Abstract

A parameter-optimized off-axis setup for digital holographic microscopy is presented for simultaneous, high-resolution, full-field quantitative amplitude and quantitative phase-contrast microscopy and the detection of changes in optical path length in transparent objects, such as undyed living cells. Numerical reconstruction with the described nondiffractive reconstruction method, which suppresses the zero order and the twin image, requires a mathematical model of the phase-difference distribution between the object wave and the reference wave in the hologram plane. Therefore an automated algorithm is explained that determines the parameters of the mathematical model by carrying out the discrete Fresnel transform. Furthermore the relationship between the axial position of the object and the reconstruction distance, which is required for optimization of the lateral resolution of the holographic images, is derived. The lateral and the axial resolutions of the system are discussed and quantified by application to technical objects and to living cells.

© 2004 Optical Society of America

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  1. T. Kreis, Holographic Interferometry, Principles and Methods: Diffraction Theory (Akademie Verlag GmbH, Berlin, 1996), pp. 27–31.
  2. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  3. G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
    [CrossRef]
  4. E. Cuche, P. Marquet, P. Magistretti, C. Depeursinge, “Quantitative phase contrast microscopy of living cells by numerical reconstruction of digital holograms,” in Optical Diagnostics of Living Cells II, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3604, 84–89 (1999).
    [CrossRef]
  5. E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
    [CrossRef]
  6. U. Schnars, W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85–101 (2002).
    [CrossRef]
  7. S. Lai, B. Kemper, G. v. Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37–43 (1999).
    [CrossRef]
  8. L. Xu, J. Miao, A. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214–3219 (2000).
    [CrossRef]
  9. W. Xu, M. H. Jerico, I. A. Meinertzhagen, H. J. Kreuzner, “Digital in-line holography of microspheres,” Appl. Opt. 41, 5367–5375 (2002).
    [CrossRef] [PubMed]
  10. M. Liebling, T. Blu, E. Cuche, P. Marquet, C. Depeursinge, M. Unser, “A novel nondiffractive reconstruction method for digital holographic microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 625–628.
    [CrossRef]
  11. H. A. Aebischer, S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
    [CrossRef]
  12. T. Kreis, Holographic Interferometry, Principles and Methods: Interference Phase Demodulation (Akademie Verlag GmbH, Berlin, 1996, pp. 161–170.
  13. S. Inoué, K. Spring, Video Microscopy: The Fundamentals (Plenum, New York, 1997).
    [CrossRef]
  14. T. Kreis, Holographic Interferometry, Principles and Methods: Principle of Digital Holography (Akademie Verlag GmbH, Berlin, 1996), pp. 150–153.
  15. B. Kemper, J. Kandulla, D. Dirksen, G. v. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
    [CrossRef]

2003

B. Kemper, J. Kandulla, D. Dirksen, G. v. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

2002

W. Xu, M. H. Jerico, I. A. Meinertzhagen, H. J. Kreuzner, “Digital in-line holography of microspheres,” Appl. Opt. 41, 5367–5375 (2002).
[CrossRef] [PubMed]

U. Schnars, W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85–101 (2002).
[CrossRef]

2000

L. Xu, J. Miao, A. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214–3219 (2000).
[CrossRef]

1999

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

H. A. Aebischer, S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

S. Lai, B. Kemper, G. v. Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37–43 (1999).
[CrossRef]

E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

1994

Aebischer, H. A.

H. A. Aebischer, S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

Asundi, A.

L. Xu, J. Miao, A. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214–3219 (2000).
[CrossRef]

Bally, G. v.

B. Kemper, J. Kandulla, D. Dirksen, G. v. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

S. Lai, B. Kemper, G. v. Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37–43 (1999).
[CrossRef]

Blu, T.

M. Liebling, T. Blu, E. Cuche, P. Marquet, C. Depeursinge, M. Unser, “A novel nondiffractive reconstruction method for digital holographic microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 625–628.
[CrossRef]

Cuche, E.

E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

E. Cuche, P. Marquet, P. Magistretti, C. Depeursinge, “Quantitative phase contrast microscopy of living cells by numerical reconstruction of digital holograms,” in Optical Diagnostics of Living Cells II, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3604, 84–89 (1999).
[CrossRef]

M. Liebling, T. Blu, E. Cuche, P. Marquet, C. Depeursinge, M. Unser, “A novel nondiffractive reconstruction method for digital holographic microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 625–628.
[CrossRef]

Depeursinge, C.

E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

E. Cuche, P. Marquet, P. Magistretti, C. Depeursinge, “Quantitative phase contrast microscopy of living cells by numerical reconstruction of digital holograms,” in Optical Diagnostics of Living Cells II, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3604, 84–89 (1999).
[CrossRef]

M. Liebling, T. Blu, E. Cuche, P. Marquet, C. Depeursinge, M. Unser, “A novel nondiffractive reconstruction method for digital holographic microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 625–628.
[CrossRef]

Dirksen, D.

B. Kemper, J. Kandulla, D. Dirksen, G. v. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

Fröning, P.

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

Inoué, S.

S. Inoué, K. Spring, Video Microscopy: The Fundamentals (Plenum, New York, 1997).
[CrossRef]

Jerico, M. H.

Jüptner, W.

U. Schnars, W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85–101 (2002).
[CrossRef]

Kandulla, J.

B. Kemper, J. Kandulla, D. Dirksen, G. v. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

Kemper, B.

B. Kemper, J. Kandulla, D. Dirksen, G. v. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

S. Lai, B. Kemper, G. v. Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37–43 (1999).
[CrossRef]

Kreis, T.

T. Kreis, Holographic Interferometry, Principles and Methods: Principle of Digital Holography (Akademie Verlag GmbH, Berlin, 1996), pp. 150–153.

T. Kreis, Holographic Interferometry, Principles and Methods: Diffraction Theory (Akademie Verlag GmbH, Berlin, 1996), pp. 27–31.

T. Kreis, Holographic Interferometry, Principles and Methods: Interference Phase Demodulation (Akademie Verlag GmbH, Berlin, 1996, pp. 161–170.

Kreuzner, H. J.

Lai, S.

S. Lai, B. Kemper, G. v. Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37–43 (1999).
[CrossRef]

Liebling, M.

M. Liebling, T. Blu, E. Cuche, P. Marquet, C. Depeursinge, M. Unser, “A novel nondiffractive reconstruction method for digital holographic microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 625–628.
[CrossRef]

Magistretti, P.

E. Cuche, P. Marquet, P. Magistretti, C. Depeursinge, “Quantitative phase contrast microscopy of living cells by numerical reconstruction of digital holograms,” in Optical Diagnostics of Living Cells II, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3604, 84–89 (1999).
[CrossRef]

Marquet, P.

E. Cuche, P. Marquet, C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

E. Cuche, P. Marquet, P. Magistretti, C. Depeursinge, “Quantitative phase contrast microscopy of living cells by numerical reconstruction of digital holograms,” in Optical Diagnostics of Living Cells II, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3604, 84–89 (1999).
[CrossRef]

M. Liebling, T. Blu, E. Cuche, P. Marquet, C. Depeursinge, M. Unser, “A novel nondiffractive reconstruction method for digital holographic microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 625–628.
[CrossRef]

Meinertzhagen, I. A.

Miao, J.

L. Xu, J. Miao, A. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214–3219 (2000).
[CrossRef]

Pedrini, G.

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

Santoyo, F. M.

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

Schnars, U.

U. Schnars, W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85–101 (2002).
[CrossRef]

U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
[CrossRef]

Spring, K.

S. Inoué, K. Spring, Video Microscopy: The Fundamentals (Plenum, New York, 1997).
[CrossRef]

Tiziani, H. J.

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

Unser, M.

M. Liebling, T. Blu, E. Cuche, P. Marquet, C. Depeursinge, M. Unser, “A novel nondiffractive reconstruction method for digital holographic microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 625–628.
[CrossRef]

Waldner, S.

H. A. Aebischer, S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

Xu, L.

L. Xu, J. Miao, A. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214–3219 (2000).
[CrossRef]

Xu, W.

Appl. Opt.

J. Opt. Soc. Am. A

Meas. Sci. Technol.

U. Schnars, W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85–101 (2002).
[CrossRef]

Opt. Commun.

S. Lai, B. Kemper, G. v. Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37–43 (1999).
[CrossRef]

G. Pedrini, P. Fröning, H. J. Tiziani, F. M. Santoyo, “Shape measurement of microscopic structures using digital holograms,” Opt. Commun. 164, 257–268 (1999).
[CrossRef]

H. A. Aebischer, S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[CrossRef]

B. Kemper, J. Kandulla, D. Dirksen, G. v. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

Opt. Eng.

L. Xu, J. Miao, A. Asundi, “Properties of digital holography based on in-line configuration,” Opt. Eng. 39, 3214–3219 (2000).
[CrossRef]

Other

E. Cuche, P. Marquet, P. Magistretti, C. Depeursinge, “Quantitative phase contrast microscopy of living cells by numerical reconstruction of digital holograms,” in Optical Diagnostics of Living Cells II, D. L. Farkas, R. C. Leif, B. J. Tromberg, eds., Proc. SPIE3604, 84–89 (1999).
[CrossRef]

M. Liebling, T. Blu, E. Cuche, P. Marquet, C. Depeursinge, M. Unser, “A novel nondiffractive reconstruction method for digital holographic microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging 2002 (Institute of Electrical and Electronics Engineers, New York, 2002), Vol. 2, pp. 625–628.
[CrossRef]

T. Kreis, Holographic Interferometry, Principles and Methods: Diffraction Theory (Akademie Verlag GmbH, Berlin, 1996), pp. 27–31.

T. Kreis, Holographic Interferometry, Principles and Methods: Interference Phase Demodulation (Akademie Verlag GmbH, Berlin, 1996, pp. 161–170.

S. Inoué, K. Spring, Video Microscopy: The Fundamentals (Plenum, New York, 1997).
[CrossRef]

T. Kreis, Holographic Interferometry, Principles and Methods: Principle of Digital Holography (Akademie Verlag GmbH, Berlin, 1996), pp. 150–153.

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Figures (10)

Fig. 1
Fig. 1

Off-axis configuration for digital holographic microscopy: O, object wave; R, reference wave; BS1, BS2, beam-splitter cube; M, mirror; ND, neutral-density filter; MO, microscope objective; PH, pinhole; L, lens; A, aperture; CCD, CCD camera.

Fig. 2
Fig. 2

Image of a captured digital hologram reconstructed with DFT without an object: (a) absolute spatial amplitude distribution (contrast enhanced); (b) phase-difference distribution for imprecisely determined reconstruction parameters; (c) phase-difference distribution for numerically optimized reconstruction parameters.

Fig. 3
Fig. 3

Cos-sin filtered11 phase difference (modulo 2π) between the reconstructed phase of the captured hologram and the synthetic hologram: (a) before optimization, (b) after a number of iterations, (c) with optimized parameters, (d)–(f) corresponding cross sections of the phase-difference distribution (represented by white lines). The standard deviation of the unwrapped lines amounts to (a) σ = 7.15, (b) σ = 1.41, and (c) σ = 0.14.

Fig. 4
Fig. 4

Imaging geometry for digital holographic microscopy: f, focal length; g 0, distance between the object plane and the microscope lens (object focused to the hologram plane); b 0, distance between the hologram plane and the microscope lens; g, distance between the object plane and the microscope lens (the object is focused to the image plane); b, distance between the image plane and the microscope lens; d, distance between the microscope’s focal point and the hologram plane; z, reconstruction distance according to the object displacement Δg.

Fig. 5
Fig. 5

Groups 8 and 9 of a negative USAF 1951 resolution chart: (a) laser illumination, (b)–(d) reconstructed absolute amplitude: (b) Δz′ = 100 mm, (c) Δz′ = 115 mm (focused), (d) Δz′ = 120 mm. Object displacement: Δg = 40 μm ± 2 μm.

Fig. 6
Fig. 6

Verification of the experimental results. The reconstruction distances Δz and Δz′ versus axial object displacement Δg are compared with theory [Eqs. (14) and (19)]: (a) DFT, (b) NDRM with subsequent DFT.

Fig. 7
Fig. 7

(a)–(c) Absolute amplitude reconstructed with the DFT: (a) Δz = 207 mm, (b) Δz = 422 mm, (c) Δz = 1180 mm. (d)–(f) Absolute amplitude reconstructed with the NDRM with subsequent DFT: (d) Δz′ = 68 mm, (e) Δz′ ′ = 113 mm, (f) Δz′ = 295 mm.

Fig. 8
Fig. 8

Part of the object arm of the interferometer for examination of living cells, e.g., tumorous human hepatocytes, in a growth medium: M, mirror; MO, microscope objective; xyz, linear translation stage with aperture.

Fig. 9
Fig. 9

Reconstructed absolute amplitudes of a single captured digital hologram of living tumorous human hepatocytes at different reconstruction distances: (a) Δz′ = 120 mm, (b) Δz′ = 130 mm, (c) Δz′ = 140 mm. The corresponding space between the reconstructed image planes is 3.3 μm.

Fig. 10
Fig. 10

Living tumorous human hepatocytes in suspension: (a) absolute amplitude of the reconstructed object wave, (b) phase distribution corresponding to (a) [reconstruction parameters calculated by application of Eqs. (10) and (11)], (c) phase distribution corresponding to (a) (reconstruction parameters numerically optimized), (d) unwrapped phase distribution of (c), (e) absolute amplitude of the reconstructed object wave after stimulation with a NaCl solution, (f) phase distribution corresponding to (e) (reconstruction parameters optimized), (g) unwrapped cross sections represented by the white lines in (c) and (f); (h) pseudo-three-dimensional image of the unwrapped phase distribution in (d).

Equations (20)

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Ex, y, Δz=iERλΔz exp-iπλΔzx2Nx2Δx2+y2Nx2Δy2x=0Nx-1y=0Ny-1 Hx, y×exp-i πλΔzx2Δx2+y2Δy2×expi2πxxNx+yyNy.
Ex, y, ΔzFFT-1Hx, yexp-i πλΔzx2Δx2+y2Δy2.
Ψx, ye-a*cb-aa-d-ac1-a*ab*-aab-aa-1-a*a1-a*a,
Φx, y:=expiΔφx, y,
a:=ax, y:=1Mm Φm, b:=bx, y:=1Mm Φm2, c:=cx, y:=1Mm Hm, d:=dx, y:=1Mm ΦmHm, e:=ex, y:=1Mm Φm*Hm.
Δx=λΔzNxΔx, Δy=λΔzNyΔy,
ΔZx=Nx2Δx2λΔz, ΔZy=Ny2Δy2λΔz,
V=ΔIxΔZx=1+Δzd,
Δφx, y=2πlxx+lyy+kx2+y2.
lx=ΔdxNx, ly=ΔdyNy,
k=Δx2V-12Δbλ+λ2V-1.
Hsynx, y=I0+γ cosΔφx, y,
1f=1g+1b,
Δz=Δgf-b02f2-b0Δg+fΔg=Δgd2f2-Δgd,
ΔIxΔz, d=Nx2Δx2λΔz1+Δzd.
ΔIxΔz, d=Nx2Δx2λΔz.
ΔIxΔz, d=ΔIxΔz, Nx2Δx2λΔz1+Δzd=Nx2Δx2λΔz, Δz=dΔzd+Δz.
d=12Δx2λk-λ.
Δz=Δx2-λ2k2fλk2Δg.
ΔzDOF=nλNA2+neNAM,

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