Abstract

One of the attractive features of hybrid holographic microscopy, in which the hologram of a microscopic object recorded by an image sensor is numerically reconstructed with a computer, is that the three-dimensional (3-D) information of a recorded object is obtained. The 3-D information has often been extracted by means of changing the reconstruction distance in the numerical reconstruction process, but here we describe an alternative technique that allows for variable viewing angles. That is, the perspective from which the object is viewed can be varied. The approximation used enables use of the fast-Fourier-transform algorithm for numerical reconstruction even in the high-resolution case in which the Fresnel approximation is no longer valid. The resolution of the proposed technique is also discussed.

© 2000 Optical Society of America

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References

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  1. L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
    [CrossRef]
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    [CrossRef]
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1999 (1)

1998 (1)

1997 (1)

1995 (1)

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

1994 (1)

1992 (1)

Boyer, K.

Cullen, D.

Doh, K. B.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Haddad, W. S.

Jüptner, W. P. O.

Kawai, H.

Longworth, J. W.

McPherson, A.

Merzlyakov, N. S.

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
[CrossRef]

Ohzu, H.

Poon, T.-C.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Rhodes, C. K.

Schilling, B. W.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Schnars, U.

Shinoda, K.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Solem, J. C.

Suzuki, Y.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Takaki, Y.

Wu, M. H.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[CrossRef]

Yamaguchi, I.

Yaroslavskii, L. P.

L. P. Yaroslavskii, N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, New York, 1980).
[CrossRef]

Zhang, T.

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Figures (9)

Fig. 1
Fig. 1

Two ways to visualize 3-D information of objects: (a) with distance z, (b) with viewing angle θ.

Fig. 2
Fig. 2

Three-dimensional coordinate system. The hologram plane and the observation plane are denoted by (x′, y′) and (X, Y), respectively. The viewing angles are θ and ϕ.

Fig. 3
Fig. 3

Coordinate transformation from hologram plane to spatial-frequency plane: the rectangular region occupied by the hologram data captured by an image sensor in the hologram plane as shown in (a) is distorted in the spatial-frequency plane as shown in (b)–(d). (b) ϕ = 0°, θ = 0°; (c) ϕ = 0°, θ = 20°; and (d) ϕ = 20°, θ = 20° (α = 30°).

Fig. 4
Fig. 4

Three-dimensional object used for the computer simulations. The object consists of one long line and six pairs of short lines.

Fig. 5
Fig. 5

Computer simulations of the proposed 3-D reconstruction technique allowing for variable viewing angles: (a), (b), (c), (g), (h), and (i) are the coordinate-transformed hologram patterns with ϕ = 0° and θ = 0°, 10°, 20°, 30°, 40°, and 50°, respectively. (d), (e), (f), (j), (k), and (l) are corresponding reconstructed images.

Fig. 6
Fig. 6

Three-dimensional reconstruction with the Fresnel–Kirchhoff integral without the approximation: ϕ = 0°, (a) θ = 0°, (b) θ = 10°, (c) θ = 20°, (d) θ = 30°, (e) θ = 40°, and (f) θ = 50°.

Fig. 7
Fig. 7

Electro-optical hologram recording system: (a) experimental system, (b) arrangement of the object beam and the reference beam on the object plane. ND, neutral density.

Fig. 8
Fig. 8

Hologram intensity distribution captured by a CCD image sensor.

Fig. 9
Fig. 9

Reconstructed images: (a), (b), (c), (d), and (e) are the intensity images with the rotation angle θ = -20°, -10°, 0°, 10°, and 20°, respectively. (f), (g), (h), (i), and (j) are the corresponding phase images.

Equations (8)

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Ox, y=i/λ  uX, Yexpikr/r×1+z/r/2dXdY,
r=x2+y2+z2+X2+Y2-2x cos θ cos ϕ+y cos θ sin ϕ+z sin θX-2-x sin ϕ+y cos ϕY1/2,
rR-x cos θ cos ϕ+y cos θ sin ϕ+z sin θX/R--x sin ϕ+y cos ϕY/R,
Ox, y=i/2λ1+z/RUνx, νyexpi2πR/λ/R,
νx=x cos θ cos ϕ+y cos θ sin ϕ+z sin θ/λR,
νy=-x sin ϕ+y cos ϕ/λR,
Rx, y=i/2λ1+z/RC expi2πR/λ/R,
4λ2R21+z/R-2Ix, y=C*Uνx, νy+CU*νx, νy+|Uνx, νy|2+|C|2,

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