Abstract

We examine the space-bandwidth product of wide field-of-view imaging systems as the systems scale in size. Our analysis is based on one conducted to examine the behavior of a plano-convex lens imaging onto a flat focal geometry. We extend this to consider systems with monocentric lenses and curved focal geometries. As a means to understand system cost, and not just performance, we also assess the volume and mass associated with these systems. Our analysis indicates monocentric lenses imaging onto a curved detector outperform other systems for the same design constraints but do so at a cost in lens weight.

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References

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    [CrossRef]
  5. H.-C. Jin, J. R. Abelson, M. K. Erhardt, and R. G. Nuzzo, “Soft lithographic fabrication of an image sensor array on a curved substrate,” J. Vac. Sci. Technol. B 22, 2548–2551 (2004).
    [CrossRef]
  6. H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
    [CrossRef]
  7. O. Iwert and B. Delabre, “The challenge of highly curved monolithic imaging detectors,” Proc. SPIE 7742, 774227 (2010).
    [CrossRef]
  8. http://www.darpa.mil/Our_Work/MTO/Programs/Hemispherical_Array_Detector_for_Imaging_(HARDI).aspx.
  9. D. L. Marks and D. J. Brady, “Gigagon: A monocentric lens design imaging 40 gigapixels,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuC2.
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    [CrossRef]
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    [CrossRef]
  14. M. P. Christensen, P. Milojkovic, M. J. McFadden, and M. W. Haney, “Multiscale optical design for global chip-to-chip optical interconnections and misalignment tolerant packaging,” J. Sel. Topics Quantum Electron. 9, 548–556 (2003).
  15. D. J. Brady and N. Hagen, “Multiscale lens design,” Opt. Express 17, 10659–10674 (2009).
    [CrossRef]

2010

O. Iwert and B. Delabre, “The challenge of highly curved monolithic imaging detectors,” Proc. SPIE 7742, 774227 (2010).
[CrossRef]

2009

2008

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

S.-B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16, 4965–4971 (2008).
[CrossRef]

2004

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

2003

M. P. Christensen, P. Milojkovic, M. J. McFadden, and M. W. Haney, “Multiscale optical design for global chip-to-chip optical interconnections and misalignment tolerant packaging,” J. Sel. Topics Quantum Electron. 9, 548–556 (2003).

1994

1989

1979

Abelson, J. R.

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

Bareket, N.

Brady, D. J.

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

D. L. Marks and D. J. Brady, “Gigagon: A monocentric lens design imaging 40 gigapixels,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuC2.

Catrysse, P. B.

Choi, W. M.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Christensen, M. P.

M. P. Christensen, P. Milojkovic, M. J. McFadden, and M. W. Haney, “Multiscale optical design for global chip-to-chip optical interconnections and misalignment tolerant packaging,” J. Sel. Topics Quantum Electron. 9, 548–556 (2003).

Cossairt, O.

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

Delabre, B.

O. Iwert and B. Delabre, “The challenge of highly curved monolithic imaging detectors,” Proc. SPIE 7742, 774227 (2010).
[CrossRef]

Dinyari, R.

Erhardt, M. K.

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

Geddes, J. B.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Hagen, N.

Haney, M. W.

M. P. Christensen, P. Milojkovic, M. J. McFadden, and M. W. Haney, “Multiscale optical design for global chip-to-chip optical interconnections and misalignment tolerant packaging,” J. Sel. Topics Quantum Electron. 9, 548–556 (2003).

Huang, K.

Huang, Y.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Iwert, O.

O. Iwert and B. Delabre, “The challenge of highly curved monolithic imaging detectors,” Proc. SPIE 7742, 774227 (2010).
[CrossRef]

Jin, H.-C.

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

Kingslake, R.

R. Kingslake, A History of the Photographic Lens (Academic Press, 1989), pp. 50–52.

Ko, H. C.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Lohmann, A. W.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (Brown University, 1944), pp. 189–213.

Malyarchuk, V.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Marks, D. L.

D. L. Marks and D. J. Brady, “Gigagon: A monocentric lens design imaging 40 gigapixels,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuC2.

McFadden, M. J.

M. P. Christensen, P. Milojkovic, M. J. McFadden, and M. W. Haney, “Multiscale optical design for global chip-to-chip optical interconnections and misalignment tolerant packaging,” J. Sel. Topics Quantum Electron. 9, 548–556 (2003).

Miau, D.

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

Milojkovic, P.

M. P. Christensen, P. Milojkovic, M. J. McFadden, and M. W. Haney, “Multiscale optical design for global chip-to-chip optical interconnections and misalignment tolerant packaging,” J. Sel. Topics Quantum Electron. 9, 548–556 (2003).

Nayar, S. K.

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

Nuzzo, R. G.

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

Ozaktas, H. M.

Peumans, P.

Rim, S.-B.

Rogers, J. A.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Song, J.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Stoykovich, M. P.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Urey, H.

Wang, S.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Xiao, J.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Yu, C.-J.

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Sel. Topics Quantum Electron.

M. P. Christensen, P. Milojkovic, M. J. McFadden, and M. W. Haney, “Multiscale optical design for global chip-to-chip optical interconnections and misalignment tolerant packaging,” J. Sel. Topics Quantum Electron. 9, 548–556 (2003).

J. Vac. Sci. Technol. B

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

Nature

H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C.-J. Yu, J. B. Geddes, J. Xiao, S. Wang, Y. Huang, and J. A. Rogers, “A hemispherical electronic eye camera based on compressible silicon optoelectronics,” Nature 454, 748–753 (2008).
[CrossRef]

Opt. Express

Proc. SPIE

O. Iwert and B. Delabre, “The challenge of highly curved monolithic imaging detectors,” Proc. SPIE 7742, 774227 (2010).
[CrossRef]

Other

http://www.darpa.mil/Our_Work/MTO/Programs/Hemispherical_Array_Detector_for_Imaging_(HARDI).aspx.

D. L. Marks and D. J. Brady, “Gigagon: A monocentric lens design imaging 40 gigapixels,” in Imaging Systems, OSA Technical Digest (CD) (Optical Society of America, 2010), paper ITuC2.

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

Handbook of Optical Systems Vol. 4: Survey of Optical Instruments, H. Gross, F. Blechinger, and B. Achtner, eds. (Wiley-VCH Verlag, 2008), pp. 109–110.

R. K. Luneburg, Mathematical Theory of Optics (Brown University, 1944), pp. 189–213.

R. Kingslake, A History of the Photographic Lens (Academic Press, 1989), pp. 50–52.

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Figures (17)

Fig. 1.
Fig. 1.

Space-bandwidth of an optical system as a function of scale. Reproduced from [1].

Fig. 2.
Fig. 2.

Imaging system scaling considered by Lohmann. (a) Base system. (b) Scaled system.

Fig. 3.
Fig. 3.

Representative imaging systems considered for analysis.

Fig. 4.
Fig. 4.

Geometry for rays assuming a (a) flat and (b) curved focal plane.

Fig. 5.
Fig. 5.

Space-bandwidth product S as a function of half-field angle β for flat and curved detectors.

Fig. 6.
Fig. 6.

Lenses analyzed. (a) Plano-convex. (b) Monocentric. (c) Luneburg.

Fig. 7.
Fig. 7.

βmax as a function of f# for variable lens diameters for a plano-convex lens imaging onto a flat detector. Reproduced from [2].

Fig. 8.
Fig. 8.

Analysis of a plano-convex lens imaging onto a flat detector. (a) βmax and (b) Smax as a function of f# for variable lens diameters.

Fig. 9.
Fig. 9.

Analysis of a plano-convex lens imaging onto a curved detector. (a) βmax and (b) Smax as a function of f# for variable lens diameters.

Fig. 10.
Fig. 10.

Analysis of a monocentric lens imaging onto a flat detector. (a) βmax and (b) Smax as a function of f# for variable lens diameters.

Fig. 11.
Fig. 11.

Analysis of a monocentric lens imaging onto a curved detector. (a) βmax and (b) Smax as a function of f# for variable lens diameters.

Fig. 12.
Fig. 12.

Analysis of a Luneburg lens imaging onto a curved detector. (a) βmax and (b) Smax as a function of f# for variable lens diameters. Since the value of βmax is independent of f# and D, all curves in (a) lie on top of one another.

Fig. 13.
Fig. 13.

Smax as a function of f# for various imaging systems with (a) D=50mm and (b) D=500mm. Labels for the graphs indicate lens type (pcx—plano-convex, mc—monocentric, lu—Luneburg) and detector geometry (flat versus curved).

Fig. 14.
Fig. 14.

Smax as a function of D for various imaging systems. (a) Plano-convex lens and flat detector. (b) Plano-convex lens and curved detector. (c) Monocentric lens and flat detector. (d) Monocentric lens and curved detector.

Fig. 15.
Fig. 15.

Physical characteristics as a function of space-bandwidth for imaging systems analyzed. (a) System volume. (b) Lens mass. (c) System density.

Fig. 16.
Fig. 16.

Optical system scaling.

Fig. 17.
Fig. 17.

Representative spot shapes from analysis.

Tables (2)

Tables Icon

Table 1. V for Imaging Systems Analyzed

Tables Icon

Table 2. Va for Imaging Systems Analyzed

Equations (13)

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

S=Aares,
ares=(δx)2+(δξ)2=(λf/D)2+ξ¯2,
f#=f/D,
Aflat=(2f#Dtanβ)2,
Acurv=2π(f#D)2(1cosβ).
ares,flat=(λfDcos3β)2,
ares,curv=(λfDcosβ)2.
aideal=(λfD)2.
Sflat=4(D/λ)2(1cos2β)cos4β,
Scurv=2π(D/λ)2(1cosβ)cos2β.
SLuneburg=1.34(D/λ)2(1cosβ).
Vs=V+Va,
ρ=mVs.

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