Abstract

Overlapping of the desired (first-order) and undesired (zero-order) terms originating from the recorded primary-fringe patterns in digital holography is a problem without a real-time solution. We propose a procedure for suppressing the zero-order disturbance that is realizable in real time. The procedure is based on the stochastic change of the speckles in the primary-fringe patterns and on the subtraction of two such subsequent patterns. The theoretical description of the procedure is given and experimental results presented.

© 2003 Optical Society of America

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References

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  1. D. Gabor, “A new microscope principle,” Nature 161, 777–778 (1948).
    [CrossRef]
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  3. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  4. T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
    [CrossRef]
  5. 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]
  6. Y. Takaki, H. Kawai, H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. 38, 4990–4996 (1999).
    [CrossRef]
  7. S. Lai, B. Kemper, G. Von Bally, “Off-axis reconstruction of in-line holograms for twin-image elimination,” Opt. Commun. 169, 37–43 (1999).
    [CrossRef]
  8. S. Lai, B. King, M. A. Neifield, “Wave front reconstruction by means of phase-shifting digital in-line holography,” Opt. Commun. 173, 155–160 (2000).
    [CrossRef]
  9. G. L. Rogers, “In-line soft-x-ray holography: the unwanted image,” Opt. Lett. 19, 67 (1994).
    [CrossRef] [PubMed]
  10. R. Spooren, “Double-pulse subtraction TV holography,” Opt. Eng. 31, 1000–1007 (1992).
    [CrossRef]

2000 (1)

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

1999 (2)

Y. Takaki, H. Kawai, H. Ohzu, “Hybrid holographic microscopy free of conjugate and zero-order images,” Appl. Opt. 38, 4990–4996 (1999).
[CrossRef]

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

1997 (1)

T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

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 (2)

1992 (1)

R. Spooren, “Double-pulse subtraction TV holography,” Opt. Eng. 31, 1000–1007 (1992).
[CrossRef]

1948 (1)

D. Gabor, “A new microscope principle,” Nature 161, 777–778 (1948).
[CrossRef]

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]

Gabor, D.

D. Gabor, “A new microscope principle,” Nature 161, 777–778 (1948).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Jüptner, W. P. O.

T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Kawai, H.

Kemper, B.

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

King, B.

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

Kreis, T. M.

T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Lai, S.

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

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

Neifield, M. A.

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

Rogers, G. L.

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]

Spooren, R.

R. Spooren, “Double-pulse subtraction TV holography,” Opt. Eng. 31, 1000–1007 (1992).
[CrossRef]

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.

Von Bally, G.

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

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]

Appl. Opt. (1)

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

Nature (1)

D. Gabor, “A new microscope principle,” Nature 161, 777–778 (1948).
[CrossRef]

Opt. Commun. (2)

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

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

Opt. Eng. (3)

T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

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]

R. Spooren, “Double-pulse subtraction TV holography,” Opt. Eng. 31, 1000–1007 (1992).
[CrossRef]

Opt. Lett. (1)

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (10)

Fig. 1
Fig. 1

Principle of quasi-Fourier off-axis digital holography.

Fig. 2
Fig. 2

First-order vs. zero-order diffraction intensities as a function of the beam ratio K.

Fig. 3
Fig. 3

Experimental setup: M—mirror, GF—gray filter, BS—beam splitter, CA—circular aperture, L—lens, SF—spatial filter.

Fig. 4
Fig. 4

Typical result for a single hologram: (a) segment showing the speckled primary fringes, (b) numerical reconstruction.

Fig. 5
Fig. 5

Typical result for a subtracted hologram: otherwise, same as in Fig. 4.

Fig. 6
Fig. 6

Results obtained for constant shifts in the horizontal direction (shifts of 1, 2, and 3 pixels from left to right, correspondingly).

Fig. 7
Fig. 7

Fourier spectrum of the vertical component of the environmental vibrations of the optical table.

Fig. 8
Fig. 8

Same as in Fig. 7, but with the environment plus stimulated vibrations of the optical table.

Fig. 9
Fig. 9

Typical segments of the digital holograms extracted from a series.

Fig. 10
Fig. 10

Typical object reconstruction obtained by subtracting two subsequent holograms from a series.

Equations (16)

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u1x1, y1=R0δx1-x0, y1-y0+sx1, y1,
u2x2, y2=C0-- u1x1, y1expi πλdx2-x12+y2-y12dx1dy1,
u2x2, y2=C0R0 expi πλdx2-x02+y2-y02+C0 expi πλdx22+y22sx1, y1×expi πλdx12+y12,
Ix2, y2=|u2x2, y2|2  R02 +sx1, y1expi πλdx12+y122 +R0C1* exp-i 2πλdx2x0+y2y0 ×sx1, y1expi πλdx12+y12* +R0C1 expi 2πλdx2x0+y2y0 ×sx1, y1expi πλdx12+y12,
Ix2, y2  R02+|scx2, y2|2+2R0|scx2, y2|cos|θcx2, y2],
θcx2, y2=cx2, y2-πλdx2-x02+y2-y02.
Kx2, y2=|scx2, y2|2R02,
Ix2, y2=R02+|scx2, y2|2×1+2Kx2, y21/21+Kx2, y2cosθcx2, y2.
ΔIx2, y2=|scx2+Δxx2, y2+Δyy2|2-|scx2, y2|2+2R0|scx2+Δxx2, y2+Δyy2|-|scx2, y2|cosθcx2, y2.
ΔIx2, y2=Δxx2x2+Δyy2y2|scx2, y2|2×1+Kx2, y2-1/2 cosθcx2, y2.
IK=F00K1+F01Kcos θc,
ΔIK=F10K1+F11Kcos θc,
F00K=1+K,
F10K=Δx x2+Δy y2K,
F01K=2K1/21+K,
F11K=1K1/2,

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