Abstract

Off-axis digital holography generally uses a 2D-FFT based spatial filtering method to extract the complex object wave from an off-axis hologram. In this paper, we describe a novel single exposure complex object wave extraction method which can provide a faster solution than the FFT based spatial filtering approach while maintaining the reconstructed phase image quality. And also, we show that the proposed direct filtering scheme can provide more robust filtering capability to the off-axis spatial carrier frequency variation than the spatial filtering method.

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References

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2011 (2)

2010 (1)

2006 (1)

2005 (1)

2004 (2)

2003 (1)

2002 (1)

2000 (1)

1999 (3)

1997 (1)

1987 (1)

1982 (1)

1948 (1)

D. Gabor, “A new microscopic principle,” Nature161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Abdelsalam, D. G.

Aspert, N.

Baek, B. J.

Beghuin, D.

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, and R. P. Salathe, “Single acquisition polarization imaging with digital holography,” Electron. Lett.35(23), 2053–2055 (1999).
[CrossRef]

Bevilacqua, F.

Blu, T.

Bourquin, S.

Charrière, F.

Chegal, W.

Cho, H. M.

Cho, Y. J.

Colomb, T.

Cuche, E.

Dahlgren, P.

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, and R. P. Salathe, “Single acquisition polarization imaging with digital holography,” Electron. Lett.35(23), 2053–2055 (1999).
[CrossRef]

Delacretaz, G.

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, and R. P. Salathe, “Single acquisition polarization imaging with digital holography,” Electron. Lett.35(23), 2053–2055 (1999).
[CrossRef]

Depeursinge, C.

Dubois, F.

Eiju, T.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature161(4098), 777–778 (1948).
[CrossRef] [PubMed]

George, N.

Hariharan, P.

Ina, H.

Istasse, E.

Javidi, B.

Kawai, H.

Khare, K.

Kim, D.

Kim, H.

Kim, S.

Kobayashi, S.

Kong, H. J.

Kühn, J.

Lee, Y.

Liebling, M.

Magnusson, R.

Marian, A.

Marquet, P.

Minetti, C.

Monnom, O.

Montfort, F.

Ohzu, H.

Oreb, B. F.

Requena, M. L.

Salathe, R. P.

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, and R. P. Salathe, “Single acquisition polarization imaging with digital holography,” Electron. Lett.35(23), 2053–2055 (1999).
[CrossRef]

Takaki, Y.

Takeda, M.

Unser, M.

Yamaguchi, I.

Zhang, T.

Appl. Opt. (5)

Electron. Lett. (1)

D. Beghuin, E. Cuche, P. Dahlgren, C. Depeursinge, G. Delacretaz, and R. P. Salathe, “Single acquisition polarization imaging with digital holography,” Electron. Lett.35(23), 2053–2055 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Korea (1)

Nature (1)

D. Gabor, “A new microscopic principle,” Nature161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (5)

Other (1)

Wikipidia, “Fast Fourier Transform,” http://en.wikipedia.org/wiki/Fast_Fourier_transform .

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the Mach-Zehnder type off-axis digital holography used for both theoretical simulations and experiments in this study.

Fig. 2
Fig. 2

Sequential reconstruction steps of the conventional spatial filtering based phase contrast off-axis digital holography: (a)off-axis hologram, (b)Fourier transformed spatial frequency domain data, (c)spatially filtered frequency domain data(undesired terms are removed), (d)-(e) inversely Fourier transformed data (amplitude and phase data, respectively), (f)phase map of the digital reference wave, and (g)-(h)reconstructed object wave (amplitude and phase data, respectively)

Fig. 3
Fig. 3

Sequential reconstruction steps of the proposed direct filtering based phase contrast off-axis digital holography: (a)modified off-axis hologram [Complex object wave direct calculation procedures: 5 consecutive hologram column vectors are used to calculate the corresponding direct filtered complex object wave column vector], (b)-(c) directly calculated complex object wave in the hologram plane (amplitude and phase data, respectively), (d)phase map of the digital reference wave, and (e)-(f)reconstructed object wave in the observation plane (amplitude and phase data, respectively).

Fig. 4
Fig. 4

Comparison between the reconstructed object phase line profiles obtained from (a)the central vertical line of Fig. 2(f) which is based on the spatial filtering and (b) that of Fig. 3(f) obtained by using the direct filtering.

Fig. 5
Fig. 5

(a) Computation time required to obtain the complex object wave in the hologram plane versus the hologram size N, and (b) ratio between the computation time of the spatial filtering method and that of the direct filtering method versus the hologram size N.

Fig. 6
Fig. 6

(a)Computer generated USAF target phase object and (b)off-axis hologram generated by using the USAF target object.

Fig. 7
Fig. 7

Reconstructed amplitude and phase images, respectively: (a) and (d) when no filtering is used, (b) and (e) when the spatial filtering applied, and (c) and (f) when the direct filtering is employed.

Fig. 8
Fig. 8

Filtering capability analysis on the variation of the off-axis spatial carrier frequency: (a)spatial frequency spectrum when kx = 1.5 × 0.00780 mm−1 and ky = 1.5 × 0.00915 mm−1, (b) when kx = 2.0 × 0.00780 mm−1 and ky = 2.0 × 0.00915 mm−1, and (c)when kx = 3.0 × 0.00780 mm−1 and ky = 3.0 × 0.00915 mm−1, (d)-(f) zoomed reconstructed phase images of the dotted inner rectangular box in Fig. 7(e), 7(g)-(i) zoomed reconstructed phase images of the dotted rectangular box in Fig. 7(f).

Fig. 9
Fig. 9

Experimental results: (a) reconstructed object phase map obtained by using the spatial filtering approach and (b) that obtained by using the proposed direct filtering method.

Equations (11)

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I H (k,l)=| O | 2 +| R | 2 + R * O+R O * = A 2 + B 2 +2ABcos( φ O φ R )
R D (k,l)= A R exp[i(2π/λ)( k x kΔx+ k y lΔy)]
Ψ SFTF (m,n)= exp(i2πd/λ) idλ exp[ iπ λd ( m 2 Δ ξ 2 + n 2 Δ η 2 )]×F{ R D (k,l)O(k,l)exp[ iπ λd ( k 2 Δ x 2 + l 2 Δ y 2 )]}
Ψ CF (m,n)= exp(i2πd/λ) idλ F -1 {F[( R D (k,l)O(k,l)]F(exp[ iπ λd ( k 2 Δ x 2 + l 2 Δ y 2 )])}
I H M = I H | R | 2 =| O | 2 + R * O+R O * = A 2 +2ABcos( φ O φ R )
I 1 =A+B+2 AB cos(ϕ2α) I 2 =A+B+2 AB cos(ϕα) I 3 =A+B+2 AB cos(ϕ) I 4 =A+B+2 AB cos(ϕ+α) I 5 =A+B+2 AB cos(ϕ+2α)
φ= tan 1 [ 1cos2α sinα ( I 2 I 4 2 I 3 I 5 I 1 )]
γ= 4 ( I 2 I 4 ) 2 + (2 I 3 I 5 I 1 ) 2 4 I 0 sinα ( sin 2 ϕ+ sin 2 α cos 2 ϕ)
I k2 M = A k 2 +2 A k B k cos[ Φ k 2(2π k y Δy/λ)] I k1 M = A k 2 +2 A k B k cos[ Φ k (2π k y Δy/λ)] I k M = A k 2 +2 A k B k cos Φ k I k+1 M = A k 2 +2 A k B k cos[ Φ k +(2π k y Δy/λ)] I k+2 M = A k 2 +2 A k B k cos[ Φ k +2(2π k y Δy/λ)]
Φ k = tan 1 [ 1cos(4π k y Δy/λ) sin(2π k y Δy/λ) ( I k1 I k+1 2 I k I k+2 I k2 )]
A k = 4 ( I k1 I k+1 ) 2 + (2 I k I k+2 I k2 ) 2 8 B k sin(2π k y Δy/λ) [ sin 2 Φ k + sin 2 (2π k y Δy/λ) cos 2 Φ k ]

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