Abstract

We present a novel technique of digital holography using digitally implemented diffraction-free vortices for a precise three-dimensional (3D) localization of point-like objects. The localization is realized by the processing of the holographic image reconstructed at arbitrarily selected plane. Separating a single radial component of the spatial spectrum and modulating its phase by a virtual spiral mask, the holographic images of individual object points are transformed to the image structures analogous to the diffraction-free vortex beams. The real part of the complex amplitude of the digital vortices creates the shape-invariant patterns rotating due to a defocusing. Determining the angular rotation, the axial positions of the individual point objects are specified over a wide axial range. In the proposed method, a single in-line hologram is processed without phase shifting and multiplane reconstruction, so that a dynamic localization and tracking of particles becomes possible. The principle of the method is presented in a unified computational model valid for both coherent and incoherent techniques of digital holography. The functionality of the method has been verified in experiments of the Fresnel incoherent correlation holography (FINCH) and its flexibility presented by controlled variations of the localization sensitivity. The application potential has been demonstrated by the defocusing image rotation of fixed fluorescent microspheres and the 3D localization and tracking of moving polystyrene beads resulting in the trajectory reconstruction of a selected particle.

© 2014 Optical Society of America

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References

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X. Yu, J. Hong, Ch. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

C. Roider, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Axial super-localization using rotating point spread functions shaped by polarisation-dependent phase modulation,” Opt. Express 22, 4029–4037 (2014).
[Crossref] [PubMed]

2013 (3)

X. Lai, S. Zeng, X. Lv, J. Yuan, and L. Fu, “Violation of the Lagrange invariant in an optical imaging system,” Opt. Lett. 38, 1896–1898 (2013).
[Crossref] [PubMed]

M. Baránek and Z. Bouchal, “Rotating vortex imaging implemented by a quantized spiral phase modulation,” J. Europ. Opt. Soc. Rap. Public. 8, 13017 (2013).
[Crossref]

P. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Europ. Opt. Soc. Rap. Public. 8, 13011 (2013).
[Crossref]

2012 (1)

2011 (3)

2010 (1)

2009 (2)

Y. S. Choi and S. J. Lee, “Three-dimensional volumetric measurement of red blood cell motion using digital holographic microscopy,” Appl. Opt. 48, 2983–2990 (2009).
[Crossref] [PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

2008 (3)

2007 (2)

F. Soulez, L. Denis, C. Fournie, E. Thiebaut, and C. Goepfert, “Inverse problem approach for particle digital holography: accurate location based on local optimisation,” J. Opt. Soc. Am. A, 24, 1164–1171 (2007).
[Crossref]

J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (3)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express. 13, 2444–2452 (2005).
[Crossref] [PubMed]

Z. Bouchal, “Physical principle of experiments with pseudo-nondiffracting fields,” Czech. J. Phys. 55, 1223–1236 (2005).
[Crossref]

2003 (1)

2002 (1)

2001 (1)

1999 (1)

1997 (1)

1987 (1)

Asundi, A.

L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express. 13, 2444–2452 (2005).
[Crossref] [PubMed]

Badieirostami, M.

Baránek, M.

M. Baránek and Z. Bouchal, “Rotating vortex imaging implemented by a quantized spiral phase modulation,” J. Europ. Opt. Soc. Rap. Public. 8, 13017 (2013).
[Crossref]

Bernet, S.

Bevilacqua, F.

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

Bouchal, P.

Bouchal, Z.

P. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Europ. Opt. Soc. Rap. Public. 8, 13011 (2013).
[Crossref]

M. Baránek and Z. Bouchal, “Rotating vortex imaging implemented by a quantized spiral phase modulation,” J. Europ. Opt. Soc. Rap. Public. 8, 13017 (2013).
[Crossref]

P. Bouchal and Z. Bouchal, “Selective edge enhancement in three-dimensional vortex imaging with incoherent light,” Opt. Lett. 37, 2949–2951 (2012).
[Crossref] [PubMed]

P. Bouchal, J. Kapitán, R. Chmelík, and Z. Bouchal, “Point spread function and two-point resolution in Fresnel incoherent correlation holography,” Opt. Express 19, 15603–15620 (2011).
[Crossref] [PubMed]

Z. Bouchal, “Physical principle of experiments with pseudo-nondiffracting fields,” Czech. J. Phys. 55, 1223–1236 (2005).
[Crossref]

Z. Bouchal, “Controlled spatial shaping of nondiffracting patterns and arrays,” Opt. Lett. 27, 1376–1378 (2002).
[Crossref]

Brooker, G.

Callens, N.

Chmelík, R.

Choi, Y. S.

Coppola, G.

Cuche, E.

De Nicola, S.

Denis, L.

J Gire, L. Denis, C. Fournier, E. Thiebaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the “inverse problem” approach,” Meas. Sci. Technol. 19, 074005 (2008).
[Crossref]

F. Soulez, L. Denis, C. Fournie, E. Thiebaut, and C. Goepfert, “Inverse problem approach for particle digital holography: accurate location based on local optimisation,” J. Opt. Soc. Am. A, 24, 1164–1171 (2007).
[Crossref]

Depeursinge, C.

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

Dubois, F.

Ducottet, C.

J Gire, L. Denis, C. Fournier, E. Thiebaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the “inverse problem” approach,” Meas. Sci. Technol. 19, 074005 (2008).
[Crossref]

Durnin, J.

Ferraro, P.

Finizio, A.

Fink, H.

Fournie, C.

F. Soulez, L. Denis, C. Fournie, E. Thiebaut, and C. Goepfert, “Inverse problem approach for particle digital holography: accurate location based on local optimisation,” J. Opt. Soc. Am. A, 24, 1164–1171 (2007).
[Crossref]

Fournier, C.

J Gire, L. Denis, C. Fournier, E. Thiebaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the “inverse problem” approach,” Meas. Sci. Technol. 19, 074005 (2008).
[Crossref]

Fu, L.

Gehri, F.

Gire, J

J Gire, L. Denis, C. Fournier, E. Thiebaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the “inverse problem” approach,” Meas. Sci. Technol. 19, 074005 (2008).
[Crossref]

Goepfert, C.

F. Soulez, L. Denis, C. Fournie, E. Thiebaut, and C. Goepfert, “Inverse problem approach for particle digital holography: accurate location based on local optimisation,” J. Opt. Soc. Am. A, 24, 1164–1171 (2007).
[Crossref]

Greengard, A.

Grilli, S.

Guo, Z.

L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express. 13, 2444–2452 (2005).
[Crossref] [PubMed]

Hong, J.

X. Yu, J. Hong, Ch. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

Jesacher, A.

Kapitán, J.

Kemper, B.

Kim, M. K.

X. Yu, J. Hong, Ch. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

Lai, X.

Latychevskaia, T.

Lee, S. F.

Lee, S. J.

Lew, M. D.

Liu, Ch.

X. Yu, J. Hong, Ch. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

Liu, N.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

Lord, S. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

Lv, X.

Magro, C.

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

Meucci, R.

Miao, J.

L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express. 13, 2444–2452 (2005).
[Crossref] [PubMed]

Moerner, W. E.

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36, 202–204 (2011).
[Crossref] [PubMed]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

Pavani, S. R. P.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
[Crossref] [PubMed]

Peng, X.

L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express. 13, 2444–2452 (2005).
[Crossref] [PubMed]

Pierattini, G.

Piestun, R.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

S. R. P. Pavani and R. Piestun, “High-efficiency rotating point spread functions,” Opt. Express 16, 3484–3489 (2008).
[Crossref] [PubMed]

A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31, 181–183 (2006).
[Crossref] [PubMed]

Ritsch-Marte, M.

Roider, C.

Rosen, J.

Schechner, Y. Y.

Schockaert, C.

Siegel, N.

Soulez, F.

J Gire, L. Denis, C. Fournier, E. Thiebaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the “inverse problem” approach,” Meas. Sci. Technol. 19, 074005 (2008).
[Crossref]

F. Soulez, L. Denis, C. Fournie, E. Thiebaut, and C. Goepfert, “Inverse problem approach for particle digital holography: accurate location based on local optimisation,” J. Opt. Soc. Am. A, 24, 1164–1171 (2007).
[Crossref]

Thiebaut, E.

J Gire, L. Denis, C. Fournier, E. Thiebaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the “inverse problem” approach,” Meas. Sci. Technol. 19, 074005 (2008).
[Crossref]

F. Soulez, L. Denis, C. Fournie, E. Thiebaut, and C. Goepfert, “Inverse problem approach for particle digital holography: accurate location based on local optimisation,” J. Opt. Soc. Am. A, 24, 1164–1171 (2007).
[Crossref]

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

von Bally, G.

Xu, L.

L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express. 13, 2444–2452 (2005).
[Crossref] [PubMed]

Yamaguchi, I.

Yourassowsky, C.

Yu, X.

X. Yu, J. Hong, Ch. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

Yuan, J.

Zeng, S.

Zhang, T.

Appl. Opt. (3)

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

Czech. J. Phys. (1)

Z. Bouchal, “Physical principle of experiments with pseudo-nondiffracting fields,” Czech. J. Phys. 55, 1223–1236 (2005).
[Crossref]

J. Europ. Opt. Soc. Rap. Public. (2)

M. Baránek and Z. Bouchal, “Rotating vortex imaging implemented by a quantized spiral phase modulation,” J. Europ. Opt. Soc. Rap. Public. 8, 13017 (2013).
[Crossref]

P. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Europ. Opt. Soc. Rap. Public. 8, 13011 (2013).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. A, (1)

F. Soulez, L. Denis, C. Fournie, E. Thiebaut, and C. Goepfert, “Inverse problem approach for particle digital holography: accurate location based on local optimisation,” J. Opt. Soc. Am. A, 24, 1164–1171 (2007).
[Crossref]

Meas. Sci. Technol. (1)

J Gire, L. Denis, C. Fournier, E. Thiebaut, F. Soulez, and C. Ducottet, “Digital holography of particles: benefits of the “inverse problem” approach,” Meas. Sci. Technol. 19, 074005 (2008).
[Crossref]

Opt. Eng. (1)

X. Yu, J. Hong, Ch. Liu, and M. K. Kim, “Review of digital holographic microscopy for three-dimensional profiling and tracking,” Opt. Eng. 53, 112306 (2014).
[Crossref]

Opt. Express (7)

Opt. Express. (1)

L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express. 13, 2444–2452 (2005).
[Crossref] [PubMed]

Opt. Lett. (8)

PNAS (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” PNAS 106, 2995–2999 (2009).
[Crossref] [PubMed]

Supplementary Material (2)

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Figures (9)

Fig. 1
Fig. 1 Block diagram with three basic parts of the holographic localization of point-like objects by the diffraction-free vortices: optical hologram acquisition, digital hologram reconstruction and conversion of the holographic images to the vortex spots whose angular rotation indicates axial position.
Fig. 2
Fig. 2 Digital conversion of the holographic point images to the diffraction-free vortices with angular rotation depending on the defocusing. The vortex axial localization is applicable to both (a) coherent holography with a global reference wave and (b) incoherent self-interference holography using local reference waves created by a microscope objective (MO) and a SLM.
Fig. 3
Fig. 3 Experimental set-up for the particle localization by the rotating diffraction-free vortices in digital holographic microscopy using incoherently illuminated and fluorescent samples (TM-transmission module for LED illumination, FM-fluorescence excitation module, ML-mercury lamp, MO-microscope objective, RL1, RL2-relay lenses, EF1-excitation filter, EF2-emission filter, P-polarizer, BS-beam splitter, CGH-computer generated hologram and SLM-spatial light modulator).
Fig. 4
Fig. 4 Experimental and computational facilities used in demonstrations of the PSF engineering: (a) point holographic record taken in the set-up shown in Fig. 3, (b) digital annular filter with a spiral phase modulation.
Fig. 5
Fig. 5 Resizing of the vortex image and control of the longitudinal period by the radial spatial frequency ν0 of the narrow annular filter (Δν = 0.05ν0, l = 1). In demonstrations, the point correlation record shown in Fig. 4(a) was processed.
Fig. 6
Fig. 6 Comparison of the sharp and the out of focus PSF obtained by the annular filters with the narrow and wide slit: (a) narrow slit and the defocusing-invariant PSF analogous to the Bessel beam, (b) wide slit with the Gaussian apodization and the PSF analogous to the Bessel-Gauss beam.
Fig. 7
Fig. 7 The theoretical dependence of the angular image rotation on the normalized defocusing (solid line) and experimental values of the angles obtained for 12 selected ratios Δz′/Λ′. The listed standard deviations were obtained from four independent measurements carried out by the digital filters with l = 1, Δν = 0.2ν0 and ν0 = 3.52, 3.96, 4.52 and 5.27l/mm. The overall standard deviation Δ φ ¯ = 1.27 ° allows to estimate the accuracy of the axial localization.
Fig. 8
Fig. 8 Defocusing spreading and rotation of the image demonstrated by 5μm fluorescent microspheres (Invitrogen Focal Check Microspheres) recorded in the set-up shown in Fig. 3: (a) portion of the holographic correlation record of the sample, (b) standard image reconstruction of the hologram, (c) rotating vortex images obtained by the spiral processing of the hologram given by Eq. (4) ( Media 1).
Fig. 9
Fig. 9 Dynamic localization of moving 0.5μm polystyrene beads by the rotating diffraction-free vortex imaging: (a) sequence of the correlation records taken with the frequency of 10Hz, (b) vortex images obtained by the spiral processing of the standard holograms given by Eq. (4), (c) tracking of the selected particle by the rotating vortex image, (d) 3D trajectory of the tracked particle ( Media 2).

Equations (16)

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T m e S m e R * exp [ i ( φ S m φ R ) ] .
T m e S m e R m * exp [ i ( φ S m φ R m ) ] .
T e S e R * exp ( i k | r | 2 2 f L ) ,
E 1 { S { F r T ( T ) } } .
E S ( F ) exp [ i k | R | 2 2 z ] exp [ i k | r | 2 2 Δ κ ] exp [ i k r R z ] d r × exp [ i k F ( R f 1 + r f 2 ) ] d R d F ,
E S ( F ) exp [ i k | F | 2 Δ z 2 f 1 2 ] exp [ i k F r f 2 ] d F ,
S ( F ) = δ ( | F | F 0 ) exp ( i l φ ) ,
E J l ( α r ) exp ( i l φ 0 + i l φ + i β Δ z ) ,
α = 2 π ν 0 ,
β = π λ ν 0 2 .
e J l ( α r ) cos ( l φ 0 + l φ + β Δ z ) .
φ max = m π l φ 0 β Δ z l , m = 1 , 2 , .
Λ min = 1 λ ν max 2 ,
Ω d φ d Δ z = β l ,
r 0 = q l 2 π ν 0 ,
ν 0 > ν max ( 1 f L f L + 0.5 f 1 ) .

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