Abstract

We present a pixel-scale sensor that uses the Talbot effect to detect the local intensity and incident angle of light. The sensor comprises two local diffraction gratings stacked above a photodiode. When illuminated by a plane wave, the upper grating generates a self-image at the half Talbot depth. The second grating, placed at this depth, blocks or passes light depending upon incident angle. Several such structures, tuned to different incident angles, are sufficient to extract local incident angle and intensity. Furthermore, arrays of such structures are sufficient to localize light sources in three dimensions without any additional optics.

© 2009 Optical Society of America

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  1. A. Gershun, “The light field,” J. Math. Phys. 18, 51-151 (1939), translated by G. Timoshenko and P. Moon.
  2. P. Moon and D. E. Spencer, The Photic Field (MIT Press, 1981).
  3. M. Levoy and P. Hanrahan, “Light field rendering,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 31-42.
  4. R. Ng, “Fourier slice photography,” ACM Trans. Graphics 24, 735-744 (2005).
    [CrossRef]
  5. H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401-407 (1836).
  6. M. Faraday, “Thoughts on ray vibrations,” Philos. Mag. 28, 346-350 (1846).
  7. E. Adelson and J. Bergen, “The plenoptic function and the elements of early vision,” in Computational Models of Visual Processing, M. Landy and J. A. Movshon, eds. (MIT Press, 1991), pp. 3-20.
  8. E. Adelson and J. Y. A. Wang, “Single lens stereo with a plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99-106 (1992).
    [CrossRef]
  9. A. Kubota, K. Aizawa, and T. Chen, “Reconstructing dense light field from array of multifocus images for novel view synthesis,” IEEE Trans. Image Process. 16, 269-279 (2007).
    [CrossRef]
  10. B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.
  11. A. Isaksen, L. McMillan, and S. J. Gortler, “Dynamically reparameterized light fields,” in Proceedings ACM SIGGRAPH 2000 (Association for Computing Machinery, 2000), pp. 297-306.
  12. A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graphics 26, 69-80 (2007).
  13. K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3D multi-aperture image sensor architecture,” in Custom Integrated Circuits Conference (IEEE, 2006), pp. 281-284.
  14. S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 43-54.
  15. M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings ACM SIGGRAPH 2006 (Association for Computing Machinery, 2006), pp. 924-934
  16. Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196-205 (1881).
  17. E. A. Hiedemann and M. A. Breazeale, “Secondary interference in the Fresnel zone of gratings,” J. Opt. Soc. Am. 49, 372-375 (1959).
    [CrossRef]
  18. J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images: I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373-381 (1965).
    [CrossRef]
  19. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772-775 (1967).
    [CrossRef]
  20. A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
    [CrossRef]
  21. J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
    [CrossRef]
  22. A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337-4340 (1990).
    [CrossRef]
  23. N. H. Salama, D. Patrignani, L. di Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269-272 (1999).
    [CrossRef]
  24. C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265-275 (2001).
    [CrossRef]
  25. P. Chavel and T. C. Strand, “Range measurement using Talbot diffraction imaging of gratings,” Appl. Opt. 23, 862-871(1984).
    [CrossRef]
  26. J. R. Leger and M. A. Snyder, “Real-time depth measurement and display using Fresnel diffraction and white-light processing,” Appl. Opt. 23, 1655-1670 (1984).
    [CrossRef]
  27. H. O. Carmesin and D. Goldbeck, “Depth map by convergent 3D Talbot interferometry,” Optik (Jena) 108, 101-116 (1998).
  28. M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167-172 (1996).
    [CrossRef]
  29. S. Teng, Y. Tan, and C. Cheng, “Quasi-Talbot effect of the high-density grating in near field,” J. Opt. Soc. Am. A 25, 2945-2951 (2008).
    [CrossRef]
  30. I. I. Smolyaninov and C. C. Davis, “Apparent superresolution in near-field optical imaging of periodic gratings,” Opt. Lett. 23, 1346-1348 (1998).
    [CrossRef]
  31. K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 0.5 μm pixel frame transfer CCD imager sensor in 110 nm CMOS,” in IEEE International Electron Devices Meeting (IEEE, 2007), pp. 1003-1006.
  32. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
    [CrossRef]
  33. S. Teng, L. Liu, J. Zu, Z. Luan, and D. Liu, “Uniform theory of the Talbot effect with partially coherent light illumination,” J. Opt. Soc. Am. A 20, 1747-1754 (2003).
    [CrossRef]
  34. Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154-2160(2006).
    [CrossRef]
  35. K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3M pixel multi-aperture image sensor with 0.7 μm pixels in 0.11 μm CMOS,” in IEEE ISSCC Digest of Technical Papers (IEEE, 2008), pp. 48-49.

2008 (2)

S. Teng, Y. Tan, and C. Cheng, “Quasi-Talbot effect of the high-density grating in near field,” J. Opt. Soc. Am. A 25, 2945-2951 (2008).
[CrossRef]

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3M pixel multi-aperture image sensor with 0.7 μm pixels in 0.11 μm CMOS,” in IEEE ISSCC Digest of Technical Papers (IEEE, 2008), pp. 48-49.

2007 (3)

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 0.5 μm pixel frame transfer CCD imager sensor in 110 nm CMOS,” in IEEE International Electron Devices Meeting (IEEE, 2007), pp. 1003-1006.

A. Kubota, K. Aizawa, and T. Chen, “Reconstructing dense light field from array of multifocus images for novel view synthesis,” IEEE Trans. Image Process. 16, 269-279 (2007).
[CrossRef]

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graphics 26, 69-80 (2007).

2006 (3)

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3D multi-aperture image sensor architecture,” in Custom Integrated Circuits Conference (IEEE, 2006), pp. 281-284.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings ACM SIGGRAPH 2006 (Association for Computing Machinery, 2006), pp. 924-934

Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154-2160(2006).
[CrossRef]

2005 (2)

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

R. Ng, “Fourier slice photography,” ACM Trans. Graphics 24, 735-744 (2005).
[CrossRef]

2003 (1)

S. Teng, L. Liu, J. Zu, Z. Luan, and D. Liu, “Uniform theory of the Talbot effect with partially coherent light illumination,” J. Opt. Soc. Am. A 20, 1747-1754 (2003).
[CrossRef]

2001 (1)

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265-275 (2001).
[CrossRef]

2000 (1)

A. Isaksen, L. McMillan, and S. J. Gortler, “Dynamically reparameterized light fields,” in Proceedings ACM SIGGRAPH 2000 (Association for Computing Machinery, 2000), pp. 297-306.

1999 (1)

N. H. Salama, D. Patrignani, L. di Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269-272 (1999).
[CrossRef]

1998 (2)

I. I. Smolyaninov and C. C. Davis, “Apparent superresolution in near-field optical imaging of periodic gratings,” Opt. Lett. 23, 1346-1348 (1998).
[CrossRef]

H. O. Carmesin and D. Goldbeck, “Depth map by convergent 3D Talbot interferometry,” Optik (Jena) 108, 101-116 (1998).

1996 (3)

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167-172 (1996).
[CrossRef]

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 43-54.

M. Levoy and P. Hanrahan, “Light field rendering,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 31-42.

1995 (1)

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
[CrossRef]

1992 (1)

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

1991 (1)

E. Adelson and J. Bergen, “The plenoptic function and the elements of early vision,” in Computational Models of Visual Processing, M. Landy and J. A. Movshon, eds. (MIT Press, 1991), pp. 3-20.

1990 (1)

A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337-4340 (1990).
[CrossRef]

1984 (2)

P. Chavel and T. C. Strand, “Range measurement using Talbot diffraction imaging of gratings,” Appl. Opt. 23, 862-871(1984).
[CrossRef]

J. R. Leger and M. A. Snyder, “Real-time depth measurement and display using Fresnel diffraction and white-light processing,” Appl. Opt. 23, 1655-1670 (1984).
[CrossRef]

1983 (1)

J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
[CrossRef]

1981 (1)

P. Moon and D. E. Spencer, The Photic Field (MIT Press, 1981).

1971 (1)

A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

1967 (1)

W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772-775 (1967).
[CrossRef]

1965 (1)

J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images: I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373-381 (1965).
[CrossRef]

1959 (1)

E. A. Hiedemann and M. A. Breazeale, “Secondary interference in the Fresnel zone of gratings,” J. Opt. Soc. Am. 49, 372-375 (1959).
[CrossRef]

1939 (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 51-151 (1939), translated by G. Timoshenko and P. Moon.

1881 (1)

Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196-205 (1881).

1846 (1)

M. Faraday, “Thoughts on ray vibrations,” Philos. Mag. 28, 346-350 (1846).

1836 (1)

H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401-407 (1836).

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings ACM SIGGRAPH 2006 (Association for Computing Machinery, 2006), pp. 924-934

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

Adelson, E.

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

E. Adelson and J. Bergen, “The plenoptic function and the elements of early vision,” in Computational Models of Visual Processing, M. Landy and J. A. Movshon, eds. (MIT Press, 1991), pp. 3-20.

Agrawal, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graphics 26, 69-80 (2007).

Aizawa, K.

A. Kubota, K. Aizawa, and T. Chen, “Reconstructing dense light field from array of multifocus images for novel view synthesis,” IEEE Trans. Image Process. 16, 269-279 (2007).
[CrossRef]

Antunez, E.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

Balmer, J. E.

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265-275 (2001).
[CrossRef]

Barth, A.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

Bergen, J.

E. Adelson and J. Bergen, “The plenoptic function and the elements of early vision,” in Computational Models of Visual Processing, M. Landy and J. A. Movshon, eds. (MIT Press, 1991), pp. 3-20.

Breazeale, M. A.

E. A. Hiedemann and M. A. Breazeale, “Secondary interference in the Fresnel zone of gratings,” J. Opt. Soc. Am. 49, 372-375 (1959).
[CrossRef]

Carmesin, H. O.

H. O. Carmesin and D. Goldbeck, “Depth map by convergent 3D Talbot interferometry,” Optik (Jena) 108, 101-116 (1998).

Chapman, M. S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
[CrossRef]

Chavel, P.

P. Chavel and T. C. Strand, “Range measurement using Talbot diffraction imaging of gratings,” Appl. Opt. 23, 862-871(1984).
[CrossRef]

Chen, T.

A. Kubota, K. Aizawa, and T. Chen, “Reconstructing dense light field from array of multifocus images for novel view synthesis,” IEEE Trans. Image Process. 16, 269-279 (2007).
[CrossRef]

Cheng, C.

S. Teng, Y. Tan, and C. Cheng, “Quasi-Talbot effect of the high-density grating in near field,” J. Opt. Soc. Am. A 25, 2945-2951 (2008).
[CrossRef]

Cohen, M. F.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 43-54.

Davis, C. C.

I. I. Smolyaninov and C. C. Davis, “Apparent superresolution in near-field optical imaging of periodic gratings,” Opt. Lett. 23, 1346-1348 (1998).
[CrossRef]

di Pasquale, L.

N. H. Salama, D. Patrignani, L. di Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269-272 (1999).
[CrossRef]

Ekstrom, C. R.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
[CrossRef]

Faraday, M.

M. Faraday, “Thoughts on ray vibrations,” Philos. Mag. 28, 346-350 (1846).

Fife, K.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3M pixel multi-aperture image sensor with 0.7 μm pixels in 0.11 μm CMOS,” in IEEE ISSCC Digest of Technical Papers (IEEE, 2008), pp. 48-49.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 0.5 μm pixel frame transfer CCD imager sensor in 110 nm CMOS,” in IEEE International Electron Devices Meeting (IEEE, 2007), pp. 1003-1006.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3D multi-aperture image sensor architecture,” in Custom Integrated Circuits Conference (IEEE, 2006), pp. 281-284.

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings ACM SIGGRAPH 2006 (Association for Computing Machinery, 2006), pp. 924-934

Gamal, A. E.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3M pixel multi-aperture image sensor with 0.7 μm pixels in 0.11 μm CMOS,” in IEEE ISSCC Digest of Technical Papers (IEEE, 2008), pp. 48-49.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 0.5 μm pixel frame transfer CCD imager sensor in 110 nm CMOS,” in IEEE International Electron Devices Meeting (IEEE, 2007), pp. 1003-1006.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3D multi-aperture image sensor architecture,” in Custom Integrated Circuits Conference (IEEE, 2006), pp. 281-284.

Gershun, A.

A. Gershun, “The light field,” J. Math. Phys. 18, 51-151 (1939), translated by G. Timoshenko and P. Moon.

Goldbeck, D.

H. O. Carmesin and D. Goldbeck, “Depth map by convergent 3D Talbot interferometry,” Optik (Jena) 108, 101-116 (1998).

Goncharenko, A. M.

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Gortler, S. J.

A. Isaksen, L. McMillan, and S. J. Gortler, “Dynamically reparameterized light fields,” in Proceedings ACM SIGGRAPH 2000 (Association for Computing Machinery, 2000), pp. 297-306.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 43-54.

Grzeszczuk, R.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 43-54.

Hammond, T. D.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
[CrossRef]

Hanrahan, P.

M. Levoy and P. Hanrahan, “Light field rendering,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 31-42.

Hiedemann, E. A.

E. A. Hiedemann and M. A. Breazeale, “Secondary interference in the Fresnel zone of gratings,” J. Opt. Soc. Am. 49, 372-375 (1959).
[CrossRef]

Horowitz, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings ACM SIGGRAPH 2006 (Association for Computing Machinery, 2006), pp. 924-934

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

Isaksen, A.

A. Isaksen, L. McMillan, and S. J. Gortler, “Dynamically reparameterized light fields,” in Proceedings ACM SIGGRAPH 2000 (Association for Computing Machinery, 2000), pp. 297-306.

Jahns, J.

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Joshi, N.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

Khilo, N. A.

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Kubota, A.

A. Kubota, K. Aizawa, and T. Chen, “Reconstructing dense light field from array of multifocus images for novel view synthesis,” IEEE Trans. Image Process. 16, 269-279 (2007).
[CrossRef]

Leger, J. R.

J. R. Leger and M. A. Snyder, “Real-time depth measurement and display using Fresnel diffraction and white-light processing,” Appl. Opt. 23, 1655-1670 (1984).
[CrossRef]

Levoy, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings ACM SIGGRAPH 2006 (Association for Computing Machinery, 2006), pp. 924-934

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

M. Levoy and P. Hanrahan, “Light field rendering,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 31-42.

Liu, D.

S. Teng, L. Liu, J. Zu, Z. Luan, and D. Liu, “Uniform theory of the Talbot effect with partially coherent light illumination,” J. Opt. Soc. Am. A 20, 1747-1754 (2003).
[CrossRef]

Liu, L.

S. Teng, L. Liu, J. Zu, Z. Luan, and D. Liu, “Uniform theory of the Talbot effect with partially coherent light illumination,” J. Opt. Soc. Am. A 20, 1747-1754 (2003).
[CrossRef]

Loewenthal, F.

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265-275 (2001).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337-4340 (1990).
[CrossRef]

A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

Lu, Y.

Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154-2160(2006).
[CrossRef]

Luan, Z.

S. Teng, L. Liu, J. Zu, Z. Luan, and D. Liu, “Uniform theory of the Talbot effect with partially coherent light illumination,” J. Opt. Soc. Am. A 20, 1747-1754 (2003).
[CrossRef]

McMillan, L.

A. Isaksen, L. McMillan, and S. J. Gortler, “Dynamically reparameterized light fields,” in Proceedings ACM SIGGRAPH 2000 (Association for Computing Machinery, 2000), pp. 297-306.

Mohan, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graphics 26, 69-80 (2007).

Montgomery, W. D.

W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772-775 (1967).
[CrossRef]

Moon, P.

P. Moon and D. E. Spencer, The Photic Field (MIT Press, 1981).

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings ACM SIGGRAPH 2006 (Association for Computing Machinery, 2006), pp. 924-934

R. Ng, “Fourier slice photography,” ACM Trans. Graphics 24, 735-744 (2005).
[CrossRef]

Ojeda-Castañeda, J.

J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
[CrossRef]

Patrignani, D.

N. H. Salama, D. Patrignani, L. di Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269-272 (1999).
[CrossRef]

Pritchard, D. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
[CrossRef]

Raskar, R.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graphics 26, 69-80 (2007).

Rayleigh, Lord

Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196-205 (1881).

Salama, N. H.

N. H. Salama, D. Patrignani, L. di Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269-272 (1999).
[CrossRef]

Schmiedmayer, J.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
[CrossRef]

Sicre, E. E.

N. H. Salama, D. Patrignani, L. di Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269-272 (1999).
[CrossRef]

J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
[CrossRef]

Siegel, C.

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265-275 (2001).
[CrossRef]

Silva, D. E.

A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov and C. C. Davis, “Apparent superresolution in near-field optical imaging of periodic gratings,” Opt. Lett. 23, 1346-1348 (1998).
[CrossRef]

Snyder, M. A.

J. R. Leger and M. A. Snyder, “Real-time depth measurement and display using Fresnel diffraction and white-light processing,” Appl. Opt. 23, 1655-1670 (1984).
[CrossRef]

Spencer, D. E.

P. Moon and D. E. Spencer, The Photic Field (MIT Press, 1981).

Strand, T. C.

P. Chavel and T. C. Strand, “Range measurement using Talbot diffraction imaging of gratings,” Appl. Opt. 23, 862-871(1984).
[CrossRef]

Szeliski, R.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 43-54.

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401-407 (1836).

Talvala, E.-V.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

Tan, Y.

S. Teng, Y. Tan, and C. Cheng, “Quasi-Talbot effect of the high-density grating in near field,” J. Opt. Soc. Am. A 25, 2945-2951 (2008).
[CrossRef]

Tannian, B. E.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
[CrossRef]

Teng, S.

S. Teng, Y. Tan, and C. Cheng, “Quasi-Talbot effect of the high-density grating in near field,” J. Opt. Soc. Am. A 25, 2945-2951 (2008).
[CrossRef]

S. Teng, L. Liu, J. Zu, Z. Luan, and D. Liu, “Uniform theory of the Talbot effect with partially coherent light illumination,” J. Opt. Soc. Am. A 20, 1747-1754 (2003).
[CrossRef]

Testorf, M.

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167-172 (1996).
[CrossRef]

Thomas, J. A.

A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337-4340 (1990).
[CrossRef]

Tumblin, J.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graphics 26, 69-80 (2007).

Vaish, V.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

Veeraraghavan, A.

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graphics 26, 69-80 (2007).

Wang, B.

Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154-2160(2006).
[CrossRef]

Wang, J. Y. A.

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

Wang, S.

Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154-2160(2006).
[CrossRef]

Wehinger, S.

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
[CrossRef]

Wilburn, B.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

Winthrop, J. T.

J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images: I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373-381 (1965).
[CrossRef]

Wong, H.-S. P.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3M pixel multi-aperture image sensor with 0.7 μm pixels in 0.11 μm CMOS,” in IEEE ISSCC Digest of Technical Papers (IEEE, 2008), pp. 48-49.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 0.5 μm pixel frame transfer CCD imager sensor in 110 nm CMOS,” in IEEE International Electron Devices Meeting (IEEE, 2007), pp. 1003-1006.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3D multi-aperture image sensor architecture,” in Custom Integrated Circuits Conference (IEEE, 2006), pp. 281-284.

Worthington, C. R.

J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images: I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373-381 (1965).
[CrossRef]

Zhou, C.

Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154-2160(2006).
[CrossRef]

Zu, J.

S. Teng, L. Liu, J. Zu, Z. Luan, and D. Liu, “Uniform theory of the Talbot effect with partially coherent light illumination,” J. Opt. Soc. Am. A 20, 1747-1754 (2003).
[CrossRef]

ACM Trans. Graphics (2)

R. Ng, “Fourier slice photography,” ACM Trans. Graphics 24, 735-744 (2005).
[CrossRef]

A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Trans. Graphics 26, 69-80 (2007).

Appl. Opt. (3)

A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337-4340 (1990).
[CrossRef]

P. Chavel and T. C. Strand, “Range measurement using Talbot diffraction imaging of gratings,” Appl. Opt. 23, 862-871(1984).
[CrossRef]

J. R. Leger and M. A. Snyder, “Real-time depth measurement and display using Fresnel diffraction and white-light processing,” Appl. Opt. 23, 1655-1670 (1984).
[CrossRef]

IEEE Trans. Image Process. (1)

A. Kubota, K. Aizawa, and T. Chen, “Reconstructing dense light field from array of multifocus images for novel view synthesis,” IEEE Trans. Image Process. 16, 269-279 (2007).
[CrossRef]

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

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

J. Math. Phys. (1)

A. Gershun, “The light field,” J. Math. Phys. 18, 51-151 (1939), translated by G. Timoshenko and P. Moon.

J. Opt. Soc. Am. (3)

E. A. Hiedemann and M. A. Breazeale, “Secondary interference in the Fresnel zone of gratings,” J. Opt. Soc. Am. 49, 372-375 (1959).
[CrossRef]

J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images: I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373-381 (1965).
[CrossRef]

W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772-775 (1967).
[CrossRef]

J. Opt. Soc. Am. A (3)

S. Teng, Y. Tan, and C. Cheng, “Quasi-Talbot effect of the high-density grating in near field,” J. Opt. Soc. Am. A 25, 2945-2951 (2008).
[CrossRef]

S. Teng, L. Liu, J. Zu, Z. Luan, and D. Liu, “Uniform theory of the Talbot effect with partially coherent light illumination,” J. Opt. Soc. Am. A 20, 1747-1754 (2003).
[CrossRef]

Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154-2160(2006).
[CrossRef]

Opt. Commun. (4)

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265-275 (2001).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167-172 (1996).
[CrossRef]

A. W. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2, 413-415 (1971).
[CrossRef]

J. Ojeda-Castañeda and E. E. Sicre, “Tunable bandstop filter for binary objects: a self-imaging technique,” Opt. Commun. 47, 183-186 (1983).
[CrossRef]

Opt. Laser Technol. (1)

N. H. Salama, D. Patrignani, L. di Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269-272 (1999).
[CrossRef]

Opt. Lett. (1)

I. I. Smolyaninov and C. C. Davis, “Apparent superresolution in near-field optical imaging of periodic gratings,” Opt. Lett. 23, 1346-1348 (1998).
[CrossRef]

Optik (Jena) (1)

H. O. Carmesin and D. Goldbeck, “Depth map by convergent 3D Talbot interferometry,” Optik (Jena) 108, 101-116 (1998).

Philos. Mag. (3)

Lord Rayleigh, “On copying diffraction gratings, and on some phenomena connected therewith,” Philos. Mag. 11, 196-205 (1881).

H. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401-407 (1836).

M. Faraday, “Thoughts on ray vibrations,” Philos. Mag. 28, 346-350 (1846).

Phys. Rev. A (1)

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: the atomic Talbot effect,” Phys. Rev. A 51, R14-R17 (1995).
[CrossRef]

Other (10)

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 0.5 μm pixel frame transfer CCD imager sensor in 110 nm CMOS,” in IEEE International Electron Devices Meeting (IEEE, 2007), pp. 1003-1006.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3M pixel multi-aperture image sensor with 0.7 μm pixels in 0.11 μm CMOS,” in IEEE ISSCC Digest of Technical Papers (IEEE, 2008), pp. 48-49.

E. Adelson and J. Bergen, “The plenoptic function and the elements of early vision,” in Computational Models of Visual Processing, M. Landy and J. A. Movshon, eds. (MIT Press, 1991), pp. 3-20.

P. Moon and D. E. Spencer, The Photic Field (MIT Press, 1981).

M. Levoy and P. Hanrahan, “Light field rendering,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 31-42.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” in Proceedings ACM SIGGRAPH 2005 (Association for Computing Machinery, 2005), pp. 765-776.

A. Isaksen, L. McMillan, and S. J. Gortler, “Dynamically reparameterized light fields,” in Proceedings ACM SIGGRAPH 2000 (Association for Computing Machinery, 2000), pp. 297-306.

K. Fife, A. E. Gamal, and H.-S. P. Wong, “A 3D multi-aperture image sensor architecture,” in Custom Integrated Circuits Conference (IEEE, 2006), pp. 281-284.

S. J. Gortler, R. Grzeszczuk, R. Szeliski, and M. F. Cohen, “The lumigraph,” in Proceedings ACM SIGGRAPH 1996 (Association for Computing Machinery, 1996), pp. 43-54.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” in Proceedings ACM SIGGRAPH 2006 (Association for Computing Machinery, 2006), pp. 924-934

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Figures (10)

Fig. 1
Fig. 1

Example of light-field imaging: (a) Light from a source strikes each pixel of an array with a distinct incident angle. (b) If each pixel in an array can determine the incident angle as well as the intensity of the light it detects, then array is able to localize a light source in three dimensions.

Fig. 2
Fig. 2

Illustration of self-imaging property of nanoscale diffraction gratings. (a) Definition of scale and dimensions. (b) FDTD simulations of the Talbot effect at the nanoscale: d = 800 nm , λ = 375 nm in Si O 2 (equivalent to 525 nm in vacuum), and θ = 0 . Note self-images at multiples of the half Talbot depth. (c) FDTD simulation showing lateral shift of the self-image at the half Talbot depth with shifting incident angle from θ = 0 ° to 5 ° .

Fig. 3
Fig. 3

FDTD simulations illustrating the effect of including an analyzer grating at the half Talbot depth. (a) When the peaks of the self-image align with the bars of the analyzer grating, little light passes through to a light detector below. (b) When the incident angle is shifted so that the peaks align with gaps in the analyzer grating, much more light passes to the detector. (c) Intensity of detected light changes periodically with swept incident angle.

Fig. 4
Fig. 4

(a) Illustration of multiple, adjacent sensors, with stacked gratings at different offset above distinct photodiodes: black dotted lines illustrate relative alignment of the gratings. (b) Simulation results, similar to Fig. 3c, but for various offsets: note that the incident angles that generate peak responses shift proportionally with the offset of the grating.

Fig. 5
Fig. 5

Microphotographs of (a) 1 ASP and (b)  8 × 8 array of ASPs, manufactured in 130 nm CMOS.

Fig. 6
Fig. 6

Measured responses of an ASP as incident angle is swept.

Fig. 7
Fig. 7

Measured effect of wavelength on angular sensitivity, b, and modulation depth, m.

Fig. 8
Fig. 8

Measured ASP array response to a light source held 500 μm above the array and slightly to the left. (a) Responses of individual sensors, where brighter squares represent more heavily illuminated sensors and white lines delimit individual ASPs. (b) Computed incident angle for each ASP (projected into the x - y plane).

Fig. 9
Fig. 9

An 8 × 8 ASP array accurately resolves light source locations in 3D space. (a) The measured light-vector field due to a source 550 μm above the array can clearly reconstruct lateral shifts in location (in this case by 100 μm ). (b) The measured light-vector field can also be used to reconstruct changes in depth (z) of a light source, in this case by 50 μm .

Fig. 10
Fig. 10

8 × 8 ASP array resolves light source locations with high resolution. All measurements were taken at a height of 550 μm . (a) Reconstructed locations of a source at three different depths separated by approximately 5 μm are clearly distinct: observed σ y = 0.19 μm and σ z = 1.74 μm . (b) Reconstruction precision is much higher in the lateral (x) direction than in the axial (z) direction: observed σ x = 0.14 μm . Three different lateral positions are shown.

Equations (6)

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

R 0 = I 0 ( 1 m cos ( b θ ) ) F ( θ ) , R 1 / 4 = I 0 ( 1 + m sin ( b θ ) ) F ( θ ) , R 1 / 2 = I 0 ( 1 + m cos ( b θ ) ) F ( θ ) , R 3 / 4 = I 0 ( 1 m sin ( b θ ) ) F ( θ ) .
I 0 F ( θ ) = R 0 + R 1 / 2 2 = R 1 / 4 + R 3 / 4 2 .
θ = 1 b tan 1 ( R 1 / 4 R 3 / 4 R 1 / 2 R 0 ) .
σ θ = 2 m b σ R R ,
σ x = z σ θ = z 2 m b σ R R ,
σ z = z 2 m b σ R R 2 csc 2 θ = σ x 2 csc 2 θ ,

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