Abstract

The ability to reproduce a high-quality image depends strongly on the image sensor light sensitivity. This sensitivity depends, in turn, on the materials, the circuitry, and the optical properties of the pixel. We calculate the optical efficiency of a complementary metal oxide semiconductor (CMOS) image sensor pixel by using a geometrical-optics phase-space approach. We compare the theoretical predictions with measurements made by using a CMOS digital pixel sensor, and we find them to be in agreement within 3%. Finally, we show how to use these optical efficiency calculations to trade off image sensor pixel sensitivity and functionality as CMOS process technology scales.

© 2002 Optical Society of America

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References

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  1. J. R. Janesick, K. Evans, T. Elliot, “Charge-coupled-device response to electron beam energies of less than 1 keV up to 20 keV,” Opt. Eng. 26, 686–691 (1987).
  2. B. Fowler, A. El Gamal, D. Yang, H. Tian, “A method for estimating quantum efficiency for CMOS image sensors,” in Solid State Sensor Arrays: Development and Applications II, M. M. Blouke, ed., Proc. SPIE3301, 178–185 (1998).
    [CrossRef]
  3. D. Yang, H. Tian, B. Fowler, X. Liu, A. El Gamal, “Characterization of CMOS image sensors with Nyquist rate pixel level ADC,” in Sensors, Cameras, and Applications for Digital Photography, N. Sampat, T. Yeh, eds., Proc. SPIE3650, 52–62 (1999).
    [CrossRef]
  4. J. Giest, H. Baltes, “High accuracy modeling of photodiode quantum efficiency,” Appl. Opt. 28, 3929–3938 (1989).
    [CrossRef]
  5. D. Yang, A. El Gamal, B. Fowler, H. Tian, “A 640×512 CMOS image sensor with ultrawide dynamic range floating-point pixel-level ADC,” IEEE J. Solid-State Circuits 34, 1821–1834 (1999).
    [CrossRef]
  6. J. A. Penkethman, “Calibrations and idiosyncrasies of micro-lensed CCD cameras,” in Current Developments in Optical Design and Optical Engineering VIII, R. E. Fischer, W. J. Smith, eds., Proc. SPIE3779, 241–249 (1999).
    [CrossRef]
  7. P. Catrysse, X. Liu, A. El Gamal, “QE reduction due to pixel vignetting in CMOS image sensors,” in Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications, M. M. Blouke, N. Sampat, G. M. Williams, T. Yeh, eds., Proc. SPIE3965, 420–430 (2000).
    [CrossRef]
  8. Luminous, Silvaco International, Santa Clara, Calif., 1995.
  9. Medici, Avanti Corporation, Fremont, Calif., 1998.
  10. M. Hideki, “Simulation for 3-D optical and electrical analysis of CCD,” IEEE Trans. Electron Devices 44, 1604–1610 (1997).
    [CrossRef]
  11. R. J. Pegis, “The modern development of Hamiltonian optics,” in Progress in Optics I, E. Wolf, ed. (North-Holland, Amsterdam, 1961), pp. 1–29.
  12. R. Winston, “Light collection within the framework of geometrical optics,” J. Opt. Soc. Am. 60, 245–247 (1970).
    [CrossRef]
  13. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1996), p. 404.
  14. M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1979).
    [CrossRef]
  15. D. Dragoman, “The Wigner distribution function in optics and optoelectronics,” in Progress in Optics XXXVII, E. Wolf, ed. (Elsevier Science, Amsterdam, 1997), pp. 1–56.
  16. A. Walther, “Gabor’s theorem and energy transfer through lenses,” J. Opt. Soc. Am. 57, 639–644 (1967).
    [CrossRef]
  17. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1986), p. 52.
  18. W. H. Steel, “Luminosity, throughput, or etendue,” Appl. Opt. 13, 704–705 (1974).
    [CrossRef] [PubMed]
  19. A. A. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
    [CrossRef]
  20. M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
    [CrossRef]
  21. P. C. S. Hayfield, G. W. T. White, “An assessment of the suitability of the Drude–Tronstad polarized light method for the study of film growth on polycrystalline metals,” in Ellipsometry in the Measurement of Surfaces and Thin Films, N. M. Bashara, A. B. Buckman, A. C. Hall, eds. (National Bureau of Standards, Washington, D.C., 1964), Vol. 256, pp. 157–200.
  22. E. R. Fossum, “Active pixel sensors: are CCD’s dinosaurs?” in Charge-Coupled Devices and Solid State Optical Sensors III, M. M. Blouke, ed., Proc. SPIE1900, 2–14 (1993).
    [CrossRef]
  23. S. Kleinfelder, S. Lim, X. Liu, A. El Gamal, “A 10kframes/s 0.18μm CMOS digital pixel sensor with pixel-level memory,” in 2001 International Solid-State Circuits Conference—Digest of Technical Papers (IEEE Press, Piscataway, N.J., 2001), pp. 88–89.
  24. B. Wandell, P. Catrysse, J. DiCarlo, D. Yang, A. El Gamal, “Multiple capture single image architecture with a CMOS sensor,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999), pp. 11–17.
  25. F. Abelès, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. (Paris) 5, 596–640 (1950).
  26. F. Abelès, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. (Paris) 5, 706–782 (1950).
  27. M. Born, E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon, Oxford, UK, 1980), pp. 38–41.

1999 (1)

D. Yang, A. El Gamal, B. Fowler, H. Tian, “A 640×512 CMOS image sensor with ultrawide dynamic range floating-point pixel-level ADC,” IEEE J. Solid-State Circuits 34, 1821–1834 (1999).
[CrossRef]

1997 (1)

M. Hideki, “Simulation for 3-D optical and electrical analysis of CCD,” IEEE Trans. Electron Devices 44, 1604–1610 (1997).
[CrossRef]

1996 (1)

1989 (1)

1987 (1)

J. R. Janesick, K. Evans, T. Elliot, “Charge-coupled-device response to electron beam energies of less than 1 keV up to 20 keV,” Opt. Eng. 26, 686–691 (1987).

1979 (1)

1978 (1)

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

1974 (1)

1970 (1)

1967 (1)

1950 (2)

F. Abelès, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. (Paris) 5, 596–640 (1950).

F. Abelès, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. (Paris) 5, 706–782 (1950).

Abelès, F.

F. Abelès, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. (Paris) 5, 596–640 (1950).

F. Abelès, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. (Paris) 5, 706–782 (1950).

Baltes, H.

Bastiaans, M. J.

M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1979).
[CrossRef]

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon, Oxford, UK, 1980), pp. 38–41.

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1986), p. 52.

Catrysse, P.

B. Wandell, P. Catrysse, J. DiCarlo, D. Yang, A. El Gamal, “Multiple capture single image architecture with a CMOS sensor,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999), pp. 11–17.

P. Catrysse, X. Liu, A. El Gamal, “QE reduction due to pixel vignetting in CMOS image sensors,” in Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications, M. M. Blouke, N. Sampat, G. M. Williams, T. Yeh, eds., Proc. SPIE3965, 420–430 (2000).
[CrossRef]

DiCarlo, J.

B. Wandell, P. Catrysse, J. DiCarlo, D. Yang, A. El Gamal, “Multiple capture single image architecture with a CMOS sensor,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999), pp. 11–17.

Dorsch, R. G.

Dragoman, D.

D. Dragoman, “The Wigner distribution function in optics and optoelectronics,” in Progress in Optics XXXVII, E. Wolf, ed. (Elsevier Science, Amsterdam, 1997), pp. 1–56.

El Gamal, A.

D. Yang, A. El Gamal, B. Fowler, H. Tian, “A 640×512 CMOS image sensor with ultrawide dynamic range floating-point pixel-level ADC,” IEEE J. Solid-State Circuits 34, 1821–1834 (1999).
[CrossRef]

D. Yang, H. Tian, B. Fowler, X. Liu, A. El Gamal, “Characterization of CMOS image sensors with Nyquist rate pixel level ADC,” in Sensors, Cameras, and Applications for Digital Photography, N. Sampat, T. Yeh, eds., Proc. SPIE3650, 52–62 (1999).
[CrossRef]

B. Fowler, A. El Gamal, D. Yang, H. Tian, “A method for estimating quantum efficiency for CMOS image sensors,” in Solid State Sensor Arrays: Development and Applications II, M. M. Blouke, ed., Proc. SPIE3301, 178–185 (1998).
[CrossRef]

P. Catrysse, X. Liu, A. El Gamal, “QE reduction due to pixel vignetting in CMOS image sensors,” in Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications, M. M. Blouke, N. Sampat, G. M. Williams, T. Yeh, eds., Proc. SPIE3965, 420–430 (2000).
[CrossRef]

S. Kleinfelder, S. Lim, X. Liu, A. El Gamal, “A 10kframes/s 0.18μm CMOS digital pixel sensor with pixel-level memory,” in 2001 International Solid-State Circuits Conference—Digest of Technical Papers (IEEE Press, Piscataway, N.J., 2001), pp. 88–89.

B. Wandell, P. Catrysse, J. DiCarlo, D. Yang, A. El Gamal, “Multiple capture single image architecture with a CMOS sensor,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999), pp. 11–17.

Elliot, T.

J. R. Janesick, K. Evans, T. Elliot, “Charge-coupled-device response to electron beam energies of less than 1 keV up to 20 keV,” Opt. Eng. 26, 686–691 (1987).

Evans, K.

J. R. Janesick, K. Evans, T. Elliot, “Charge-coupled-device response to electron beam energies of less than 1 keV up to 20 keV,” Opt. Eng. 26, 686–691 (1987).

Ferreira, C.

Fossum, E. R.

E. R. Fossum, “Active pixel sensors: are CCD’s dinosaurs?” in Charge-Coupled Devices and Solid State Optical Sensors III, M. M. Blouke, ed., Proc. SPIE1900, 2–14 (1993).
[CrossRef]

Fowler, B.

D. Yang, A. El Gamal, B. Fowler, H. Tian, “A 640×512 CMOS image sensor with ultrawide dynamic range floating-point pixel-level ADC,” IEEE J. Solid-State Circuits 34, 1821–1834 (1999).
[CrossRef]

D. Yang, H. Tian, B. Fowler, X. Liu, A. El Gamal, “Characterization of CMOS image sensors with Nyquist rate pixel level ADC,” in Sensors, Cameras, and Applications for Digital Photography, N. Sampat, T. Yeh, eds., Proc. SPIE3650, 52–62 (1999).
[CrossRef]

B. Fowler, A. El Gamal, D. Yang, H. Tian, “A method for estimating quantum efficiency for CMOS image sensors,” in Solid State Sensor Arrays: Development and Applications II, M. M. Blouke, ed., Proc. SPIE3301, 178–185 (1998).
[CrossRef]

Giest, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1996), p. 404.

Hayfield, P. C. S.

P. C. S. Hayfield, G. W. T. White, “An assessment of the suitability of the Drude–Tronstad polarized light method for the study of film growth on polycrystalline metals,” in Ellipsometry in the Measurement of Surfaces and Thin Films, N. M. Bashara, A. B. Buckman, A. C. Hall, eds. (National Bureau of Standards, Washington, D.C., 1964), Vol. 256, pp. 157–200.

Hideki, M.

M. Hideki, “Simulation for 3-D optical and electrical analysis of CCD,” IEEE Trans. Electron Devices 44, 1604–1610 (1997).
[CrossRef]

Janesick, J. R.

J. R. Janesick, K. Evans, T. Elliot, “Charge-coupled-device response to electron beam energies of less than 1 keV up to 20 keV,” Opt. Eng. 26, 686–691 (1987).

Kleinfelder, S.

S. Kleinfelder, S. Lim, X. Liu, A. El Gamal, “A 10kframes/s 0.18μm CMOS digital pixel sensor with pixel-level memory,” in 2001 International Solid-State Circuits Conference—Digest of Technical Papers (IEEE Press, Piscataway, N.J., 2001), pp. 88–89.

Lim, S.

S. Kleinfelder, S. Lim, X. Liu, A. El Gamal, “A 10kframes/s 0.18μm CMOS digital pixel sensor with pixel-level memory,” in 2001 International Solid-State Circuits Conference—Digest of Technical Papers (IEEE Press, Piscataway, N.J., 2001), pp. 88–89.

Liu, X.

S. Kleinfelder, S. Lim, X. Liu, A. El Gamal, “A 10kframes/s 0.18μm CMOS digital pixel sensor with pixel-level memory,” in 2001 International Solid-State Circuits Conference—Digest of Technical Papers (IEEE Press, Piscataway, N.J., 2001), pp. 88–89.

P. Catrysse, X. Liu, A. El Gamal, “QE reduction due to pixel vignetting in CMOS image sensors,” in Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications, M. M. Blouke, N. Sampat, G. M. Williams, T. Yeh, eds., Proc. SPIE3965, 420–430 (2000).
[CrossRef]

D. Yang, H. Tian, B. Fowler, X. Liu, A. El Gamal, “Characterization of CMOS image sensors with Nyquist rate pixel level ADC,” in Sensors, Cameras, and Applications for Digital Photography, N. Sampat, T. Yeh, eds., Proc. SPIE3650, 52–62 (1999).
[CrossRef]

Lohmann, A. A.

Mendlovic, D.

Pegis, R. J.

R. J. Pegis, “The modern development of Hamiltonian optics,” in Progress in Optics I, E. Wolf, ed. (North-Holland, Amsterdam, 1961), pp. 1–29.

Penkethman, J. A.

J. A. Penkethman, “Calibrations and idiosyncrasies of micro-lensed CCD cameras,” in Current Developments in Optical Design and Optical Engineering VIII, R. E. Fischer, W. J. Smith, eds., Proc. SPIE3779, 241–249 (1999).
[CrossRef]

Steel, W. H.

Tian, H.

D. Yang, A. El Gamal, B. Fowler, H. Tian, “A 640×512 CMOS image sensor with ultrawide dynamic range floating-point pixel-level ADC,” IEEE J. Solid-State Circuits 34, 1821–1834 (1999).
[CrossRef]

D. Yang, H. Tian, B. Fowler, X. Liu, A. El Gamal, “Characterization of CMOS image sensors with Nyquist rate pixel level ADC,” in Sensors, Cameras, and Applications for Digital Photography, N. Sampat, T. Yeh, eds., Proc. SPIE3650, 52–62 (1999).
[CrossRef]

B. Fowler, A. El Gamal, D. Yang, H. Tian, “A method for estimating quantum efficiency for CMOS image sensors,” in Solid State Sensor Arrays: Development and Applications II, M. M. Blouke, ed., Proc. SPIE3301, 178–185 (1998).
[CrossRef]

Walther, A.

Wandell, B.

B. Wandell, P. Catrysse, J. DiCarlo, D. Yang, A. El Gamal, “Multiple capture single image architecture with a CMOS sensor,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999), pp. 11–17.

White, G. W. T.

P. C. S. Hayfield, G. W. T. White, “An assessment of the suitability of the Drude–Tronstad polarized light method for the study of film growth on polycrystalline metals,” in Ellipsometry in the Measurement of Surfaces and Thin Films, N. M. Bashara, A. B. Buckman, A. C. Hall, eds. (National Bureau of Standards, Washington, D.C., 1964), Vol. 256, pp. 157–200.

Winston, R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon, Oxford, UK, 1980), pp. 38–41.

Yang, D.

D. Yang, A. El Gamal, B. Fowler, H. Tian, “A 640×512 CMOS image sensor with ultrawide dynamic range floating-point pixel-level ADC,” IEEE J. Solid-State Circuits 34, 1821–1834 (1999).
[CrossRef]

D. Yang, H. Tian, B. Fowler, X. Liu, A. El Gamal, “Characterization of CMOS image sensors with Nyquist rate pixel level ADC,” in Sensors, Cameras, and Applications for Digital Photography, N. Sampat, T. Yeh, eds., Proc. SPIE3650, 52–62 (1999).
[CrossRef]

B. Fowler, A. El Gamal, D. Yang, H. Tian, “A method for estimating quantum efficiency for CMOS image sensors,” in Solid State Sensor Arrays: Development and Applications II, M. M. Blouke, ed., Proc. SPIE3301, 178–185 (1998).
[CrossRef]

B. Wandell, P. Catrysse, J. DiCarlo, D. Yang, A. El Gamal, “Multiple capture single image architecture with a CMOS sensor,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999), pp. 11–17.

Zalevsky, Z.

Ann. Phys. (Paris) (2)

F. Abelès, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. (Paris) 5, 596–640 (1950).

F. Abelès, “Recherches sur la propagation des ondes electromagnetiques sinusoidales dans les milieux stratifies: application aux couches minces,” Ann. Phys. (Paris) 5, 706–782 (1950).

Appl. Opt. (2)

IEEE J. Solid-State Circuits (1)

D. Yang, A. El Gamal, B. Fowler, H. Tian, “A 640×512 CMOS image sensor with ultrawide dynamic range floating-point pixel-level ADC,” IEEE J. Solid-State Circuits 34, 1821–1834 (1999).
[CrossRef]

IEEE Trans. Electron Devices (1)

M. Hideki, “Simulation for 3-D optical and electrical analysis of CCD,” IEEE Trans. Electron Devices 44, 1604–1610 (1997).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

M. J. Bastiaans, “The Wigner distribution function applied to optical signals and systems,” Opt. Commun. 25, 26–30 (1978).
[CrossRef]

Opt. Eng. (1)

J. R. Janesick, K. Evans, T. Elliot, “Charge-coupled-device response to electron beam energies of less than 1 keV up to 20 keV,” Opt. Eng. 26, 686–691 (1987).

Other (15)

B. Fowler, A. El Gamal, D. Yang, H. Tian, “A method for estimating quantum efficiency for CMOS image sensors,” in Solid State Sensor Arrays: Development and Applications II, M. M. Blouke, ed., Proc. SPIE3301, 178–185 (1998).
[CrossRef]

D. Yang, H. Tian, B. Fowler, X. Liu, A. El Gamal, “Characterization of CMOS image sensors with Nyquist rate pixel level ADC,” in Sensors, Cameras, and Applications for Digital Photography, N. Sampat, T. Yeh, eds., Proc. SPIE3650, 52–62 (1999).
[CrossRef]

R. J. Pegis, “The modern development of Hamiltonian optics,” in Progress in Optics I, E. Wolf, ed. (North-Holland, Amsterdam, 1961), pp. 1–29.

J. A. Penkethman, “Calibrations and idiosyncrasies of micro-lensed CCD cameras,” in Current Developments in Optical Design and Optical Engineering VIII, R. E. Fischer, W. J. Smith, eds., Proc. SPIE3779, 241–249 (1999).
[CrossRef]

P. Catrysse, X. Liu, A. El Gamal, “QE reduction due to pixel vignetting in CMOS image sensors,” in Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications, M. M. Blouke, N. Sampat, G. M. Williams, T. Yeh, eds., Proc. SPIE3965, 420–430 (2000).
[CrossRef]

Luminous, Silvaco International, Santa Clara, Calif., 1995.

Medici, Avanti Corporation, Fremont, Calif., 1998.

P. C. S. Hayfield, G. W. T. White, “An assessment of the suitability of the Drude–Tronstad polarized light method for the study of film growth on polycrystalline metals,” in Ellipsometry in the Measurement of Surfaces and Thin Films, N. M. Bashara, A. B. Buckman, A. C. Hall, eds. (National Bureau of Standards, Washington, D.C., 1964), Vol. 256, pp. 157–200.

E. R. Fossum, “Active pixel sensors: are CCD’s dinosaurs?” in Charge-Coupled Devices and Solid State Optical Sensors III, M. M. Blouke, ed., Proc. SPIE1900, 2–14 (1993).
[CrossRef]

S. Kleinfelder, S. Lim, X. Liu, A. El Gamal, “A 10kframes/s 0.18μm CMOS digital pixel sensor with pixel-level memory,” in 2001 International Solid-State Circuits Conference—Digest of Technical Papers (IEEE Press, Piscataway, N.J., 2001), pp. 88–89.

B. Wandell, P. Catrysse, J. DiCarlo, D. Yang, A. El Gamal, “Multiple capture single image architecture with a CMOS sensor,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999), pp. 11–17.

D. Dragoman, “The Wigner distribution function in optics and optoelectronics,” in Progress in Optics XXXVII, E. Wolf, ed. (Elsevier Science, Amsterdam, 1997), pp. 1–56.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1996), p. 404.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1986), p. 52.

M. Born, E. Wolf, Principles of Optics, 6th (corrected) ed. (Pergamon, Oxford, UK, 1980), pp. 38–41.

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Figures (11)

Fig. 1
Fig. 1

Scanning electron microscope image of a CMOS image sensor pixel. The image shows a cross section. The white areas show the metal layers and the connection vias. The top white layer is a dielectric passivation layer (Si3N4) sitting on top of a metal light shield. The shield has a square aperture so that incident light can reach the photodetector. The photodetector (Si) is located at the bottom of a dielectric tunnel (SiO2) of width 5.5 µm and depth 7.08 µm.

Fig. 2
Fig. 2

Geometrical-optics PS: The parameters (x0, p0) define a geometrical ray incident on a surface in (a) one-dimensional real space and (b) two-dimensional phase space.

Fig. 3
Fig. 3

PS representation of optical signals: (a) plane wave, (b) point source, (c) area source.

Fig. 4
Fig. 4

PS representations of several surface photodetector configurations: (a) photodetector covering the entire pixel area (100% fill factor), (b) photodetector covering half of the pixel area (50% fill factor), (c) photodetector covering half of the pixel area placed on axis in the imaging plane of a lens. The light-shaded area represents the PS representation of the lens at the image plane, and the black rectangle indicates the intersection of the surface photodetector PS and the lens PS.

Fig. 5
Fig. 5

PS representations of a pixel (50% fill factor): (a) pixel with surface photodetector, (b) pixel with buried photodetector [PS is given with respect to the photodetector plane (xo, po)], (c) pixel with buried photodetector. The input-referred PS is given with respect to the aperture plane (xi, pi). In the pixel cross-sectional diagram, the light-shaded areas indicate Si3N4, SiO2, and Si, the black rectangles represent metal wires, and the dark-shaded rectangle represents the photodetector.

Fig. 6
Fig. 6

Transmission efficiency of a CMOS image sensor pixel as a function of the angle of incidence of a plane wave calculated by using a scattering matrix approach. The curve represents the average transmission over visible wavelengths.

Fig. 7
Fig. 7

Experimental setups: (a) plane-wave experiment, (b) imaging experiment.

Fig. 8
Fig. 8

Plane-wave experimental results: Pixel response, normalized with respect to on-axis pixel response, is plotted as a function of angle of incidence of a plane wave. The error bars and solid curve represent measured and predicted values, respectively.

Fig. 9
Fig. 9

Imaging experimental results: Pixel response, normalized with respect to on-axis pixel response, is shown as a function of angle of incidence of the chief ray from an f/1.8 imaging lens with a 23-deg full FOV. The error bars and solid curve represent measured and predicted values, respectively.

Fig. 10
Fig. 10

OE predictions based on geometrical-optics PS. (a) On-axis pixel response (f/1.8 imaging lens) is shown as a function of number of metal layers in a 0.18-µm standard CMOS process. Aperture width is equal to 1.92 µm, and tunnel depths vary from 3.73 to 9.05 µm. (b) On-axis pixel response for a standard APS pixel with a 30% fill factor using two metal layers as a function of feature size of the CMOS technology used. Aperture width and tunnel depth vary from 3.72 to 1.92 µm and from 4.37 to 3.73 µm, respectively.

Fig. 11
Fig. 11

Comparison of geometrical-optics PS and wave-optics approaches to calculating pixel OE as a function of angle of incidence of the chief ray of an f/1.8 imaging lens with a full FOV of 23 deg. The computed pixel OE includes both geometric and transmission efficiency. When these theoretical curves are plotted with the data in Fig. 9, both the theory and the data are normalized to the on-axis pixel OE, effectively removing the transmission loss.

Equations (38)

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

p=n sin θx,q=n sin θy,
W(x, ν)=u(x+x/2)u*(x-x/2)exp(-2πiνx)dx.
W(x/2, ν)exp(2πiνx)dν=u(x)u*(0),
|u(0)|2=W(0, ν)dν.
Wgeom(x, p)=1W(x, ν)>Wthresh0otherwise,
p=λν.
WI(x, p)=δ(x-x0, p-p0)=δ(x-x0)δ(p-p0).
WI(x, p)=δ(p-p0).
WI(x, p)=δ(x-x0).
WI(x, p)=x-x0Δ,p-p02NA=x-x0Δp-p02NA.
x-x0Δx0=1,x0-Δx02xx0+Δx020,else.
Φ=WI(x, p)dxdp.
WY(x, p)=1withinacceptancerange0else.
WY(x, p)=xwp2n.
WY(x, p)=xw/2p2n.
WY(x, p)=xw/2p2NA.
G=WY(x, p)dxdp.
WIY(x, p)=WI(x, p)WY(x, p).
xopo=ABCDxipi.
xopo=1-d/n01xipi,
xo=xi-dpin1-pin21/2,po=pi.
ηgeom=GdetectorGaperture,
RMSE=n(Lmodel-Lmeasn)2N1/2,
E=maxnLmodel-LmeasnLmeasn.
E(z)=E+(z)E-(z).
E+(z)E-(z)=S11S12S21S22E+(z)E-(z).
S=I01L1  I(j-1)jLj  LmIm(m+1).
I(j-1)j=[1/t(j-1)j]1r(j-1)jr(j-1)j1.
n0 sin θ0==nj sin θj==nm+1 sin θm+1.
Lj=exp(jβj)00exp(-jβj),
βj=2πλdj nj cos θj.
R=S21S11,
T=1S21.
Aoαλ,βλ; 0=--Uo(x, y, 0)×exp-j2παλx+βλydxdy.
Aoαλ,βλ; zo=Aoαλ,βλ; 0expj2πλzo×exp-jπλzoαλ2+βλ2,
Aoαλ,βλ; zo=Aoαλ,βλ; 0×expj2πλ(1-α2-β2)1/2zo.
Uo(x, y, zo)=--Aoαλ,βλ; zo×expj2παλx+βλydαλdβλ,
Ul(x, y, zo)=P(x, y)expjk2 f(x2+y2)Uo(x, y, zo).

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