Abstract

The use of complementary engineered point spread functions is proposed for the joint tasks of depth estimation and image recovery over an extended depth of field. A digital imaging system with a dynamically adjustable pupil is demonstrated experimentally. The implementation of a broadband, passive camera is demonstrated with a fractional ranging error of 4/104 at a working distance of 1 m. Once the depth and brightness information of a scene are obtained, a synthetic camera is defined and images rendered computationally to emphasize particular features such as image focusing at different depths.

© 2012 Optical Society of America

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2011 (1)

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for super-resolution microscopy with engineered point spread functions,” Proc. Natl. Acad. Sci. USA 109, 675–679 (2011).
[CrossRef]

2010 (1)

2009 (4)

S. Bagheri, P. E. X. Silveira, and G. Barbastathis, “Signal-to-noise-ratio limit to the depth-of-field extension for imaging systems with an arbitrary pupil function,” J. Opt. Soc. Am. A 26, 895–908 (2009).
[CrossRef]

S. R. P. Pavani, J. G. DeLuca, and R. Piestun, “Polarization sensitive, three-dimensional, single-molecule imaging of cells with a double-helix system,” Opt. Express 17, 19644–19655 (2009).
[CrossRef]

S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. 95, 021103 (2009).
[CrossRef]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef]

2008 (3)

2007 (2)

H. Barrett, C. Dainty, and D. Lara, “Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions,” J. Opt. Soc. Am. A 24, 391–414(2007).
[CrossRef]

S. Ram, J. Chao, P. Prabhat, R. J. Ober, and E. S. Ward, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[CrossRef]

2006 (2)

2002 (1)

2001 (1)

2000 (3)

1997 (1)

1996 (1)

1995 (1)

1994 (1)

S. K. Nayar and Y. Nakagawa, “Shape from Focus,” IEEE Trans. Pattern Anal. 16, 824–831 (1994).
[CrossRef]

1992 (1)

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

1987 (1)

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. PAMI-9, 523–531 (1987).
[CrossRef]

1908 (1)

G. Lippman, “Épreuves réversibles donnant la sensation du relief,” J. Phys. Théor. Appl. 7, 821–825 (1908).
[CrossRef]

Adelson, E. H.

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

Arimoto, H.

Bagheri, S.

Barbastathis, G.

Barrett, H.

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef]

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef]

Bredif, M.

R. Ng, M. Levoy, M. Bredif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (Stanford University, 2005).

Cathey, W. T.

Chao, J.

S. Ram, J. Chao, P. Prabhat, R. J. Ober, and E. S. Ward, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[CrossRef]

Chaudhuri, S.

S. Chaudhuri and A. N. Rajagopalan, Depth from Defocus: A Real Aperture Imaging Approach (Springer-Verlag, 1999).

Curless, B.

T. Georgeiv, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoff in integral photography,” in Proceedings of the 17th Eurographics Conference on Rendering Techniques (Eurographics Association, 2006), pp. 263–272.

Dainty, C.

Darrell, T.

T. Darrell and K. Wohn, “Pyramid based depth from focus,” in Proceedings of Computer Vision and Pattern Recognition (IEEE, 1988), pp. 504–509.

de Farias, D. Pucci

Deaver, D. M.

del Pozo, F.

DeLuca, J. G.

Dowski, E.

Dowski, E. R.

Durand, F.

A. Levin, R. Fergus, F. Durand, and B. Freeman, “Image and depth from a conventional camera with a coded aperture,” SIGGRAPH 2007 (ACM, 2007), article 70.

Duval, G.

R. Ng, M. Levoy, M. Bredif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (Stanford University, 2005).

Favaro, P.

P. Favaro and S. Soatto, 3-D Shape Estimation and Image Restoration—Exploiting Defocus and Motion Blur (Springer-Verlag, 2007).

Fergus, R.

A. Levin, R. Fergus, F. Durand, and B. Freeman, “Image and depth from a conventional camera with a coded aperture,” SIGGRAPH 2007 (ACM, 2007), article 70.

Freeman, B.

A. Levin, R. Fergus, F. Durand, and B. Freeman, “Image and depth from a conventional camera with a coded aperture,” SIGGRAPH 2007 (ACM, 2007), article 70.

Gaya, F.

Georgeiv, T.

T. Georgeiv, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoff in integral photography,” in Proceedings of the 17th Eurographics Conference on Rendering Techniques (Eurographics Association, 2006), pp. 263–272.

Greengard, A.

S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. 95, 021103 (2009).
[CrossRef]

A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31, 181–183 (2006).
[CrossRef]

Grover, G.

Hanrahan, P.

R. Ng, M. Levoy, M. Bredif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (Stanford University, 2005).

Horowitz, M.

R. Ng, M. Levoy, M. Bredif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (Stanford University, 2005).

Huang, B.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef]

Intwala, C.

T. Georgeiv, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoff in integral photography,” in Proceedings of the 17th Eurographics Conference on Rendering Techniques (Eurographics Association, 2006), pp. 263–272.

Javidi, B.

Johnson, G. E.

Juskaitis, R.

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (Prentice Hall, 1993).

Kiryati, N.

Y. Y. Schechner and N. Kiryati, “Depth from defocus vs. stereo: how different really are they?” Int. J. Comput. Vis. 39, 141–162 (2000).
[CrossRef]

Lara, D.

Levin, A.

A. Levin, R. Fergus, F. Durand, and B. Freeman, “Image and depth from a conventional camera with a coded aperture,” SIGGRAPH 2007 (ACM, 2007), article 70.

Levoy, M.

R. Ng, M. Levoy, M. Bredif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (Stanford University, 2005).

Lin, S.

C. Zhou, S. Lin, and S. Nayar, “Coded aperture pairs for depth from defocus,” IEEE International Conference on Computer Vision (IEEE, 2009), pp. 325–332.

Lippman, G.

G. Lippman, “Épreuves réversibles donnant la sensation du relief,” J. Phys. Théor. Appl. 7, 821–825 (1908).
[CrossRef]

Liu, N.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef]

Lord, S. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef]

Medina, A.

Moerner, W. E.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef]

Nakagawa, Y.

S. K. Nayar and Y. Nakagawa, “Shape from Focus,” IEEE Trans. Pattern Anal. 16, 824–831 (1994).
[CrossRef]

Narayanswamy, R.

Nayar, S.

T. Georgeiv, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoff in integral photography,” in Proceedings of the 17th Eurographics Conference on Rendering Techniques (Eurographics Association, 2006), pp. 263–272.

C. Zhou, S. Lin, and S. Nayar, “Coded aperture pairs for depth from defocus,” IEEE International Conference on Computer Vision (IEEE, 2009), pp. 325–332.

Nayar, S. K.

S. K. Nayar and Y. Nakagawa, “Shape from Focus,” IEEE Trans. Pattern Anal. 16, 824–831 (1994).
[CrossRef]

Neil, M. A. A.

Ng, R.

R. Ng, M. Levoy, M. Bredif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Stanford University Computer Science Tech Report CSTR 2005-02 (Stanford University, 2005).

Ober, R. J.

S. Ram, J. Chao, P. Prabhat, R. J. Ober, and E. S. Ward, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[CrossRef]

Pavani, S. R. P.

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for super-resolution microscopy with engineered point spread functions,” Proc. Natl. Acad. Sci. USA 109, 675–679 (2011).
[CrossRef]

G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett. 35, 3306–3308 (2010).
[CrossRef]

S. R. P. Pavani, J. G. DeLuca, and R. Piestun, “Polarization sensitive, three-dimensional, single-molecule imaging of cells with a double-helix system,” Opt. Express 17, 19644–19655 (2009).
[CrossRef]

S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. 95, 021103 (2009).
[CrossRef]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
[CrossRef]

Pentland, A. P.

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. PAMI-9, 523–531 (1987).
[CrossRef]

Piestun, R.

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for super-resolution microscopy with engineered point spread functions,” Proc. Natl. Acad. Sci. USA 109, 675–679 (2011).
[CrossRef]

G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett. 35, 3306–3308 (2010).
[CrossRef]

S. R. P. Pavani, J. G. DeLuca, and R. Piestun, “Polarization sensitive, three-dimensional, single-molecule imaging of cells with a double-helix system,” Opt. Express 17, 19644–19655 (2009).
[CrossRef]

S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. 95, 021103 (2009).
[CrossRef]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
[CrossRef]

A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31, 181–183 (2006).
[CrossRef]

R. Piestun, Y. Y. Schechner, and J. Shamir, “Propagation-invariant wave fields with finite energy,” J. Opt. Soc. Am. A 17, 294–303 (2000).
[CrossRef]

Prabhat, P.

S. Ram, J. Chao, P. Prabhat, R. J. Ober, and E. S. Ward, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[CrossRef]

Quirin, S.

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for super-resolution microscopy with engineered point spread functions,” Proc. Natl. Acad. Sci. USA 109, 675–679 (2011).
[CrossRef]

Rajagopalan, A. N.

S. Chaudhuri and A. N. Rajagopalan, Depth from Defocus: A Real Aperture Imaging Approach (Springer-Verlag, 1999).

Ram, S.

S. Ram, J. Chao, P. Prabhat, R. J. Ober, and E. S. Ward, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[CrossRef]

Salesin, D.

T. Georgeiv, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoff in integral photography,” in Proceedings of the 17th Eurographics Conference on Rendering Techniques (Eurographics Association, 2006), pp. 263–272.

Schechner, Y. Y.

Shafer, S. A.

Y. Xiong and S. A. Shafer, “Depth from focusing and defocusing,” Technical report CMU-RI-TR-93-07 (Robotics Institute, Carnegie Mellon University, 1993).

Shamir, J.

Silveira, P. E. X.

Soatto, S.

P. Favaro and S. Soatto, 3-D Shape Estimation and Image Restoration—Exploiting Defocus and Motion Blur (Springer-Verlag, 2007).

Taylor, M. G.

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef]

Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[CrossRef]

van der Gracht, J.

Wang, J. Y.

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

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef]

Ward, E. S.

S. Ram, J. Chao, P. Prabhat, R. J. Ober, and E. S. Ward, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[CrossRef]

Wilson, T.

Wohn, K.

T. Darrell and K. Wohn, “Pyramid based depth from focus,” in Proceedings of Computer Vision and Pattern Recognition (IEEE, 1988), pp. 504–509.

Xiong, Y.

Y. Xiong and S. A. Shafer, “Depth from focusing and defocusing,” Technical report CMU-RI-TR-93-07 (Robotics Institute, Carnegie Mellon University, 1993).

Zheng, K. C.

T. Georgeiv, K. C. Zheng, B. Curless, D. Salesin, S. Nayar, and C. Intwala, “Spatio-angular resolution tradeoff in integral photography,” in Proceedings of the 17th Eurographics Conference on Rendering Techniques (Eurographics Association, 2006), pp. 263–272.

Zhou, C.

C. Zhou, S. Lin, and S. Nayar, “Coded aperture pairs for depth from defocus,” IEEE International Conference on Computer Vision (IEEE, 2009), pp. 325–332.

Zhuang, X.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. R. P. Pavani, A. Greengard, and R. Piestun, “Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system,” Appl. Phys. Lett. 95, 021103 (2009).
[CrossRef]

IEEE Trans. Pattern Anal. (2)

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. PAMI-9, 523–531 (1987).
[CrossRef]

S. K. Nayar and Y. Nakagawa, “Shape from Focus,” IEEE Trans. Pattern Anal. 16, 824–831 (1994).
[CrossRef]

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

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

Int. J. Comput. Vis. (1)

Y. Y. Schechner and N. Kiryati, “Depth from defocus vs. stereo: how different really are they?” Int. J. Comput. Vis. 39, 141–162 (2000).
[CrossRef]

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