Abstract

We present a digital method for holographic microscopy involving a CCD camera as a recording device. Off-axis holograms recorded with a magnified image of microscopic objects are numerically reconstructed in amplitude and phase by calculation of scalar diffraction in the Fresnel approximation. For phase-contrast imaging the reconstruction method involves the computation of a digital replica of the reference wave. A digital method for the correction of the phase aberrations is presented. We present a detailed description of the reconstruction procedure and show that the transverse resolution is equal to the diffraction limit of the imaging system.

© 1999 Optical Society of America

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  1. J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
    [CrossRef]
  2. M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).
  3. W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, C. K. Rhodes, “Fourier-transform holographic microscope,” Appl. Opt. 31, 4973–4978 (1992).
    [CrossRef] [PubMed]
  4. K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and X-ray wavelength,” Nat. Med. (N.Y.) 2, 939–941 (1996).
    [CrossRef]
  5. U. Schnars, W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  6. K. Yoshinori, U. Hiroaki, T. Kenji, H. Okamoto, E. Shimizu, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2716, 272–282 (1994).
  7. O. Coquoz, R. Conde, F. Taleblou, C. Depeursinge, “Performances of endoscopic holography with a multicore optical fiber,” Appl. Opt. 34, 7186–7193 (1995).
    [CrossRef] [PubMed]
  8. J. Pomarico, U. Schnars, H.-J. Hartmann, W. Jüptner, “Digital recording and numerical reconstruction of holograms: a new method for displaying light in flight,” Appl. Opt. 34, 8095–8099 (1995).
    [CrossRef] [PubMed]
  9. E. Cuche, P. Poscio, C. Depeursinge, “Optical tomography at the microscopic scale by means of a numerical low coherence holographic technique,” in Optical and Imaging Techniques for Biomonitoring II, H. J. Foth, R. Marchesini, H. Pobielska, eds., Proc. SPIE2927, 61–66 (1996).
    [CrossRef]
  10. E. Cuche, P. Poscio, C. Depeursinge, “Tomographie optique par une technique d’holographie numérique en faible cohérence,” J. Opt. (Paris) 28, 260–264 (1997).
    [CrossRef]
  11. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  12. T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
    [CrossRef]
  13. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  14. U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
    [CrossRef]
  15. E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  16. See, for example, M. Pluta, “Holographic microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosslett, eds. (Academic, London, 1987), Vol. 10, pp. 99–213.
  17. R. F. VanLigten, H. Osterberg, “Holographic microscopy,” Nature 211, 282–283 (1966).
    [CrossRef]
  18. J. E. Greivenkamp, J. H. Brunning, “Phase shifting interferometry”; K. Creath, A. Morales, “Contact and noncontact profilers,” in Optical Shop Testing, 2nd ed., Wiley Series in Pure and Applied Optics, D. Malacara, ed. (Wiley, New York, 1992), Chaps. 14 and 17.
  19. P. C. Sun, E. Arons, “Nonscanning confocal ranging system,” Appl. Opt. 34, 1254–1261 (1995).
    [CrossRef] [PubMed]
  20. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), Chap. 5.

1999 (1)

1998 (1)

1997 (2)

E. Cuche, P. Poscio, C. Depeursinge, “Tomographie optique par une technique d’holographie numérique en faible cohérence,” J. Opt. (Paris) 28, 260–264 (1997).
[CrossRef]

I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef] [PubMed]

1996 (2)

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and X-ray wavelength,” Nat. Med. (N.Y.) 2, 939–941 (1996).
[CrossRef]

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

1995 (3)

1994 (2)

1992 (1)

1972 (1)

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

1967 (1)

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

1966 (1)

R. F. VanLigten, H. Osterberg, “Holographic microscopy,” Nature 211, 282–283 (1966).
[CrossRef]

Arons, E.

Bevilacqua, F.

Borisov, A. B.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and X-ray wavelength,” Nat. Med. (N.Y.) 2, 939–941 (1996).
[CrossRef]

Boyer, K.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and X-ray wavelength,” Nat. Med. (N.Y.) 2, 939–941 (1996).
[CrossRef]

W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, C. K. Rhodes, “Fourier-transform holographic microscope,” Appl. Opt. 31, 4973–4978 (1992).
[CrossRef] [PubMed]

Conde, R.

Coquoz, O.

Cuche, E.

E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
[CrossRef]

E. Cuche, P. Poscio, C. Depeursinge, “Tomographie optique par une technique d’holographie numérique en faible cohérence,” J. Opt. (Paris) 28, 260–264 (1997).
[CrossRef]

E. Cuche, P. Poscio, C. Depeursinge, “Optical tomography at the microscopic scale by means of a numerical low coherence holographic technique,” in Optical and Imaging Techniques for Biomonitoring II, H. J. Foth, R. Marchesini, H. Pobielska, eds., Proc. SPIE2927, 61–66 (1996).
[CrossRef]

Cullen, D.

Depeursinge, C.

E. Cuche, F. Bevilacqua, C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
[CrossRef]

E. Cuche, P. Poscio, C. Depeursinge, “Tomographie optique par une technique d’holographie numérique en faible cohérence,” J. Opt. (Paris) 28, 260–264 (1997).
[CrossRef]

O. Coquoz, R. Conde, F. Taleblou, C. Depeursinge, “Performances of endoscopic holography with a multicore optical fiber,” Appl. Opt. 34, 7186–7193 (1995).
[CrossRef] [PubMed]

E. Cuche, P. Poscio, C. Depeursinge, “Optical tomography at the microscopic scale by means of a numerical low coherence holographic technique,” in Optical and Imaging Techniques for Biomonitoring II, H. J. Foth, R. Marchesini, H. Pobielska, eds., Proc. SPIE2927, 61–66 (1996).
[CrossRef]

Goodman, J. W.

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), Chap. 5.

Haddad, W. S.

Hartmann, H.-J.

Hiroaki, U.

K. Yoshinori, U. Hiroaki, T. Kenji, H. Okamoto, E. Shimizu, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2716, 272–282 (1994).

Jüptner, W.

Jüptner, W. P. O.

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

Kenji, T.

K. Yoshinori, U. Hiroaki, T. Kenji, H. Okamoto, E. Shimizu, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2716, 272–282 (1994).

Kreis, T. M.

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Lawrence, R. W.

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

Longworth, J. W.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and X-ray wavelength,” Nat. Med. (N.Y.) 2, 939–941 (1996).
[CrossRef]

W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, C. K. Rhodes, “Fourier-transform holographic microscope,” Appl. Opt. 31, 4973–4978 (1992).
[CrossRef] [PubMed]

McPherson, A.

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Okamoto, H.

K. Yoshinori, U. Hiroaki, T. Kenji, H. Okamoto, E. Shimizu, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2716, 272–282 (1994).

Osterberg, H.

R. F. VanLigten, H. Osterberg, “Holographic microscopy,” Nature 211, 282–283 (1966).
[CrossRef]

Pluta, M.

See, for example, M. Pluta, “Holographic microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosslett, eds. (Academic, London, 1987), Vol. 10, pp. 99–213.

Pomarico, J.

Poscio, P.

E. Cuche, P. Poscio, C. Depeursinge, “Tomographie optique par une technique d’holographie numérique en faible cohérence,” J. Opt. (Paris) 28, 260–264 (1997).
[CrossRef]

E. Cuche, P. Poscio, C. Depeursinge, “Optical tomography at the microscopic scale by means of a numerical low coherence holographic technique,” in Optical and Imaging Techniques for Biomonitoring II, H. J. Foth, R. Marchesini, H. Pobielska, eds., Proc. SPIE2927, 61–66 (1996).
[CrossRef]

Rhodes, C. K.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and X-ray wavelength,” Nat. Med. (N.Y.) 2, 939–941 (1996).
[CrossRef]

W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, C. K. Rhodes, “Fourier-transform holographic microscope,” Appl. Opt. 31, 4973–4978 (1992).
[CrossRef] [PubMed]

Schnars, U.

Shimizu, E.

K. Yoshinori, U. Hiroaki, T. Kenji, H. Okamoto, E. Shimizu, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2716, 272–282 (1994).

Solem, J. C.

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and X-ray wavelength,” Nat. Med. (N.Y.) 2, 939–941 (1996).
[CrossRef]

W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, C. K. Rhodes, “Fourier-transform holographic microscope,” Appl. Opt. 31, 4973–4978 (1992).
[CrossRef] [PubMed]

Sun, P. C.

Taleblou, F.

VanLigten, R. F.

R. F. VanLigten, H. Osterberg, “Holographic microscopy,” Nature 211, 282–283 (1966).
[CrossRef]

Yamaguchi, I.

Yaroslavskii, L. P.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Yoshinori, K.

K. Yoshinori, U. Hiroaki, T. Kenji, H. Okamoto, E. Shimizu, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2716, 272–282 (1994).

Zhang, T.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

J. W. Goodman, R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[CrossRef]

J. Opt. (Paris) (1)

E. Cuche, P. Poscio, C. Depeursinge, “Tomographie optique par une technique d’holographie numérique en faible cohérence,” J. Opt. (Paris) 28, 260–264 (1997).
[CrossRef]

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

Nat. Med. (N.Y.) (1)

K. Boyer, J. C. Solem, J. W. Longworth, A. B. Borisov, C. K. Rhodes, “Biomedical three-dimensional holographic microimaging at visible, ultraviolet and X-ray wavelength,” Nat. Med. (N.Y.) 2, 939–941 (1996).
[CrossRef]

Nature (1)

R. F. VanLigten, H. Osterberg, “Holographic microscopy,” Nature 211, 282–283 (1966).
[CrossRef]

Opt. Eng. (1)

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

Opt. Lett. (3)

Sov. Phys. Tech. Phys. (1)

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Other (5)

E. Cuche, P. Poscio, C. Depeursinge, “Optical tomography at the microscopic scale by means of a numerical low coherence holographic technique,” in Optical and Imaging Techniques for Biomonitoring II, H. J. Foth, R. Marchesini, H. Pobielska, eds., Proc. SPIE2927, 61–66 (1996).
[CrossRef]

K. Yoshinori, U. Hiroaki, T. Kenji, H. Okamoto, E. Shimizu, “Three-dimensional shape measurement using images reconstructed by the computer from a hologram,” in Practical Holography VIII, S. A. Benton, ed., Proc. SPIE2716, 272–282 (1994).

J. E. Greivenkamp, J. H. Brunning, “Phase shifting interferometry”; K. Creath, A. Morales, “Contact and noncontact profilers,” in Optical Shop Testing, 2nd ed., Wiley Series in Pure and Applied Optics, D. Malacara, ed. (Wiley, New York, 1992), Chaps. 14 and 17.

See, for example, M. Pluta, “Holographic microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosslett, eds. (Academic, London, 1987), Vol. 10, pp. 99–213.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), Chap. 5.

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Figures (9)

Fig. 1
Fig. 1

Schematic of the holographic microscope for transmission imaging. NF, neutral density filter; PBS, polarizing beam splitter; BE, beam expander with spatial filter; λ/2, half-wave plate; M, mirror; BS, beam splitter; O, object wave; R, reference wave. Inset: detail showing the off-axis geometry at the incidence on the CCD.

Fig. 2
Fig. 2

Schematic of the holographic microscope for reflection imaging. NF, neutral density filter; PBS, polarizing beam splitter; BE, beam expander with spatial filter; λ/2, half-wave plate; M, mirror; BS, beam splitter; O, object wave; R, reference wave.

Fig. 3
Fig. 3

Configuration for holographic microscopy.

Fig. 4
Fig. 4

Geometry for hologram reconstruction. 0xy, hologram plane; 0ξη, observation plane; d, reconstruction distance; Ψ(ξ, η), reconstructed wave front.

Fig. 5
Fig. 5

Schematic of the wave-front deformation by the MO.

Fig. 6
Fig. 6

Digital hologram recorded by the CCD camera.

Fig. 7
Fig. 7

Reconstructed images corresponding to the hologram presented in Fig. 6. (a) Amplitude-contrast image, (b) phase-contrast image, (c) the reconstructed phase distribution presented in a three-dimensional perspective.

Fig. 8
Fig. 8

Amplitude-contrast images obtained for different values of the reconstruction distance d. (a) Out of focus image (d too short), (b) in-focus image, (c) out of focus image (d too long).

Fig. 9
Fig. 9

Phase-contrast images obtained for different values of k x , k y , and D. (a) Without digital reference wave and without digital phase mask (k x = 0.0, k y = 0.0, no phase mask), (b) without digital reference wave and with proper digital phase mask (k x = 0.0, k y = 0.0, D = 0.258), (c) with proper digital phase mask and wrong digital reference wave (k x = 9.0 × 10-3, k y = 1.0 × 10-3, D = 0.258), (d) with proper digital reference wave and wrong digital phase mask (k x = 11.08 × 10-3, k y = 2.05 10-3, D = 0.240), (e) with proper digital reference wave and proper digital phase mask (k x = 11.08 × 10-3, k y = 2.05 10-3, D = 0.258).

Equations (17)

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IHx, y=|R|2+|O|2+R*O+RO*,
IHk, l=IHx, yrectxL, yL×k=-N/2N/2l=-N/2N/2 δx-kΔx, y-lΔy,
Ψ=RIH=R|R|2+R|O|2+|R|2O+R2O*.
Ψξ, η=A expiπλdξ2+η2× IHx, yexpiπλdx2+y2×expi2πλdxξ+yηdxdy,
IHx, yexpiπλdx2+y2.
Ψm, n=A expiπλdm2Δξ2+n2Δη2×FFTIHk, lexpiπλdk2Δx2+l2Δy2m,n,
Δξ=Δη=λdNΔx=λdL,
RDk, l=AR expi2π/λkxkΔx+kylΔy,
Uixi, yi= hxi, yi; xo, yoUxo, yodxodyo,
1di+1do=1f,
hxi, xo=C expiπλdi xi2expiπλdo xo2× Pxϕexp-i2πλxodo+xidixϕdxϕ,
hxi, yi; xo, yoC expiπλdi1+dodixi2+yi2×δxi+Mxo, yi+Myo.
Φm, n=exp-iπλDm2Δξ2+n2Δη2,
1D=1di1+dodi.
Ψm, n=AΦm, nexpiπλdm2Δξ2+n2Δη2×FFTRDk, lIHk, l×expiπλdk2Δx2+l2Δy2m,n.
Im, n=ReΨm, n2+ImΨm, n2,
ϕm, n=arc tanImΨm, nReΨm, n.

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