Abstract

We discuss image formation in phase-shifting digital holography by developing an analytical formulation based on the Fresnel–Kirchhoff diffraction theory. Image-plane position and imaging magnification are derived for general configurations in which a spherical reference is employed. The influences of discrete sampling of the resulting interference patterns by a CCD and numerical reconstruction on qualities of point images are investigated. Dependence of the point images on the ratio of the minimum fringe spacing to pixel pitch of the CCD is numerically analyzed. Two-point resolution and magnification are also investigated as a function of pixel numbers by a simulation using a one-dimensional model. In experiments magnified images of biological objects and a resolution target were reconstructed with the same quality as by conventional microscopy.

© 2001 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. L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
    [CrossRef]
  4. U. Schnars, W. Juptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  5. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  6. B. Skarman, J. Becker, K. Wozniak, “Simultaneous 3D-PIV and temperature measurements using a new CCD-based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
    [CrossRef]
  7. T. Zhang, I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
    [CrossRef]
  8. Y. Takaki, H. Kawai, H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. 38, 4990–4996 (1999).
    [CrossRef]
  9. S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. E. Tajahuerce, O. Matoba, S. C. Verrall, B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
    [CrossRef]
  14. I. Yamaguchi, S. Ohta, J. Kato, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

2001 (2)

I. Yamaguchi, S. Ohta, J. Kato, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[CrossRef]

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

2000 (5)

1999 (4)

1998 (1)

1997 (1)

1996 (1)

B. Skarman, J. Becker, K. Wozniak, “Simultaneous 3D-PIV and temperature measurements using a new CCD-based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[CrossRef]

1994 (1)

1992 (1)

1987 (1)

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

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 (2)

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

E. B. Champagne, “Nonparaaxial imaging, magnification, and aberration properties in holography,” J. Opt. Soc. Am. 57, 51–55 (1967).
[CrossRef]

Becker, J.

B. Skarman, J. Becker, K. Wozniak, “Simultaneous 3D-PIV and temperature measurements using a new CCD-based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[CrossRef]

Boyer, K.

Champagne, E. B.

Cuche, E.

Cullen, D.

Depeursinge, C.

Dubois, F.

Goodman, J. W.

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

Haddad, W. S.

Javidi, B.

Joannes, L.

Juptner, W.

Kato, J.

I. Yamaguchi, S. Ohta, J. Kato, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[CrossRef]

Kawai, H.

King, B.

S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[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).

Lai, S.

S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

S. Lai, M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178, 283–289 (2000).
[CrossRef]

Lawrence, R. W.

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

Legros, J.-C.

Longworth, J. W.

Marquet, P.

Matoba, O.

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).

Neifeld, M. A.

S. Lai, M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178, 283–289 (2000).
[CrossRef]

S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

Ohta, S.

I. Yamaguchi, S. Ohta, J. Kato, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[CrossRef]

Ohzu, H.

Onural, L.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Pedrini, G.

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

Rhodes, C. K.

Schedin, S.

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

Schnars, U.

Scott, P. D.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Skarman, B.

B. Skarman, J. Becker, K. Wozniak, “Simultaneous 3D-PIV and temperature measurements using a new CCD-based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[CrossRef]

Solem, J. C.

Tajahuerce, E.

Takaki, Y.

Tiziani, H. J.

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

Verrall, S. C.

Wozniak, K.

B. Skarman, J. Becker, K. Wozniak, “Simultaneous 3D-PIV and temperature measurements using a new CCD-based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[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).

Zhang, T.

Appl. Opt. (8)

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]

Flow Meas. Instrum. (1)

B. Skarman, J. Becker, K. Wozniak, “Simultaneous 3D-PIV and temperature measurements using a new CCD-based holographic interferometer,” Flow Meas. Instrum. 7, 1–6 (1996).
[CrossRef]

J. Mod. Opt. (1)

G. Pedrini, S. Schedin, H. J. Tiziani, “Aberration compensation in digital holographic reconstruction of microscopic objects,” J. Mod. Opt. 48, 1035–1041 (2001).

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

S. Lai, B. King, M. A. Neifeld, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
[CrossRef]

S. Lai, M. A. Neifeld, “Digital wavefront reconstruction and its application to image encryption,” Opt. Commun. 178, 283–289 (2000).
[CrossRef]

Opt. Eng. (1)

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Opt. Lett. (3)

Opt. Rev. (1)

I. Yamaguchi, S. Ohta, J. Kato, “Surface shape measurement by phase-shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[CrossRef]

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).

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Figures (12)

Fig. 1
Fig. 1

Fundamental setup of phase-shifting digital holography. PZT, piezoelectric transducer.

Fig. 2
Fig. 2

Coordinate system for image formation.

Fig. 3
Fig. 3

CCD images for various distances of a point object.

Fig. 4
Fig. 4

Reconstructed point images at the focal plane and their cross sections.

Fig. 5
Fig. 5

Dependence of the size of point images and the Nyquist factor on object distance.

Fig. 6
Fig. 6

Data appearing in one-dimensional simulation: (a) CCD output; (b) real and (c) imaginary parts of the derived complex amplitude.

Fig. 7
Fig. 7

Two-point images obtained from various pixel numbers.

Fig. 8
Fig. 8

Two-point images resulting from a diverging reference beam.

Fig. 9
Fig. 9

Experimental setup for microscopy with phase-shifting digital holography. PZT, piezoelectric transducer.

Fig. 10
Fig. 10

Reconstructed images of onion peels at various distances.

Fig. 11
Fig. 11

Comparison between holographic images at different wavelengths and a microscopic image.

Fig. 12
Fig. 12

Reconstructed images of a resolution target.

Equations (28)

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

Ux, y= UOx, yexpikzO+ik x-x2+y-y22zOdxdy,
IHx, y; δ=|URx, yexpiδ+Ux, y|2=|UR|2+|U|2+2URU * expiδ,
Ux, y=14UR*IHx, y; 0-IHx, y; π+iIHx, y; π/2-IHx, y; 3π/2
Ux, y=1-i4UR*IHx, y; 0-IHx, y; π/2+iIHx, y; π/2-IHx, y; π
UIX, Y, Z= Ux, yexpikZ+ik X-x2+Y-y22Zdxdy,
UIX, Y, Z=expikzO+Z+X2+Y22Z   UOx, y×expikx2+y221zO+1Z+x2+y22zO-xxzO+XZ-yyzO+YZdxdydxdy.
Z=-zO,
UIX, Y, -zO=UOX, Y
UMx, y=expik x2+y22zM,
1zO+1Z+1zM1Q,
Z=ZI=-11zO+1zM.
X=-ZIzO x=x1+zOzM,Y=-ZIzO y=y1+zOzM.
m=1+zOzM-1,
UIX, Y, Z=expikZ+X2+Y22Z  Ux, y×expik x2+y22Z×exp-ik Xx+YyZdxdy,
UˆIξ, η; Z=expiπλZξ2+η2Uˆξ, η,
Uˆξ, η= Ux, yexpi2πξx+ηydxdy,
UˆIξ, η; Z= UIX, Y, Zexpi2πξX+ηYdXdY.
UIX, Y, Z= UˆIξ, η; Zexp-i2πξX+ηYdξdη.
IHlmδ=mpy-dy/2mpy+dy/2dy lpx-dx/2lpx+dx/2 IHx, y; δdx.
Ulm=1-i4UR*IHlm0-IHlmπ/2+iIHlmπ/2-IHlmπ.
ΔX, ΔY=λZ1/Nxpx, 1/Nypy=λZ1/Lx, 1/Ly,
ΔX, ΔY=px, py,
IHx; δ  1+cosπλ1zO-1zRx2+δ,
ξ=xλ1zO-1zR.
CNξmax1/2px=pxLxλ1zO-1zR=Nxpx2λ1zO-1zR1,
ZI=-11zO-1zR.
ΔZ=2λZI2/Nxpx2=2λZI2/Lx2.
δX=λZI/Lx,

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