Abstract

We present a theoretical framework for recording and reconstructing incoherent correlation holograms of real-existing three-dimensional scenes observed from multiple viewpoints. This framework is demonstrated by generating and reconstructing a modified Fresnel hologram as well as a new correlation hologram called a protected correlation hologram. The reconstructed scene obtained from the protected correlation hologram has a significantly improved transverse resolution for the far objects in the scene compared to the modified Fresnel hologram. Additionally, the three-dimensional information encoded into the protected correlation hologram is scrambled by a secretive point spread function and thus the hologram can be used for encrypting the observed scene. The proposed holography methods are demonstrated by both simulations and experiments.

© 2008 Optical Society of America

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References

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2008 (2)

2007 (1)

2006 (1)

2003 (3)

2001 (1)

1997 (1)

B. Javidi and A. Sergent, “Fully phase encoded key and biometrics for security verification,” Opt. Eng. 36, 935-942 (1997).
[CrossRef]

1987 (1)

H.Stark, ed., Image Recovery: Theory and Application (Academic, 1987), pp. 29-78 and 277-320.

1982 (1)

1976 (1)

Abookasis, D.

Fienup, J. R.

Itoh, M.

Javidi, B.

B. Javidi and A. Sergent, “Fully phase encoded key and biometrics for security verification,” Opt. Eng. 36, 935-942 (1997).
[CrossRef]

Katz, B.

Li, Y.

Rosen, J.

Sando, Y.

Sergent, A.

B. Javidi and A. Sergent, “Fully phase encoded key and biometrics for security verification,” Opt. Eng. 36, 935-942 (1997).
[CrossRef]

Shaked, N. T.

Stern, A.

Yatagai, T.

Appl. Opt. (5)

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

D. Abookasis and J. Rosen, “Digital correlation holograms implemented on a joint transform correlator,” Opt. Commun. 225, 31-37 (2003).
[CrossRef]

Opt. Eng. (1)

B. Javidi and A. Sergent, “Fully phase encoded key and biometrics for security verification,” Opt. Eng. 36, 935-942 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (1)

H.Stark, ed., Image Recovery: Theory and Application (Academic, 1987), pp. 29-78 and 277-320.

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Figures (10)

Fig. 1
Fig. 1

Optical system for acquiring MVPs of the 3D scene along the horizontal axis.

Fig. 2
Fig. 2

Top view of the optical system of the MVP acquisition.

Fig. 3
Fig. 3

Schematics of the POCS algorithm for finding the PSF of the DIPCH.

Fig. 4
Fig. 4

Examples of the phase distributions of the generating random-constrained PSFs of (a) a 1D DIPCH and (b) a 2D DIPCH.

Fig. 5
Fig. 5

Several projections taken from the entire computer-generated set containing 600 × 600 projections, used for generating the 2D DIMFH and the 2D DIPCH.

Fig. 6
Fig. 6

Generating and reconstructing the 2D DIMFH: (a) magnitude and phase of the hologram; (b) the phase distributions of the reconstructing PSFs used for obtaining the three best in-focus reconstructed planes; (c) the corresponding three best in-focus reconstructed planes along the optical axis; (d) same as (c), but after the 2D resampling process; (e) zoomed-in images of the corresponding best in-focus reconstructed objects.

Fig. 7
Fig. 7

Generating and reconstructing the 2D DIPCH: (a) magnitude and phase of the hologram; (b) the phase distributions of the reconstructing PSFs used for obtaining the three best in-focus reconstructed planes; (c) the corresponding three best in-focus reconstructed planes along the optical axis; (d) same as (c), but after the 2D resampling process; (e) zoomed-in images of the corresponding best in-focus reconstructed objects.

Fig. 8
Fig. 8

Several projections taken from the entire experimentally obtained set containing 1200 projections, used for generating the 1D DIMFH and the 1D DIPCH.

Fig. 9
Fig. 9

Generating and reconstructing the 1D DIMFH: (a) magnitude and phase of the hologram; (b) the phase distributions of the reconstructing PSFs used for obtaining the three best in-focus reconstructed planes; (c) the corresponding three best in-focus reconstructed planes along the optical axis; (d) same as (c), but after the 1D resampling process; (e) zoomed-in images of the corresponding best in-focus reconstructed objects.

Fig. 10
Fig. 10

Generating and reconstructing the 1D DIPCH: (a) magnitude and phase of the hologram; (b) the phase distributions of the reconstructing PSFs used for obtaining the three best in-focus reconstructed planes; (c) the corresponding three best in-focus reconstructed planes along the optical axis; (d) same as (c), but after the 1D resampling process; (e) zoomed-in images of the corresponding best in-focus reconstructed objects

Equations (19)

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H 2 ( m , n ) = P m , n ( x p , y p ) E 2 ( x p , y p ) d x p d y p ,
E 2 ( x p , y p ) = A 2 ( b x p , b y p ) exp [ i g 2 ( b x p , b y p ) ] ,
s 2 ( m , n ; z r ) = H 2 ( m , n ) R 2 ( m , n ; z r ) ,
R 2 ( m , n ; z r ) = A 2 ( m Δ p z r , n Δ p z r ) exp [ i g 2 ( m Δ p z r , n Δ p z r ) ] ,
x p = f ( x s m α ) z s , y p = f ( y s n α ) z s ,
E 2 ( x p , y p ) = A 2 ( b x p , b y p ) exp [ i g 2 ( b x p , b y p ) ] = A 2 ( ξ , η ) exp [ i g 2 ( ξ , η ) ] = E 2 ( x s m α , y s n α ; z s ) ,
ξ = b f ( x s m α ) z s = b f α z s Δ p ( x s Δ p α m Δ p ) ,
η = b f ( y s n α ) z s = b f α z s Δ p ( y s Δ p α n Δ p ) .
H ̃ 2 ( m , n ; x s , y s , z s ) = [ h ( x s , y s , z s ) Δ x s Δ y s Δ z s δ ( x p x p , y p y p ) ] E 2 ( x p , y p ) d x p d y p = h ( x s , y s , z s ) E 2 ( x p , y p ) Δ x s Δ y s Δ z s = h ( x s , y s , z s ) E 2 ( x s m α , y s n α ; z s ) Δ x s Δ y s Δ z s .
H 2 ( m , n ) = H ̃ 2 ( m , n ; x s , y s , z s ) d x s d y s d z s = h ( x s , y s , z s ) E 2 ( x s m α , y s n α ; z s ) d x s d y s d z s .
s 2 ( m , n ; z r ) = H 2 ( m , n ) R 2 ( m , n ; z r ) = [ h ( x s , y s , z s ) E 2 ( x s m α , y s n α ; z s ) d x s d y s d z s ] R 2 ( m m , n n ; z r ) d m d n = h ( x s , y s , z s ) [ E 2 ( x s m α , y s n α ; z s ) R 2 ( m m , n n ; z r ) d m d n ] d x s d y s d z s = h ( x s , y s , z s ) E 2 ( x s m α , y s n α ; z s ) R 2 ( m , n ; z r ) d x s d y s d z s .
E 2 ( x s m α , y s n α ; z s ) R 2 ( m , n ; z r ) = FT 1 { FT { E 2 ( x s m α , y s n α ; z s ) } FT { R 2 ( m , n ; z r ) } } = FT 1 { FT { A 2 ( ξ , η ) exp [ i g 2 ( ξ , η ) ] } FT { A 2 ( m Δ p z r , n Δ p z r ) exp [ i g 2 ( m Δ p z r , n Δ p z r ) ] } } = C FT 1 { exp [ i ϕ ( z s Δ p α b f ν m , z s Δ p α b f ν n ) ] exp [ i ( x s Δ p α ν m + y s Δ p α ν n ) ] exp [ i ϕ ( z r ν m , z r ν n ) ] } = C δ ( m Δ p x s Δ p α , n Δ p y s Δ p α ; z r z s Δ p α b f ) ,
s 2 ( m , n ; z r ) = C h ( x s , y s , z s ) δ ( m Δ p x s Δ p α , n Δ p y s Δ p α ; z r z s Δ p b f α ) d x s d y s d z s = C h ( m Δ p α Δ p , n Δ p α Δ p ; z r b f α Δ p ) .
M 2 , x = M 2 , y = Δ p α , M 2 , z = Δ p b f α .
x p = f ( x s m α ) z s , y p = f y s z s .
s 1 ( m , n ; z r ) = C h ( m Δ p α Δ p , n Δ p z s f ; z r b f α Δ p ) ,
M 1 , x = Δ p α , M 1 , y = f z s , M 1 , z = Δ p b f α .
E 1 ( x p , y p ) = exp ( i 2 π b 2 x p 2 ) δ ( y p ) .
E 2 ( x p , y p ) = exp [ i 2 π b 2 ( x p 2 + y p 2 ) ] .

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