Abstract

While lenses of aperture less than 1000λ frequently form images with pixel counts approaching the space-bandwidth limit, only heroic designs approach the theoretical information capacity at larger scales. We propose to use the field processing capabilities of small-scale secondary lens arrays to correct aberrations due to larger scale objective lenses, with an ultimate goal of achieving diffraction-limited imaging for apertures greater than 10,000λ. We present an example optical design using an 8 mm entrance pupil capable of resolving 20 megapixels.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. T. di Francia, "Degrees of freedom of an image," J. Opt. Soc. Am. 59, 799-804 (1969).
    [CrossRef]
  2. J. Kopf, M. Uyttendaele, O. Deussen, and M. F. Cohen, "Capturing and viewing gigapixel images," ACM Trans. Graphics 26, 93 (2007).
    [CrossRef]
  3. A. W. Lohmann, "Scaling laws for lens systems," Appl. Opt. 28, 4996-4998 (1989).
    [CrossRef] [PubMed]
  4. T. Matsuyama, Y. Ohmura, and D. M. Williamson, "The lithographic lens: its history and evolution," in Optical Microlithography XIX, D. G. Flagello, ed., vol. 6154 of Proc. SPIE (2006).
  5. R. Völkel, M. Eisner, and K. J. Weible, "Miniaturized imaging systems," Microelectron. Eng. 67-68, 461-472 (2003).
  6. Y. Dagan, "Wafer-level optics enables low cost camera phones," in Integrated Optics: Devices, Materials, and Technologies XIII, J.-E. Broquin and C. M. Greiner, eds., vol. 7218 of Proc. SPIE (2009).
  7. J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
    [CrossRef]
  8. M. Shankar, R. Willett, N. Pitsianis, T. Schulz, R. Gibbons, R. T. Kolste, J. Carriere, C. Chen, D. Prather, and D. Brady, "Thin infrared imaging systems through multichannel sampling," Appl. Opt. 47, B1-B10 (2008).
    [CrossRef] [PubMed]
  9. T. Mirani, D. Rajan, M. P. Christensen, S. C. Douglas, and S. L. Wood, "Computational imaging systems: joint design and end-to-end optimality," Appl. Opt. 47, B86-B103 (2008).
    [CrossRef] [PubMed]
  10. K. Choi and T. J. Schulz, "Signal-processing approaches for image-resolution restoration for TOMBO imagery," Appl. Opt. 47, B104-B116 (2008).
    [CrossRef] [PubMed]
  11. A. V. Kanaev, D. A. Scribner, J. R. Ackerman, and E. F. Fleet, "Analysis and application of multiframe superresolution processing for conventional imaging systems and lenslet arrays," Appl. Opt. 46, 4320-4328 (2007).
    [CrossRef] [PubMed]
  12. A. D. Portnoy, N. P. Pitsianis, X. Sun, and D. J. Brady, "Multichannel sampling schemes for optical imaging systems," Appl. Opt. 47, B76-B85 (2008).
    [CrossRef] [PubMed]
  13. R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, "Three-dimensional information acquisition using a compound imaging system," Opt. Rev. 14, 347-350 (2007).
    [CrossRef]
  14. E. H. Adelson and J. Y. Wang, "Single lens stereo with a plenoptic camera," IEEE Trans. Pattern Anal. Mach. Intel. 14, 99-106 (1992).
    [CrossRef]
  15. M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, "Light field microscopy," ACM Trans. Graphics 25, 924-934 (2006).
    [CrossRef]
  16. H.-J. Lee, D.-H. Shin, H. Yoo, J.-J. Lee, and E.-S. Kim, "Computational integral imaging reconstruction scheme of far 3D objects by additional use of an imaging lens," Opt. Comm. 281, 2026-2032 (2007).
    [CrossRef]
  17. J. Duparré, P. Schreiber, A. Matthes, E. Pshenay-Severin, A. Bräuer, A. Tünnermann, R. Völkel, M. Eisner, and T. Scharf, "Microoptical telescope compound eye," Opt. Express 13, 889-903 (2005).
    [CrossRef] [PubMed]
  18. J. A. Cox and B. S. Fritz, "Variable focal length micro lens array field curvature corrector," (2003). US Patent 6556349.
  19. R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
    [CrossRef]
  20. http://www.gmto.org/codrfolder/GMT-ID-01467-Chapter 6 Optics.pdf/.
  21. http://www2.keck.hawaii.edu/inst/hires/.
  22. http://www.zemax.com.
  23. M. V. R. K. Murty, "On the theoretical limit of resolution," J. Opt. Soc. Am. 47, 667-668 (1957).
    [CrossRef]

2008 (4)

2007 (4)

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, "Three-dimensional information acquisition using a compound imaging system," Opt. Rev. 14, 347-350 (2007).
[CrossRef]

H.-J. Lee, D.-H. Shin, H. Yoo, J.-J. Lee, and E.-S. Kim, "Computational integral imaging reconstruction scheme of far 3D objects by additional use of an imaging lens," Opt. Comm. 281, 2026-2032 (2007).
[CrossRef]

A. V. Kanaev, D. A. Scribner, J. R. Ackerman, and E. F. Fleet, "Analysis and application of multiframe superresolution processing for conventional imaging systems and lenslet arrays," Appl. Opt. 46, 4320-4328 (2007).
[CrossRef] [PubMed]

J. Kopf, M. Uyttendaele, O. Deussen, and M. F. Cohen, "Capturing and viewing gigapixel images," ACM Trans. Graphics 26, 93 (2007).
[CrossRef]

2006 (1)

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, "Light field microscopy," ACM Trans. Graphics 25, 924-934 (2006).
[CrossRef]

2005 (1)

2003 (1)

R. Völkel, M. Eisner, and K. J. Weible, "Miniaturized imaging systems," Microelectron. Eng. 67-68, 461-472 (2003).

2001 (2)

J. Tanida, T. Kumagai, K. Yamada, S. Miyatake, K. Ishida, T. Morimoto, N. Kondou, D. Miyazaki, and Y. Ichioka, "Thin observation module by bound optics (TOMBO): concept and experimental verification," Appl. Opt. 40, 1806-1813 (2001).
[CrossRef]

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

1992 (1)

E. H. Adelson and J. Y. Wang, "Single lens stereo with a plenoptic camera," IEEE Trans. Pattern Anal. Mach. Intel. 14, 99-106 (1992).
[CrossRef]

1989 (1)

1969 (1)

1957 (1)

Ackerman, J. R.

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, "Light field microscopy," ACM Trans. Graphics 25, 924-934 (2006).
[CrossRef]

Adelson, E. H.

E. H. Adelson and J. Y. Wang, "Single lens stereo with a plenoptic camera," IEEE Trans. Pattern Anal. Mach. Intel. 14, 99-106 (1992).
[CrossRef]

Allington-Smith, J. R.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Bacon, R.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Brady, D.

Brady, D. J.

Bräuer, A.

Bureau, M.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Carollo, C. M.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Carriere, J.

Chen, C.

Choi, K.

Christensen, M. P.

Cohen, M. F.

J. Kopf, M. Uyttendaele, O. Deussen, and M. F. Cohen, "Capturing and viewing gigapixel images," ACM Trans. Graphics 26, 93 (2007).
[CrossRef]

Copin, P. Y.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Davies, R. L.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

de Zeeuw, P. T.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Deussen, O.

J. Kopf, M. Uyttendaele, O. Deussen, and M. F. Cohen, "Capturing and viewing gigapixel images," ACM Trans. Graphics 26, 93 (2007).
[CrossRef]

di Francia, G. T.

Douglas, S. C.

Duparré, J.

Eisner, M.

Emsellem, E.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Fleet, E. F.

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, "Light field microscopy," ACM Trans. Graphics 25, 924-934 (2006).
[CrossRef]

Gibbons, R.

Horisaki, R.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, "Three-dimensional information acquisition using a compound imaging system," Opt. Rev. 14, 347-350 (2007).
[CrossRef]

Horowitz, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, "Light field microscopy," ACM Trans. Graphics 25, 924-934 (2006).
[CrossRef]

Ichioka, Y.

Irie, S.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, "Three-dimensional information acquisition using a compound imaging system," Opt. Rev. 14, 347-350 (2007).
[CrossRef]

Ishida, K.

Kanaev, A. V.

Kim, E.-S.

H.-J. Lee, D.-H. Shin, H. Yoo, J.-J. Lee, and E.-S. Kim, "Computational integral imaging reconstruction scheme of far 3D objects by additional use of an imaging lens," Opt. Comm. 281, 2026-2032 (2007).
[CrossRef]

Kolste, R. T.

Kondou, N.

Kopf, J.

J. Kopf, M. Uyttendaele, O. Deussen, and M. F. Cohen, "Capturing and viewing gigapixel images," ACM Trans. Graphics 26, 93 (2007).
[CrossRef]

Kumagai, T.

Kuntschner, H.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Lee, H.-J.

H.-J. Lee, D.-H. Shin, H. Yoo, J.-J. Lee, and E.-S. Kim, "Computational integral imaging reconstruction scheme of far 3D objects by additional use of an imaging lens," Opt. Comm. 281, 2026-2032 (2007).
[CrossRef]

Lee, J.-J.

H.-J. Lee, D.-H. Shin, H. Yoo, J.-J. Lee, and E.-S. Kim, "Computational integral imaging reconstruction scheme of far 3D objects by additional use of an imaging lens," Opt. Comm. 281, 2026-2032 (2007).
[CrossRef]

Levoy, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, "Light field microscopy," ACM Trans. Graphics 25, 924-934 (2006).
[CrossRef]

Lohmann, A. W.

Matthes, A.

Miller, B. W.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Mirani, T.

Miyatake, S.

Miyazaki, D.

Monnet, G.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Morimoto, T.

Murty, M. V. R. K.

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, "Light field microscopy," ACM Trans. Graphics 25, 924-934 (2006).
[CrossRef]

Ogura, Y.

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, "Three-dimensional information acquisition using a compound imaging system," Opt. Rev. 14, 347-350 (2007).
[CrossRef]

Peletier, R. F.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Pitsianis, N.

Pitsianis, N. P.

Portnoy, A. D.

Prather, D.

Pshenay-Severin, E.

Rajan, D.

Scharf, T.

Schreiber, P.

Schulz, T.

Schulz, T. J.

Scribner, D. A.

Shankar, M.

Shin, D.-H.

H.-J. Lee, D.-H. Shin, H. Yoo, J.-J. Lee, and E.-S. Kim, "Computational integral imaging reconstruction scheme of far 3D objects by additional use of an imaging lens," Opt. Comm. 281, 2026-2032 (2007).
[CrossRef]

Sun, X.

Tanida, J.

Tünnermann, A.

Uyttendaele, M.

J. Kopf, M. Uyttendaele, O. Deussen, and M. F. Cohen, "Capturing and viewing gigapixel images," ACM Trans. Graphics 26, 93 (2007).
[CrossRef]

Verolme, E. K.

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Völkel, R.

Wang, J. Y.

E. H. Adelson and J. Y. Wang, "Single lens stereo with a plenoptic camera," IEEE Trans. Pattern Anal. Mach. Intel. 14, 99-106 (1992).
[CrossRef]

Weible, K. J.

R. Völkel, M. Eisner, and K. J. Weible, "Miniaturized imaging systems," Microelectron. Eng. 67-68, 461-472 (2003).

Willett, R.

Wood, S. L.

Yamada, K.

Yoo, H.

H.-J. Lee, D.-H. Shin, H. Yoo, J.-J. Lee, and E.-S. Kim, "Computational integral imaging reconstruction scheme of far 3D objects by additional use of an imaging lens," Opt. Comm. 281, 2026-2032 (2007).
[CrossRef]

ACM Trans. Graphics (2)

J. Kopf, M. Uyttendaele, O. Deussen, and M. F. Cohen, "Capturing and viewing gigapixel images," ACM Trans. Graphics 26, 93 (2007).
[CrossRef]

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, "Light field microscopy," ACM Trans. Graphics 25, 924-934 (2006).
[CrossRef]

Appl. Opt. (7)

IEEE Trans. Pattern Anal. Mach. Intel. (1)

E. H. Adelson and J. Y. Wang, "Single lens stereo with a plenoptic camera," IEEE Trans. Pattern Anal. Mach. Intel. 14, 99-106 (1992).
[CrossRef]

J. Opt. Soc. Am. (2)

Microelectron. Eng. (1)

R. Völkel, M. Eisner, and K. J. Weible, "Miniaturized imaging systems," Microelectron. Eng. 67-68, 461-472 (2003).

Monthly Notices of the Royal Astronomical Society (1)

R. Bacon, P. Y. Copin, G. Monnet, B. W. Miller, J. R. Allington-Smith, M. Bureau, C. M. Carollo, R. L. Davies, E. Emsellem, H. Kuntschner, R. F. Peletier, E. K. Verolme, and P. T. de Zeeuw, "The SAURON project—I. The panoramic integral-field spectrograph," Monthly Notices of the Royal Astronomical Society 326, 23-35 (2001).
[CrossRef]

Opt. Comm. (1)

H.-J. Lee, D.-H. Shin, H. Yoo, J.-J. Lee, and E.-S. Kim, "Computational integral imaging reconstruction scheme of far 3D objects by additional use of an imaging lens," Opt. Comm. 281, 2026-2032 (2007).
[CrossRef]

Opt. Express (1)

Opt. Rev. (1)

R. Horisaki, S. Irie, Y. Ogura, and J. Tanida, "Three-dimensional information acquisition using a compound imaging system," Opt. Rev. 14, 347-350 (2007).
[CrossRef]

Other (6)

Y. Dagan, "Wafer-level optics enables low cost camera phones," in Integrated Optics: Devices, Materials, and Technologies XIII, J.-E. Broquin and C. M. Greiner, eds., vol. 7218 of Proc. SPIE (2009).

J. A. Cox and B. S. Fritz, "Variable focal length micro lens array field curvature corrector," (2003). US Patent 6556349.

T. Matsuyama, Y. Ohmura, and D. M. Williamson, "The lithographic lens: its history and evolution," in Optical Microlithography XIX, D. G. Flagello, ed., vol. 6154 of Proc. SPIE (2006).

http://www.gmto.org/codrfolder/GMT-ID-01467-Chapter 6 Optics.pdf/.

http://www2.keck.hawaii.edu/inst/hires/.

http://www.zemax.com.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1.

The basic layout and example raw measurements from the three imager types: (a) conventional, (b) 3×3 multiaperture, and (c) 5×5 two-level multiscale.

Fig. 2.
Fig. 2.

An example three-level multiscale imager design.

Fig. 3.
Fig. 3.

Ray tracing for a simple lens, and the corresponding spot diagrams for the image evaluated at three field angles. The RMS spotsizes (in units of microns) are given below each diagram.

Fig. 4.
Fig. 4.

Information efficiency γ vs. scale M for ξ1/(1.22λ f #)=0,0.25,0.5. While the information efficiency of an unaberrated system is scale-invariant, the aberrated systems’ efficiency declines sharply with M above the default scale (M=1).

Fig. 5.
Fig. 5.

F-number scaling for (1) photographic cameras, (2) the giant Magellan telescope [20], (3) the Keck telescope (using the HIRES instrument) [21], (4) 1988 VLSI lithography lens, (5) 2004 lithography lens, (6) aerial photography lens, (7) 10×microscope objective, (8) 60×microscope objective. Lenses lying well above the Lohmann line indicate that other design tradeoffs have been made, either in system complexity or reduced field of view.

Fig. 6.
Fig. 6.

A wavefront having 10λ of field curvature (FC) aberration is shown at left. For a processor consisting of a 3×3 lenslet array, the aberration expressed locally across each lenslet is shown on the right hand side: the off-axis lenslets see a large defocus (4.9λ) and linear variation in defocus across the field (4.6λ), but only a small conventional field curvature (0.7λ).

Fig. 7.
Fig. 7.

(a) An f/8 objective lens, used with (b) a spherical focal surface, and (c) its corresponding planar and (d) curved multiscale designs. The entrance pupil diameter for each design is 8 mm. In (c) and (d), only those lenslets mapping to positive field angles in the meridional plane are shown for clarity, and each lenslet is labeled with the field angle of its corresponding chief ray. In (c) rays from three field angles are shown for each lenslet, whereas in (d) only the chief ray for each lenslet is drawn for clarity. The locally linear multiscale design is depicted with a series of small detector arrays placed near the focal sphere in (d).

Fig. 8.
Fig. 8.

The “subfield” of a given lenslet, where the central point is the lenslet chief ray, and the 3×3 Cartesian grid of distributed points indicate the field angles on which the merit function is defined.

Fig. 9.
Fig. 9.

A closeup of three field angles (32.5°±1.25°) incident on the 10th lenslet of the curved multiscale design. The tangential, medial, and sagittal focal surfaces are shown together with the ideal location of a local subimage (where one could place a small detector array). Only rays in the meridional plane are shown here.

Fig. 10.
Fig. 10.

The RMS geometric spotsize of each design as a function of field angle, sampled every 0.25°. The five designs compared are: the conventional lens with (“conv”) planar or (“conv. sphere”) spherical focal surface; and the multiscale designs using (“multi-local”) only a series of small detector arrays placed in 3D, (“multi-planar”) a planar arrangement processor array, and (“multi-sphere”) a curved focal surface arrangement. “Multi-local” refers to the technique of tiling a series of small detector arrays along the focal surface.

Fig. 11.
Fig. 11.

The estimated number N of resolvable spots for each design per unit field angle.

Tables (1)

Tables Icon

Table 1. Shannon number (in megapixels) as a function of FOV and aperture.

Equations (13)

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

S=π(A2)2π[2λsin(FOV2)]2=π2A2λ2sin2(FOV2).
Nmax=0.67A2λ2tan2(FOV2)
γ=Nλ20.67A2tan2(FOV2)
NM2D124[32λ2f#2+M2ξ12],
γ=11+M2(ξ11.22λf#)2.
W(H,ρ,ϕ)=W040ρ4+W131Hρ3cosϕ+W222H2ρ2cos2ϕ+W220H2cos2ϕ+W311H3ρcosϕ,
W(HHn,ρ,ϕ)=W040ρ4+W131(HHn)ρcosϕ+W222(HHn)2ρ2cos2ϕ
+W220(HHn)2ρ2+W311(HHn)3ρcosϕ
=[W040ρ4sphericalaberration]
+[W131Hnρ3cosϕconstantcoma+W131Hρ3cosϕlinearcoma]
+[W222Hn2ρ2cos2ϕconstantastigmatism2W222HHnρ2cos2ϕlinearastigmatism+W222H2ρ2cos2ϕquadraticastigmatism]
+[W220Hn2ρ2defocus2W220HHnρ2lineardefocus+W220H2ρ2quadraticdefocus(i.e.FC)]
+[W311Hn3ρcosϕfielddisplacement+3W311HHn2ρcosϕtilt(i.e.magnificationerror)3W311H2Hnρcosϕquadraticdistortion+W311H3ρcosϕcubicdistortion]

Metrics