optical Design (Cambridge University, 1997).

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 (Optical Society of America, 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 (Optical Society of America, 2011), paper JTuE2.

Son, H. S.

D. L. Marks, H. S. Son, J. Kim, and D. Brady, “Engineering a gigapixel monocentric multiscale camera,” Opt. Eng. 51, 083202 (2012).
[CrossRef]

Stack, R.

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

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 (Optical Society of America, 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]

Stamenov, I.

I. Stamenov, I. Agurok, and J. Ford, “Optimization of two-glass monocentric lenses for compact panoramic imagers: general aberration analysis and specific designs,” Appl. Opt. 51, 7648–7661 (2012).
[CrossRef]

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

I. Stamenov, I. Agurok, and J. Ford, “Capabilities of monocentric objective lenses,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper ITu3E.4.

Tremblay, E.

J. E. Ford and E. Tremblay, “Extreme form factor imagers,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 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 (Optical Society of America, 2011), paper JTuE2.

Van Loan, C.

G. Golub and C. Van Loan, Matrix Computations (John Hopkins, 1989).

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. patent3,166,623 (19January1965).

Wilson, B. A.

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics7th ed. (Cambridge University, 1999).

Wright, M.

P. Gill, W. Murray, and M. Wright, Practical Optimization (Academic, 1981).

Zheng, N.

N. Zheng, S. C. Schmidler, D. Marks, and D. Brady, “Computer experiment and global optimization of layered monocentric lens systems,” Optik 123, 1249–1259 (2012).
[CrossRef]

Appl. Opt.

Nature

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. Eng.

D. L. Marks, H. S. Son, J. Kim, and D. Brady, “Engineering a gigapixel monocentric multiscale camera,” Opt. Eng. 51, 083202 (2012).
[CrossRef]

Optik

N. Zheng, S. C. Schmidler, D. Marks, and D. Brady, “Computer experiment and global optimization of layered monocentric lens systems,” Optik 123, 1249–1259 (2012).
[CrossRef]

Proc. SPIE

J. F. Kordas, I. T. Lewis, B. A. Wilson, D. P. Nielsen, H. Park, R. E. Priest, R. Hills, M. J. Shannon, A. G. Ledebuhr, and L. D. Pleasance, “Star tracker stellar compass for the Clementine mission,” Proc. SPIE 2466, 70 (1995).
[CrossRef]

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

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

Other

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

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

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 (Optical Society of America, 2011), paper JTuE2.

G. Golub and C. Van Loan, Matrix Computations (John Hopkins, 1989).

R. Shannon, The Art and Science of Optical Design (Cambridge University, 1997).

http://www.andor.com/learning-academy/ccd-spectral-response-(qe)-defining-the-qe-of-a-ccd .

M. Kruger, B. Panov, B. Kulagin, G. Pogarev, Y. Kruger, and A. Levinson, “Handbook of opto-mechanics,” Moscow, 1963.

www.norlandprod.com .

M. Rusinov, Composition of Optical Systems (Mashinostroenie, 1989).

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D. Dayton, J. Gonglewsky, C. Arnauld, I. Mons, and D. Burns, SWIR Sky Glow Cloud Correlation with NIR and Visible Clouds: An Urban and Rural Comparison (AFRL, 2009).

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www.schott.com , TIE-41 Large Optical Glass Blanks, Technical information document.

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

J. Ford, I. Stamenov, S. Olivas, G. Schuster, N. Motamedi, I. Agurok, R. Stack, A. Johnson, and R. Morrison, “Fiber-coupled monocentric lens imaging,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper CW4C.2.

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

J. A. Waidelich, “Spherical lens imaging device,” U.S. patent3,166,623 (19January1965).

T. S. Axelrod, N. J. Colella, and A. G. Ledebuhr, “The wide-field-of-view camera,” in Energy and Technology Review, (Lawrence Livermore National Laboratory, 1988).

C. Akerlof, M. Fatuzzo, B. Lee, R. Bionta, A. Ledebuhr, H. Park, S. Barthelmy, T. Cline, and N. Gehrels, “Gamma-ray optical counterpart search experiment (GROCSE),” in AIP Conference Proceedings (American Institute of Physics, 1994), Vol. 307, pp. 633–637.

M. Born and E. Wolf, Principles of Optics7th ed. (Cambridge University, 1999).

I. Stamenov, I. Agurok, and J. Ford, “Capabilities of monocentric objective lenses,” in Imaging and Applied Optics, J. Christou and D. Miller, eds. OSA Technical Digest (online) (Optical Society of America, 2013), paper ITu3E.4.

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

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

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P. Gill, W. Murray, and M. Wright, Practical Optimization (Academic, 1981).

S. A. Rodionov, Computer Lens Design (Mashinostroenie, 1982).

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Figures (24)

Fig. 1.
Fig. 1.

MTF performance curves showing the limits of the globally optimized 2GS monocentric geometries. The examples are derived from an initial high-performing lens (a), which is pushed to improve spectral bandwidth (b), numerical aperture (c), or focal length (d) [using a 3× scale change to the illustration]. For each, the resolution of the two-glass structure drops well below the diffraction limit, indicating a need for greater complexity.

Fig. 2.
Fig. 2.

Monocentric lens design space showing glass only (upper half) and glass with air gap (lower half) regions divided by the seven preferred design architectures in between.

Fig. 3.
Fig. 3.

Optimization of preferred monocentric lens geometries.

Fig. 4.
Fig. 4.

New f=70mm AWARE 2 2GS candidates.

Fig. 5.
Fig. 5.

Monocentric three-glass symmetric (3GS) architecture.

Fig. 6.
Fig. 6.

Top 12 mm F/1.7 435–850 nm 3GS monocentric lens candidate (a) optimization space, (b) MTF comparison curves with top 2GS candidate, and (c) apochromatic shaped focal shift curve.

Fig. 7.
Fig. 7.

MTF performance comparison of globally optimized 2GS and 3GS monocentric lenses for extension of the original lens specifications. The plots show only on-axis MTF, to allow comparison of 2GS and 3GS architectures.

Fig. 8.
Fig. 8.

MTF performance curves of the 4GA-8 lens geometries derived from the original lens specifications through seeded Hammer optimization.

Fig. 9.
Fig. 9.

Four-glass asymmetric with air gap (4GA-8) monocentric lens architecture.

Fig. 10.
Fig. 10.

Gradient descent method applied for normal minimum and degraded minimum shape.

Fig. 11.
Fig. 11.

Optimization criterion ravine of minimums (projection onto 3D space).

Fig. 12.
Fig. 12.

Optimization procedure inside the 4GA-8 optimization space.

Fig. 13.
Fig. 13.

MTF curves for 12 mm, F/1.7, 400–1000 nm lenses obtained through seeded Hammer search and near global five-dimensional optimization (shown on layout).

Fig. 14.
Fig. 14.

Spectral response of front and back-illuminated silicon sensor.

Fig. 15.
Fig. 15.

MTF curves for 12 mm, F/1.7 lens operating with 400–1000 nm front-illuminated silicon sensor sensitivity spectrum.

Fig. 16.
Fig. 16.

MTF curves for 12 mm, F/1.7 lens operating with 435–1000 nm back-illuminated silicon sensor sensitivity spectrum.

Fig. 17.
Fig. 17.

Longitudinal aberrations of the (a) top 3GS and (b) top 4GA-8 architecture 12 mm F/1.7 monocentric lenses for 400–1000 nm spectral band.

Fig. 18.
Fig. 18.

Monocentric lens geometries optimization behavior for two different scales operating in 486–656 nm spectral range.

Fig. 19.
Fig. 19.

Monocentric objective lens performance trade-off for different scales and three spectral bands (486–656 nm, 435–850 nm, 400–1000 nm).

Fig. 20.
Fig. 20.

Underwater monocentric lens (9mm/12mm image/object space focal length, F/1.79, 380–550 nm).

Fig. 21.
Fig. 21.

Gen III Night Vision monocentric lens (16 mm focal length, F/1.2, 500–900 nm).

Fig. 22.
Fig. 22.

SWIR monocentric lens (12 mm focal length, F/1.19, 900–1500 nm).

Fig. 23.
Fig. 23.

Medium scale monocentric lens 5GA-10 diffraction limited candidate possible to fabricate (112 mm focal length, F/2.33, 486–656 nm).

Fig. 24.
Fig. 24.

Polychromatic MTF comparison of previously reported 5GA-10 optimal solution for the Gigagon 40GPix lens and a simpler 4GA-8 solution (280 mm focal length, F/2.8, 450–700 nm).

Tables (14)

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Table 1. Updated List of Top Solutions for the SCENICC F/1.7 f=12mm 470–650 nm 120° Monocentric Lensa

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Table 2. Array of Local Minimums Over the Main Ravine in 4GA-8 Optimization Space.a

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Table 3. Optical Prescription of the 400–1000 nm F/1.7 f=12mm MC Lens Example Solution A=5.63g

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Table 4. Optical Prescription of the 400–1000 nm F/1.7 f=12mm MC Lens Example Solution B=5.71g

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Table 5. Optical Prescription of the 400–1000 nm F/1.7 f=12mm MC Lens Example Solution C=5.72g

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Table 6. Families of Solutions for F/1.7 12 mm Monocentric 4GA-8 400–1000 nm Lens Obtained Through Near-Global Search

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Table 7. Optical Prescription of the 400–1000 nm F/1.7 f=12mm Monocentric Near Global Solution

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Table 8. Optical Prescription of the 400–1000 nm F/1.7 f=12mm Monocentric Lens Operating with Front-Illuminated Silicon Sensor

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Table 9. Optical Prescription of the 435–1000 nm F/1.7 f=12mm Monocentric Lens Operating with Back-Illuminated Silicon Sensor

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Table 10. Optical Prescription of the Water Immersed Monocentric Lens

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Table 11. Optical Prescription of the Night Vision Monocentric Lens

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Table 12. Optical Prescription of the Short-Wave Infrared Monocentric Lens

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Table 13. Optical Prescription of the f=112mm Monocentric Lens Candidate

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Table 14. Optical Prescription of the Optimal 40GPix Monocentric 4GA-8 Lens

Equations (11)

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

Q=m=15{i=13Abs(ΔS(hi,λm))+j=13kjAbs[ΔS(hj,λm)ΔS(hk,λm)]},
(ΔΦ)2=15i=15{[C20new(λi)]23+[C40(λi)]25+[C60(λi)]27+[C80(λi)]29+[C100(λi)]211}.
1f=2r1(11n2)+2r2(1n21n3)+2r3(1n31n4)
OE¯=hsin{2[arcsin(hr1)arcsin(hr1n2)+arcsin(hr2n2)arcsin(hr2n3)+arcsin(hr3n3)arcsin(hr3n4)]}.
ΔS(hi)=OE¯(hi)f
Q=i=19j=18pj·Abs(ΔS(hj,λi))=i=19j=18pj·Abs(ΔS(pj·f·NA,λi)),
OG¯=h/sin{arcsin(hR1)+arcsin(hR2n2)+arcsin(hR2n4)arcsin(hR1n2)2arcsin(hR2n3)+arcsin(hR4)arcsin(hR4n4)arcsin(hR5)+arcsin(hR5n5)+arcsin(hR6)arcsin(hR6n5)}
ΔS(hi)=OG¯(hi)f,
hi=NA·f·pi,
p=[10.970.880.80.70.60.50.40.05].
C=i=19j=19[pj·ΔS(hi)λj]2+[ΔS(h9,λ1)ΔS(h9,λ9)]2+[ΔS(h3,λ1)ΔS(h3,λ9)]2+[ΔS(h1,λ1)ΔS(h1,λ9)]2,

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