Abstract

A method is presented for the reconstruction of sectional images without the out-of-focus haze from a hologram generated by optical scanning holography. A random-phase pupil is adopted in the process of recovering individual sections from the hologram. The main idea of this approach is to recover a prescribed section while dispersing the energy from other sections into “specklelike patterns,” which can be eliminated subsequently by averaging of multiple section images.

© 2010 Optical Society of America

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References

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2009 (2)

2008 (3)

2006 (1)

2003 (1)

1995 (1)

1982 (1)

1972 (1)

R. Gerchberg and W. Saxton, Optik (Stuttgart) 35, 237 (1972).

Badizadegan, K.

Choi, W.

Dasari, R.

Doh, K.

Feld, M. S.

Fienup, J.

Gerchberg, R.

R. Gerchberg and W. Saxton, Optik (Stuttgart) 35, 237 (1972).

Hennelly, B. M.

Javidi, B.

Kelly, D. P.

Kim, H.

Kim, T.

Lai, D.

D. Lai, X. Zhou, D.-F. Zhou, and D.-H. Li, J. Mod. Opt. 55, 167 (2008).
[CrossRef]

Lam, E. Y.

Lee, B.

Li, D.-H.

D. Lai, X. Zhou, D.-F. Zhou, and D.-H. Li, J. Mod. Opt. 55, 167 (2008).
[CrossRef]

Min, S.-W.

Monaghan, D. S.

Pandey, N.

Park, Y.

Poon, T.-C.

Refregier, P.

Saxton, W.

R. Gerchberg and W. Saxton, Optik (Stuttgart) 35, 237 (1972).

Yaqoob, Z.

Zhang, X.

Zhou, D.-F.

D. Lai, X. Zhou, D.-F. Zhou, and D.-H. Li, J. Mod. Opt. 55, 167 (2008).
[CrossRef]

Zhou, X.

D. Lai, X. Zhou, D.-F. Zhou, and D.-H. Li, J. Mod. Opt. 55, 167 (2008).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of OSH. p 1 ( x , y ) and p 2 ( x , y ) are pupil functions; I ( x , y ; z ) , input transmittance intensity function; f, focal length of lens L; z, distance of object from focal plane of lens L; ⊗, electronic multiplier; LPF, low-pass filter; PD, photodetector.

Fig. 2
Fig. 2

Probability distribution versus a: (a) real part; (b) imaginary part.

Fig. 3
Fig. 3

(a) Multisection object used in the system; (b) and (c) reconstruction images by conventional holographic reconstruction, where the image section at z 2 and z 3 is focused, respectively.

Fig. 4
Fig. 4

(a) and (c) are reconstruction images by our proposed method where the image section at z 2 and z 3 is focused, respectively; (b) and (d) are averaging results corresponding, respectively, to (a) and (c) of ten section images obtained by ten independent random-phase pupils.

Equations (9)

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i ( x , y ) = F 1 { F { I ( x , y ; z = z c ) } · OTF Ω ( k x , k y ; z = z c ) } ,
OTF Ω ( k x , k y ; z c ) = exp [ j z c 2 k 0 ( k x 2 + k y 2 ) ] × p 1 c * ( x , y ) p 2 c ( x + f k 0 k x , y + f k 0 k y ) exp [ j z c f ( x k x + y k y ) ] d x d y ,
ϕ out ( x , y ) = F 1 { F { I ( x , y ; z c ) } · OTF Ω ( k x , k y ; z c ) · OTF Ω ( k x , k y ; z d ) } .
ϕ out ( x , y ) = F 1 { F { I ( x , y ; z c ) } exp [ j z d z c 2 k 0 ( k x 2 + k y 2 ) ] } .
ϕ haze ( x , y ) = z i z d F 1 { F { I ( x , y ; z i ) } exp [ j z d z i 2 k 0 ( k x 2 + k y 2 ) ] } .
p 1 c * ( x , y ) · p 2 d ( x , y ) = 1 .
ϕ out ( x , y ) = z i F 1 { F { I ( x , y ; z i ) } × P 1 c * ( z i f k x , z i f k y ) · P 2 d ( z d f k x , z d f k y ) · exp [ j z d z i 2 k 0 ( k x 2 + k y 2 ) ] } ,
P 1 c * ( z i f k x , z i f k y ) · P 2 d ( z d f k x , z d f k y ) = 1 .
| z d z i | = a N 2 λ π D 2 / f 2 .

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