Abstract

Optical eigenmode imaging (OEI) is an interesting nonlocal imaging method but has the drawback that the completeness of eigenmodes used in OEI is hard guarantee. This may lead to significant blurring of the reconstructed images. Here we show that in OEI with a sparse constraint, the correlation between the original target and the recovered image can be extremely close to 1 by retrieving lost information, and the compressibility is enhanced. In addition, high-quality images can be received for a wide range of both object and system parameters.

© 2014 Optical Society of America

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  1. A. C. D. Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, Phys. Rev. A 84, 021803(R) (2011).
    [CrossRef]
  2. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
    [CrossRef]
  3. N. Tian, Q. C. Guo, A. Wang, D. L. Xu, and L. Fu, Opt. Lett. 36, 003302 (2011).
    [CrossRef]
  4. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
    [CrossRef]
  5. B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
    [CrossRef]
  6. P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804(R) (2011).
    [CrossRef]
  7. J. Du, W. L. Gong, and S. S. Han, Opt. Lett. 37, 001067 (2012).
    [CrossRef]
  8. X. Tsampoula, M. Mazilu, T. Vettenburg, F. Gunn-Moore, and K. Dholakia, Photon. Res. 1, 000042 (2013).
    [CrossRef]
  9. O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
    [CrossRef]
  10. O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
    [CrossRef]
  11. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).
  12. C. B. Li, W. T. Yin, and Y. Zhang, http://www.caam.rice.edu/~optimization/L1/TVAL3/ .
  13. T. Sun, J. G. Liu, H. S. Yan, G. Morgan, and W. L. Chen, Opt. Lett. 38, 003471 (2013).
    [CrossRef]
  14. K. Piche, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, Opt. Express 20, 026424 (2012).
    [CrossRef]
  15. E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
    [CrossRef]

2013 (4)

X. Tsampoula, M. Mazilu, T. Vettenburg, F. Gunn-Moore, and K. Dholakia, Photon. Res. 1, 000042 (2013).
[CrossRef]

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

T. Sun, J. G. Liu, H. S. Yan, G. Morgan, and W. L. Chen, Opt. Lett. 38, 003471 (2013).
[CrossRef]

2012 (3)

K. Piche, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, Opt. Express 20, 026424 (2012).
[CrossRef]

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

J. Du, W. L. Gong, and S. S. Han, Opt. Lett. 37, 001067 (2012).
[CrossRef]

2011 (3)

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804(R) (2011).
[CrossRef]

A. C. D. Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, Phys. Rev. A 84, 021803(R) (2011).
[CrossRef]

N. Tian, Q. C. Guo, A. Wang, D. L. Xu, and L. Fu, Opt. Lett. 36, 003302 (2011).
[CrossRef]

2010 (1)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

2009 (1)

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

2008 (1)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).

2005 (1)

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Allain, M.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).

Belkebir, K.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Bowman, A.

B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Bowman, R.

B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Boyd, R. W.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

K. Piche, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, Opt. Express 20, 026424 (2012).
[CrossRef]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804(R) (2011).
[CrossRef]

Bromberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Chan, K. W. C.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804(R) (2011).
[CrossRef]

Chen, W. L.

T. Sun, J. G. Liu, H. S. Yan, G. Morgan, and W. L. Chen, Opt. Lett. 38, 003471 (2013).
[CrossRef]

D’Angelo, M.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).

Dholakia, K.

X. Tsampoula, M. Mazilu, T. Vettenburg, F. Gunn-Moore, and K. Dholakia, Photon. Res. 1, 000042 (2013).
[CrossRef]

A. C. D. Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, Phys. Rev. A 84, 021803(R) (2011).
[CrossRef]

Du, J.

J. Du, W. L. Gong, and S. S. Han, Opt. Lett. 37, 001067 (2012).
[CrossRef]

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).

Edger, M. P.

B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Fu, L.

N. Tian, Q. C. Guo, A. Wang, D. L. Xu, and L. Fu, Opt. Lett. 36, 003302 (2011).
[CrossRef]

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Girard, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Gong, W. L.

J. Du, W. L. Gong, and S. S. Han, Opt. Lett. 37, 001067 (2012).
[CrossRef]

Gunn-Moore, F.

X. Tsampoula, M. Mazilu, T. Vettenburg, F. Gunn-Moore, and K. Dholakia, Photon. Res. 1, 000042 (2013).
[CrossRef]

Guo, Q. C.

N. Tian, Q. C. Guo, A. Wang, D. L. Xu, and L. Fu, Opt. Lett. 36, 003302 (2011).
[CrossRef]

Han, S. S.

J. Du, W. L. Gong, and S. S. Han, Opt. Lett. 37, 001067 (2012).
[CrossRef]

Howell, J. C.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804(R) (2011).
[CrossRef]

Howland, G. A.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

Johnson, A. S.

K. Piche, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, Opt. Express 20, 026424 (2012).
[CrossRef]

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).

Kolobov, M. I.

K. Piche, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, Opt. Express 20, 026424 (2012).
[CrossRef]

Kosmeier, S.

A. C. D. Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, Phys. Rev. A 84, 021803(R) (2011).
[CrossRef]

Laske, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).

Leach, J.

K. Piche, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, Opt. Express 20, 026424 (2012).
[CrossRef]

Liu, J. G.

T. Sun, J. G. Liu, H. S. Yan, G. Morgan, and W. L. Chen, Opt. Lett. 38, 003471 (2013).
[CrossRef]

Luca, A. C. D.

A. C. D. Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, Phys. Rev. A 84, 021803(R) (2011).
[CrossRef]

Lugiato, L. A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Magana-Loaiza, O. S.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

Magatti, D.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

Malik, M.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

Mazilu, M.

X. Tsampoula, M. Mazilu, T. Vettenburg, F. Gunn-Moore, and K. Dholakia, Photon. Res. 1, 000042 (2013).
[CrossRef]

A. C. D. Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, Phys. Rev. A 84, 021803(R) (2011).
[CrossRef]

Moal, E. L.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Morgan, G.

T. Sun, J. G. Liu, H. S. Yan, G. Morgan, and W. L. Chen, Opt. Lett. 38, 003471 (2013).
[CrossRef]

Mudry, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Nicoletti, C.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Padgett, M. J.

B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Piche, K.

K. Piche, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, Opt. Express 20, 026424 (2012).
[CrossRef]

Salvail, J. Z.

K. Piche, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, Opt. Express 20, 026424 (2012).
[CrossRef]

Savatier, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Scarcelli, G.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Sentenac, A.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Shih, Y.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Silberberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Sun, B.

B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Sun, T.

T. Sun, J. G. Liu, H. S. Yan, G. Morgan, and W. L. Chen, Opt. Lett. 38, 003471 (2013).
[CrossRef]

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).

Takhar, D.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).

Tian, N.

N. Tian, Q. C. Guo, A. Wang, D. L. Xu, and L. Fu, Opt. Lett. 36, 003302 (2011).
[CrossRef]

Tsampoula, X.

X. Tsampoula, M. Mazilu, T. Vettenburg, F. Gunn-Moore, and K. Dholakia, Photon. Res. 1, 000042 (2013).
[CrossRef]

Valencia, A.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Vettenburg, T.

X. Tsampoula, M. Mazilu, T. Vettenburg, F. Gunn-Moore, and K. Dholakia, Photon. Res. 1, 000042 (2013).
[CrossRef]

Vittert, L. E.

B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Wang, A.

N. Tian, Q. C. Guo, A. Wang, D. L. Xu, and L. Fu, Opt. Lett. 36, 003302 (2011).
[CrossRef]

Welsh, S.

B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Xu, D. L.

N. Tian, Q. C. Guo, A. Wang, D. L. Xu, and L. Fu, Opt. Lett. 36, 003302 (2011).
[CrossRef]

Yan, H. S.

T. Sun, J. G. Liu, H. S. Yan, G. Morgan, and W. L. Chen, Opt. Lett. 38, 003471 (2013).
[CrossRef]

Zerom, P.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804(R) (2011).
[CrossRef]

Appl. Phys. Lett. (2)

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, Appl. Phys. Lett. 102, 231104 (2013).
[CrossRef]

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

IEEE Signal Process. Mag. (1)

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laske, T. Sun, K. F. Kelly, and R. G. Baraniuk, IEEE Signal Process. Mag. 10(83), 1109 (2008).

Nat. Photonics (1)

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. L. Moal, C. Nicoletti, M. Allain, and A. Sentenac, Nat. Photonics 6, 312 (2012).
[CrossRef]

Opt. Express (1)

K. Piche, J. Leach, A. S. Johnson, J. Z. Salvail, M. I. Kolobov, and R. W. Boyd, Opt. Express 20, 026424 (2012).
[CrossRef]

Opt. Lett. (3)

J. Du, W. L. Gong, and S. S. Han, Opt. Lett. 37, 001067 (2012).
[CrossRef]

T. Sun, J. G. Liu, H. S. Yan, G. Morgan, and W. L. Chen, Opt. Lett. 38, 003471 (2013).
[CrossRef]

N. Tian, Q. C. Guo, A. Wang, D. L. Xu, and L. Fu, Opt. Lett. 36, 003302 (2011).
[CrossRef]

Photon. Res. (1)

X. Tsampoula, M. Mazilu, T. Vettenburg, F. Gunn-Moore, and K. Dholakia, Photon. Res. 1, 000042 (2013).
[CrossRef]

Phys. Rev. A (2)

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, Phys. Rev. A 84, 061804(R) (2011).
[CrossRef]

A. C. D. Luca, S. Kosmeier, K. Dholakia, and M. Mazilu, Phys. Rev. A 84, 021803(R) (2011).
[CrossRef]

Phys. Rev. Lett. (2)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, Phys. Rev. Lett. 104, 253603 (2010).
[CrossRef]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef]

Science (1)

B. Sun, M. P. Edger, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, Science 340, 844 (2013).
[CrossRef]

Other (1)

C. B. Li, W. T. Yin, and Y. Zhang, http://www.caam.rice.edu/~optimization/L1/TVAL3/ .

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Figures (7)

Fig. 1.
Fig. 1.

Proposed experiment configuration of OEISC. Laser is expanded by focal mirrors F1 and F2 to cover the SLM. Light deflected from the SLM experiences different degrees of modulation controlled by the computer, then is focused by F3 on the target plane. Finally, the single pixel photodiode (PD) collects the coefficients between eigenmodes and the target (O).

Fig. 2.
Fig. 2.

(a) and (b) First and second object. (c) and (d) Corresponding DCT and space coefficients of the second object.

Fig. 3.
Fig. 3.

Red, 1D profile of one bar in Fig. 2(a). Blue, 1D profile of the bar recovered by OEISC. Black, 1D profile of the bar recovered by OEI.

Fig. 4.
Fig. 4.

Upper row, original images with different K1 numbers. Middle row, images from OEI. Bottom row, images from OEISC, w1=10, N=400.

Fig. 5.
Fig. 5.

(a) Relationship between MSE and w1, N=400. (b) Log(MSE) versus w1. (c) Relationship between MSE and effective pixel number K1. (d) MSE versus N. All results here correspond to the object in Fig. 2(a).

Fig. 6.
Fig. 6.

Upper row, original object and recovered images when w1 is between 9 and 11. Bottom row, recovered images when w1 is between 17 and 20. Eigenmode number N equals 400.

Fig. 7.
Fig. 7.

Upper and bottom rows, images from OEI and OEISC, respectively, with eigenmode number N=50, 100, 200, 300, and 400.

Equations (4)

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

El=1λlj=1Nvjl*Ej,
sl=ROIO(r)×El(r)dr.
minTDT1+u2AT1J22,
MSE=1Npixij(O(i,j)T(i,j))2,

Metrics