Abstract

This Letter reports a demonstration of off-axis compressed holography in low-light level imaging conditions. An acquisition protocol relying on a single exposure of a randomly undersampled diffraction map of the optical field, recorded in the high heterodyne gain regime, is proposed. The image acquisition scheme is based on compressed sensing, a theory establishing that near-exact recovery of an unknown sparse signal is possible from a small number of nonstructured measurements. Image reconstruction is further enhanced by introducing an off-axis spatial support constraint to the image estimation algorithm. We report accurate experimental recovering of holographic images of a resolution target in low-light conditions with a frame exposure of 5μs, scaling down measurements to 9% of random pixels within the array detector.

© 2011 Optical Society of America

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References

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  1. M. Gross and M. Atlan, Opt. Lett. 32, 909 (2007).
    [CrossRef] [PubMed]
  2. E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
    [CrossRef]
  3. E. Candes and J. Romberg, Inverse Probl. 23, 969 (2007).
    [CrossRef]
  4. D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
    [CrossRef]
  5. D. Brady, K. Choi, D. Marks, R. Horisaki, and S. Lim, Opt. Express 17, 13040 (2009).
    [CrossRef] [PubMed]
  6. L. Denis, D. Lorenz, E. Thibaut, C. Fournier, and D. Trede, Opt. Lett. 34, 3475 (2009).
    [CrossRef] [PubMed]
  7. K. Choi, R. Horisaki, J. Hahn, S. Lim, D. L. Marks, T. J. Schulz, and D. J. Brady, Appl. Opt. 49, H1 (2010).
    [CrossRef] [PubMed]
  8. C. Fernandez Cull, D. A. Wikner, J. N. Mait, M. Mattheiss, and D. J. Brady, Appl. Opt. 49, E67 (2010).
    [CrossRef]
  9. M. Marim, M. Atlan, E. Angelini, and J.-C. Olivo-Marin, Opt. Lett. 35, 871 (2010).
    [CrossRef] [PubMed]
  10. U. Schnars and W. Juptner, Appl. Opt. 33, 179 (1994).
    [CrossRef] [PubMed]

2010 (3)

2009 (2)

2007 (2)

E. Candes and J. Romberg, Inverse Probl. 23, 969 (2007).
[CrossRef]

M. Gross and M. Atlan, Opt. Lett. 32, 909 (2007).
[CrossRef] [PubMed]

2006 (2)

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

1994 (1)

Angelini, E.

Atlan, M.

Brady, D.

Brady, D. J.

Candes, E.

E. Candes and J. Romberg, Inverse Probl. 23, 969 (2007).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Choi, K.

Denis, L.

Donoho, D. L.

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

Fernandez Cull, C.

Fournier, C.

Gross, M.

Hahn, J.

Horisaki, R.

Juptner, W.

Lim, S.

Lorenz, D.

Mait, J. N.

Marim, M.

Marks, D.

Marks, D. L.

Mattheiss, M.

Olivo-Marin, J.-C.

Romberg, J.

E. Candes and J. Romberg, Inverse Probl. 23, 969 (2007).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Schnars, U.

Schulz, T. J.

Tao, T.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Thibaut, E.

Trede, D.

Wikner, D. A.

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Figures (3)

Fig. 1
Fig. 1

Experimental image acquisition setup.

Fig. 2
Fig. 2

Compressed holographic reconstruction of g without support constraint. (a) Reconstruction with TV minimization over the region R . (b) In both cases, n = 2.4 e ( D = 0 ) and M / N = 9 % . (c), (d) Magnified views over 330 × 330 pixels.

Fig. 3
Fig. 3

Amount of digital counts in the object channel averaged over N pixels for three different attenuations: (a)  D = 0 , (b)  D = 0.5 , (c)  D = 1 . The LO beam is turned off. The optical field E impinges onto the detector (i) and is blocked (ii) sequentially by the optical chopper, from one frame to the next. The horizontal axis is the frame number; the vertical axis is the average number of counts per pixels. Standard holographic reconstructions at (d)  D = 0 , (e)  D = 0.5 , and (f)  D = 1 . CS reconstructions at (g)  D = 0 with M / N = 9 % , (h) at D = 0.5 with M / N = 13 % , and at (i)  D = 1 with M / N = 19 % .

Equations (3)

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I = | E LO | 2 + | E | 2 + E E LO * + E * E LO ,
f k , l = i λ Δ z e i π λ Δ z ( k 2 N x 2 d x 2 + l 2 N y d y 2 ) × p = 1 N x q = 1 N y F p , q e i π λ Δ z ( p 2 d x 2 + q 2 d y 2 ) e 2 i π ( k p N x + l q N y ) ,
g ^ = argmin R g 1 subject to     F ^ | Γ F | Γ 2 δ .

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