Abstract

A method to improve the image quality of a digital holographic reconstructed image by means of speckle reduction is proposed. The size and position of the speckles are changed according to the wavelengths to record a digital hologram. By superposing reconstructed images with different wavelengths, the effect of speckle is reduced so that the image quality is improved. Optical experiments are given to confirm the proposed method.

© 2008 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).
    [CrossRef] [PubMed]
  2. W. Osten, T. Baumbach, and W. Jüptner, “Comparative digital holography,” Opt. Lett. 27, 1764-1766 (2002).
    [CrossRef]
  3. T. Kreis, Handbook of Holographic Interferometry (Wiley VCH, 2005).
  4. Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
    [CrossRef]
  5. J. W. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
    [CrossRef]
  6. J. Rosen, “Three-dimensional optical Fourier transform and correlation,” Opt. Lett. 22, 964-966 (1997).
    [CrossRef] [PubMed]
  7. P. Ferraro, S. Grilli, D. Alfieri, S. D. Nicola, A. Finizio, G. Pierattini, B. Javidi, G. Coppola, and V. Striano, “Extended focused image in microscopy by digital holography,” Opt. Express 13, 6738-6749 (2005).
    [CrossRef] [PubMed]
  8. E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595-6601 (2000).
    [CrossRef]
  9. 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]
  10. T.-C. Poon and T. Kim, “Optical image recognition of three-dimensional objects,” Appl. Opt. 38, 370-381 (1999).
    [CrossRef]
  11. 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]
  12. 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]
  13. B. Javidi, P. Ferraro, S.-H. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144-146 (2005).
    [CrossRef] [PubMed]
  14. C. M. Do, S.-H. Hong, T. Nomura, and B. Javidi, “Multi-wavelength holographic image fusions using discrete wavelet transform,” Proc. SPIE 6016, 60160Z-1-6 (2005).
  15. J. Maycock, C. P. Mc Elhinney, J. B. McDonald, T. J. Naughton, and B. Javidi, “Independent component analysis applied to digital holograms of three-dimensional objects,” Proc. SPIE 5908, 590806-1-9 (2005).
  16. T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
    [CrossRef]
  17. 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]
  18. B. W. Schilling and G. C. Templeton, “Three-dimensional remote sensing by optical scanning holography,” Appl. Opt. 40, 5474-5481 (2001).
    [CrossRef]
  19. T.-C. Poon, “Recent progress in optical scanning holography,” J. Hologr. Speckle 1 , 6-25 (2004).
    [CrossRef]

2007 (1)

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[CrossRef]

2006 (1)

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
[CrossRef]

2005 (5)

2004 (2)

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]

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

2002 (1)

2001 (2)

2000 (2)

1999 (1)

1997 (2)

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

J. Rosen, “Three-dimensional optical Fourier transform and correlation,” Opt. Lett. 22, 964-966 (1997).
[CrossRef] [PubMed]

1967 (1)

J. W. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Alfieri, D.

Baumbach, T.

Coppola, G.

De Nicola, S.

Do, C. M.

C. M. Do, S.-H. Hong, T. Nomura, and B. Javidi, “Multi-wavelength holographic image fusions using discrete wavelet transform,” Proc. SPIE 6016, 60160Z-1-6 (2005).

Ferraro, P.

Finizio, A.

Frauel, Y.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Grilli, S.

Hong, S.-H.

B. Javidi, P. Ferraro, S.-H. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144-146 (2005).
[CrossRef] [PubMed]

C. M. Do, S.-H. Hong, T. Nomura, and B. Javidi, “Multi-wavelength holographic image fusions using discrete wavelet transform,” Proc. SPIE 6016, 60160Z-1-6 (2005).

Indebetouw, G.

Javidi, B.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
[CrossRef]

C. M. Do, S.-H. Hong, T. Nomura, and B. Javidi, “Multi-wavelength holographic image fusions using discrete wavelet transform,” Proc. SPIE 6016, 60160Z-1-6 (2005).

J. Maycock, C. P. Mc Elhinney, J. B. McDonald, T. J. Naughton, and B. Javidi, “Independent component analysis applied to digital holograms of three-dimensional objects,” Proc. SPIE 5908, 590806-1-9 (2005).

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]

B. Javidi, P. Ferraro, S.-H. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144-146 (2005).
[CrossRef] [PubMed]

P. Ferraro, S. Grilli, D. Alfieri, S. D. Nicola, A. Finizio, G. Pierattini, B. Javidi, G. Coppola, and V. Striano, “Extended focused image in microscopy by digital holography,” Opt. Express 13, 6738-6749 (2005).
[CrossRef] [PubMed]

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]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595-6601 (2000).
[CrossRef]

Jüptner, W.

Kim, D.

Kim, T.

Kreis, T.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[CrossRef]

T. Kreis, Handbook of Holographic Interferometry (Wiley VCH, 2005).

Lawrence, R.

J. W. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Matoba, O.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
[CrossRef]

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]

Maycock, J.

J. Maycock, C. P. Mc Elhinney, J. B. McDonald, T. J. Naughton, and B. Javidi, “Independent component analysis applied to digital holograms of three-dimensional objects,” Proc. SPIE 5908, 590806-1-9 (2005).

Mc Elhinney, C. P.

J. Maycock, C. P. Mc Elhinney, J. B. McDonald, T. J. Naughton, and B. Javidi, “Independent component analysis applied to digital holograms of three-dimensional objects,” Proc. SPIE 5908, 590806-1-9 (2005).

McDonald, J. B.

J. Maycock, C. P. Mc Elhinney, J. B. McDonald, T. J. Naughton, and B. Javidi, “Independent component analysis applied to digital holograms of three-dimensional objects,” Proc. SPIE 5908, 590806-1-9 (2005).

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]

Naughton, T.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
[CrossRef]

Naughton, T. J.

J. Maycock, C. P. Mc Elhinney, J. B. McDonald, T. J. Naughton, and B. Javidi, “Independent component analysis applied to digital holograms of three-dimensional objects,” Proc. SPIE 5908, 590806-1-9 (2005).

Nicola, S. D.

Nomura, T.

C. M. Do, S.-H. Hong, T. Nomura, and B. Javidi, “Multi-wavelength holographic image fusions using discrete wavelet transform,” Proc. SPIE 6016, 60160Z-1-6 (2005).

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]

Osten, W.

Pierattini, G.

Poon, T.-C.

Rosen, J.

J. Rosen, “Three-dimensional optical Fourier transform and correlation,” Opt. Lett. 22, 964-966 (1997).
[CrossRef] [PubMed]

Schilling, B. W.

Schlüter, K.

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[CrossRef]

Shinoda, K.

Striano, V.

Suzuki, Y.

Tahajuerce, E.

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
[CrossRef]

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. (4)

Appl. Phys. Lett. (1)

J. W. Goodman and R. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Hologr. Speckle (1)

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

Opt. Eng. (2)

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]

T. Kreis and K. Schlüter, “Resolution enhancement by aperture synthesis in digital holography,” Opt. Eng. 46, 055803 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Proc. IEEE (1)

Y. Frauel, T. Naughton, O. Matoba, E. Tahajuerce, and B. Javidi, “Three-dimensional imaging and processing using computational holographic imaging,” Proc. IEEE 94, 636-653 (2006).
[CrossRef]

Proc. SPIE (2)

C. M. Do, S.-H. Hong, T. Nomura, and B. Javidi, “Multi-wavelength holographic image fusions using discrete wavelet transform,” Proc. SPIE 6016, 60160Z-1-6 (2005).

J. Maycock, C. P. Mc Elhinney, J. B. McDonald, T. J. Naughton, and B. Javidi, “Independent component analysis applied to digital holograms of three-dimensional objects,” Proc. SPIE 5908, 590806-1-9 (2005).

Other (1)

T. Kreis, Handbook of Holographic Interferometry (Wiley VCH, 2005).

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of compensation of the pixel value based on a linear interpolation.

Fig. 2
Fig. 2

Experimental setup: L, lens; SF, spatial filter; BS, beam splitter; M, mirror.

Fig. 3
Fig. 3

White board as an object.

Fig. 4
Fig. 4

Reconstructed images from a single digital hologram with a wavelength of (a) 616 n m and (b) 624 n m . (c) and (d) Magnified portions of (a) and (b), respectively.

Fig. 5
Fig. 5

(a) Superposed image using eight reconstructed images and (b) its magnified portion.

Fig. 6
Fig. 6

Relation between the variance value and the number of superpositions.

Fig. 7
Fig. 7

Reconstructed image by spatial averaging filtering with 3 by 3 windows.

Fig. 8
Fig. 8

Cross sections of (a) the reconstructed image of a single hologram shown in Fig. 4(b), (b) the superposed reconstructed image using eight digital holograms shown in Fig. 5(a), and (c) the reconstructed image by spatial averaging filtering with 3 by 3 windows shown in Fig. 7.

Fig. 9
Fig. 9

Miniature pitcher as a three-dimensional object.

Fig. 10
Fig. 10

Reconstructed images by (a) the proposed superposition method, (b) the superposition without sampling period compensation, and (c) a conventional single hologram.

Fig. 11
Fig. 11

Reconstructed images by the proposed superposition method at a distance of (a) 320 m m (out of focus), (b) 420 m m (out of focus), and (c) 520 m m (in focus) from the CCD.

Equations (18)

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u ( X , Y ) = exp ( i 2 π λ X 2 + Y 2 2 d ) × [ g ( x 0 , y 0 ) exp ( i 2 π λ x 0 2 + y 0 2 2 d ) ] ,
u ( X , Y ) = u ( X , Y ) r e c t ( X a ) r e c t ( Y b ) .
U ( x , y ) = exp ( i 2 π λ x 2 + y 2 2 d ) × [ u ( X , Y ) exp ( i 2 π λ X 2 + Y 2 2 d ) ] = exp ( i 2 π λ x 2 + y 2 2 d ) × { g ( x 0 , y 0 ) exp ( i 2 π λ x 0 2 + y 0 2 2 d ) ∗  sinc ( a x 0 λ d ) sinc ( b y 0 λ d ) } ,
Δ S x = λ d a ,
Δ S y = λ d b .
I ( x , y ) = I ( x , y ) + s i ( x , y ) ,
i = 1 N I ( x , y ) = i = 1 N I ( x , y ) + i = 1 N s i ( x , y ) ,
N I ( x , y ) = N I ( x , y ) + S ,
i = 1 N s i ( x , y ) = S .
I ( x , y ) = I ( x , y ) .
Δ x = λ d N X Δ X ,
Δ y = λ d N Y Δ Y ,
Δ x = λ i λ c Δ x ,
I ( m + 1 ) = I ( n + 1 ) I ( n ) Δ x { ( m + 1 ) Δ x n Δ x } + I ( n ) .
| U s ( x , y ) | 2 = 1 N i = 1 N | U i ( x , y ) | 2 .
I b = 1 N n = 1 N I n ,
I t = 1 N n = m m + N I m ,
g r a d . = I t I b m N .

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