Abstract

In previous work [Opt. Lett. 44, 2827 (2019) [CrossRef]  ], we presented a method based on digital holography and orthogonal matching pursuit, which is able to determine the 3D positions of small objects moving within a larger motionless object. Indeed, if the scattering density is sparse in direct 3D space, compressive sensing algorithms can be used. The method was validated by imaging red blood cell trajectories in the trunk vascular system of a zebrafish (Danio rerio) larva. We give here further details on the reconstruction technique and present a more robust version of the algorithm based on multiple illuminations.

© 2019 Optical Society of America

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References

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2019 (1)

2017 (3)

2016 (2)

D. Donnarumma, A. Brodoline, D. Alexandre, and M. Gross, “4d holographic microscopy of zebrafish larvae microcirculation,” Opt. Express 24, 26887–26900 (2016).
[Crossref]

X. Quan, P. Xia, O. Matoba, K. Nitta, and Y. Awatsuji, “Multi-modal digital holographic microscopy for wide-field fluorescence and 3d phase imaging,” Proc. SPIE 9718, 971821 (2016).
[Crossref]

2015 (1)

2014 (1)

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 36, 248–260 (2014).
[Crossref]

2012 (1)

2011 (3)

2010 (4)

2009 (5)

2008 (5)

2007 (1)

2006 (3)

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

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

T. Colomb, E. Cuche, F. Charrière, J. Kühn, N. Aspert, F. Montfort, P. Marquet, and C. Depeursinge, “Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation,” Appl. Opt. 45, 851–863 (2006).
[Crossref]

2005 (1)

2001 (1)

S. Isogai, M. Horiguchi, and B. M. Weinstein, “The vascular anatomy of the developing zebrafish: an atlas of embryonic and early larval development,” Dev. Biol. 230, 278–301 (2001).
[Crossref]

2000 (3)

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
[Crossref]

T. Schwerte and B. Pelster, “Digital motion analysis as a tool for analysing the shape and performance of the circulatory system in transparent animals,” J. Exp. Biol. 203, 1659–1669 (2000).

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[Crossref]

1999 (1)

1996 (1)

R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. B 58, 267–288 (1996).
[Crossref]

1994 (1)

1948 (1)

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

Absil, E.

Alexandre, D.

Angelini, E.

Aspert, N.

Atlan, M.

Awatsuji, Y.

X. Quan, P. Xia, O. Matoba, K. Nitta, and Y. Awatsuji, “Multi-modal digital holographic microscopy for wide-field fluorescence and 3d phase imaging,” Proc. SPIE 9718, 971821 (2016).
[Crossref]

Badizadegan, K.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. Dasari, and M. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[Crossref]

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref]

Barbastathis, G.

Barman, I.

Beck, A.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2, 183–202 (2009).
[Crossref]

Best-Popescu, C.

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref]

Bettens, S.

Blinder, D.

Brady, D.

Brodoline, A.

A. Brodoline, N. Rawat, D. Alexandre, N. Cubedo, and M. Gross, “4d compressive sensing holographic microscopy imaging of small moving objects,” Opt. Lett. 44, 2827–2830 (2019).
[Crossref]

D. Donnarumma, A. Brodoline, D. Alexandre, and M. Gross, “4d holographic microscopy of zebrafish larvae microcirculation,” Opt. Express 24, 26887–26900 (2016).
[Crossref]

A. Brodoline, N. Rawat, D. Donnarumma, D. Alexandre, N. Cubedo, and M. Gross, “Compressive sensing holographic microscopy for imaging of sparse moving objects in 3D,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2019), paper Th2B.7.

Buraga-Lefebvre, C.

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[Crossref]

Candes, E.

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

Carin, L.

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56, 2346–2356 (2008).
[Crossref]

Charrière, F.

Chen, H.

Chen, J.

Choi, K.

Choi, W.

Coëtmellec, S.

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[Crossref]

Colomb, T.

Coppey-Moisan, M.

Cossairt, O.

Z. Wang, L. Spinoulas, K. He, L. Tian, O. Cossairt, A. K. Katsaggelos, and H. Chen, “Compressive holographic video,” Opt. Express 25, 250–262 (2017).
[Crossref]

O. Cossairt, K. He, R. Shang, N. Matsuda, M. Sharma, X. Huang, A. Katsaggelos, L. Spinoulas, and S. Yoo, “Compressive reconstruction for 3d incoherent holographic microscopy,” in International Conference on Image Processing (ICIP) (2016), pp. 958–962.

Z. Wang, Q. Dai, D. Ryu, K. He, R. Horstmeyer, A. K. Katsaggelos, and O. Cossairt, “Dictionary-based phase retrieval for space-time super resolution using lens-free on-chip holographic video,” in Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP) (Optical Society of America, 2017), paper CTu2B.3.

Cubedo, N.

A. Brodoline, N. Rawat, D. Alexandre, N. Cubedo, and M. Gross, “4d compressive sensing holographic microscopy imaging of small moving objects,” Opt. Lett. 44, 2827–2830 (2019).
[Crossref]

A. Brodoline, N. Rawat, D. Donnarumma, D. Alexandre, N. Cubedo, and M. Gross, “Compressive sensing holographic microscopy for imaging of sparse moving objects in 3D,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2019), paper Th2B.7.

Cuche, E.

Dai, Q.

Z. Wang, Q. Dai, D. Ryu, K. He, R. Horstmeyer, A. K. Katsaggelos, and O. Cossairt, “Dictionary-based phase retrieval for space-time super resolution using lens-free on-chip holographic video,” in Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP) (Optical Society of America, 2017), paper CTu2B.3.

Dasari, R.

Dasari, R. R.

J. W. Kang, N. Lue, C.-R. Kong, I. Barman, N. C. Dingari, S. J. Goldfless, J. C. Niles, R. R. Dasari, and M. S. Feld, “Combined confocal Raman and quantitative phase microscopy system for biomedical diagnosis,” Biomed. Opt. Express 2, 2484–2492 (2011).
[Crossref]

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref]

Debailleul, M.

Deflores, L.

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref]

Denis, L.

Depeursinge, C.

Desbiolles, P.

Dingari, N. C.

Domínguez-Caballero, J.

Donnarumma, D.

D. Donnarumma, A. Brodoline, D. Alexandre, and M. Gross, “4d holographic microscopy of zebrafish larvae microcirculation,” Opt. Express 24, 26887–26900 (2016).
[Crossref]

A. Brodoline, N. Rawat, D. Donnarumma, D. Alexandre, N. Cubedo, and M. Gross, “Compressive sensing holographic microscopy for imaging of sparse moving objects in 3D,” in Digital Holography and Three-Dimensional Imaging (Optical Society of America, 2019), paper Th2B.7.

Donoho, D.

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

Fang-Yen, C.

Feld, M.

Feld, M. S.

J. W. Kang, N. Lue, C.-R. Kong, I. Barman, N. C. Dingari, S. J. Goldfless, J. C. Niles, R. R. Dasari, and M. S. Feld, “Combined confocal Raman and quantitative phase microscopy system for biomedical diagnosis,” Biomed. Opt. Express 2, 2484–2492 (2011).
[Crossref]

G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008).
[Crossref]

Ferraro, P.

Finizio, A.

Fournier, C.

Gabor, D.

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

Gao, J.

Georges, V.

Goepfert, C.

Goldfless, S. J.

Gross, M.

Gu, J.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 36, 248–260 (2014).
[Crossref]

Gupta, M.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 36, 248–260 (2014).
[Crossref]

Haeberlé, O.

Hahn, J.

He, K.

Z. Wang, L. Spinoulas, K. He, L. Tian, O. Cossairt, A. K. Katsaggelos, and H. Chen, “Compressive holographic video,” Opt. Express 25, 250–262 (2017).
[Crossref]

O. Cossairt, K. He, R. Shang, N. Matsuda, M. Sharma, X. Huang, A. Katsaggelos, L. Spinoulas, and S. Yoo, “Compressive reconstruction for 3d incoherent holographic microscopy,” in International Conference on Image Processing (ICIP) (2016), pp. 958–962.

Z. Wang, Q. Dai, D. Ryu, K. He, R. Horstmeyer, A. K. Katsaggelos, and O. Cossairt, “Dictionary-based phase retrieval for space-time super resolution using lens-free on-chip holographic video,” in Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP) (Optical Society of America, 2017), paper CTu2B.3.

Hitomi, Y.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 36, 248–260 (2014).
[Crossref]

Horiguchi, M.

S. Isogai, M. Horiguchi, and B. M. Weinstein, “The vascular anatomy of the developing zebrafish: an atlas of embryonic and early larval development,” Dev. Biol. 230, 278–301 (2001).
[Crossref]

Horisaki, R.

Horstmeyer, R.

Z. Wang, Q. Dai, D. Ryu, K. He, R. Horstmeyer, A. K. Katsaggelos, and O. Cossairt, “Dictionary-based phase retrieval for space-time super resolution using lens-free on-chip holographic video,” in Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP) (Optical Society of America, 2017), paper CTu2B.3.

Huang, X.

O. Cossairt, K. He, R. Shang, N. Matsuda, M. Sharma, X. Huang, A. Katsaggelos, L. Spinoulas, and S. Yoo, “Compressive reconstruction for 3d incoherent holographic microscopy,” in International Conference on Image Processing (ICIP) (2016), pp. 958–962.

Isogai, S.

S. Isogai, M. Horiguchi, and B. M. Weinstein, “The vascular anatomy of the developing zebrafish: an atlas of embryonic and early larval development,” Dev. Biol. 230, 278–301 (2001).
[Crossref]

Javidi, B.

Ji, S.

S. Ji, Y. Xue, and L. Carin, “Bayesian compressive sensing,” IEEE Trans. Signal Process. 56, 2346–2356 (2008).
[Crossref]

Jiang, X.

Jüptner, W.

Kang, J. W.

Katsaggelos, A.

O. Cossairt, K. He, R. Shang, N. Matsuda, M. Sharma, X. Huang, A. Katsaggelos, L. Spinoulas, and S. Yoo, “Compressive reconstruction for 3d incoherent holographic microscopy,” in International Conference on Image Processing (ICIP) (2016), pp. 958–962.

Katsaggelos, A. K.

Z. Wang, L. Spinoulas, K. He, L. Tian, O. Cossairt, A. K. Katsaggelos, and H. Chen, “Compressive holographic video,” Opt. Express 25, 250–262 (2017).
[Crossref]

Z. Wang, Q. Dai, D. Ryu, K. He, R. Horstmeyer, A. K. Katsaggelos, and O. Cossairt, “Dictionary-based phase retrieval for space-time super resolution using lens-free on-chip holographic video,” in Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP) (Optical Society of America, 2017), paper CTu2B.3.

Kemper, B.

Kim, M.

Kong, C.-R.

Krishnaprasad, P.

Y. Pati, R. Rezaiifar, and P. Krishnaprasad, “Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition,” in 27th Asilomar Conference on Signals, Systems and Computers (IEEE, 1993), pp. 40–44.

Kühn, J.

Lebrun, D.

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, “Application of wavelet transform to hologram analysis: three-dimensional location of particles,” Opt. Lasers Eng. 33, 409–421 (2000).
[Crossref]

Lim, S.

Liu, D.

D. Liu, J. Gu, Y. Hitomi, M. Gupta, T. Mitsunaga, and S. K. Nayar, “Efficient space-time sampling with pixel-wise coded exposure for high-speed imaging,” IEEE Trans. Pattern Anal. Mach. Intell. 36, 248–260 (2014).
[Crossref]

Liu, J.

Loomis, N.

Lorenz, D.

Lue, N.

J. W. Kang, N. Lue, C.-R. Kong, I. Barman, N. C. Dingari, S. J. Goldfless, J. C. Niles, R. R. Dasari, and M. S. Feld, “Combined confocal Raman and quantitative phase microscopy system for biomedical diagnosis,” Biomed. Opt. Express 2, 2484–2492 (2011).
[Crossref]

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Proc. SPIE (1)

X. Quan, P. Xia, O. Matoba, K. Nitta, and Y. Awatsuji, “Multi-modal digital holographic microscopy for wide-field fluorescence and 3d phase imaging,” Proc. SPIE 9718, 971821 (2016).
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M. Westerfield, The zebrafish book: a guide for the laboratory use of zebrafish (Danio rerio) (University of Oregon press, 2007).

Z. Wang, Q. Dai, D. Ryu, K. He, R. Horstmeyer, A. K. Katsaggelos, and O. Cossairt, “Dictionary-based phase retrieval for space-time super resolution using lens-free on-chip holographic video,” in Imaging and Applied Optics 2017 (3D, AIO, COSI, IS, MATH, pcAOP) (Optical Society of America, 2017), paper CTu2B.3.

O. Cossairt, K. He, R. Shang, N. Matsuda, M. Sharma, X. Huang, A. Katsaggelos, L. Spinoulas, and S. Yoo, “Compressive reconstruction for 3d incoherent holographic microscopy,” in International Conference on Image Processing (ICIP) (2016), pp. 958–962.

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Supplementary Material (3)

NameDescription
» Visualization 1       3D reconstruction of the red blood cells positions in the vascular system of a 5-days zebrafish larva. Positions are obtained for one camera frame.
» Visualization 2       3D reconstruction of the blood vessels by averaging the trajectories of the red blood cells over 256 frames. Vascular system of a 5-days zebrafish larva.
» Visualization 3       Reconstruction of the vascular system of a 5-days zebrafish larva. The instantaneous 3D positions of the red blood cells are represented. The shapes of the blood vessels are obtained by averaging the trajectories of the red blood cells over 256 frames

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Figures (8)

Fig. 1.
Fig. 1. Triple illumination off-axis holographic microscopy setup. BS, beam splitters; M, mirrors; MO, microscope objective; $\theta$ , off-axis angle; $C^\prime$ , camera plane; ${E_{I\!L}}$ , illumination beam; $E$ , scattered object field; and ${E_R}$ , reference field.
Fig. 2.
Fig. 2. Typical off-axis holographic microscopy setup. L, laser; $C^\prime$ , camera; BS, beam splitter; M, mirror; MO, microscope objective; C, conjugate plane of plane $C^\prime$ by objective MO; V, imaged volume; S, scattering object; $E$ , object field; and ${E_R}$ , reference field.
Fig. 3.
Fig. 3. (a) Schematic representation of the transformations. Matrix $A$ describes the emission by the 3D sources ${\textbf v}\equiv S$ resulting in a 2D field in Fourier space ${\textbf u}\equiv {\tilde E_C}$ . Matrix ${A^\dagger}$ represents the 3D field reconstruction from the 2D field in the camera conjugate plane. (b) Normalization procedure diagram: ${{\textbf u}^{(n)}}$ is the hologram at the iteration $n$ , ${{\textbf u}_n}$ the field radiated by the sources selected at iteration $n$ , ${a_n}$ the normalization coefficient, and ${{\textbf u}^{(n+1)}}$ the hologram at the iteration $n+1$ , orthogonal to ${{\textbf u}_n}$ .
Fig. 4.
Fig. 4. (a) Fourier transform of the off-axis hologram. The bright spots inside the $+1$ and $-1$ orders correspond to the three illumination beams. (b) Crop of the $+1$ order of the hologram, filtering of the center of the pupil and of the zero order. (c) Separation of the three illumination beams inside the $+1$ order with circular masks (red, green, and blue). (d) Intensity of the three fields (red, green, and blue) reconstructed in the camera conjugate plane.
Fig. 5.
Fig. 5. (a) Representation of RBCs considering a single 3D reconstruction at one camera frame. View at 0°. (b), (c) Representations of the vascular system considering a summation of a sequence of 256 holograms. Views at 96° and 120°. (d) The RBC positions are superimposed with the shape of the blood vessels. DA, dorsal aorta; CV, caudal vein; ISV, intersegmental vessels; and DLAV, dorsal longitudinal anastomotic vessels can be clearly seen. View at 0°. Reconstructions performed with operator $T_{\cal C}^{(n)}$ and a selection threshold ${\cal C}_{\textrm{th}}^{(n)}=0.8\, \textrm{Corr}_{n,\textrm{max}}$ . For a 360° rotation, see Visualizations in supplement.
Fig. 6.
Fig. 6. Comparison between the reconstructions with the two operators ${T^{(n)}}$ : (a) reconstruction using triple illumination with $T_{\cal C}^{(n)}$ and selection threshold ${\cal C}_{\textrm {th}}^{(n)}=0.8\, \textrm{Corr}_{n,\textrm{max}}$ . (b) Reconstruction based on energy with $T_{\cal E}^{(n)}$ and selection threshold ${\cal E}_{\textrm{th}}^{(n)}=0.8 \,{\cal E}_{\textrm{max}}^{(n)}$ . Views at 96°. White arrows: reconstruction artifacts.
Fig. 7.
Fig. 7. (a) Mean decrease in energy of the hologram with time. (b) Temporal variation of the ratio between the mean maximum energy or correlation and its value at the first iteration. The averages of energy, correlation, and time are performed on 256 images. Plots are given for the cases where ${T^{(n)}}$ considers total energy (red circles) or correlation between the three beams (blue diamonds) as well as for two selection thresholds: 0.8 (empty) and 0.5 (full). Each point corresponds to one iteration of the algorithm.
Fig. 8.
Fig. 8. (a) Reconstruction by selection of the sources based on energy with $T_{\cal E}^{(n)}$ and a threshold ${\cal E}_{\textrm{th}}^{(n)}=0.5\,{\cal E}_{\textrm{max}}^{(n)}$ . (b) Reconstruction by selection of the sources based on the correlation between the three beams with $T_{\cal C}^{(n)}$ and a threshold ${\cal C}_{\textrm {th}}^{(n)}=0.5 \,{\cal C}_{\textrm {max}}^{(n)}$ . White arrows: reconstruction artifacts.

Equations (10)

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H C ( x , y ) = m η m I m ( x , y ) with m η m = 0.
H C ( x , y ) = k = 0 N 1 sin ( 2 π k N ) I m ( x , y ) .
E ~ C ( k x , k y ) = z exp ( + i k z . z ) FT [ S ( x , y , z ) ] ,
u = A v ,
S ( x , y , z ) = FT 1 [ exp ( i k z . z ) E ~ C ( k x , k y ) ] .
u ( n + 1 ) = u ( n ) a n A T ( n ) A u ( n ) ,
a n = u n u ( n ) | u n | 2 .
v = n a n T ( n ) A u ( n ) .
S ( x , y , z ) = n a n S n ( x , y , z ) .
Corr n 3 ( x , y , z ) = | S ( n , 1 ) ( x , y , z ) | 2 × | S ( n , 2 ) ( x , y , z ) | 2 × | S ( n , 3 ) ( x , y , z ) | 2 .

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