Abstract

I propose a novel digital technique that reduces defocus noise in the reconstruction of the sectional images from the complex hologram of a thick object. In three-dimensional microscopy applications of holography, reducing the defocused light scattered from outside the focused plane is an important issue. In this technique I first extract a complex hologram of a thick object by using optical scanning holography. After that, I separate the power spectra of the focused and defocused planes from the complex hologram. Finally, I construct a Wiener filter by use of the power spectra. The Wiener filter reduces the defocus noise in the reconstruction of the sectional image of the focused plane. Computer simulations show that the proposed Wiener filter reduces the defocus noise and provides the sectional images.

© 2006 Optical Society of America

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References

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2003 (1)

2002 (1)

2001 (1)

2000 (2)

1999 (1)

J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

1998 (1)

1997 (3)

1996 (1)

K. Doh, T.-C. Poon, and G. Indebetouw, "Twin-image noise in optical scanning holography," Opt. Eng. 35, 1550-1555 (1996).

1995 (1)

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, "Three-dimensional microscopy by optical scanning holography," Opt. Eng. 34, 1338-1344 (1995).

1985 (1)

T.-C. Poon, "Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis," J. Opt. Soc. Am. 2, 521-527 (1985).

1984 (1)

1983 (1)

1979 (1)

1977 (1)

Athey, B. D.

Banerjee, P. P.

P. P. Banerjee and T.-C. Poon, Principles of Applied Optics (Irwin, 1991).

Berriel, L. R.

Bescos, J.

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice-Hall, 1996).

Chien, W.-C.

Corle, T. R.

T. R. Corle and G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, 1996).

Couch, L. W.

L. W. Couch, Digital and Analog Communication Systems, 5th ed. (Prentice-Hall, 1997).

Dilworth, D. S.

Doh, K.

K. Doh, T.-C. Poon, and G. Indebetouw, "Twin-image noise in optical scanning holography," Opt. Eng. 35, 1550-1555 (1996).

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, "Three-dimensional microscopy by optical scanning holography," Opt. Eng. 34, 1338-1344 (1995).

Ghiglia, D. G.

Goodman, J. W.

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

Huisken, J.

Ichioka, Y.

Indebetouw, G.

Kim, E.-S.

Kim, S.-G.

Kim, T.

Kino, G. S.

T. R. Corle and G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, 1996).

Klysubun, P.

Kondo, K.

Korpel, A.

Lee, B.

Martinez-Corral, M.

Mils, K. D.

Neith, E. N.

Poon, T.-C.

Satisteban, A.

Schilling, B.

Schmitt, J. M.

J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

Shinoda, K.

Stark, H.

H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd ed. (Prentice-Hall, 2002).

Stelzer, E. H. K.

Storrie, B.

Suzuki, T.

Suzuki, Y.

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).

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, "Three-dimensional microscopy by optical scanning holography," Opt. Eng. 34, 1338-1344 (1995).

Swoger, J.

Woods, J. W.

H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd ed. (Prentice-Hall, 2002).

Wu, M.

B. Schilling, T.-C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, and M. Wu, "Three-dimensional holographic fluorescence microscopy," Opt. Lett. 22, 1506-1508 (1997).

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, "Three-dimensional microscopy by optical scanning holography," Opt. Eng. 34, 1338-1344 (1995).

Wu, M. H.

Yamaguchi, I.

Zhang, T.

Appl. Opt. (3)

IEEE J. Sel. Top. Quantum Electron. (1)

J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron. 5, 1205-1215 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

T.-C. Poon, "Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis," J. Opt. Soc. Am. 2, 521-527 (1985).

J. Opt. Soc. Am. A (5)

Opt. Eng. (2)

K. Doh, T.-C. Poon, and G. Indebetouw, "Twin-image noise in optical scanning holography," Opt. Eng. 35, 1550-1555 (1996).

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, "Three-dimensional microscopy by optical scanning holography," Opt. Eng. 34, 1338-1344 (1995).

Opt. Lett. (5)

Other (6)

P. P. Banerjee and T.-C. Poon, Principles of Applied Optics (Irwin, 1991).

K. R. Castleman, Digital Image Processing (Prentice-Hall, 1996).

T. R. Corle and G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, 1996).

H. Stark and J. W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd ed. (Prentice-Hall, 2002).

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

L. W. Couch, Digital and Analog Communication Systems, 5th ed. (Prentice-Hall, 1997).

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Figures (6)

Fig. 1
Fig. 1

(Color online) Optical scanning holography: M1–M3, mirrors; AOM, acousto-optic modulator; BS1–BS3, beam splitters; BE1, BE2, beam expanders; L1, focusing lens; L2, collecting lens with focal length fc ; PD, photodetector with a large detecting area; ⊗, electronic multiplexer; LPF, low-pass filter.

Fig. 2
Fig. 2

Thick object (Lx = Ly = 2 mm and Lz = 1 mm).

Fig. 3
Fig. 3

(a) Cosine hologram and (b) sine hologram.

Fig. 4
Fig. 4

Reconstructed image at (a) z 1 = 10 mm and (b) z1 = 11 mm by the conventional manner.

Fig. 5
Fig. 5

SNR against L Re with L Im = 6.5 mm−1.

Fig. 6
Fig. 6

Reconstructed sectional image at (a) z 1 = 10 mm and (b) z 1 = 11 mm by the proposed Wiener filter.

Equations (27)

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A o ( x , y ) = exp [ ( x 2 + y 2 ) ω o     2 ] ,
ν ( x , y ) = A o ( x , y ) h ( x , y ) ,
g 1 ( x , y ) g 2 ( x , y ) = g 1 ( x , y ) × g 2 ( x x , y y ) d x d y
h ( x , y , z ) = j 1 λ z exp [ j π λ z ( x 2 + y 2 ) ]
i r [ x ( t ) , y ( t ) ] = Re [ u * ( x , y ) ν ( x , y ) ] | O [ x ( t ) + x , y ( t ) + y , z ] | 2 d x d y d z ,
i i [ x ( t ) , y ( t ) ] = Im [ u * ( x , y ) ν ( x , y ) ] | O [ x ( t ) + x , y ( t ) + y , z ] | 2  d x d y d z ,
φ ( x , y ) = i r ( x , y ) + j i i ( x , y )
= | O ( x , y , z ) | 2 [ u * ( x , y ) ν ( x , y ) ] d z
= | O ( x , y , z ) | 2 [ A o ( x , y ) h ( x , y , z ) ] d z .
s z R ( x , y ) = φ ( x , y ) h * ( x , y , z R )
= | O ( x , y , z R ) | 2 A o ( x , y ) + z z R | O ( x , y , z ) | 2 A o ( x , y ) h ( x , y , z z R ) d z .
z z R | O ( x , y , z ) | 2 A o ( x , y ) h ( x , y , z z R ) d z
s z R ( x , y ) = Re [ s z R ( x , y ) ] + j Im [ s z R ( x , y ) ]
= | O ( x , y , z R ) | 2 A o ( x , y ) + z z R | O ( x , y , z ) | 2 A o ( x , y ) 1 λ ( z z R ) sin [ π λ ( z z R ) ( x 2 + y 2 ) ] d z + j z z R | O ( x , y , z ) | 2 A o ( x , y ) 1 λ ( z z R ) cos [ π λ ( z z R ) ( x 2 + y 2 ) ] d z .
S Re ( k x , k y ) = F { Re [ s z R ( x , y ) ] } ,
S Im ( k x , k y ) = F { Im [ s z R ( x , y ) ] } ,
P Re ( k x , k y ) = | S Re ( k x , k y ) | 2 rect ( k x L R e , k y L R e ) ,
P Im ( k x , k y ) = | S Im ( k x , k y ) | 2 rect ( k x L I m , k y L I m ) ,
rect ( k x L R e , k y L R e )
rect ( k x L R e , k y L Re ) = { 1 L R e / 2 k x , k y L R e / 2 0 otherwise .          
F w ( k x , k y ) = H z R * ( k x , k y ) | H z R ( k x , k y ) | 2 + P Im ( k x , k y ) P Re ( k x , k y ) P Im ( k x , k y ) ,
H output ( k x , k y ) = F [ φ ( x , y ) ] F w ( k x , k y )
= F [ φ ( x , y ) ] H z R * ( k x , k y ) | H z R ( k x , k y ) | 2 + P Im ( k x , k y ) P Re ( k x , k y ) P Im ( k x , k y ) .
P Im ( k x , k y ) P Re ( k x , k y ) P Im ( k x , k y ) 1 ,
F w ( k x , k y ) = H z o * ( k x , k y ) | H z o ( k x , k y ) | 2 ,
P Im ( k x , k y ) P Re ( k x , k y ) P Im ( k x , k y ) 1 ,
H output ( x , y ) = F 1 [ H output ( k x , k y ) ]

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