Abstract

In computational imaging by pattern projection, a sequence of microstructured light patterns codified onto a programmable spatial light modulator is used to sample an object. The patterns are used as generalized measurement modes where the object information is expressed. In this Letter, we show that the resolution of the recovered image is only limited by the numerical aperture of the projecting optics regardless of the quality of the collection optics. We provide proof-of-principle experiments where the single-pixel detection strategy outperforms the resolution achieved using a conventional optical array detector for optical imaging. It is advantageous in the presence of real-world conditions, such as optical aberrations and optical imperfections in between the sample and the sensor. We provide experimental verification of image retrieval even when an optical diffuser prevents imaging with a megapixel array camera.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  19. Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
    [CrossRef]

2013 (5)

2012 (5)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

T. Shirai, H. Kellock, T. Setälä, and A. T. Friberg, J. Opt. Soc. Am. A 29, 1288 (2012).
[CrossRef]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[CrossRef]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Opt. Lett. 37, 824 (2012).
[CrossRef]

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, Proc. Natl. Acad. Sci. USA 109, E1679 (2012).

2011 (2)

B. M. Davis, A. J. Hemphill, D. Cebeci Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, Anal. Chem. 83, 5086 (2011).
[CrossRef]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

2010 (1)

2008 (3)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

J. H. Shapiro, Phys. Rev. A 78, 061802 (2008).
[CrossRef]

E. J. Candes and M. B. Wakin, IEEE Signal Process. Mag. 25(5), 682 (2008).

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Ben-Amotz, D.

B. M. Davis, A. J. Hemphill, D. Cebeci Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, Anal. Chem. 83, 5086 (2011).
[CrossRef]

Bo, Z.

Bobin, J.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, Proc. Natl. Acad. Sci. USA 109, E1679 (2012).

Bullkich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Candes, E.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, Proc. Natl. Acad. Sci. USA 109, E1679 (2012).

Candes, E. J.

E. J. Candes and M. B. Wakin, IEEE Signal Process. Mag. 25(5), 682 (2008).

Cebeci Maltas, D.

B. M. Davis, A. J. Hemphill, D. Cebeci Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, Anal. Chem. 83, 5086 (2011).
[CrossRef]

Chahid, M.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, Proc. Natl. Acad. Sci. USA 109, E1679 (2012).

Cho, Y.-W.

Choi, W.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Choi, Y.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Clemente, P.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Appl. Phys. B 113, 551 (2013).
[CrossRef]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Opt. Lett. 37, 824 (2012).
[CrossRef]

Cohen, O.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Cohen-Hyams, T.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Dahan, M.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, Proc. Natl. Acad. Sci. USA 109, E1679 (2012).

Dana, H.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Dasari, R. R.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Davis, B. M.

B. M. Davis, A. J. Hemphill, D. Cebeci Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, Anal. Chem. 83, 5086 (2011).
[CrossRef]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Durán, V.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Appl. Phys. B 113, 551 (2013).
[CrossRef]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Opt. Lett. 37, 824 (2012).
[CrossRef]

Eldar, Y. C.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Erkmen, B. I.

Fang-Yen, C.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Feld, M. S.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Fernández-Alonso, M.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Appl. Phys. B 113, 551 (2013).
[CrossRef]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Opt. Lett. 37, 824 (2012).
[CrossRef]

Fink, M.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[CrossRef]

Friberg, A. T.

Gazit, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Gong, W.

Han, S.

Hemphill, A. J.

B. M. Davis, A. J. Hemphill, D. Cebeci Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, Anal. Chem. 83, 5086 (2011).
[CrossRef]

Howell, J. C.

Howland, G. A.

Irles, E.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Appl. Phys. B 113, 551 (2013).
[CrossRef]

Kang, P.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Kellock, H.

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Kim, Y.-H.

Kley, E. B.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[CrossRef]

Lancis, J.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Appl. Phys. B 113, 551 (2013).
[CrossRef]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Opt. Lett. 37, 824 (2012).
[CrossRef]

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Lee, K. J.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[CrossRef]

Li, E.

Lu, R.-W.

Lum, D. J.

Mendlovic, D.

Z. Zalevsky and D. Mendlovic, Optical Superresolution (Springer, 2003).

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[CrossRef]

Mousavi, H. S.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, Proc. Natl. Acad. Sci. USA 109, E1679 (2012).

Oh, J.-E.

Osherovich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Scarcelli, G.

Segev, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Setälä, T.

Shapiro, J. H.

Shechtman, Y.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Shirai, T.

Shoham, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Sidorenko, P.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Soldevila, F.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Appl. Phys. B 113, 551 (2013).
[CrossRef]

Steiner, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Studer, V.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, Proc. Natl. Acad. Sci. USA 109, E1679 (2012).

Szameit, A.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Tajahuerce, E.

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Appl. Phys. B 113, 551 (2013).
[CrossRef]

V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Opt. Lett. 37, 824 (2012).
[CrossRef]

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

Wakin, M. B.

E. J. Candes and M. B. Wakin, IEEE Signal Process. Mag. 25(5), 682 (2008).

Wang, B.-Q.

Wang, P.

B. M. Davis, A. J. Hemphill, D. Cebeci Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, Anal. Chem. 83, 5086 (2011).
[CrossRef]

Ware, M. R.

Wilson, T.

T. Wilson, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Yang, T. D.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Yao, X.-C.

Yavneh, I.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Zalevsky, Z.

Z. Zalevsky and D. Mendlovic, Optical Superresolution (Springer, 2003).

Zhang, Q.-X.

Zibulevsky, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Zipper, M. A.

B. M. Davis, A. J. Hemphill, D. Cebeci Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, Anal. Chem. 83, 5086 (2011).
[CrossRef]

Adv. Opt. Photon. (1)

Anal. Chem. (1)

B. M. Davis, A. J. Hemphill, D. Cebeci Maltaş, M. A. Zipper, P. Wang, and D. Ben-Amotz, Anal. Chem. 83, 5086 (2011).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

F. Soldevila, E. Irles, V. Durán, P. Clemente, M. Fernández-Alonso, E. Tajahuerce, and J. Lancis, Appl. Phys. B 113, 551 (2013).
[CrossRef]

Biomed. Opt. Express (1)

IEEE Signal Process. Mag. (2)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 25(2), 83 (2008).
[CrossRef]

E. J. Candes and M. B. Wakin, IEEE Signal Process. Mag. 25(5), 682 (2008).

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

Nat. Mater. (1)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Steiner, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, Nat. Mater. 11, 455 (2012).
[CrossRef]

Nat. Photonics (1)

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

J. H. Shapiro, Phys. Rev. A 78, 061802 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, Proc. Natl. Acad. Sci. USA 109, E1679 (2012).

Other (3)

E. J. Candes, http://users.ece.gatech.edu/justin/l1magic .

T. Wilson, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Z. Zalevsky and D. Mendlovic, Optical Superresolution (Springer, 2003).

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup for image resolution analysis via Hadamard illumination using a single-pixel architecture. See text for details.

Fig. 2.
Fig. 2.

Experimental results for image resolution analysis. (a) Part of the USAF test image. (b) Image obtained with CCD camera. (c) Reconstructed image of 128×128 pixels via single-pixel imaging (CR=2). Panels (d) and (e) show intensity profiles for USAF elements 6-6 and 7-5, respectively. Blue lines correspond to the CCD camera and red lines to the single-pixel image. The curves have been smoothed.

Fig. 3.
Fig. 3.

Images taken through a commercial diffuser placed between OB and O2 (see Fig. 1). (a) Image obtained with CCD camera. (b) Reconstructed image via single-pixel imaging (CR=2).

Equations (2)

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y=Sx,
minxl1such thaty=Sx,

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