Abstract

A single-exposure in-line (SEOL) holography is a digital holographic setup that has been used in the study of cell identification. In this paper we demonstrate improved three-dimensional performance of the SEOL holography setup by applying the principles of the recently introduced compressive-sensing theory. This, along with proper modeling of the sensing process, enables improved depth-resolution features, especially when considering noisy environments. We then study and demonstrate that by using the proper reference and object-beam amplitude partition, the compressive SEOL holography setup is found to be almost ideal. This occurs since it allows the recovery of low-signal-to-noise-ratio objects and rapid acquisition rate associated with the off-axis holography setup, combined with the high resolution and field of view associated with the in-line holography setup.

© 2012 Optical Society of America

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2012

2011

2010

2009

D. J. Brady, K. Choi, D. L. Marks, R. Horisaki, and S. Lim, “Compressive holography,” Opt. Express 17, 13040–13049 (2009).
[CrossRef]

L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, and D. Trede, “Inline hologram reconstruction with sparsity constraints,” Opt. Lett. 34, 3475–3477 (2009).
[CrossRef]

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional imaging, identification and tracking of micro/nano biological organisms by holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

2008

A. Stern and B. Javidi, “3D optical microscopy using digital holography,” Proc. SPIE. 6983, 69830O (2008).
[CrossRef]

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

2007

G. B. Esmer, V. Uzunov, L. Onural, H. M. Ozaktas, and A. Gotchev, “Diffraction field computation from arbitrarily distributed data points in space,” Signal Process. Image Commun. 22, 178–187 (2007).
[CrossRef]

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, 2992–3004(2007).
[CrossRef]

A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A 24, 163–168 (2007).
[CrossRef]

2006

F. Charrière, T. Colomb, F. Montfort, E. Cuche, P. Marquet, and C. Depeursinge, “Shot-noise influence on the reconstructed phase image signal-to-noise ratio in digital holographic microscopy,” Appl. Opt. 45, 7667–7673 (2006).
[CrossRef]

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

S. Yeom and B. Javidi, “Automatic identification of biological microorganisms using three-dimensional complex morphology,” J. Biomed. Opt. 11, 024017 (2006).
[CrossRef]

2005

1999

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Angelini, E.

Atlan, M.

Balber, S.

Barbastathis, G.

Bernardo, L. M.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

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, 2992–3004(2007).
[CrossRef]

Brady, D. J.

Bryanston-Cross, P.

Candes, E.

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

Candès, E. J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Carapezza, E.

Charrière, F.

Choi, K.

Claus, D.

Colomb, T.

Coskun, A. F.

Cuche, E.

Cull, C. Fernandez

Daneshpanah, M.

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional imaging, identification and tracking of micro/nano biological organisms by holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

Denis, L.

Depeursinge, C.

Esmer, G. B.

G. B. Esmer, V. Uzunov, L. Onural, H. M. Ozaktas, and A. Gotchev, “Diffraction field computation from arbitrarily distributed data points in space,” Signal Process. Image Commun. 22, 178–187 (2007).
[CrossRef]

Ferreira, C.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Fienup, J.

A. Tippie and J. Fienup, “Weak-object image reconstructions with single-shot digital holography,” in Digital Holography and Three-Dimensional Imaging, Technical Digest (Optical Society of America, 2012), p. DM4C.5.

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, 2992–3004(2007).
[CrossRef]

Fournier, C.

Garcia, J.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Gotchev, A.

G. B. Esmer, V. Uzunov, L. Onural, H. M. Ozaktas, and A. Gotchev, “Diffraction field computation from arbitrarily distributed data points in space,” Signal Process. Image Commun. 22, 178–187 (2007).
[CrossRef]

Hahn, J.

Horisaki, R.

Huang, H. Y. H.

Iliescu, D.

Javidi, B.

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

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional imaging, identification and tracking of micro/nano biological organisms by holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

A. Stern and B. Javidi, “3D optical microscopy using digital holography,” Proc. SPIE. 6983, 69830O (2008).
[CrossRef]

A. Stern and B. Javidi, “Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope,” J. Opt. Soc. Am. A 24, 163–168 (2007).
[CrossRef]

S. Yeom and B. Javidi, “Automatic identification of biological microorganisms using three-dimensional complex morphology,” J. Biomed. Opt. 11, 024017 (2006).
[CrossRef]

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13, 4492–4506 (2005).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry (Wiley-VCH, 2004).

Lam, E. Y.

Lee, J. W.

Lim, S.

Liu, Y.

Lorenz, D.

Mait, J. N.

Marim, M.

Marim, M. M.

Marinho, F.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Marks, D. L.

Marquet, P.

Mas, D.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Mattheiss, M.

Montfort, F.

Moon, I.

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional imaging, identification and tracking of micro/nano biological organisms by holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13, 4492–4506 (2005).
[CrossRef]

Olivo-Marin, J.

Olivo-Marin, J.-C.

Onural, L.

G. B. Esmer, V. Uzunov, L. Onural, H. M. Ozaktas, and A. Gotchev, “Diffraction field computation from arbitrarily distributed data points in space,” Signal Process. Image Commun. 22, 178–187 (2007).
[CrossRef]

Ozaktas, H. M.

G. B. Esmer, V. Uzunov, L. Onural, H. M. Ozaktas, and A. Gotchev, “Diffraction field computation from arbitrarily distributed data points in space,” Signal Process. Image Commun. 22, 178–187 (2007).
[CrossRef]

Ozcan, A.

Paganin, D. M.

D. M. Paganin, Coherent X-ray Optics (Oxford Science Publications, 2006).

Rivenson, Y.

Romberg, J.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Rosen, J.

Rot, A.

Schulz, T. J.

Sencan, I.

Stern, A.

Su, T.-W.

Tao, T.

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Thiébaut, E.

Tian, L.

Tippie, A.

A. Tippie and J. Fienup, “Weak-object image reconstructions with single-shot digital holography,” in Digital Holography and Three-Dimensional Imaging, Technical Digest (Optical Society of America, 2012), p. DM4C.5.

Trede, D.

Triantafyllou, M. S.

Uzunov, V.

G. B. Esmer, V. Uzunov, L. Onural, H. M. Ozaktas, and A. Gotchev, “Diffraction field computation from arbitrarily distributed data points in space,” Signal Process. Image Commun. 22, 178–187 (2007).
[CrossRef]

Wakin, M.

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[CrossRef]

Wikner, D. A.

Yeom, S.

S. Yeom and B. Javidi, “Automatic identification of biological microorganisms using three-dimensional complex morphology,” J. Biomed. Opt. 11, 024017 (2006).
[CrossRef]

B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express 13, 4492–4506 (2005).
[CrossRef]

Zhang, X.

Appl. Opt.

IEEE Signal Process. Mag.

E. Candes and M. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008).
[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, 2992–3004(2007).
[CrossRef]

IEEE Trans. Inf. Theory

E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

J. Biomed. Opt.

S. Yeom and B. Javidi, “Automatic identification of biological microorganisms using three-dimensional complex morphology,” J. Biomed. Opt. 11, 024017 (2006).
[CrossRef]

J. Disp. Technol.

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

J. Opt. Soc. Am. A

Opt. Commun.

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. IEEE

I. Moon, M. Daneshpanah, B. Javidi, and A. Stern, “Automated three-dimensional imaging, identification and tracking of micro/nano biological organisms by holographic microscopy,” Proc. IEEE 97, 990–1010 (2009).
[CrossRef]

Proc. SPIE.

A. Stern and B. Javidi, “3D optical microscopy using digital holography,” Proc. SPIE. 6983, 69830O (2008).
[CrossRef]

Signal Process. Image Commun.

G. B. Esmer, V. Uzunov, L. Onural, H. M. Ozaktas, and A. Gotchev, “Diffraction field computation from arbitrarily distributed data points in space,” Signal Process. Image Commun. 22, 178–187 (2007).
[CrossRef]

Other

A. Tippie and J. Fienup, “Weak-object image reconstructions with single-shot digital holography,” in Digital Holography and Three-Dimensional Imaging, Technical Digest (Optical Society of America, 2012), p. DM4C.5.

T. Kreis, Handbook of Holographic Interferometry (Wiley-VCH, 2004).

D. M. Paganin, Coherent X-ray Optics (Oxford Science Publications, 2006).

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Figures (7)

Fig. 1.
Fig. 1.

SEOL holography setup: (a) optical setup and (b) equivalent block scheme.

Fig. 2.
Fig. 2.

Sectioning performance of the SEOL holographic system on spherical alga diatoms at depth plane. Reconstruction using conventional angular spectrum propagation, i.e., a 2D–2D model at (a) z=3.2μm, (b) z=6.4μm, and (c) z=9.6μm. (d)–(f) Same corresponding planes reconstructed with the CS SEOL holography approach.

Fig. 3.
Fig. 3.

Numerical experiment setup.

Fig. 4.
Fig. 4.

Noiseless numerical experiment: reconstruction results of planes z=Δz, 2Δz, 3Δz, 4Δz. (a) Original grating object. (b) Backpropagation reconstruction. (c) Compressive-holography reconstruction. The line denotes the examined cross section. (d) Cross section of the original object shown in (a). (e) Cross section of (b), where IPIR0. (f) Cross section of (c), where IPIR=0.67.

Fig. 5.
Fig. 5.

Reconstruction improvement, as measured by the interplaned interference rejection ratio IPIR [defined in Eq. (9)], as a function of separation between the object’s depth plane, Δz, and the theoretical resolution limit for the noiseless holographic system, δz195μm.

Fig. 6.
Fig. 6.

Noisy hologram reconstruction results. (a) Conventional backpropagation, with ξ=1.5. (b) Reconstruction using the compressive-holography approach on the Gabor recorded hologram with ξ=1.5. (c) Reconstruction using the compressive-holography approach with ξ=37.5, on the SEOL recorded hologram. (d) Row m0 of (b). (e) Row m0 of (c).

Fig. 7.
Fig. 7.

Influence of reference wave-to-object ratio on the reconstructed object resolution, quantified by the IPIR value [Eq. (9)].

Equations (9)

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

ISEOL=|U+R|2=|U|2+|R|2+R*U+RU*,
O(u,v;d)=jλdexp(j2πλd)exp(j2πλd(u2+v2))×U(x,y)exp(j2πλd(x2+y2))exp(j2πλd(ux+vy))dxdy,
U(x,y)+U*(x,y)={ISEOL|U|2|R|2}/R,
U(kΔx,lΔy)=r=1NzF2D1{exp[jπλrΔd(Δυxm)2+(Δυyn)2]F2D{O(p,q;rΔz)}}
min{UΦOT22+τOTV}.
U=[F2D1Qλ2ΔzF2D;;F2D1Qλ2NzΔzF2D][oΔz;;oNZΔz]T=ΦOT,
OTV=li,j(oi+1,j,loi,j,l)2+(oi,j+1,loi,j,l)2,
ξ=|RU|.
IPIR=O˜r(υF)O˜s(υF)Or(υF),0r,sNz1.

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