Abstract

A simple method to decode the stored phase signal of volume holographic data storage with adequate wave aberration tolerance is highly demanded. We proposed and demonstrated a one-shot scheme to decode a binary-phase encoding signal through double-frequency-grating based shearing interferometry (DFGSI). The lateral shearing amount is dependent on the focal length of the collimated lens and the frequency difference between the gratings. Diffracted waves with phase encoding were successfully decoded through experimentation. An optical model for the DFGSI was built to analyze phase-error induction and phase-difference control by shifting the double-frequency grating longitudinally and laterally, respectively. The optical model was demonstrated experimentally. Finally, a high aberration tolerance of the DFGSI was demonstrated using the optical model.

© 2016 Optical Society of America

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References

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  1. H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds., Holographic Data Storage, Springer Series in Optical Sciences (Springer-Verlag, 2000)
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    [Crossref]
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    [Crossref]
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2010 (1)

2009 (2)

B. Das, J. Joseph, and K. Singh, “Phase-image-based sparse-gray-level data pages for holographic data storage,” Appl. Opt. 48(28), 5240–5250 (2009).
[Crossref] [PubMed]

M. He, L. Cao, Q. Tan, Q. He, and G. Jin, “Novel phase detection method for a holographic data storage system using two interferograms,” J. Opt. A. 11(6), 065705 (2009).
[Crossref]

2008 (1)

M. Hara, K. Tanaka, K. Tokuyama, M. Toishi, K. Hirooka, A. Fukumoto, and K. Watanabe, “Linear reproduction of a holographic storage channel using coherent addition of optical DC components,” Jpn. J. Appl. Phys. 47(7), 5885–5890 (2008).
[Crossref]

2006 (2)

2005 (1)

2004 (1)

1998 (1)

1973 (1)

Asundi, A.

Bhagatji, A.

Bjornson, E.

Boyd, C.

Campbell, S.

Cao, L.

M. He, L. Cao, Q. Tan, Q. He, and G. Jin, “Novel phase detection method for a holographic data storage system using two interferograms,” J. Opt. A. 11(6), 065705 (2009).
[Crossref]

Curtis, K.

Das, B.

Dhar, L.

Fukumoto, A.

M. Hara, K. Tanaka, K. Tokuyama, M. Toishi, K. Hirooka, A. Fukumoto, and K. Watanabe, “Linear reproduction of a holographic storage channel using coherent addition of optical DC components,” Jpn. J. Appl. Phys. 47(7), 5885–5890 (2008).
[Crossref]

Furuki, M.

Guo, Z.

Haga, K.

Hara, M.

M. Hara, K. Tanaka, K. Tokuyama, M. Toishi, K. Hirooka, A. Fukumoto, and K. Watanabe, “Linear reproduction of a holographic storage channel using coherent addition of optical DC components,” Jpn. J. Appl. Phys. 47(7), 5885–5890 (2008).
[Crossref]

Harris, A.

Hayashi, K.

He, M.

M. He, L. Cao, Q. Tan, Q. He, and G. Jin, “Novel phase detection method for a holographic data storage system using two interferograms,” J. Opt. A. 11(6), 065705 (2009).
[Crossref]

He, Q.

M. He, L. Cao, Q. Tan, Q. He, and G. Jin, “Novel phase detection method for a holographic data storage system using two interferograms,” J. Opt. A. 11(6), 065705 (2009).
[Crossref]

Hesselink, L.

Hill, A.

Hirooka, K.

M. Hara, K. Tanaka, K. Tokuyama, M. Toishi, K. Hirooka, A. Fukumoto, and K. Watanabe, “Linear reproduction of a holographic storage channel using coherent addition of optical DC components,” Jpn. J. Appl. Phys. 47(7), 5885–5890 (2008).
[Crossref]

Jin, G.

M. He, L. Cao, Q. Tan, Q. He, and G. Jin, “Novel phase detection method for a holographic data storage system using two interferograms,” J. Opt. A. 11(6), 065705 (2009).
[Crossref]

Joseph, J.

Kawano, K.

Kwan, D.

Levinos, N.

Miao, J.

Minabe, J.

Ogasawara, Y.

Okas, R.

Orlov, S. S.

Peng, X.

Phillips, W.

Schilling, M.

Singh, K.

Snyder, R.

Sundaram, P.

Tackitt, M.

Takashima, Y.

Tan, Q.

M. He, L. Cao, Q. Tan, Q. He, and G. Jin, “Novel phase detection method for a holographic data storage system using two interferograms,” J. Opt. A. 11(6), 065705 (2009).
[Crossref]

Tanaka, K.

M. Hara, K. Tanaka, K. Tokuyama, M. Toishi, K. Hirooka, A. Fukumoto, and K. Watanabe, “Linear reproduction of a holographic storage channel using coherent addition of optical DC components,” Jpn. J. Appl. Phys. 47(7), 5885–5890 (2008).
[Crossref]

Toishi, M.

M. Hara, K. Tanaka, K. Tokuyama, M. Toishi, K. Hirooka, A. Fukumoto, and K. Watanabe, “Linear reproduction of a holographic storage channel using coherent addition of optical DC components,” Jpn. J. Appl. Phys. 47(7), 5885–5890 (2008).
[Crossref]

Tokuyama, K.

M. Hara, K. Tanaka, K. Tokuyama, M. Toishi, K. Hirooka, A. Fukumoto, and K. Watanabe, “Linear reproduction of a holographic storage channel using coherent addition of optical DC components,” Jpn. J. Appl. Phys. 47(7), 5885–5890 (2008).
[Crossref]

Waldman, D. A.

Watanabe, K.

M. Hara, K. Tanaka, K. Tokuyama, M. Toishi, K. Hirooka, A. Fukumoto, and K. Watanabe, “Linear reproduction of a holographic storage channel using coherent addition of optical DC components,” Jpn. J. Appl. Phys. 47(7), 5885–5890 (2008).
[Crossref]

Wilson, W.

Wyant, J. C.

Xu, L.

Yasuda, S.

Yoshizawa, H.

Appl. Opt. (5)

J. Opt. A. (1)

M. He, L. Cao, Q. Tan, Q. He, and G. Jin, “Novel phase detection method for a holographic data storage system using two interferograms,” J. Opt. A. 11(6), 065705 (2009).
[Crossref]

Jpn. J. Appl. Phys. (1)

M. Hara, K. Tanaka, K. Tokuyama, M. Toishi, K. Hirooka, A. Fukumoto, and K. Watanabe, “Linear reproduction of a holographic storage channel using coherent addition of optical DC components,” Jpn. J. Appl. Phys. 47(7), 5885–5890 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Other (4)

K. Curtis, L. Dhar, W. Wilson, A. Hill, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

M. R. Ayres, “Method for holographic data retrieval by quadrature homodyne detection,” United States Patent, US 8,233,205 B2 (2012).

T. Nobukawa and T. Nomura, “Complex amplitude-modulated data page recording in coaxial holographic data storage with phase-shifting digital holography,” in Imaging and Applied Optics 2014, OSA Technical Digest (OSA, 2014), paper JTu4A.11.

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds., Holographic Data Storage, Springer Series in Optical Sciences (Springer-Verlag, 2000)

Supplementary Material (11)

NameDescription
» Visualization 1: MP4 (7696 KB)      The simulated interferogram of homodyne detection obtained through inline interferometry after inducing a wavefront aberration of 0.25 ? rms and 10% pseudorandom coherent noise.
» Visualization 2: MP4 (168 KB)      Experimental result of the phase change by adjusting the DFG longitudinally.
» Visualization 3: MP4 (1521 KB)      Simulation result of the phase change by adjusting the DFG longitudinally.
» Visualization 4: MP4 (147 KB)      Experimental result of the phase change by adjusting the DFG laterally.
» Visualization 5: MP4 (1543 KB)      Simulation result of the phase change by adjusting the DFG laterally.
» Visualization 6: MP4 (7253 KB)      The simulated interferogram of the inline interferometry when linear wavefront aberration varying from 0 to 10? rms was induced.
» Visualization 7: MP4 (7292 KB)      The simulated interferogram of DFGSI when linear wavefront aberration varying from 0 to 10? rms was induced.
» Visualization 8: MP4 (8264 KB)      The simulated interferogram of the inline interferometry when quadratic wavefront aberration varying from 0 to 10? rms was induced.
» Visualization 9: MP4 (8117 KB)      The simulated interferogram of DFGSI when quadratic wavefront aberration varying from 0 to 10? rms was induced.
» Visualization 10: MP4 (6771 KB)      The simulated interferogram of the inline interferometry when biquadratic wavefront aberration varying from 0 to 10? rms was induced.
» Visualization 11: MP4 (6728 KB)      The simulated interferogram of DFGSI when biquadratic wavefront aberration varying from 0 to 10? rms was induced.

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Figures (14)

Fig. 1
Fig. 1 The simulated interferogram of homodyne detection obtained through inline interferometry after inducing a wavefront aberration of 0.25 λ rms, 10% pseudorandom coherent noise, and unstable dc phase shift (see Visualization 1).
Fig. 2
Fig. 2 A schematic diagram of the shearing interferometry with the DFG.
Fig. 3
Fig. 3 (a) The 2-D encoded binary phase distribution, where the phase difference between the yellow and green pixels is π. (b) Schema of one-pixel shearing through the DFG. (c) The interference result by the original image and the one-pixel sheared image with destructive interference. The first and last columns blocked by red dash lines are out of the interference region.
Fig. 4
Fig. 4 (a)The geometry of the shearing interferometry with the DFG. (b) The schema when the DFG shifts ∆z along z axis.
Fig. 5
Fig. 5 The interferogram is changed by adjusting the DFG longitudinally. When the DFG locates exactly at the back-focal plane of lens1, the interferogram is uniform. (a) Experimental result for shifting DFG longitudinally (see Visualization 2), (b) the corresponding theoretical simulation (see Visualization 3).
Fig. 6
Fig. 6 The phase change by adjusting the DFG laterally can be observed as fringes shifting. (a) Experimental result for shifting DFG laterally (see Visualization 4), (b) the corresponding theoretical simulation (see Visualization 5).
Fig. 7
Fig. 7 (a) The phase encoding without passing the lateral shearing interferometer. (b) The interferogram by the lateral shearing interferometer, where the effective pixel size is 417 μm.
Fig. 8
Fig. 8 (a) The interferogram by the lateral shearing interferometer, where the effective pixel size is 417 μm. (b) The corresponding destructive interference between two diffracted waves in the case of constant phase encoding.
Fig. 9
Fig. 9 The simulated interferogram when linear wavefront aberration from 0 to 10λ rms was induced, (a) The interferogram of the inline interferometry (see Visualization 6), (b) The interferogram of DFGSI (see Visualization 7).
Fig. 10
Fig. 10 The simulated inteferogram when quadratic wavefront aberration varying from 0 to 10λ rms was induced. (a) The interferogram of the inline interferometry (see Visualization 8), (b) The interferogram of DFGSI (see Visualization 9).
Fig. 11
Fig. 11 The simulated inteferogram when biquadratic wavefront aberration varying from 0 to 10λ rms was induced. (a) The interferogram of the inline interferometry (see Visualization 10), (b) The interferogram of DFGSI (see Visualization 11).
Fig. 12
Fig. 12 BER depended on linear wave-front aberration for different lateral shearing.
Fig. 13
Fig. 13 BER depended on quadratic wave-front aberration for different lateral shearing.
Fig. 14
Fig. 14 BER depended on biquadratic wave-front aberration for different lateral shearing.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

x 1 =Δzsin θ 1 ,
z 1 =Δz( 1cos θ 1 ),
x 2 =Δzsin θ 2 ,
z 2 =Δz( 1cos θ 2 ).
x 1 =Δzsin( θ 1 θ )+Δzsinθ,
z 1 =Δzcos( θ 1 θ )+Δzcosθ,
x 2 =Δzsin( θ 2 θ )+Δzsinθ,
z 2 =Δzcos( θ 2 θ )+Δzcosθ,
u 1 ( x , y )=, { [ U( u,v ) ]| u x λ f 1 v y λ f 1 exp[ iksin( θ 1 θ ) x ] }δ( x λ f 2 x 1 λ f 2 )exp[ ik( x 2 + y 2 ) 2 z 1 ]
u 2 ( x , y )=, { [ U( u,v ) ]| u x λ f 1 v y λ f 1 exp[ iksin( θ 2 θ ) x ] }δ( x λ f 2 x 2 λ f 2 )exp[ ik( x 2 + y 2 ) 2 z 2 ]
U 1 ( ξ,η )=exp[ jπ z 1 ( ξ 2 + η 2 ) λ f 2 2 ]exp( j2π x 1 ξ λ f 2 )U{ f 1 f 2 [ ξ f 2 sin( θ 1 θ ) ], f 1 η f 2 },
U 2 ( ξ,η )=exp[ jπ z 2 ( ξ 2 + η 2 ) λ f 2 2 ]exp( j2π x 2 ξ λ f 2 )U{ f 1 f 2 [ ξ f 2 sin( θ 2 θ ) ], f 1 η f 2 },
I( ξ,η )= | exp[ iΔ ϕ 0 + iπΔzcos( θ θ 1 )( ξ 2 + η 2 ) λ f 2 2 + i2πΔzsin( θ θ 1 )ξ λ f 2 ] U{ f 1 f 2 [ ξ f 2 sin( θ 1 θ ) ], f 1 η f 2 } +exp[ iΔ ϕ x + iπΔzcos( θ θ 2 )( ξ 2 + η 2 ) λ f 2 2 + i2πΔzsin( θ θ 2 )ξ λ f 2 ] U{ f 1 f 2 [ ξ f 2 sin( θ 2 θ ) ], f 1 η f 2 } | 2 ,
Δ ϕ x = 2π λ ( sin θ 1 sin θ 2 )Δx.
G 0 (v)= 1 δ 0 2π e ( v μ 0 ) 2 2 σ 0 2 ,
G 1 (v)= 1 δ 1 2π e ( v μ 1 ) 2 2 σ 1 2 ,
V th = ( μ 0 σ 0 2 μ 1 σ 1 2 )± ( μ 0 σ 0 2 μ 1 σ 1 2 ) 2 4( 1 2 σ 1 2 1 2 σ 0 2 )[ μ 1 2 2 σ 1 2 μ 0 2 2 σ 0 2 ln( δ 0 δ 1 ) ] 2( 1 2 σ 1 2 1 2 σ 0 2 ) ,

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