Abstract

Compressive holography enables 3D reconstruction from a single 2D holographic snapshot for objects that can be sparsely represented in some basis. The snapshot mode enables tomographic imaging of microscopic moving objects. We demonstrate video-rate tomographic image acquisition of two live water cyclopses with 5.2 μm spatial resolution and 60 μm axial resolution.

© 2011 OSA

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References

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  1. D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
    [CrossRef] [PubMed]
  2. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52(10), 1123–1130 (1962).
    [CrossRef]
  3. D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17(15), 13040–13049 (2009).
    [CrossRef] [PubMed]
  4. E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
    [CrossRef]
  5. E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
    [CrossRef]
  6. D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
    [CrossRef]
  7. L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, and D. Trede, “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34(22), 3475–3477 (2009).
    [CrossRef] [PubMed]
  8. C. Fournier, L. Denis, and T. Fournel, “On the single point resolution of on-axis digital holography,” J. Opt. Soc. Am. A 27(8), 1856–1862 (2010).
    [CrossRef]
  9. A. F. Coskun, I. Sencan, T.-W. Su, and A. Ozcan, “Lensless wide-field fluorescent imaging on a chip using compressive decoding of sparse objects,” Opt. Express 18(10), 10510–10523 (2010).
    [CrossRef] [PubMed]
  10. M. M. Marim, M. Atlan, E. Angelini, and J.-C. Olivo-Marin, “Compressed sensing with off-axis frequency-shifting holography,” Opt. Lett. 35(6), 871–873 (2010).
    [CrossRef] [PubMed]
  11. Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
    [CrossRef]
  12. H. Kim, S.-W. Min, B. Lee, and T.-C. Poon, “Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions,” Appl. Opt. 47(19), D164–D175 (2008).
    [CrossRef] [PubMed]
  13. E. Y. Lam, X. Zhang, H. Vo, T.-C. Poon, and G. Indebetouw, “Three-dimensional microscopy and sectional image reconstruction using optical scanning holography,” Appl. Opt. 48(34), H113–H119 (2009).
    [CrossRef] [PubMed]
  14. J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
    [CrossRef] [PubMed]
  15. S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, “Lensfree holographic imaging for on-chip cytometry and diagnostics,” Lab Chip 9(6), 777–787 (2009).
    [CrossRef] [PubMed]
  16. J. Hahn, S. Lim, K. Choi, R. Horisaki, D. L. Marks, and D. J. Brady, “Compressive Holographic Microscopy,” in Biomedical Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JMA1.
  17. R. E. Blahurt, Theory of Remote Image Formation (Cambridge University Press, 2005).
  18. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
    [CrossRef]
  19. J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
    [CrossRef] [PubMed]
  20. D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2009).
  21. D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48(9), 095801 (2009).
    [CrossRef]
  22. A. C. Kak, and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
  23. D. L. Marks, “A family of approximations spanning the Born and Rytov scattering series,” Opt. Express 14(19), 8837–8848 (2006).
    [CrossRef] [PubMed]
  24. J. Chae and S. Nishida, “Integumental ultrastructure and colour patterns in the iridescent copepods of the family Sapphirinidae (Copepoda: Poecilostomatoida),” Mar. Biol. 119(2), 205–210 (1994).
    [CrossRef]

2010

2009

2008

2007

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[CrossRef] [PubMed]

2006

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

D. L. Marks, “A family of approximations spanning the Born and Rytov scattering series,” Opt. Express 14(19), 8837–8848 (2006).
[CrossRef] [PubMed]

1994

J. Chae and S. Nishida, “Integumental ultrastructure and colour patterns in the iridescent copepods of the family Sapphirinidae (Copepoda: Poecilostomatoida),” Mar. Biol. 119(2), 205–210 (1994).
[CrossRef]

1992

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[CrossRef]

1962

1948

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Angelini, E.

Atlan, M.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[CrossRef] [PubMed]

Brady, D. J.

Candes, E. J.

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[CrossRef]

Candès, E. J.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

Chae, J.

J. Chae and S. Nishida, “Integumental ultrastructure and colour patterns in the iridescent copepods of the family Sapphirinidae (Copepoda: Poecilostomatoida),” Mar. Biol. 119(2), 205–210 (1994).
[CrossRef]

Choi, K.

Coskun, A. F.

Denis, L.

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

Erlinger, A.

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, “Lensfree holographic imaging for on-chip cytometry and diagnostics,” Lab Chip 9(6), 777–787 (2009).
[CrossRef] [PubMed]

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[CrossRef]

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[CrossRef] [PubMed]

Fournel, T.

Fournier, C.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Garcia-Sucerquia, J.

Hennelly, B. M.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48(9), 095801 (2009).
[CrossRef]

Horisaki, R.

Indebetouw, G.

Javidi, B.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[CrossRef]

Jericho, M. H.

Jericho, S. K.

Kelly, D. P.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48(9), 095801 (2009).
[CrossRef]

Kim, H.

Klages, P.

Kreuzer, H. J.

Lam, E. Y.

Lee, B.

Leith, E. N.

Lim, S.

Lorenz, D.

Marim, M. M.

Marks, D. L.

Min, S.-W.

Naughton, T. J.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48(9), 095801 (2009).
[CrossRef]

Nishida, S.

J. Chae and S. Nishida, “Integumental ultrastructure and colour patterns in the iridescent copepods of the family Sapphirinidae (Copepoda: Poecilostomatoida),” Mar. Biol. 119(2), 205–210 (1994).
[CrossRef]

Olivo-Marin, J.-C.

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[CrossRef]

Ozcan, A.

A. F. Coskun, I. Sencan, T.-W. Su, and A. Ozcan, “Lensless wide-field fluorescent imaging on a chip using compressive decoding of sparse objects,” Opt. Express 18(10), 10510–10523 (2010).
[CrossRef] [PubMed]

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, “Lensfree holographic imaging for on-chip cytometry and diagnostics,” Lab Chip 9(6), 777–787 (2009).
[CrossRef] [PubMed]

Pandey, N.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48(9), 095801 (2009).
[CrossRef]

Poon, T.-C.

Rhodes, W. T.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48(9), 095801 (2009).
[CrossRef]

Rivenson, Y.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[CrossRef]

Romberg, J. K.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[CrossRef]

Sencan, I.

Seo, S.

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, “Lensfree holographic imaging for on-chip cytometry and diagnostics,” Lab Chip 9(6), 777–787 (2009).
[CrossRef] [PubMed]

Stern, A.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[CrossRef]

Su, T. W.

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, “Lensfree holographic imaging for on-chip cytometry and diagnostics,” Lab Chip 9(6), 777–787 (2009).
[CrossRef] [PubMed]

Su, T.-W.

Tao, T.

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[CrossRef]

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

Thiébaut, E.

Trede, D.

Tseng, D. K.

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, “Lensfree holographic imaging for on-chip cytometry and diagnostics,” Lab Chip 9(6), 777–787 (2009).
[CrossRef] [PubMed]

Upatnieks, J.

Vo, H.

Xu, W.

Zhang, X.

Appl. Opt.

Commun. Pure Appl. Math.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

IEEE Trans. Image Process.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new twIst: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory

E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?” IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[CrossRef]

J. Disp. Technol.

Y. Rivenson, A. Stern, and B. Javidi, “Compressive Fresnel holography,” J. Disp. Technol. 6(10), 506–509 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Lab Chip

S. Seo, T. W. Su, D. K. Tseng, A. Erlinger, and A. Ozcan, “Lensfree holographic imaging for on-chip cytometry and diagnostics,” Lab Chip 9(6), 777–787 (2009).
[CrossRef] [PubMed]

Mar. Biol.

J. Chae and S. Nishida, “Integumental ultrastructure and colour patterns in the iridescent copepods of the family Sapphirinidae (Copepoda: Poecilostomatoida),” Mar. Biol. 119(2), 205–210 (1994).
[CrossRef]

Nature

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Opt. Eng.

D. P. Kelly, B. M. Hennelly, N. Pandey, T. J. Naughton, and W. T. Rhodes, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48(9), 095801 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Physica D

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[CrossRef]

Other

A. C. Kak, and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).

J. Hahn, S. Lim, K. Choi, R. Horisaki, D. L. Marks, and D. J. Brady, “Compressive Holographic Microscopy,” in Biomedical Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JMA1.

R. E. Blahurt, Theory of Remote Image Formation (Cambridge University Press, 2005).

D. J. Brady, Optical Imaging and Spectroscopy (Wiley, 2009).

Supplementary Material (5)

» Media 1: MPEG (2668 KB)     
» Media 2: MPEG (1792 KB)     
» Media 3: MPEG (1774 KB)     
» Media 4: MPEG (3884 KB)     
» Media 5: MPEG (3846 KB)     

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Figures (8)

Fig. 1
Fig. 1

A schematic of the compressive holographic microscope.

Fig. 2
Fig. 2

Photographs of (a) the holographic microscope and (b) a water container in which water cyclopses are swimming.

Fig. 3
Fig. 3

Raw image of a Gabor hologram.

Fig. 4
Fig. 4

A comparison of reconstructions at chosen axial positions: (a-b) the backpropagation reconstructions and by (c-d) the compressive holographic reconstructions using the data shown in Fig. 3. All the transverse slices of the reconstructions are sequentially shown in (e) obtained by the backpropagation method (Media 1) and in (f) obtained by the compressive holography method (Media 2) for the full range of water container.

Fig. 5
Fig. 5

A comparison of the magnified tails, marked by rectangles in Figs. 4(b) and 4(d), of (a) the backpropagation reconstruction and (b) the compressive holography reconstruction.

Fig. 6
Fig. 6

A 3D visualization of the compressive holography reconstruction (Media 3).

Fig. 7
Fig. 7

Images of (a) the maximum intensity values of the reconstructed density (f) along the propagation directions and (b) a map of the axial positions corresponding to the maximum values in Fig. 7(a). (c) A range colormap represents the HSV space.

Fig. 8
Fig. 8

Videos of (a) raw measurements (Media 4) and (b) range maps of the compressive holography reconstructions (Media 5).

Equations (11)

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

I ( x , y ; z F P A ) = | U ( x , y ; z F P A ) | 2 = | U 0 ( x , y ; z F P A ) | 2 + | U s ( x , y ; z F P A ) | 2 + 2 Re { U 0 * ( x , y ; z F P A ) U s ( x , y ; z F P A ) } ,
U s ( x , y ;   z F P A ) = U ( x , y ; z F P A ) U 0 ( x , y ; z F P A ) = d x d y d z U 0 ( x , y ; z ) β ( x , y , z ) h ( x x , y y ; z F P A z ) .
U s ( x , y ; z F P A ) = d x d y d z h F ( x , y ; z ) β ( x , y , z ) h F ( x x , y y ; z F P A z ) = h F ( x , y ; z F P A ) d x d y d z C ( z ) β ( x z z F P A , y z z F P A , z ) h F ( x x , y y ; z F P A z z / z F P A ) = h F ( x , y ; z F P A ) d z C ( z ) F 2 D 1 { F 2 D { β ( x z z F P A , y z z F P A , z ) } H F ( k x , k y ; z F P A z z / z F P A ) } .
C ( z ) = exp [ j k z F P A ( 1 z F P A / z ) ] .
U 0 * ( n 1 Δ , n 2 Δ , z F P A ) U s ( n 1 Δ , n 2 Δ , z F P A ) = h F * ( n 1 Δ , n 2 Δ , z F P A ) U s ( n 1 Δ , n 2 Δ , z F P A ) = 1 N 2 l C ( l Δ z z F P A ) m 1 m 2 n 1 n 2 β ( n 1 Δ , n 2 Δ , l Δ z ) exp ( 2 π j m 1 n 1 1 + m 2 n 2 N ) × H F ( m 1 Δ k , m 2 Δ k , z F P A l Δ z l Δ z / z F P A ) exp ( 2 π j n 1 m 1 + n 2 m 2 N ) ,
U 0 , n 1 n 2 * U s , n 1 n 2 = l C l F 2 D 1 { F 2 D { β n 1 n 2 l } m 1 m 2 H F , m 1 m 2 l } n 1 n 2 .
g = 2 Re { H f } + e + n ,
f ^ = arg min f 1 2 g 2 Re ( H f ) 2 + τ f T V .
f T V = z x y | ( f z ) x , y | ,
Δ x = λ 2 N A ,
Δ z = 2 λ N A 2 ,

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