Abstract

We analyze the diffraction of the picture obtained by the subtraction of two in-line holograms recorded in two planes at distances of z and z+Δz apart from the object plane. Our theoretical analysis reveals that the reconstructed field at the object plane is approximately equal to the Laplacian second-order differentiation of the object wave in transverse direction when Δz is much smaller than the distance z, that is, the reconstructed image presents a high quality of edge enhancement. We further investigate the dependence of the edge-enhancement quality on the longitudinal differential distance Δz and find that the reconstructed images have the sharpest edge-enhancement and high signal-to-noise ratio at the same time only when the value of Δzz lies between 0.7% and 0.9% under our experimental condition. We also construct a criteria function, named the entropy of the image, to automatically focus the edge-enhanced image and demonstrate its adaptability in experiments.

© 2008 Optical Society of America

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2008 (1)

2007 (1)

2006 (4)

2005 (1)

2004 (1)

2003 (2)

2000 (2)

1999 (1)

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, Opt. Commun. 164, 257 (1999).
[CrossRef]

1998 (1)

1997 (1)

1948 (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Banerjee, P. P.

Brown, W. J.

Cai, L. Z.

Cao, D.

Chalut, K. J.

Dong, G. Y.

Fröning, P.

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, Opt. Commun. 164, 257 (1999).
[CrossRef]

Garcia-Sucerquia, J.

Gopinathan, U.

Ishikawa, T.

Javidi, B.

Jericho, M. H.

Jericho, S. K.

Joseph, J.

Klages, P.

Kohmura, Y.

Kreuzer, H. J.

Liu, Q.

Meng, X. F.

Nelleri, A.

Osten, W.

Pedrini, G.

Poon, T. C.

Ryle, J. P.

Sakurai, T.

Santoyo, F. M.

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, Opt. Commun. 164, 257 (1999).
[CrossRef]

Shannon, C. E.

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Shen, X. X.

Sheridan, J. T.

Singh, K.

Situ, G.

Tajahuerce, E.

Tiziani, H.

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, Opt. Commun. 164, 257 (1999).
[CrossRef]

Tiziani, H. J.

Wang, Y. R.

Wax, A.

Xu, W.

Xu, X. F.

Yamaguchi, I.

Yamazaki, H.

Yang, X. L.

Zhang, T.

Zhang, X.

Zhang, Y.

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

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

Opt. Commun. (1)

G. Pedrini, P. Fröning, H. Tiziani, and F. M. Santoyo, Opt. Commun. 164, 257 (1999).
[CrossRef]

Opt. Express (3)

Opt. Lett. (6)

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Figures (3)

Fig. 1
Fig. 1

Geometry for recording in-line holograms.

Fig. 2
Fig. 2

(a) In-line holograms recorded at z = 160 mm . (b) Reconstructed image by one hologram shown in (a). (c) Laplacian differential reconstruction of two holograms with Δ z = 1.3 mm . (d) Laplacian differential reconstructions when Δ z is taken as 0.1 mm .

Fig. 3
Fig. 3

Curve between the entropy of the reconstructed image and the reconstruction distance.

Equations (12)

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o ( x , y , z ) = F 1 { O ( ξ , η , 0 ) exp [ i 2 π z 1 λ 2 ( ξ 2 + η 2 ) ] } ,
I ( x , y , z ) = r ( x , y ) 2 + o ( x , y , z ) 2 + r ( x , y ) o * ( x , y , z ) + r ( x , y ) * o ( x , y , z ) ,
Δ I = I ( x , y , z + Δ z ) I ( x , y , z ) ,
= [ o ( x , y , z + Δ z ) 2 o ( x , y , z ) 2 ] + r ( x , y , ) [ o * ( x , y , z + Δ z ) o * ( x , y , z ) ] + r * ( x , y ) [ o ( x , y , z + Δ z ) o ( x , y , z ) ] .
Δ I = Δ z r ( x , y ) F 1 { j 2 π 1 λ 2 ( ξ 2 + η 2 ) O * ( ξ , η , 0 ) exp [ j 2 π z 1 λ 2 ( ξ 2 + η 2 ) ] } + Δ z r * ( x , y ) F 1 { j 2 π 1 λ 2 ( ξ 2 + η 2 ) O ( ξ , η , 0 ) exp [ j 2 π z 1 λ 2 ( ξ 2 + η 2 ) ] } .
D f z { Δ I } = Δ z r ( x , y ) F 1 { j 2 π 1 λ 2 ( ξ 2 + η 2 ) O * ( ξ , η , 0 ) exp [ j 4 π z 1 λ 2 ( ξ 2 + η 2 ) ] } + Δ z r * ( x , y ) j 2 π F 1 { 1 λ 2 ( ξ 2 + η 2 ) O ( ξ , η , 0 ) } ,
D f z { Δ I } = Δ z r ( x , y ) F 1 { j π λ ( ξ 2 + η 2 ) O * ( ξ , η , 0 ) exp [ j 2 π λ z ( ξ 2 + η 2 ) ] } Δ z r * ( x , y ) F 1 { j π λ ( ξ 2 + η 2 ) O ( ξ , η , 0 ) } .
F 1 { ( ξ 2 + η 2 ) O ( ξ , η , 0 ) } = 1 4 π 2 { 2 o ( x , y , 0 ) x 2 + 2 o ( x , y , 0 ) y 2 } = 1 4 π 2 x y 2 o ( x , y ) ,
F 1 { ( ξ 2 + η 2 ) O ( ξ , η , 0 ) exp [ j π λ z ( ξ 2 + η 2 ) ] } = 1 4 π 2 x y 2 o ( x , y , z ) .
D f z { Δ I } = j λ Δ z 4 π r ( x , y , z ) x y 2 o * ( x , y , 2 z ) j λ Δ z 4 π r * ( x , y , z ) x y 2 o ( x , y , 0 ) .
D f z { Δ I } j λ Δ z 4 π r * ( x , y , z ) x y 2 { o ( x , y , 0 ) } .
H z = m , n I z ( m , n ) E z log 2 [ I z ( m , n ) E z ] ,

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