Abstract

A new method for three-dimensional image formation is proposed in which the distribution of complex amplitude at a plane is measured by phase-shifting interferometry and then Fresnel transformed by a digital computer. The method can reconstruct an arbitrary cross section of a three-dimensional object with higher image quality and a wider viewing angle than from conventional digital holography using an off-axis configuration. Basic principles and experimental verification are described.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).
  2. L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).
    [CrossRef]
  3. U. Schnars, J. Opt. Soc. Am. 11, 2011 (1994).
    [CrossRef]
  4. G. Pedrini, B. Pfister, and H. Tiziani, J. Mod. Opt. 40, 367 (1995).
    [CrossRef]
  5. T.-C. Poon, K. B. Doh, M. S. Wu, K. Shinoda, and Y. Suzuki, Opt. Eng. 34, 567 (1995).
    [CrossRef]
  6. J. C. Marron and K. S. Schroeder, Appl. Opt. 31, 255 (1992).
    [CrossRef] [PubMed]
  7. J. H. Brunning, D. R. Herriot, J. E. Gallapfer, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, Appl. Opt. 13, 2693 (1974).
    [CrossRef]
  8. J. Kato and I. Yamaguchi, in Fringe “93, Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner and W. Osten, eds. (Akademie-Verlag, Berlin, 1993), pp. 66–71.
  9. L. B. Lesem, P. M. Hirsch, and J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]

1995

G. Pedrini, B. Pfister, and H. Tiziani, J. Mod. Opt. 40, 367 (1995).
[CrossRef]

T.-C. Poon, K. B. Doh, M. S. Wu, K. Shinoda, and Y. Suzuki, Opt. Eng. 34, 567 (1995).
[CrossRef]

1994

U. Schnars, J. Opt. Soc. Am. 11, 2011 (1994).
[CrossRef]

1992

1987

L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).
[CrossRef]

1974

1972

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

1969

L. B. Lesem, P. M. Hirsch, and J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Brangaccio, D. J.

Brunning, J. H.

Doh, K. B.

T.-C. Poon, K. B. Doh, M. S. Wu, K. Shinoda, and Y. Suzuki, Opt. Eng. 34, 567 (1995).
[CrossRef]

Gallapfer, J. E.

Herriot, D. R.

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Jordon, J. A.

L. B. Lesem, P. M. Hirsch, and J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Kato, J.

J. Kato and I. Yamaguchi, in Fringe “93, Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner and W. Osten, eds. (Akademie-Verlag, Berlin, 1993), pp. 66–71.

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Marron, J. C.

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

Onural, L.

L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).
[CrossRef]

Pedrini, G.

G. Pedrini, B. Pfister, and H. Tiziani, J. Mod. Opt. 40, 367 (1995).
[CrossRef]

Pfister, B.

G. Pedrini, B. Pfister, and H. Tiziani, J. Mod. Opt. 40, 367 (1995).
[CrossRef]

Poon, T.-C.

T.-C. Poon, K. B. Doh, M. S. Wu, K. Shinoda, and Y. Suzuki, Opt. Eng. 34, 567 (1995).
[CrossRef]

Rosenfeld, D. P.

Schnars, U.

U. Schnars, J. Opt. Soc. Am. 11, 2011 (1994).
[CrossRef]

Schroeder, K. S.

Scott, P. D.

L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).
[CrossRef]

Shinoda, K.

T.-C. Poon, K. B. Doh, M. S. Wu, K. Shinoda, and Y. Suzuki, Opt. Eng. 34, 567 (1995).
[CrossRef]

Suzuki, Y.

T.-C. Poon, K. B. Doh, M. S. Wu, K. Shinoda, and Y. Suzuki, Opt. Eng. 34, 567 (1995).
[CrossRef]

Tiziani, H.

G. Pedrini, B. Pfister, and H. Tiziani, J. Mod. Opt. 40, 367 (1995).
[CrossRef]

White, A. D.

Wu, M. S.

T.-C. Poon, K. B. Doh, M. S. Wu, K. Shinoda, and Y. Suzuki, Opt. Eng. 34, 567 (1995).
[CrossRef]

Yamaguchi, I.

J. Kato and I. Yamaguchi, in Fringe “93, Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner and W. Osten, eds. (Akademie-Verlag, Berlin, 1993), pp. 66–71.

Yaroslavskii, L. P.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

Appl. Opt.

IBM J. Res. Dev.

L. B. Lesem, P. M. Hirsch, and J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

J. Mod. Opt.

G. Pedrini, B. Pfister, and H. Tiziani, J. Mod. Opt. 40, 367 (1995).
[CrossRef]

J. Opt. Soc. Am.

U. Schnars, J. Opt. Soc. Am. 11, 2011 (1994).
[CrossRef]

Opt. Eng.

T.-C. Poon, K. B. Doh, M. S. Wu, K. Shinoda, and Y. Suzuki, Opt. Eng. 34, 567 (1995).
[CrossRef]

L. Onural and P. D. Scott, Opt. Eng. 26, 1124 (1987).
[CrossRef]

Sov. Phys. Tech. Phys.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavskii, Sov. Phys. Tech. Phys. 17, 333 (1972).

Other

J. Kato and I. Yamaguchi, in Fringe “93, Proceedings of the 2nd International Workshop on Automatic Processing of Fringe Patterns, W. Jüptner and W. Osten, eds. (Akademie-Verlag, Berlin, 1993), pp. 66–71.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Arrangement for phase-shifting digital holography: BS1, BS2, beam splitters; M, mirror.

Fig. 2
Fig. 2

Coordinate system for hologram recording and reconstruction.

Fig. 3
Fig. 3

Reconstructions of (a) a point object located at x0=y0=0 and z0=-60 cm and (b) its cross section cut by the plane Y=0, where p is the pixel size (11  µm) of the CCD.

Fig. 4
Fig. 4

(a) Phase and (b) amplitude maps of a diffusely reflecting object.

Fig. 5
Fig. 5

Numerically reconstructed images of a diffusely reflecting object: (a) focused image, (b) defocused image.

Fig. 6
Fig. 6

Reconstructed image from a single interference pattern corresponding to a Gabor hologram.

Equations (6)

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

Ux, y=A expiϕ=A0z0 expiϕ0+ikz0+ikx-x02+y-y022z0,
Ix, y; ϕR=URϕR+Ux, y2=AR2+A2+2ARA cosϕR-ϕ.
ϕx, y=tan-1Ix, y; 3π/2-Ix, y; π/2Ix, y; 0-Ix, y; π,
U1X, Y, Z=Ux, y×expikX-x2+Y-y22Zdxdy.
U1X, Y, Z=A0z0×expiϕ0+ikz0+ik2X2+Y2Z+x02+y02z0×exp-ikxx0z0+XZ+yy0z0+YZ-x2+y221z0+1Zdxdy,
P=αz0ξ=a/p=N.

Metrics