Abstract

Conventional digital in-line holography requires at least two phase-shifting holograms to reconstruct an original object without zero-order and conjugate image noise. We present a novel approach in which only one in-line hologram and two intensity values (namely the object wave intensity and the reference wave intensity) are required. First, by subtracting the two intensity values the zero-order diffraction can be completely eliminated. Then, an algorithm, called partition calculation, is proposed to numerically remove the conjugate image. A preliminary experimental result is given to confirm the proposed method. The method can simplify the procedure of phase-shifting digital holography and improve the practical feasibility for digital in-line holography.

© 2012 OSA

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References

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  1. H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55(18), 2989–3000 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2010 (2)

2009 (1)

L. H. Ma, H. Wang, Y. Li, and H. J. Zhang, “Elimination of zero-order diffraction and conjugate image in off-axis digital holography,” J. Mod. Opt. 56(21), 2377–2383 (2009).
[CrossRef]

2008 (3)

2007 (1)

2000 (1)

1997 (2)

T. M. Kreis and W. P. P. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36(8), 2357–2360 (1997).
[CrossRef]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[CrossRef] [PubMed]

Awatsuji, Y.

Chang, C. C.

Chen, G. L.

Cuche, E.

Deperursinge, C.

Dong, Y. C.

Hu, C. Y.

Imbe, M.

Jin, H. Z.

H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55(18), 2989–3000 (2008).
[CrossRef]

Jüptner, W. P. P.

T. M. Kreis and W. P. P. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36(8), 2357–2360 (1997).
[CrossRef]

Kaneko, A.

Koyama, T.

Kreis, T. M.

T. M. Kreis and W. P. P. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36(8), 2357–2360 (1997).
[CrossRef]

Kubota, T.

Kuo, M. K.

Li, Y.

L. H. Ma, H. Wang, Y. Li, and H. J. Zhang, “Elimination of zero-order diffraction and conjugate image in off-axis digital holography,” J. Mod. Opt. 56(21), 2377–2383 (2009).
[CrossRef]

H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55(18), 2989–3000 (2008).
[CrossRef]

Lin, C. Y.

Ma, L. H.

L. H. Ma, H. Wang, Y. Li, and H. J. Zhang, “Elimination of zero-order diffraction and conjugate image in off-axis digital holography,” J. Mod. Opt. 56(21), 2377–2383 (2009).
[CrossRef]

Marquet, P.

Matoba, O.

Nishio, K.

Nomura, T.

Qiu, P. Z.

H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55(18), 2989–3000 (2008).
[CrossRef]

Tahara, T.

Ura, S.

Wang, H.

L. H. Ma, H. Wang, Y. Li, and H. J. Zhang, “Elimination of zero-order diffraction and conjugate image in off-axis digital holography,” J. Mod. Opt. 56(21), 2377–2383 (2009).
[CrossRef]

H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55(18), 2989–3000 (2008).
[CrossRef]

Weng, J. W.

Wu, J.

Yamaguchi, I.

Zhang, H. J.

L. H. Ma, H. Wang, Y. Li, and H. J. Zhang, “Elimination of zero-order diffraction and conjugate image in off-axis digital holography,” J. Mod. Opt. 56(21), 2377–2383 (2009).
[CrossRef]

Zhang, T.

Zhang, Y. P.

H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55(18), 2989–3000 (2008).
[CrossRef]

Zhong, J. G.

Appl. Opt. (2)

J. Mod. Opt. (2)

H. Z. Jin, H. Wang, Y. P. Zhang, Y. Li, and P. Z. Qiu, “The influence of structural parameters of CCD on the reconstruction image of digital holograms,” J. Mod. Opt. 55(18), 2989–3000 (2008).
[CrossRef]

L. H. Ma, H. Wang, Y. Li, and H. J. Zhang, “Elimination of zero-order diffraction and conjugate image in off-axis digital holography,” J. Mod. Opt. 56(21), 2377–2383 (2009).
[CrossRef]

Opt. Eng. (1)

T. M. Kreis and W. P. P. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36(8), 2357–2360 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

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Figures (12)

Fig. 1
Fig. 1

A typical digital in-line holographic setup.

Fig. 2
Fig. 2

The schematic diagram of the four regions and new coordinate system

Fig. 3
Fig. 3

(a)-(d) are the schematic maps for the frequency spectrum distribution in each region.

Fig. 4
Fig. 4

A schematic diagram of the implementation of partition calculation.

Fig. 5
Fig. 5

Image-plane in-line holography geometry.

Fig. 6
Fig. 6

(a) digital in-line hologram, (b) the frequency spectrum of the hologram, (c) the frequency spectrum without zero-order term.

Fig. 7
Fig. 7

Sub-complex-hologram in each region

Fig. 8
Fig. 8

Frequency spectrum in each region corresponding with Fig. 8.

Fig. 9
Fig. 9

Extracted frequency spectrum of conjugate object wave in each region.

Fig. 10
Fig. 10

The whole frequency spectrum

Fig. 11
Fig. 11

The reconstructed phase image

Fig. 12
Fig. 12

(a) the reconstructed image with the presence of the zero-order term and the conjugate image, (b) the reconstructed image with removing the zero-order term, (c) the reconstructed image with removing the conjugate image.

Equations (20)

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R(x,y)=Aexp[i2π( x 2 + y 2 2λz )]rect( x MΔx )rect( y NΔy )
I(x,y)= | O(x,y)+R(x,y) | 2 = | O | 2 + | R | 2 +O R * + O * R
I O (x,y)= | O(x,y) | 2
I R (x,y)= | R(x,y) | 2
I C (x,y)=O R * + O * R
x Rk = (-1) k MΔx 4 = (-1) k x R , y Rk = (1) k1 NΔy 4 = (1) k1 y R k=1,2 x Rk = (-1) k1 MΔx 4 = (-1) k1 x R , y Rk = (1) k1 NΔy 4 = (1) k1 y R k=3,4
R k ( x + x Rk , y + y Rk )=Aexp[i2π ( x + x Rk ) 2 + ( y + y Rk ) 2 2λz ] =Aexp[i2π x R 2 + y R 2 2λz ]exp[i2π x 2 + y 2 2λz ]exp[i2π( x x Rk + y y Rk λz )] = R (x,y)exp[i2π( x x Rk + y y Rk λz )] k=1,2,3,4
I Ck (x,y)= I Ck ( x + x Rk , y + y Rk )= O k R k * + O k * R k k=1,2,3,4
R k (ξ,η)=F{ R k ( x + x Rk , y + y Rk )}= R (ξ x Rk λz ,η y Rk λz ) R k * (ξ,η)=F{ R k ( x + x Rk , y + y Rk )}= R * ( x Rk λz ξ, y Rk λz η)
Ι k (ξ,η)=F{ I Ck ( x + x Rk ,y'+ y Rk )} =F{ O k ( x , y )}exp[i2π(ξ x Rk +η y Rk )] R k (ξ,η) +F{ O k ( x , y )}exp[-i2π(ξ x Rk +η y Rk )] R k (ξ,η) =F{ O k ( x , y )}exp[i2π(ξ x Rk +η y Rk )] R ( x Rk λz ξ, y Rk λz η) +F{ O k ( x , y )}exp[-i2π(ξ x Rk +η y Rk )] R (ξ x Rk λz ,η y Rk λz )
ρ omax 1 4λz (MΔx) 2 + (NΔy) 2
z min =max( M (Δx) 2 λ , N (Δy) 2 λ )
ρ omax 2 4Δx
sw= L x L y B x B y =MΔxMΔx2 2 4Δx 2 2 4Δx = 1 2 M 2 = 1 2 s w CCD
REC T 1 =[ 1 ... 1 0 ... 0 1 ... 1 0 ... 0 1 ... 1 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 ] REC T 2 =[ 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 1 ... 1 0 ... 0 1 ... 1 0 ... 0 1 ... 1 ] REC T 3 =[ 0 ... 0 1 ... 1 0 ... 0 1 ... 1 0 ... 0 1 ... 1 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 ] REC T 4 =[ 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 0 ... 0 1 ... 1 0 ... 0 1 ... 1 0 ... 0 1 ... 1 0 ... 0 ]
I C1 (x,y)= I C (x,y)REC T 1 I C2 (x,y)= I C (x,y)REC T 2 I C3 (x,y)= I C (x,y)REC T 3 I C4 (x,y)= I C (x,y)REC T 4
TR I 1 =[ 0 0 ..... 0 0 0 0 ..... 0 1 0 0 .... 1 1 0 0 1 1 1 0 1 ..... 1 1 ] TR I 2 =[ 1 1 ..... 1 0 1 1 ..... 0 0 1 1 .... 0 0 1 0 0 0 0 0 0 ..... 0 0 ] TR I 3 =[ 0 0 ..... 0 0 1 0 ..... 0 0 1 1 .... 0 0 1 1 1 0 0 1 1 ..... 1 0 ] TR I 4 =[ 0 1 ..1.. 1 1 0 0 ..... 1 1 0 0 .... 1 1 0 0 0 0 1 0 0 ..... 0 0 ]
O R1 (ξ,η)=F{ I C1 (x,y)}TR I 1 = I 1 (ξ,η)TR I 1 O R2 (ξ,η)=F{ I C2 (x,y)}TR I 2 = I 2 (ξ,η)TR I 2 O R3 (ξ,η)=F{ I C3 (x,y)}TR I 3 = I 3 (ξ,η)TR I 3 O R4 (ξ,η)=F{ I C4 (x,y)}TR I 4 = I 4 (ξ,η)TR I 4
O 1 (x,y)= F 1 { O R1 (ξ,η)} R 1 (x,y) O 2 (x,y)= F 1 { O R2 (ξ,η)} R 2 (x,y) O 3 (x,y)= F 1 { O R3 (ξ,η)} R 3 (x,y) O 4 (x,y)= F 1 { O R4 (ξ,η)} R 4 (x,y)
O(x,y)= F 1 { O R1 (ξ,η)+ O R2 (ξ,η)+ O R3 (ξ,η)+ O R4 (ξ,η)}R(x,y)

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