Abstract

In standard (four-exposure) quadrature phase-shifting holography (QPSH), two holograms and two intensity maps are acquired for zero-order-free and twin-image-free reconstruction. The measurement of the intensity map of the object light can be omitted in three-exposure QPSH. Furthermore, the measurements of the two intensity maps can be omitted in two-exposure QPSH, and the acquisition time of the overall holographic recording process is reduced. In this paper we examine the quality of the reconstructed images in two-, three-, and four-exposure QPSH, in simulations as well as in optical experiments. Various intensity ratios of the object light and the reference light are taken into account. Simulations show that two- and three-exposure QPSH can provide reconstructed images with quality comparable to that of four-exposure QPSH at a low intensity ratio. In practice the intensity ratio is limited by visibility, and thus four-exposure QPSH exhibits the best quality of the reconstructed image. The uniformity and the phase error of the reference light are also discussed. We found in most cases there is no significant difference between the reconstructed images in two- and three-exposure QPSH, and the quality of the reconstructed images is acceptable for visual applications such as the acquisition of three-dimensional scene for display or particle tracking.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T.-C.Poon, ed., Digital Holography and Three-Dimensional Display (Springer, 2006).
    [CrossRef]
  2. U. Schnars and W. Jueptner, Digital Holography(Springer, 2005).
  3. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
    [CrossRef]
  4. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39, 4070–4075 (2000).
    [CrossRef]
  5. W. Pan, W. Lu, Y. Zhu, and J. Wang, “One-shot in-line digital holography based Hilbert phase-shifting,” Chin. Opt. Lett. 7, 1123–1125 (2009).
    [CrossRef]
  6. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [CrossRef] [PubMed]
  7. T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23, 1221–1223 (1998).
    [CrossRef]
  8. 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]
  9. 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]
  10. X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
    [CrossRef]
  11. W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
    [CrossRef]
  12. X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry” J. Opt. 12, 015301 (2010).
    [CrossRef]
  13. 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]
  14. X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, J. P. Guo, and Y. R. Wang, “Wavefront reconstruction and three-dimensional shape measurement by two-step dc-term-suppressed phase-shifted intensities,” Opt. Lett. 34, 1210–1212(2009).
    [CrossRef] [PubMed]
  15. N. T. Shaked, Y. Zhu, M. T. Rinehart, and A. Wax, “Two-step-only phase-shifting interferometry with optimized detector bandwidth for microscopy of live cells,” Opt. Express 17, 15585–15591 (2009).
    [CrossRef] [PubMed]
  16. J.-P. Liu and T.-C. Poon, “Two-step-only quadrature phase-shifting digital holography,” Opt. Lett. 34, 250–252(2009).
    [CrossRef] [PubMed]
  17. J. Hahn, H. Kim, S.-W. Cho, and B. Lee, “Phase-shifting interferometry with genetic algorithm-based twin image noise elimination,” Appl. Opt. 47, 4068–4076 (2008).
    [CrossRef] [PubMed]

2010 (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry” J. Opt. 12, 015301 (2010).
[CrossRef]

2009 (5)

2008 (2)

J. Hahn, H. Kim, S.-W. Cho, and B. Lee, “Phase-shifting interferometry with genetic algorithm-based twin image noise elimination,” Appl. Opt. 47, 4068–4076 (2008).
[CrossRef] [PubMed]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

2006 (2)

2005 (1)

U. Schnars and W. Jueptner, Digital Holography(Springer, 2005).

2004 (1)

2003 (1)

2000 (1)

1999 (1)

1998 (1)

1997 (1)

Cai, L. Z.

Chen, W.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

Cheng, X. C.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

Cho, S.-W.

Cuche, E.

Depeursinge, C.

Devaney, A. J.

Dong, G. Y.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

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]

Fu, Y.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

Guo, J. P.

Guo, P.

Hahn, J.

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography(Springer, 2005).

Kim, H.

Lee, B.

Li, A. M.

Liu, J.-P.

Liu, Q.

Lu, W.

Marquet, P.

Meng, X. F.

Pan, W.

Peng, X.

Poon, T.-C.

Quan, C.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

Rinehart, M. T.

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography(Springer, 2005).

Shaked, N. T.

Shen, X. X.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

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]

Tay, C. J.

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

Wang, J.

Wang, Y. R.

X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry” J. Opt. 12, 015301 (2010).
[CrossRef]

X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, J. P. Guo, and Y. R. Wang, “Wavefront reconstruction and three-dimensional shape measurement by two-step dc-term-suppressed phase-shifted intensities,” Opt. Lett. 34, 1210–1212(2009).
[CrossRef] [PubMed]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

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]

Wax, A.

Xu, X. F.

X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry” J. Opt. 12, 015301 (2010).
[CrossRef]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

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]

Yamaguchi, I.

Yan, R. S.

X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry” J. Opt. 12, 015301 (2010).
[CrossRef]

Yang, X. L.

Zhang, T.

Zhu, Y.

Appl. Opt. (3)

Chin. Opt. Lett. (1)

J. Opt. (1)

X. F. Xu, L. Z. Cai, Y. R. Wang, and R. S. Yan, “Direct phase shift extraction and wavefront reconstruction in two-step generalized phase-shifting interferometry” J. Opt. 12, 015301 (2010).
[CrossRef]

Opt. Commun. (2)

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, and X. C. Cheng, “Wavefront reconstruction by two-step generalized phase-shifting interferometry,” Opt. Commun. 281, 5701–5705 (2008).
[CrossRef]

W. Chen, C. Quan, C. J. Tay, and Y. Fu, “Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography,” Opt. Commun. 282, 2800–2805 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (7)

Other (2)

T.-C.Poon, ed., Digital Holography and Three-Dimensional Display (Springer, 2006).
[CrossRef]

U. Schnars and W. Jueptner, Digital Holography(Springer, 2005).

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 (15)

Fig. 1
Fig. 1

Schematic diagram of QPSH.

Fig. 2
Fig. 2

RMSE as a function of intensity ratio.

Fig. 3
Fig. 3

Error pixels as a function of the intensity ratio for the simulation of curve B in Fig. 2.

Fig. 4
Fig. 4

Error of the calculated intensity of reference light ( E r ) as a function of the intensity ratio.

Fig. 5
Fig. 5

RMSE as a function of E r .

Fig. 6
Fig. 6

Intensity distribution of the reference light with (a)  Gaussian-distributed variation, (b) linear variation.

Fig. 7
Fig. 7

RMSE as a function of intensity ratio while the reference light is the one shown in Fig. 6a.

Fig. 8
Fig. 8

RMSE as a function of intensity ratio while the reference light is the one shown in Fig. 6b.

Fig. 9
Fig. 9

RMSE as a function of phase difference while the intensity ratio is 0.1.

Fig. 10
Fig. 10

E r as a function of phase difference while the intensity ratio is 0.1.

Fig. 11
Fig. 11

RMSE as a function of intensity ratio (experiment).

Fig. 12
Fig. 12

Standard deviation of the measured reference light at various intensity ratios. The average brightness of all the calculated photos is normalized to unity.

Fig. 13
Fig. 13

Reconstructed images by methods (a) A, (b) B, (c) C, and (d) D while the intensity ratio is 0.05.

Fig. 14
Fig. 14

Same as Fig. 13 except that the intensity ratio is 0.26.

Fig. 15
Fig. 15

Same as Fig. 13 except that the intensity ratio is 0.62

Equations (9)

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

I H i = I O + I R + O · R * e j θ i + O * · R e j θ i , for     i = 1 , 2 ,
2 ( I O + I R ) 2 ( 4 I R + 2 I H 1 + 2 I H 2 ) ( I O + I R ) + ( I H 1 2 + I H 2 2 + 4 I R 2 ) = 0 ,
I O + I R = 2 I R + I H 1 + I H 2 2 ( 2 I R + I H 1 + I H 2 ) 2 2 ( I H 1 2 + I H 2 2 + 4 I R 2 ) 2 .
H QPSH = ( I H 1 I O I R ) + j ( I H 2 I O I R ) 2 = O R * .
NCP real { [ H t H r ] MAX } [ H r H r ] MAX ,
H t / n = ( 1 j ) 2 ( I H 1 I H 2 ) = O R * j O * R .
RMSE { 1 M N m = 1 M n = 1 N [ F ( m , n ) f ( m , n ) ] 2 } 1 / 2 ,
intensity ratio 1 M N m = 1 M n = 1 N I O ( m , n ) 1 M N m = 1 M n = 1 N I R ( m , n ) = I ¯ O I ¯ R ,
E r ( I r I ¯ R ) / I ¯ R ,

Metrics