Abstract

Phase-shifting digital holography with a phase difference between orthogonal polarizations is proposed. The use of orthogonal polarizations can make it possible to record two phase-shifted holograms simultaneously. By combining the holograms with the distributions of a reference wave and an object wave, the complex field of the object's wavefront can be obtained. Preliminary experimental results are shown to confirm the proposed method.

© 2006 Optical Society of America

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References

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  1. I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 1268-1270 (1997).
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    [CrossRef]
  3. T. Nomura, K. Uota, and Y. Morimoto, "Hybrid optical encryption of a 3-D object using a digital holographic technique," Opt. Eng. 43, 2228-2232 (2004).
    [CrossRef]
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    [CrossRef]
  5. E. Tajahuerce, O. Matoba, and B. Javidi, "Shift-invariant three-dimensional object recognition by means of digital holography," Appl. Opt. 40, 3877-3888 (2001).
    [CrossRef]
  6. B. Javidi and D. Kim, "Three-dimensional-object recognition by use of single-exposure on-axis digital holography," Opt. Lett. 30, 236-238 (2005).
    [CrossRef] [PubMed]
  7. T.-C. Poon, T. Kim, G. Indebetouw, M. H. Wu, K. Shinoda, and Y. Suzuki, "Twin-image elimination experiments for three-dimensional images in optical scanning holography," Opt. Lett. 25, 215-217 (2000).
    [CrossRef]
  8. T.-C. Poon, "Recent progress in optical scanning holography," J. Holography Speckle 1, 6-25 (2004).
    [CrossRef]
  9. B. W. Schilling and G. C. Templeton, "Three-dimensional remote sensing by optical scanning holography," Appl. Opt. 40, 5474-5481 (2001).
    [CrossRef]
  10. R. Smythe and R. Moore, "Instantaneous phase measuring interferometry," Opt. Eng. 23, 361-364 (1984).
  11. C. Dunsby, Y. Gu, and P. M. W. French, "Single-shot phase-stepped wide-field coherence-gated imaging," Opt. Express 11, 105-115 (2003).
    [CrossRef] [PubMed]
  12. J. A. Ferrari, E. M. Frins, and C. D. Perciante, "A new scheme for phase-shifting ESPI using polarized light," Opt. Commun. 202, 233-237 (2002).
    [CrossRef]
  13. J. A. Ferrari, E. M. Frins, D. Perciante, and A. Dubra, "Robust one-beam interferometer with phase-delay control," Opt. Lett. 24, 1272-1274 (1999).
    [CrossRef]
  14. D. Kim and B. Javidi, "In-line digital holography using a quarter wave plate and averaging method," in Proc. SPIE 5599, 106-113 (2004).
    [CrossRef]
  15. M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187-188.
  16. Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
    [CrossRef]
  17. M. Sasada, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by a simple optical setup and effective use of image-sensor pixles," in Technical Digest of the 2004 ICO International Conference Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

2005

2004

T.-C. Poon, "Recent progress in optical scanning holography," J. Holography Speckle 1, 6-25 (2004).
[CrossRef]

T. Nomura, K. Uota, and Y. Morimoto, "Hybrid optical encryption of a 3-D object using a digital holographic technique," Opt. Eng. 43, 2228-2232 (2004).
[CrossRef]

D. Kim and B. Javidi, "In-line digital holography using a quarter wave plate and averaging method," in Proc. SPIE 5599, 106-113 (2004).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

2003

2002

J. A. Ferrari, E. M. Frins, and C. D. Perciante, "A new scheme for phase-shifting ESPI using polarized light," Opt. Commun. 202, 233-237 (2002).
[CrossRef]

2001

2000

1999

1997

1984

R. Smythe and R. Moore, "Instantaneous phase measuring interferometry," Opt. Eng. 23, 361-364 (1984).

Awatsuji, Y.

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187-188.

M. Sasada, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by a simple optical setup and effective use of image-sensor pixles," in Technical Digest of the 2004 ICO International Conference Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

Dubra, A.

Dunsby, C.

Ferrari, J. A.

J. A. Ferrari, E. M. Frins, and C. D. Perciante, "A new scheme for phase-shifting ESPI using polarized light," Opt. Commun. 202, 233-237 (2002).
[CrossRef]

J. A. Ferrari, E. M. Frins, D. Perciante, and A. Dubra, "Robust one-beam interferometer with phase-delay control," Opt. Lett. 24, 1272-1274 (1999).
[CrossRef]

French, P. M. W.

Frins, E. M.

J. A. Ferrari, E. M. Frins, and C. D. Perciante, "A new scheme for phase-shifting ESPI using polarized light," Opt. Commun. 202, 233-237 (2002).
[CrossRef]

J. A. Ferrari, E. M. Frins, D. Perciante, and A. Dubra, "Robust one-beam interferometer with phase-delay control," Opt. Lett. 24, 1272-1274 (1999).
[CrossRef]

Fujii, A.

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187-188.

Gu, Y.

Indebetouw, G.

Javidi, B.

Kim, D.

B. Javidi and D. Kim, "Three-dimensional-object recognition by use of single-exposure on-axis digital holography," Opt. Lett. 30, 236-238 (2005).
[CrossRef] [PubMed]

D. Kim and B. Javidi, "In-line digital holography using a quarter wave plate and averaging method," in Proc. SPIE 5599, 106-113 (2004).
[CrossRef]

Kim, T.

Kubota, T.

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187-188.

M. Sasada, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by a simple optical setup and effective use of image-sensor pixles," in Technical Digest of the 2004 ICO International Conference Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

Matoba, O.

Moore, R.

R. Smythe and R. Moore, "Instantaneous phase measuring interferometry," Opt. Eng. 23, 361-364 (1984).

Morimoto, Y.

T. Nomura, K. Uota, and Y. Morimoto, "Hybrid optical encryption of a 3-D object using a digital holographic technique," Opt. Eng. 43, 2228-2232 (2004).
[CrossRef]

Nomura, T.

T. Nomura, K. Uota, and Y. Morimoto, "Hybrid optical encryption of a 3-D object using a digital holographic technique," Opt. Eng. 43, 2228-2232 (2004).
[CrossRef]

Perciante, C. D.

J. A. Ferrari, E. M. Frins, and C. D. Perciante, "A new scheme for phase-shifting ESPI using polarized light," Opt. Commun. 202, 233-237 (2002).
[CrossRef]

Perciante, D.

Poon, T.-C.

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

M. Sasada, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by a simple optical setup and effective use of image-sensor pixles," in Technical Digest of the 2004 ICO International Conference Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187-188.

Schilling, B. W.

Shinoda, K.

Smythe, R.

R. Smythe and R. Moore, "Instantaneous phase measuring interferometry," Opt. Eng. 23, 361-364 (1984).

Suzuki, Y.

Tajahuerce, E.

Templeton, G. C.

Uota, K.

T. Nomura, K. Uota, and Y. Morimoto, "Hybrid optical encryption of a 3-D object using a digital holographic technique," Opt. Eng. 43, 2228-2232 (2004).
[CrossRef]

Wu, M. H.

Yamaguchi, I.

Zhang, T.

Appl. Opt.

Appl. Phys. Lett.

Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett. 85, 1069-1071 (2004).
[CrossRef]

J. Holography Speckle

T.-C. Poon, "Recent progress in optical scanning holography," J. Holography Speckle 1, 6-25 (2004).
[CrossRef]

Opt. Commun.

J. A. Ferrari, E. M. Frins, and C. D. Perciante, "A new scheme for phase-shifting ESPI using polarized light," Opt. Commun. 202, 233-237 (2002).
[CrossRef]

Opt. Eng.

R. Smythe and R. Moore, "Instantaneous phase measuring interferometry," Opt. Eng. 23, 361-364 (1984).

T. Nomura, K. Uota, and Y. Morimoto, "Hybrid optical encryption of a 3-D object using a digital holographic technique," Opt. Eng. 43, 2228-2232 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

D. Kim and B. Javidi, "In-line digital holography using a quarter wave plate and averaging method," in Proc. SPIE 5599, 106-113 (2004).
[CrossRef]

Other

M. Sasada, A. Fujii, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement," in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187-188.

M. Sasada, Y. Awatsuji, and T. Kubota, "Parallel quasi-phase-shifting digital holography implemented by a simple optical setup and effective use of image-sensor pixles," in Technical Digest of the 2004 ICO International Conference Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

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Figures (4)

Fig. 1
Fig. 1

Optical setup for phase-shifted digital holography when the phase difference between orthogonal polarization is used: SF1, SF2, spatial filters; CL1, CL2, collimating lenses.

Fig. 2
Fig. 2

(a) Pixelated polarizers of the polarization CCD; (b) interpolation method of a one-shot digital hologram.

Fig. 3
Fig. 3

Schematic diagram for obtaining two phase-shifted digital holograms from a one-shot digital hologram.

Fig. 4
Fig. 4

Reconstructed objects when we used (a) conventional phase-shifting digital holography, (b) the proposed method in which a checkerboard layout is used, (c) an averaging method, and (d) on-axis digital holography.

Tables (2)

Tables Icon

Table 1 Mean-Squared Errors for Amplitude (MSE a ) and Phase (MSE p ) between Reconstructed Images by Various Methods and the Reconstructed Image by Conventional Phase-Shifting Digital Holography

Tables Icon

Table 2 Mean-Squared Errors for Amplitude (MSE a ) and Phase (MSE p ) between Reconstructed Images of Shifting Objects and an Object That Is Not Shifting

Equations (45)

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

A o ( x , y )
A r ( x , y )
a o ( x , y )
ϕ o ( x , y )
a r ( x , y )
ϕ r ( x , y )
A o ( x , y ) = a o ( x , y ) exp [ i ϕ o ( x , y ) ] ,
A r ( x , y ) = a r ( x , y ) exp { i [ ϕ r ( x , y ) + α ] } ,
I ( x , y , α ) = a o 2 ( x , y ) + a r 2 ( x , y ) + 2 a o ( x , y ) a r ( x , y ) × cos [ ϕ o ( x , y ) { ϕ r ( x , y ) + α } ] .
π / 2
I ( x , y , 0 ) = a o 2 ( x , y ) + a r 2 ( x , y ) + 2 a o ( x , y ) a r ( x , y ) × cos { ϕ o ( x , y ) ϕ r ( x , y ) } ,
I ( x , y , π / 2 ) = a o 2 ( x , y ) + a r 2 ( x , y ) + 2 a o ( x , y ) a r ( x , y ) × sin { ϕ o ( x , y ) ϕ r ( x , y ) } ,
I r ( x , y )
I o ( x , y )
I r ( x , y ) = a r     2 ( x , y ) ,
I o ( x , y ) = a o     2 ( x , y ) ,
a o ( x , y ) = [ I o ( x , y ) ] 1 / 2 ,
ϕ o ( x , y ) = tan 1 I ( x , y , π / 2 ) I o ( x , y ) I r ( x , y ) I ( x , y , 0 ) I o ( x , y ) I r ( x , y ) + ϕ r ( x , y ) .
ϕ r ( x , y )
I r ( x , y )
π / 2
45 deg
I ( i , j ) = [ I ( i 1 , j ) + I ( i + 1 , j ) + I ( i , j 1 ) + I ( i , j + 1 ) ] .
632.8   nm
8   mm × 8   mm × 8   mm
1024 × 768
4.65 μm × 4.65 μm
230   mm
45 deg
π / 2
45 deg
( MSE a )
( MSE p )
MSE a = 1 M N i = 1 M j = 1 N { | r ( i , j ) | | r c ( i , j ) | } 2 ,
MSE p = 1 M N i = 1 M j = 1 N { arg [ r ( i , j ) ] arg [ r c ( i , j ) ] } 2 ,
arg ( )
r ( i , j )
r c ( i , j )
MSE a
MSE p
2 π
I o ( x , y )
I ( x , y , 0 )
I ( x , y , π / 2 )
4.65   μm

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