Abstract

We present the range of optical architectures for imaging systems based on a single optical component, an aperture stop, and a detector. Thanks to the formalism of third-order Seidel aberrations, several strategies of simplification and miniaturization of optical systems are examined. Figures of merit are also introduced to assess the basic optical properties and performance capabilities of such systems; by this way, we show the necessary trade-off between simplicity, miniaturization, and optical performance.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
  8. 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]
  9. G. Druart, N. Guérineau, J. Taboury, S. Rommeluère, R. Haïdar, J. Primot, M. Fendler, and J. C. Cigna, “Compact infrared pinhole fisheye for wide field applications,” Appl. Opt. 48, 1104–1113 (2009).
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    [CrossRef]
  15. G. Druart, J. Taboury, N. Guérineau, R. Haïdar, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett. 33, 366–368 (2008).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  29. D. J. Brady, “Micro-optics and megapixels,” Opt. Photonics News , 17(11), 24–29 (2006).
    [CrossRef]
  30. F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, and M. Fendler, “Integration of advanced optical functions near the focal plane array: First steps towards the on-chip infrared camera,” Proc. SPIE 7787, 778706 (2010).
    [CrossRef]
  31. G. Druart, N. Guérineau, R. Haïdar, J. Primot, P. Chavel, and J. Taboury, “Nonparaxial analysis of continuous self-imaging gratings in oblique illumination,” J. Opt. Soc. Am. A 24, 3379–3387 (2007).
    [CrossRef]
  32. N. A. Ahuja and N. K. Bose, “Design of large field-of-view high-resolution miniaturized imaging system,” EURASIP J. Adv. Signal Process. 2007, 1 (2007).
    [CrossRef]
  33. L. C. Laycock and V. A. Handerek, “Multi-aperture imaging device for airborne platforms,” Proc. SPIE 6737, 673709 (2007).
    [CrossRef]
  34. F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
    [CrossRef] [PubMed]
  35. A. Papoulis, “Generalized sampling expansion,” IEEE Trans. Circuits Syst. 24, 652–654 (1977).
    [CrossRef]
  36. A. V. Kanaev, J. R. Ackerman, E. F. Fleet, and D. A. Scribner, “TOMBO sensor with scene-independent superresolution processing,” Opt. Lett. 32, 2855–2857 (2007).
    [CrossRef] [PubMed]

2010

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, and M. Fendler, “Integration of advanced optical functions near the focal plane array: First steps towards the on-chip infrared camera,” Proc. SPIE 7787, 778706 (2010).
[CrossRef]

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
[CrossRef] [PubMed]

2009

2008

2007

2006

M. W. Haney, “Performance scaling in flat imagers,” Appl. Opt. 45, 2901–2910 (2006).
[CrossRef] [PubMed]

J. W. Duparré, and F. C. Wipermann, “Micro-optical artificial compound eyes,” Bioinsp. Biomim. 1, R1–R16 (2006).
[CrossRef]

S. R. Wilk, “Ancient optics: Producing magnification without lenses,” Opt. Photonics News 17 (4), 12–13 (2006).

D. J. Brady, “Micro-optics and megapixels,” Opt. Photonics News , 17(11), 24–29 (2006).
[CrossRef]

2005

2004

2003

R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67–68, 461–472 (2003).
[CrossRef]

2001

1991

1989

1978

1977

A. Papoulis, “Generalized sampling expansion,” IEEE Trans. Circuits Syst. 24, 652–654 (1977).
[CrossRef]

Ackerman, J. R.

Ahuja, N. A.

N. A. Ahuja and N. K. Bose, “Design of large field-of-view high-resolution miniaturized imaging system,” EURASIP J. Adv. Signal Process. 2007, 1 (2007).
[CrossRef]

Andersen, G.

Barrière, F. de la

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
[CrossRef] [PubMed]

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, and M. Fendler, “Integration of advanced optical functions near the focal plane array: First steps towards the on-chip infrared camera,” Proc. SPIE 7787, 778706 (2010).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1989), p. 228.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1989), p. 468.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1989), p. 211.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1989), p. 213.

Bose, N. K.

N. A. Ahuja and N. K. Bose, “Design of large field-of-view high-resolution miniaturized imaging system,” EURASIP J. Adv. Signal Process. 2007, 1 (2007).
[CrossRef]

Brady, D. J.

D. J. Brady, “Micro-optics and megapixels,” Opt. Photonics News , 17(11), 24–29 (2006).
[CrossRef]

Bräuer, A.

Cannon, T. M.

Catrysse, P. B.

Chavel, P.

Cigna, J. C.

Dannberg, P.

Davidson, N.

Deschamps, J.

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, M. Tauvy, S. Thétas, S. Rommeluère, J. Primot, J. Deschamps, and E. Lambert, “MULTICAM: A miniature cryogenic camera for infrared detection,” Proc. SPIE 6992, 699215 (2008).

Dinyari, R.

Druart, G.

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
[CrossRef] [PubMed]

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, and M. Fendler, “Integration of advanced optical functions near the focal plane array: First steps towards the on-chip infrared camera,” Proc. SPIE 7787, 778706 (2010).
[CrossRef]

G. Druart, N. Guérineau, R. Haïdar, S. Thétas, J. Taboury, S. Rommeluère, J. Primot, and M. Fendler, “Demonstration of an infrared microcamera inspired by Xenos Peckii vision,” Appl. Opt. 48, 3368–3374 (2009).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, J. Taboury, S. Rommeluère, R. Haïdar, J. Primot, M. Fendler, and J. C. Cigna, “Compact infrared pinhole fisheye for wide field applications,” Appl. Opt. 48, 1104–1113 (2009).
[CrossRef]

G. Druart, J. Taboury, N. Guérineau, R. Haïdar, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett. 33, 366–368 (2008).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, M. Tauvy, S. Thétas, S. Rommeluère, J. Primot, J. Deschamps, and E. Lambert, “MULTICAM: A miniature cryogenic camera for infrared detection,” Proc. SPIE 6992, 699215 (2008).

G. Druart, N. Guérineau, R. Haïdar, J. Primot, A. Kattnig, and J. Taboury, “Image formation by use of continuously self-imaging gratings and diffractive axicons,” Proc. SPIE 6712, 671208 (2007).
[CrossRef]

G. Druart, N. Guérineau, R. Haïdar, J. Primot, P. Chavel, and J. Taboury, “Nonparaxial analysis of continuous self-imaging gratings in oblique illumination,” J. Opt. Soc. Am. A 24, 3379–3387 (2007).
[CrossRef]

Duparré, J.

Duparré, J. W.

J. W. Duparré, and F. C. Wipermann, “Micro-optical artificial compound eyes,” Bioinsp. Biomim. 1, R1–R16 (2006).
[CrossRef]

Eisner, M.

Fendler, M.

Fenimore, E. E.

Fleet, E. F.

Ford, J. E.

Friesem, A. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts and Company, 2005), p. 107.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts and Company, 2005), p. 146.

Gottesman, S. R.

Guérineau, N.

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, and M. Fendler, “Integration of advanced optical functions near the focal plane array: First steps towards the on-chip infrared camera,” Proc. SPIE 7787, 778706 (2010).
[CrossRef]

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, S. Thétas, J. Taboury, S. Rommeluère, J. Primot, and M. Fendler, “Demonstration of an infrared microcamera inspired by Xenos Peckii vision,” Appl. Opt. 48, 3368–3374 (2009).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, J. Taboury, S. Rommeluère, R. Haïdar, J. Primot, M. Fendler, and J. C. Cigna, “Compact infrared pinhole fisheye for wide field applications,” Appl. Opt. 48, 1104–1113 (2009).
[CrossRef]

G. Druart, J. Taboury, N. Guérineau, R. Haïdar, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett. 33, 366–368 (2008).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, M. Tauvy, S. Thétas, S. Rommeluère, J. Primot, J. Deschamps, and E. Lambert, “MULTICAM: A miniature cryogenic camera for infrared detection,” Proc. SPIE 6992, 699215 (2008).

G. Druart, N. Guérineau, R. Haïdar, J. Primot, A. Kattnig, and J. Taboury, “Image formation by use of continuously self-imaging gratings and diffractive axicons,” Proc. SPIE 6712, 671208 (2007).
[CrossRef]

G. Druart, N. Guérineau, R. Haïdar, J. Primot, P. Chavel, and J. Taboury, “Nonparaxial analysis of continuous self-imaging gratings in oblique illumination,” J. Opt. Soc. Am. A 24, 3379–3387 (2007).
[CrossRef]

Haïdar, R.

Handerek, V. A.

L. C. Laycock and V. A. Handerek, “Multi-aperture imaging device for airborne platforms,” Proc. SPIE 6737, 673709 (2007).
[CrossRef]

Haney, M. W.

Hasman, E.

Huang, K.

Ichioka, Y.

Ishida, K.

Kanaev, A. V.

Karp, J. H.

Kattnig, A.

G. Druart, J. Taboury, N. Guérineau, R. Haïdar, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett. 33, 366–368 (2008).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, J. Primot, A. Kattnig, and J. Taboury, “Image formation by use of continuously self-imaging gratings and diffractive axicons,” Proc. SPIE 6712, 671208 (2007).
[CrossRef]

Kolodziejczyk, A.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. (Bellingham, Wash.) 44, 058001 (2005).
[CrossRef]

Kondou, N.

Kumagai, T.

Lambert, E.

G. Druart, N. Guérineau, R. Haïdar, M. Tauvy, S. Thétas, S. Rommeluère, J. Primot, J. Deschamps, and E. Lambert, “MULTICAM: A miniature cryogenic camera for infrared detection,” Proc. SPIE 6992, 699215 (2008).

Laycock, L. C.

L. C. Laycock and V. A. Handerek, “Multi-aperture imaging device for airborne platforms,” Proc. SPIE 6737, 673709 (2007).
[CrossRef]

Lohmann, A. W.

Makowski, M.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. (Bellingham, Wash.) 44, 058001 (2005).
[CrossRef]

Matthes, A.

Mikula, G.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. (Bellingham, Wash.) 44, 058001 (2005).
[CrossRef]

Miyatake, S.

Miyazaki, D.

Morimoto, T.

Morrison, R. L.

Papoulis, A.

A. Papoulis, “Generalized sampling expansion,” IEEE Trans. Circuits Syst. 24, 652–654 (1977).
[CrossRef]

Peumans, P.

Primot, J.

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, S. Thétas, J. Taboury, S. Rommeluère, J. Primot, and M. Fendler, “Demonstration of an infrared microcamera inspired by Xenos Peckii vision,” Appl. Opt. 48, 3368–3374 (2009).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, J. Taboury, S. Rommeluère, R. Haïdar, J. Primot, M. Fendler, and J. C. Cigna, “Compact infrared pinhole fisheye for wide field applications,” Appl. Opt. 48, 1104–1113 (2009).
[CrossRef]

G. Druart, J. Taboury, N. Guérineau, R. Haïdar, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett. 33, 366–368 (2008).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, M. Tauvy, S. Thétas, S. Rommeluère, J. Primot, J. Deschamps, and E. Lambert, “MULTICAM: A miniature cryogenic camera for infrared detection,” Proc. SPIE 6992, 699215 (2008).

G. Druart, N. Guérineau, R. Haïdar, J. Primot, A. Kattnig, and J. Taboury, “Image formation by use of continuously self-imaging gratings and diffractive axicons,” Proc. SPIE 6712, 671208 (2007).
[CrossRef]

G. Druart, N. Guérineau, R. Haïdar, J. Primot, P. Chavel, and J. Taboury, “Nonparaxial analysis of continuous self-imaging gratings in oblique illumination,” J. Opt. Soc. Am. A 24, 3379–3387 (2007).
[CrossRef]

Prokopowicz, C.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. (Bellingham, Wash.) 44, 058001 (2005).
[CrossRef]

Pshenay-Severin, E.

Rim, S. B.

Rommeluère, S.

Sauer, H.

Scharf, T.

Schreiber, P.

Scribner, D. A.

Stack, R. A.

Sypek, M.

G. Mikula, A. Kolodziejczyk, M. Makowski, C. Prokopowicz, and M. Sypek, “Diffractive elements for imaging with extended depth of focus,” Opt. Eng. (Bellingham, Wash.) 44, 058001 (2005).
[CrossRef]

Taboury, J.

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, and M. Fendler, “Integration of advanced optical functions near the focal plane array: First steps towards the on-chip infrared camera,” Proc. SPIE 7787, 778706 (2010).
[CrossRef]

F. de la Barrière, G. Druart, N. Guérineau, J. Taboury, J. Primot, and J. Deschamps, “Modulation transfer function measurement of a multichannel optical system,” Appl. Opt. 49, 2879–2890 (2010).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, S. Thétas, J. Taboury, S. Rommeluère, J. Primot, and M. Fendler, “Demonstration of an infrared microcamera inspired by Xenos Peckii vision,” Appl. Opt. 48, 3368–3374 (2009).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, J. Taboury, S. Rommeluère, R. Haïdar, J. Primot, M. Fendler, and J. C. Cigna, “Compact infrared pinhole fisheye for wide field applications,” Appl. Opt. 48, 1104–1113 (2009).
[CrossRef]

G. Druart, J. Taboury, N. Guérineau, R. Haïdar, H. Sauer, A. Kattnig, and J. Primot, “Demonstration of image-zooming capability for diffractive axicons,” Opt. Lett. 33, 366–368 (2008).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, J. Primot, P. Chavel, and J. Taboury, “Nonparaxial analysis of continuous self-imaging gratings in oblique illumination,” J. Opt. Soc. Am. A 24, 3379–3387 (2007).
[CrossRef]

G. Druart, N. Guérineau, R. Haïdar, J. Primot, A. Kattnig, and J. Taboury, “Image formation by use of continuously self-imaging gratings and diffractive axicons,” Proc. SPIE 6712, 671208 (2007).
[CrossRef]

Tanida, J.

Tauvy, M.

G. Druart, N. Guérineau, R. Haïdar, M. Tauvy, S. Thétas, S. Rommeluère, J. Primot, J. Deschamps, and E. Lambert, “MULTICAM: A miniature cryogenic camera for infrared detection,” Proc. SPIE 6992, 699215 (2008).

Thétas, S.

G. Druart, N. Guérineau, R. Haïdar, S. Thétas, J. Taboury, S. Rommeluère, J. Primot, and M. Fendler, “Demonstration of an infrared microcamera inspired by Xenos Peckii vision,” Appl. Opt. 48, 3368–3374 (2009).
[CrossRef] [PubMed]

G. Druart, N. Guérineau, R. Haïdar, M. Tauvy, S. Thétas, S. Rommeluère, J. Primot, J. Deschamps, and E. Lambert, “MULTICAM: A miniature cryogenic camera for infrared detection,” Proc. SPIE 6992, 699215 (2008).

Tremblay, E. J.

Tullson, D.

Tünnermann, A.

Vo¨lkel, R.

Völkel, R.

R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67–68, 461–472 (2003).
[CrossRef]

Weible, K. J.

R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67–68, 461–472 (2003).
[CrossRef]

Wilk, S. R.

S. R. Wilk, “Ancient optics: Producing magnification without lenses,” Opt. Photonics News 17 (4), 12–13 (2006).

Wipermann, F. C.

J. W. Duparré, and F. C. Wipermann, “Micro-optical artificial compound eyes,” Bioinsp. Biomim. 1, R1–R16 (2006).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1989), p. 213.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1989), p. 211.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1989), p. 468.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1989), p. 228.

Yamada, K.

Appl. Opt.

E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Appl. Opt. 17, 337–347 (1978).
[CrossRef] [PubMed]

S. R. Gottesman and E. E. Fenimore, “New family of binary arrays for coded aperture imaging,” Appl. Opt. 28, 4344–4352 (1989).
[CrossRef] [PubMed]

A. W. Lohmann, “Scaling laws for lens systems,” Appl. Opt. 28, 4996–4998 (1989).
[CrossRef] [PubMed]

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]

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Figures (6)

Fig. 1
Fig. 1

Illustration of the pupil coordinates r and φ and of the image plane coordinate r .

Fig. 2
Fig. 2

Illustration of a thin lens, an aperture stop (which is the entrance pupil), and a detector. t is the distance between the entrance pupil and the lens.

Fig. 3
Fig. 3

Illustration of a multichannel optical system (a) with curved components, (b) with planar components.

Fig. 4
Fig. 4

Illustration of an apposition compound eye (which corresponds to the eye of the fly), with a curved microlens array and a curved retina in a convex shape (see [7]).

Fig. 5
Fig. 5

(a) Illustration of the miniaturization of an optical system by decreasing its focal length f, while maintaining a constant f-number and a constant field of view, and illustration of the decrease of the number of resolved points. (b) Method to compensate for the loss of resolved points by replicating an optical miniaturized system.

Fig. 6
Fig. 6

Illustration of the different strategies used to design a simple imaging system with a minimal number of optical elements.

Equations (29)

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p s ( r , φ , r ) = p s 0 ( r , φ ) exp [ i 2 Π λ W ( r , φ , r ) ] .
W = W ( 0 ) + W ( 4 ) + W ( 6 ) + W ( 8 ) + .
W ( 4 ) ( r , φ , r ) = 1 4 B r 4 + F r 3 r cos φ C r 2 r 2 cos 2 φ 1 2 D r 2 r 2 + E r r 3 cos φ ,
P = 1 f = ( n 1 ) ( C 1 C 2 ) ,
γ = 1 2 ( C 1 + C 2 ) .
B = U ,
F = t U + V ,
C = t 2 U 2 t V + P 2 ,
D = t 2 U 2 t V + n + 1 2 n P ,
E = t 3 U + 3 t 2 V t 3 n + 1 2 n P ,
U = β 2 + n ( 4 n 1 ) 8 ( n 1 ) 2 ( n + 2 ) P 3 + P 2 n ( n + 2 ) [ ( n + 2 ) γ ( n + 1 ) P ] 2 ,
V = P 2 n [ ( n + 1 ) γ ( n + 1 2 ) P ] .
W max ( 4 ) ( f , # , FOV ) = B 2 6 f 4 # 4 + F 2 4 FOV f 4 # 3 C 2 4 FOV 2 f 4 # 2 D 2 5 FOV 2 f 4 # 2 + E 2 4 FOV 3 f 4 # .
W max ( 4 ) ( n , γ , f , # , FOV ) = 1 2 9 n ( 4 n 1 ) ( n 1 ) 2 ( n + 2 ) f # 4 1 2 7 ( n + 2 ) f 3 # 4 [ ( n + 2 ) γ 1 f ( n + 1 ) ] 2 + n + 1 2 5 n γ f 3 FOV # 3 2 n + 1 2 6 n f 2 FOV # 3 1 2 5 f 3 FOV 2 # 2 1 2 6 n + 1 n f 3 FOV 2 # 2 .
IFOV = λ # f .
N b = ( FOV IFOV ) 2 .
N b = f 2 FOV 2 λ 2 # 2 .
G = Π t pix 2 4 # 2 .
G = 1.17 λ 2 .
γ min = 1 f n + 1 n + 2 .
γ ( coma = 0 ) = 1 f 2 n + 1 2 ( n + 1 ) .
# curved = 1 θ + FOV e ,
# planar = 1 FOV e ,
FOV e t det f ,
θ t det e .
# curved = 1 2 FOV e ,
# curved = # planar 2 .
F = ( t pix p s ) 2 .
N ch = 2 F .

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