Abstract

This work discusses a novel approach for numerical wavefront reconstruction, which utilizes arbitrary phase step digital holography. The experimental results reveal that only two digital holograms and a simple estimation procedure are required for twin-image suppression, and for numerical reconstruction. One advantage of this approach is its simplicity. Only one estimate equation needs to be applied. Additionally, the optical system can be constructed from inexpensive, generally available elements. Another advantage is the effectiveness of the approach. The tolerance of the estimated value is less than 1% of the actual value, such that the quality of the reconstructed image is excellent. This novel approach should facilitate the application of digital holography and promote its use.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
    [CrossRef] [PubMed]
  2. I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 1268-1270 (1997).
    [CrossRef] [PubMed]
  3. G. D. Lassahn, J. K. Lassahn, P. L. Taylor and V. A. Deason, "Multiphase fringe analysis with unknown phase shifts," Opt. Eng. 33, 2039-2044 (1994).
    [CrossRef]
  4. G. Stoilov and T. Dragostinov, "Phase-stepping interferometry: five-frame algorithm with an arbitrary step," Opt. Lasers Eng. 28, 61-69 (1997).
    [CrossRef]
  5. X. Chen, M. Gramaglia, and J. A. Yeazell, "Phase-shifting interferometry with uncalibrated phase shifts," Appl. Opt. 39, 585-591 (2000).
    [CrossRef]
  6. C. S. Guo, L. Zhang, H. T. Wang, J. Liao, and Y. Y. Zhu, "Phase-shifting error and its elimination in phase-shifting digital holography," Opt. Lett. 27, 1687-1689 (2002).
    [CrossRef]
  7. L. Z. Cai, Q. Liu, and X. L. Yang, "Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps," Opt. Lett. 28, 1808-1810 (2003).
    [CrossRef] [PubMed]
  8. L. Z. Cai, Q. Liu, and X. L. Yang, "Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects," Opt. Lett. 29, 183-185 (2004).
    [CrossRef] [PubMed]
  9. L. Z. Cai, Q. Liu, and X. L. Yang, "Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors," Opt. Commun. 233, 21-26 (2004).
    [CrossRef]
  10. S. Zhang, "A non-iterative method for phase-shift estimation and wave-front reconstruction in phase-shifting digital holography," Opt. Commun. 268, 231-234 (2006).
    [CrossRef]
  11. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, "Two-step phase-shifting interferometry and its application in image encryption," Opt. Lett. 31, 1414-1416 (2006).
    [CrossRef] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw Hill, New York, 1996).
  13. G. L. Chen, C. Y. Lin, M. K. Kuo, and C. C. Chang, "Numerical suppression of zero-order image in digital holography," Opt. Express 15, 8851-8856 (2007).
    [CrossRef] [PubMed]
  14. P. Guo and A. J. Devaney, "Digital microscopy using phase-shifting digital holography with two reference waves," Opt. Lett. 29, 857-859 (2004).
    [CrossRef] [PubMed]

2007 (1)

2006 (2)

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, "Two-step phase-shifting interferometry and its application in image encryption," Opt. Lett. 31, 1414-1416 (2006).
[CrossRef] [PubMed]

S. Zhang, "A non-iterative method for phase-shift estimation and wave-front reconstruction in phase-shifting digital holography," Opt. Commun. 268, 231-234 (2006).
[CrossRef]

2004 (3)

2003 (1)

2002 (1)

2000 (1)

1997 (2)

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

G. Stoilov and T. Dragostinov, "Phase-stepping interferometry: five-frame algorithm with an arbitrary step," Opt. Lasers Eng. 28, 61-69 (1997).
[CrossRef]

1994 (1)

G. D. Lassahn, J. K. Lassahn, P. L. Taylor and V. A. Deason, "Multiphase fringe analysis with unknown phase shifts," Opt. Eng. 33, 2039-2044 (1994).
[CrossRef]

1948 (1)

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Appl. Opt. (1)

Nature (1)

D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
[CrossRef] [PubMed]

Opt. Commun. (2)

L. Z. Cai, Q. Liu, and X. L. Yang, "Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors," Opt. Commun. 233, 21-26 (2004).
[CrossRef]

S. Zhang, "A non-iterative method for phase-shift estimation and wave-front reconstruction in phase-shifting digital holography," Opt. Commun. 268, 231-234 (2006).
[CrossRef]

Opt. Eng. (1)

G. D. Lassahn, J. K. Lassahn, P. L. Taylor and V. A. Deason, "Multiphase fringe analysis with unknown phase shifts," Opt. Eng. 33, 2039-2044 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (1)

G. Stoilov and T. Dragostinov, "Phase-stepping interferometry: five-frame algorithm with an arbitrary step," Opt. Lasers Eng. 28, 61-69 (1997).
[CrossRef]

Opt. Lett. (6)

Other (1)

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

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 (3)

Fig. 1.
Fig. 1.

Schematic diagram of the optical setup, where SF: spatial filter, PBS: polarized beam splitter, BS: beam splitter.

Fig. 2.
Fig. 2.

Experimental results; (a) the first acquired digital hologram; (b) the 2D Fourier spectrum of (a); (c) the arbitrary step digital hologram; (d) the 2D Fourier spectrum of (c); (e) the intensity obtained from the numerical reconstruction of (a); (f) the intensity of the reconstructed object wave obtained using this novel approach; (g) the 2D Fourier spectrum of (f); (h) a more detailed of (f).

Fig. 3.
Fig. 3.

The performance of estimation of arbitrary step phase.

Equations (16)

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

ψ O ( x , y ) = 1 { { ψ Obj ( x , y ) } { h ( x , y ; z 1 ) } }
= a o ( x , y ) exp [ j φ o ( x , y ) ]
ψ R ( x , y ) = a r ( x , y ) exp [ j φ r ( x , y ) ]
I H 1 = ψ O + ψ R 2 = ψ O 2 + ψ R 2 + ψ O ψ R * + ψ O * ψ R
= a o 2 + a r 2 + 2 a o a r cos ( φ o φ r ) ,
I H 2 = = a o 2 + a r 2 + 2 a o a r cos ( φ o φ r Δ ϕ )
a o 2 + a r 2 + 2 a o a r cos ( φ o φ r ) cos ( Δ ϕ ) .
( For the det ailed derivation see Appendix A . )
{ I H 1 } = { a o 2 + a r 2 } + { 2 a o a r cos ( φ o φ r ) }
{ I H 2 } { I H 1 } = { α o 2 + α r 2 } + { 2 α o α r cos ( ϕ o ϕ r ) cos ( Δ ϕ ) } { α o 2 + α r 2 } + { 2 α o α r cos ( ϕ o ϕ r ) } .
{ I H 2 } { I H 1 } { a o 2 + a r 2 } { a o 2 + a r 2 } + { 2 a o a r cos ( φ o φ r ) } { cos ( Δ φ ) } { 2 a o a r cos ( φ o φ r ) }
= 1 + { cos ( Δ φ ) }
1 { { I H 2 } { I H 1 } } = δ + cos ( Δ φ ) cos ( Δ φ ) .
I H 1 = I H 1 ψ R 2 ( I H 1 ψ R 2 ) 2 ( I H 1 + ψ R 2 )
I H 2 = I H 2 ψ R 2 ( I H 2 ψ R 2 ) 2 ( I H 2 + ψ R 2 )
ψ O bj ψ R * = 1 { { I H 1 exp ( j Δ φ ) I H 2 } { h ( z 1 ) } } .

Metrics