Abstract

The significant optical and size benefits of using a curved focal surface for imaging systems have been well studied yet never brought to market for lack of a high-quality, mass-producible, curved image sensor. In this work we demonstrate that commercial silicon CMOS image sensors can be thinned and formed into accurate, highly curved optical surfaces with undiminished functionality. Our key development is a pneumatic forming process that avoids rigid mechanical constraints and suppresses wrinkling instabilities. A combination of forming-mold design, pressure membrane elastic properties, and controlled friction forces enables us to gradually contact the die at the corners and smoothly press the sensor into a spherical shape. Allowing the die to slide into the concave target shape enables a threefold increase in the spherical curvature over prior approaches having mechanical constraints that resist deformation, and create a high-stress, stretch-dominated state. Our process creates a bridge between the high precision and low-cost but planar CMOS process, and ideal non-planar component shapes such as spherical imagers for improved optical systems. We demonstrate these curved sensors in prototype cameras with custom lenses, measuring exceptional resolution of 3220 line-widths per picture height at an aperture of f/1.2 and nearly 100% relative illumination across the field. Though we use a 1/2.3” format image sensor in this report, we also show this process is generally compatible with many state of the art imaging sensor formats. By example, we report photogrammetry test data for an APS-C sized silicon die formed to a 30° subtended spherical angle. These gains in sharpness and relative illumination enable a new generation of ultra-high performance, manufacturable, digital imaging systems for scientific, industrial, and artistic use.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2015 (2)

2014 (1)

2013 (2)

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

2012 (5)

2010 (2)

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

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

2008 (5)

X. Xu, M. Davanco, X. Qi, and S. R. Forrest, “Direct transfer patterning on three dimensionally deformed surfaces at micrometer resolutions and its application to hemispherical focal plane detector arrays,” Org. Electron. 9(6), 1122–1127 (2008).
[Crossref]

R. Dinyari, S. B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

S. B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

2005 (1)

X. Li, T. Kasai, S. Nakao, H. Tanaka, T. Ando, M. Shikida, and K. Sato, “Measurement for fracture toughness of single crystal silicon film with tensile test,” Sens. Actuators A Phys. 119(1), 229–235 (2005).
[Crossref]

2004 (1)

P. Swain, D. Channin, G. Taylor, S. Lipp, and D. Mark, “Curved CCD’s and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).

2000 (1)

K. Y. Chen, R. L. D. Zenner, M. Ameson, and D. Mountain, “Ultra-thin electronic device package,” IEEE Trans. Adv. Packag. 23(1), 22–26 (2000).
[Crossref]

Agurok, I. P.

Ameson, M.

K. Y. Chen, R. L. D. Zenner, M. Ameson, and D. Mountain, “Ultra-thin electronic device package,” IEEE Trans. Adv. Packag. 23(1), 22–26 (2000).
[Crossref]

Ando, T.

X. Li, T. Kasai, S. Nakao, H. Tanaka, T. Ando, M. Shikida, and K. Sato, “Measurement for fracture toughness of single crystal silicon film with tensile test,” Sens. Actuators A Phys. 119(1), 229–235 (2005).
[Crossref]

Arianpour, A.

Baier, N.

Brady, D. J. M. E.

D. J. M. E. 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(7403), 386–389 (2012).
[Crossref] [PubMed]

Cao, Y.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Catrysse, P. B.

R. Dinyari, S. B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (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(7), 4965–4971 (2008).
[Crossref] [PubMed]

Ceballos, A.

T. Wu, S. S. Hamann, A. Ceballos, O. Solgaard, and R. T. Howe, “Design and fabrication of curved silicon image planes for miniature monocentric imagers,” in 2015 18th International Conference on Solid-State Sensors, Actuators and Microsystems, TRANSDUCERS 2015 (2015), pp. 2073–2076.
[Crossref]

Channin, D.

P. Swain, D. Channin, G. Taylor, S. Lipp, and D. Mark, “Curved CCD’s and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).

Chen, K. Y.

K. Y. Chen, R. L. D. Zenner, M. Ameson, and D. Mountain, “Ultra-thin electronic device package,” IEEE Trans. Adv. Packag. 23(1), 22–26 (2000).
[Crossref]

Choi, K. J.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Clark, H. R.

Crozier, K. B.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Davanco, M.

X. Xu, M. Davanco, X. Qi, and S. R. Forrest, “Direct transfer patterning on three dimensionally deformed surfaces at micrometer resolutions and its application to hemispherical focal plane detector arrays,” Org. Electron. 9(6), 1122–1127 (2008).
[Crossref]

DeCew, A. E.

DeFranzo, C. M.

Delabre, B.

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

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

Dinyari, R.

S. B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

R. Dinyari, S. B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

Dolat, V. S.

Dumas, D.

Evans, R. A.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Feller, S. D.

D. J. M. E. 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(7403), 386–389 (2012).
[Crossref] [PubMed]

Fendler, M.

Ford, J. E.

Forman, S. E.

Forrest, S. R.

X. Xu, M. Davanco, X. Qi, and S. R. Forrest, “Direct transfer patterning on three dimensionally deformed surfaces at micrometer resolutions and its application to hemispherical focal plane detector arrays,” Org. Electron. 9(6), 1122–1127 (2008).
[Crossref]

Gan, Z.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Gehm, M. E.

D. J. M. E. 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(7403), 386–389 (2012).
[Crossref] [PubMed]

Golish, D. R.

D. J. M. E. 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(7403), 386–389 (2012).
[Crossref] [PubMed]

Gregory, J. A.

Gu, M.

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Ha, J. S.

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

Hamann, S. S.

T. Wu, S. S. Hamann, A. Ceballos, O. Solgaard, and R. T. Howe, “Design and fabrication of curved silicon image planes for miniature monocentric imagers,” in 2015 18th International Conference on Solid-State Sensors, Actuators and Microsystems, TRANSDUCERS 2015 (2015), pp. 2073–2076.
[Crossref]

Howe, R. T.

T. Wu, S. S. Hamann, A. Ceballos, O. Solgaard, and R. T. Howe, “Design and fabrication of curved silicon image planes for miniature monocentric imagers,” in 2015 18th International Conference on Solid-State Sensors, Actuators and Microsystems, TRANSDUCERS 2015 (2015), pp. 2073–2076.
[Crossref]

Huang, K.

R. Dinyari, S. B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (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(7), 4965–4971 (2008).
[Crossref] [PubMed]

Huang, Y.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Iwert, O.

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

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

Johnson, A. R.

Jung, I.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

Kasai, T.

X. Li, T. Kasai, S. Nakao, H. Tanaka, T. Ando, M. Shikida, and K. Sato, “Measurement for fracture toughness of single crystal silicon film with tensile test,” Sens. Actuators A Phys. 119(1), 229–235 (2005).
[Crossref]

Kim, R. H.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Kittle, D. S.

D. J. M. E. 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(7403), 386–389 (2012).
[Crossref] [PubMed]

Ko, H. C.

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Lambour, R. L.

le Coarer, E.

Lesser, M.

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

Li, R.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Li, X.

X. Li, T. Kasai, S. Nakao, H. Tanaka, T. Ando, M. Shikida, and K. Sato, “Measurement for fracture toughness of single crystal silicon film with tensile test,” Sens. Actuators A Phys. 119(1), 229–235 (2005).
[Crossref]

Lipp, S.

P. Swain, D. Channin, G. Taylor, S. Lipp, and D. Mark, “Curved CCD’s and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).

Liu, Z.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Loomis, A. H.

Lu, C.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Mait, J. N.

Malyarchuk, V.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Mark, D.

P. Swain, D. Channin, G. Taylor, S. Lipp, and D. Mark, “Curved CCD’s and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).

Marks, D. L.

D. J. M. E. 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(7403), 386–389 (2012).
[Crossref] [PubMed]

Mendenhall, L.

Milojkovic, P.

Morrison, R. L.

Mountain, D.

K. Y. Chen, R. L. D. Zenner, M. Ameson, and D. Mountain, “Ultra-thin electronic device package,” IEEE Trans. Adv. Packag. 23(1), 22–26 (2000).
[Crossref]

Nakao, S.

X. Li, T. Kasai, S. Nakao, H. Tanaka, T. Ando, M. Shikida, and K. Sato, “Measurement for fracture toughness of single crystal silicon film with tensile test,” Sens. Actuators A Phys. 119(1), 229–235 (2005).
[Crossref]

Olivas, S. J.

Osgood, R. M.

Ouellette, D.

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

Park, H.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Pearce, E. C.

Peumans, P.

S. B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

R. Dinyari, S. B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

Primot, J.

Qi, X.

X. Xu, M. Davanco, X. Qi, and S. R. Forrest, “Direct transfer patterning on three dimensionally deformed surfaces at micrometer resolutions and its application to hemispherical focal plane detector arrays,” Org. Electron. 9(6), 1122–1127 (2008).
[Crossref]

Reshidko, D.

Rim, S. B.

S. B. Rim, P. B. Catrysse, R. Dinyari, K. Huang, and P. Peumans, “The optical advantages of curved focal plane arrays,” Opt. Express 16(7), 4965–4971 (2008).
[Crossref] [PubMed]

R. Dinyari, S. B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

Rogers, J. A.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Sasian, J.

Sato, K.

X. Li, T. Kasai, S. Nakao, H. Tanaka, T. Ando, M. Shikida, and K. Sato, “Measurement for fracture toughness of single crystal silicon film with tensile test,” Sens. Actuators A Phys. 119(1), 229–235 (2005).
[Crossref]

Shah, R. Y.

Shikida, M.

X. Li, T. Kasai, S. Nakao, H. Tanaka, T. Ando, M. Shikida, and K. Sato, “Measurement for fracture toughness of single crystal silicon film with tensile test,” Sens. Actuators A Phys. 119(1), 229–235 (2005).
[Crossref]

Shin, G.

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

Smith, A. M.

Solgaard, O.

T. Wu, S. S. Hamann, A. Ceballos, O. Solgaard, and R. T. Howe, “Design and fabrication of curved silicon image planes for miniature monocentric imagers,” in 2015 18th International Conference on Solid-State Sensors, Actuators and Microsystems, TRANSDUCERS 2015 (2015), pp. 2073–2076.
[Crossref]

Song, J.

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Song, Y. M.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Stack, R. A.

I. Stamenov, A. Arianpour, S. J. Olivas, I. P. Agurok, A. R. Johnson, R. A. Stack, R. L. Morrison, and J. E. Ford, “Panoramic monocentric imaging using fiber-coupled focal planes,” Opt. Express 22(26), 31708–31721 (2014).
[Crossref] [PubMed]

D. J. M. E. 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(7403), 386–389 (2012).
[Crossref] [PubMed]

Stamenov, I.

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Swain, P.

P. Swain, D. Channin, G. Taylor, S. Lipp, and D. Mark, “Curved CCD’s and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).

Tanaka, H.

X. Li, T. Kasai, S. Nakao, H. Tanaka, T. Ando, M. Shikida, and K. Sato, “Measurement for fracture toughness of single crystal silicon film with tensile test,” Sens. Actuators A Phys. 119(1), 229–235 (2005).
[Crossref]

Taylor, G.

P. Swain, D. Channin, G. Taylor, S. Lipp, and D. Mark, “Curved CCD’s and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).

Vera, E. M.

D. J. M. E. 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(7403), 386–389 (2012).
[Crossref] [PubMed]

Wang, S.

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Warner, K.

Woods, D. F.

Wu, T.

T. Wu, S. S. Hamann, A. Ceballos, O. Solgaard, and R. T. Howe, “Design and fabrication of curved silicon image planes for miniature monocentric imagers,” in 2015 18th International Conference on Solid-State Sensors, Actuators and Microsystems, TRANSDUCERS 2015 (2015), pp. 2073–2076.
[Crossref]

Xiao, J.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Xie, Y.

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Xu, X.

X. Xu, M. Davanco, X. Qi, and S. R. Forrest, “Direct transfer patterning on three dimensionally deformed surfaces at micrometer resolutions and its application to hemispherical focal plane detector arrays,” Org. Electron. 9(6), 1122–1127 (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(7205), 748–753 (2008).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Zenner, R. L. D.

K. Y. Chen, R. L. D. Zenner, M. Ameson, and D. Mountain, “Ultra-thin electronic device package,” IEEE Trans. Adv. Packag. 23(1), 22–26 (2000).
[Crossref]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

R. Dinyari, S. B. Rim, K. Huang, P. B. Catrysse, and P. Peumans, “Curving monolithic silicon for nonplanar focal plane array applications,” Appl. Phys. Lett. 92(9), 091114 (2008).
[Crossref]

IEEE Trans. Adv. Packag. (1)

K. Y. Chen, R. L. D. Zenner, M. Ameson, and D. Mountain, “Ultra-thin electronic device package,” IEEE Trans. Adv. Packag. 23(1), 22–26 (2000).
[Crossref]

Nat. Commun. (1)

Z. Gan, Y. Cao, R. A. Evans, and M. Gu, “Three-dimensional deep sub-diffraction optical beam lithography with 9 nm feature size,” Nat. Commun. 4, 2061 (2013).
[Crossref] [PubMed]

Nature (4)

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(7205), 748–753 (2008).
[Crossref] [PubMed]

D. J. M. E. 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(7403), 386–389 (2012).
[Crossref] [PubMed]

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(7205), 748–753 (2008).
[Crossref] [PubMed]

Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, and J. A. Rogers, “Digital cameras with designs inspired by the arthropod eye,” Nature 497(7447), 95–99 (2013).
[Crossref] [PubMed]

Opt. Express (2)

Org. Electron. (1)

X. Xu, M. Davanco, X. Qi, and S. R. Forrest, “Direct transfer patterning on three dimensionally deformed surfaces at micrometer resolutions and its application to hemispherical focal plane detector arrays,” Org. Electron. 9(6), 1122–1127 (2008).
[Crossref]

Proc. SPIE (3)

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

P. Swain, D. Channin, G. Taylor, S. Lipp, and D. Mark, “Curved CCD’s and their application with astronomical telescopes and stereo panoramic cameras,” Proc. SPIE 5301, 109–129 (2004).

O. Iwert, D. Ouellette, M. Lesser, and B. Delabre, “First results from a novel curving process for large area scientific imagers,” Proc. SPIE 8453, 84531W (2012).
[Crossref]

Sens. Actuators A Phys. (1)

X. Li, T. Kasai, S. Nakao, H. Tanaka, T. Ando, M. Shikida, and K. Sato, “Measurement for fracture toughness of single crystal silicon film with tensile test,” Sens. Actuators A Phys. 119(1), 229–235 (2005).
[Crossref]

Small (1)

G. Shin, I. Jung, V. Malyarchuk, J. Song, S. Wang, H. C. Ko, Y. Huang, J. S. Ha, and J. A. Rogers, “Micromechanics and advanced designs for curved photodetector arrays in hemispherical electronic-eye cameras,” Small 6(7), 851–856 (2010).
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J. N. Burghartz, “Ultra-thin chip technology and applications,” in Ultra-thin Chip Technology and Applications (Springer, 2011), pp. 197–215.

T. Wu, S. S. Hamann, A. Ceballos, O. Solgaard, and R. T. Howe, “Design and fabrication of curved silicon image planes for miniature monocentric imagers,” in 2015 18th International Conference on Solid-State Sensors, Actuators and Microsystems, TRANSDUCERS 2015 (2015), pp. 2073–2076.
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K. Tekaya, M. Fendler, K. Inal, E. Massoni, and H. Ribot, “Mechanical behavior of flexible silicon devices curved in spherical configurations,” in 2013 14th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE, 2013), paper 6529978.
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S. Timonshenko, Theory of Plates and Shell (McGraw-Hill, 1940), p. 332.

K. Itonaga, T. Arimura, K. Matsumoto, G. Kondo, K. Terahata, S. Makimoto, M. Baba, Y. Honda, S. Bori, T. Kai, K. Kasahara, M. Nagano, M. Kimura, Y. Kinoshita, E. Kishida, T. Baba, S. Baba, Y. Nomura, N. Tanabe, N. Kimizuka, Y. Matoba, T. Takachi, E. Takagi, T. Haruta, N. Ikebe, K. Matsuda, T. Niimi, T. Ezaki, and T. Hirayama, “A novel curved CMOS image sensor integrated with imaging system,”Digest of Technical Papers - Symposium on VLSI Technology, 6894341 (2014).
[Crossref]

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (2403 KB)      Video of the strains and deformation of a 28 x 23.5 mm, 60 um thick silicon die during the forming process, measured using digital image correlation. The final shape has a 60.45 mm radius of curvature, and a 30-degree subtended angle.

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Figures (11)

Fig. 1
Fig. 1

A) The eye focuses onto photosensitive cells arranged along the curved focal surface inherent of a thick lens. Typical optical lenses require more elements and complexity to focus on flat focal planes and correct the aberrations these compensating elements introduce, losing performance compared to a curved focal plane. B) Functional, 18 megapixel (1/2.3” 7.6 mm x 7.7 mm die) BSI CMOS curved image sensor bonded to a precise 18.74 mm curved mold surface.

Fig. 2
Fig. 2

A) In conventional micro-device 3D membrane formation (red) edges are fixed while pressure or vacuum is applied and deformation is resisted by radial in-plane tensile loads that grow nonlinearly with increasing deflection. By comparison, our pneumatic forming process forms an unconstrained die (blue) through a pressurized flexible membrane that leaves the edges free to translate, thus largely eliminating radial tensile forces and reducing the strain energy density. B) Curving a free standing die into a concave mold introduces in-plane transverse (hoop) compressive strains that grow with increasing curvature. The resulting unstable buckling behavior is prevented through the normal forces applied though the membrane.

Fig. 3
Fig. 3

Finite element predictions for the peak stresses and volumetric strain energy density developed as a function of normalized center displacement for the fixed perimeter and free edge molding operations for thicknesses ranging from 40 µm to 100 µm and a die size of 22.3 mm x 28 mm.

Fig. 4
Fig. 4

A) Predicted evolution of radial and transverse stress on the surface of a die as it is forced into a spherical curvature with increasing pneumatic pressure up to 800 MPa. Near the edge, the deformation pattern is compressive in the loop and radial directions, transitioning to biaxial tension near the center. B) Comparison of strains measured using digital image correlation (DIC) on the top surface of the die (upper row, see Visualization 1 for a time-lapse video) and FEA model estimates (lower row) reveal purely tensile strains along the radial direction, and larger tangential strains that shift from large compression near the edges to tension near the center. Close correspondence of the measured and model results illustrates that our FEM models are a good predictor of the strains in bending actual CMOS die.

Fig. 5
Fig. 5

Comparative graph of curvature achieved in working sensors between this work and the significant work from the literature. A wirebonded sensor used for one camera in this study is shown in the lower right, having a spherical curvature of 23.7°. The working sensor in the upper right has a curvature of 26.7° but could not be used for this study as it does not match the lens.

Fig. 6
Fig. 6

A) SEM cross-sectional image of the CMOS sensor used in this work, demonstrating the variety and complexity of the materials undergoing deformation. The silicon substrate shown at the bottom has a 16 μm thickness and is outside the field of view. B) Interferometer measurement of the shape accuracy of a camera sensor at 2.2 μm peak-to-valley. C) Plot of the measured dark current versus temperature of all wirebonded sensors curved to the lens prescription. Most of the curved samples have slightly lower dark current than the unmodified flat sensor.

Fig. 7
Fig. 7

As-designed MTF for curved vs. flat designs for f/1.2, 1/2.3” CMOS sensor with 50 ° field of view. A) Curved sensor, optimized for an 18.74 mm radius of curvature sensor. B) Flat sensor optimized design. The curved system has almost double the sharpness at every field angle, despite having 1 less element and 2 fewer aspherical surfaces. The flat sensor design is also much larger.

Fig. 8
Fig. 8

Measured MTF results and relative illumination performance with comparisons to two high-quality commercial f/1.2 cameras. Curved refers to the prototype curved CMOS sensor camera. Canon refers to a Canon 50 mm f/1.2 lens mounted on a Canon 1DS Mark III body. Flat refers to an Edmund Optics 6 mm f/1.2 lens mounted on a flat version of our CMOS sensor. The data show more than double the sharpness in the center and more than triple in the corner, as measured in Line-Width/Picture-Height (LW/PH) at MTF30. Relative illumination measurements show virtually no light lost from center to corner for our curved sensor prototype compared to over 90% loss for the Canon lens.

Fig. 9
Fig. 9

Image captured with the curved sensor prototype camera. The zoomed-in portion shows excellent sharpness far from center. The large depth range in the scene illustrates pleasing shallow depth of field enabled by the wide aperture of the f/1.2 lens.

Fig. 10
Fig. 10

Design study comparison between the curved sensor optical system A) and flat sensor B). 28 mm focal length, f/1.7, 75° diagonal field of view, 43 mm image circle. Flat lens B) has 10 elements and 2 aspherical surfaces. Curved sensor lens A) has seven elements and one aspherical surface. At MTF50 the curved sensor design A) has 1.3x the spatial frequency response of the flat design B) despite having fewer elements.

Fig. 11
Fig. 11

Design study comparison for 80 mm, f/1.8, 30° field of view, 43 mm image circle. Flat sensor lens B) has eight spherical elements. Curved sensor lens A) has five spherical elements. At MTF50 the curved sensor design A) has 1.2x the spatial frequency response of the flat design B) despite having three fewer elements.

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