Abstract

Fast non-interferometric phase retrieval is a very important technique for phase-encoded holographic data storage and other phase based applications due to its advantage of easy implementation, simple system setup, and robust noise tolerance. Here we present an iterative non-interferometric phase retrieval for 4-level phase encoded holographic data storage based on an iterative Fourier transform algorithm and known portion of the encoded data, which increases the storage code rate to two-times that of an amplitude based method. Only a single image at the Fourier plane of the beam is captured for the iterative reconstruction. Since beam intensity at the Fourier plane of the reconstructed beam is more concentrated than the reconstructed beam itself, the requirement of diffractive efficiency of the recording media is reduced, which will improve the dynamic range of recording media significantly. The phase retrieval only requires 10 iterations to achieve a less than 5% phase data error rate, which is successfully demonstrated by recording and reconstructing a test image data experimentally. We believe our method will further advance the holographic data storage technique in the era of big data.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

M. Walde, A. Jost, W. Kai, and R. Heintzmann, “Engineering an achromatic Bessel beam using a phase-only spatial light modulator and an iterative Fourier transformation algorithm,” Opt. Commun. 383, 64–68 (2017).

Y. Liu, F. Fan, Y. Hong, J. Zang, G. Kang, and X. Tan, “Volume holographic recording in Irgacure 784-doped PMMA photopolymer,” Opt. Express 25(17), 20654–20662 (2017).
[PubMed]

2014 (1)

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

2013 (2)

2011 (2)

S. H. Jeon and S. K. Gil, “2-step phase-shifting digital holographic optical encryption and error analysis,” J. Opt. Soc. Korea 15(3), 244–251 (2011).

J. A. M. Noriega, B. M. Kurkoski, M. N. Miyatake, and H. P. Meana, “Image authentication and recovery using BCH error-correcting codes,” Int. J. Comput. 5(1), 26–33 (2011).

2009 (2)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[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, Pure Appl. Opt. 11(6), 377–378 (2009).

2007 (2)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, “Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift,” Opt. Commun. 273(1), 54–59 (2007).

H. Horimai and X. Tan, “Holographic Information Storage System: Today and Future,” IEEE Trans. Magn. 43(2), 943–947 (2007).

2005 (1)

2003 (1)

M. Haw, “Holographic data storage: The light fantastic,” Nature 422(6932), 556–558 (2003).
[PubMed]

2002 (2)

V. V. Volkov, Y. Zhu, and M. De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[PubMed]

C. Desset, B. Macq, and L. Vandendorpe, “Block error-correcting codes for systems with a very high BER: Theoretical analysis and application to the protection of watermarks,” Signal Process. Image Commun. 17(5), 409–421 (2002).

2001 (1)

M. Takabayashi, A. Okamoto, A. Tomita, and M. Bunsen, “Symbol error characteristics of hybrid-modulated holographic data storage by intensity and multi phase modulation,” Jpn. J. Appl. Phys. 50(9), 09ME05 (2001).

2000 (2)

1997 (1)

1987 (2)

1986 (1)

1982 (1)

1972 (1)

R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Bunsen, M.

M. Takabayashi, A. Okamoto, A. Tomita, and M. Bunsen, “Symbol error characteristics of hybrid-modulated holographic data storage by intensity and multi phase modulation,” Jpn. J. Appl. Phys. 50(9), 09ME05 (2001).

Cai, L. Z.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, “Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift,” Opt. Commun. 273(1), 54–59 (2007).

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, Pure Appl. Opt. 11(6), 377–378 (2009).

Cho, B. C.

Chou, W. C.

De Graef, M.

V. V. Volkov, Y. Zhu, and M. De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[PubMed]

Desset, C.

C. Desset, B. Macq, and L. Vandendorpe, “Block error-correcting codes for systems with a very high BER: Theoretical analysis and application to the protection of watermarks,” Signal Process. Image Commun. 17(5), 409–421 (2002).

Dong, G. Y.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, “Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift,” Opt. Commun. 273(1), 54–59 (2007).

Eiju, T.

Fan, F.

Fienup, J. R.

Gao, P.

Gerchberg, R. W.

R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Gil, S. K.

Hariharan, P.

Haw, M.

M. Haw, “Holographic data storage: The light fantastic,” Nature 422(6932), 556–558 (2003).
[PubMed]

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, Pure Appl. Opt. 11(6), 377–378 (2009).

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, Pure Appl. Opt. 11(6), 377–378 (2009).

Heintzmann, R.

M. Walde, A. Jost, W. Kai, and R. Heintzmann, “Engineering an achromatic Bessel beam using a phase-only spatial light modulator and an iterative Fourier transformation algorithm,” Opt. Commun. 383, 64–68 (2017).

Hong, Y.

Horimai, H.

H. Horimai and X. Tan, “Holographic Information Storage System: Today and Future,” IEEE Trans. Magn. 43(2), 943–947 (2007).

H. Horimai, X. Tan, and J. Li, “Collinear holography,” Appl. Opt. 44(13), 2575–2579 (2005).
[PubMed]

Jeon, S. H.

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, Pure Appl. Opt. 11(6), 377–378 (2009).

Jost, A.

M. Walde, A. Jost, W. Kai, and R. Heintzmann, “Engineering an achromatic Bessel beam using a phase-only spatial light modulator and an iterative Fourier transformation algorithm,” Opt. Commun. 383, 64–68 (2017).

Kai, W.

M. Walde, A. Jost, W. Kai, and R. Heintzmann, “Engineering an achromatic Bessel beam using a phase-only spatial light modulator and an iterative Fourier transformation algorithm,” Opt. Commun. 383, 64–68 (2017).

Kang, G.

Kim, E. S.

Kim, K. T.

Kreske, K.

Kurkoski, B. M.

J. A. M. Noriega, B. M. Kurkoski, M. N. Miyatake, and H. P. Meana, “Image authentication and recovery using BCH error-correcting codes,” Int. J. Comput. 5(1), 26–33 (2011).

Li, J.

Li, Y.

Lin, Q.

Liu, C.

Liu, Y.

Lu, H.

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

Macq, B.

C. Desset, B. Macq, and L. Vandendorpe, “Block error-correcting codes for systems with a very high BER: Theoretical analysis and application to the protection of watermarks,” Signal Process. Image Commun. 17(5), 409–421 (2002).

Maiden, A. M.

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[PubMed]

Meana, H. P.

J. A. M. Noriega, B. M. Kurkoski, M. N. Miyatake, and H. P. Meana, “Image authentication and recovery using BCH error-correcting codes,” Int. J. Comput. 5(1), 26–33 (2011).

Meng, X. F.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, “Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift,” Opt. Commun. 273(1), 54–59 (2007).

Miyatake, M. N.

J. A. M. Noriega, B. M. Kurkoski, M. N. Miyatake, and H. P. Meana, “Image authentication and recovery using BCH error-correcting codes,” Int. J. Comput. 5(1), 26–33 (2011).

Neifeld, M. A.

Ning, X.

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

Noriega, J. A. M.

J. A. M. Noriega, B. M. Kurkoski, M. N. Miyatake, and H. P. Meana, “Image authentication and recovery using BCH error-correcting codes,” Int. J. Comput. 5(1), 26–33 (2011).

Okamoto, A.

M. Takabayashi, A. Okamoto, A. Tomita, and M. Bunsen, “Symbol error characteristics of hybrid-modulated holographic data storage by intensity and multi phase modulation,” Jpn. J. Appl. Phys. 50(9), 09ME05 (2001).

Oreb, B. F.

Osten, W.

Pan, X.

Pedrini, G.

Rodenburg, J. M.

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[PubMed]

Rosen, J.

Saxton, W.

R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Shen, X. X.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, “Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift,” Opt. Commun. 273(1), 54–59 (2007).

Sui, L.

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

Takabayashi, M.

M. Takabayashi, A. Okamoto, A. Tomita, and M. Bunsen, “Symbol error characteristics of hybrid-modulated holographic data storage by intensity and multi phase modulation,” Jpn. J. Appl. Phys. 50(9), 09ME05 (2001).

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, Pure Appl. Opt. 11(6), 377–378 (2009).

Tan, X.

Tomita, A.

M. Takabayashi, A. Okamoto, A. Tomita, and M. Bunsen, “Symbol error characteristics of hybrid-modulated holographic data storage by intensity and multi phase modulation,” Jpn. J. Appl. Phys. 50(9), 09ME05 (2001).

Vandendorpe, L.

C. Desset, B. Macq, and L. Vandendorpe, “Block error-correcting codes for systems with a very high BER: Theoretical analysis and application to the protection of watermarks,” Signal Process. Image Commun. 17(5), 409–421 (2002).

Volkov, V. V.

V. V. Volkov, Y. Zhu, and M. De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[PubMed]

Wackerman, C. C.

Walde, M.

M. Walde, A. Jost, W. Kai, and R. Heintzmann, “Engineering an achromatic Bessel beam using a phase-only spatial light modulator and an iterative Fourier transformation algorithm,” Opt. Commun. 383, 64–68 (2017).

Wang, Y.

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

Wang, Y. R.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, “Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift,” Opt. Commun. 273(1), 54–59 (2007).

Xu, X. F.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, “Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift,” Opt. Commun. 273(1), 54–59 (2007).

Zang, J.

Zhang, H.

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, “Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift,” Opt. Commun. 273(1), 54–59 (2007).

Zhu, J.

Zhu, Y.

V. V. Volkov, Y. Zhu, and M. De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[PubMed]

Appl. Opt. (6)

IEEE Trans. Magn. (1)

H. Horimai and X. Tan, “Holographic Information Storage System: Today and Future,” IEEE Trans. Magn. 43(2), 943–947 (2007).

Int. J. Comput. (1)

J. A. M. Noriega, B. M. Kurkoski, M. N. Miyatake, and H. P. Meana, “Image authentication and recovery using BCH error-correcting codes,” Int. J. Comput. 5(1), 26–33 (2011).

J. Opt. A, Pure Appl. Opt. (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, Pure Appl. Opt. 11(6), 377–378 (2009).

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

J. Opt. Soc. Korea (1)

Jpn. J. Appl. Phys. (1)

M. Takabayashi, A. Okamoto, A. Tomita, and M. Bunsen, “Symbol error characteristics of hybrid-modulated holographic data storage by intensity and multi phase modulation,” Jpn. J. Appl. Phys. 50(9), 09ME05 (2001).

Micron (1)

V. V. Volkov, Y. Zhu, and M. De Graef, “A new symmetrized solution for phase retrieval using the transport of intensity equation,” Micron 33(5), 411–416 (2002).
[PubMed]

Nature (1)

M. Haw, “Holographic data storage: The light fantastic,” Nature 422(6932), 556–558 (2003).
[PubMed]

Opt. Commun. (2)

X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, G. Y. Dong, and X. X. Shen, “Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift,” Opt. Commun. 273(1), 54–59 (2007).

M. Walde, A. Jost, W. Kai, and R. Heintzmann, “Engineering an achromatic Bessel beam using a phase-only spatial light modulator and an iterative Fourier transformation algorithm,” Opt. Commun. 383, 64–68 (2017).

Opt. Eng. (1)

L. Sui, H. Lu, X. Ning, and Y. Wang, “Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain,” Opt. Eng. 53(2), 026108 (2014).

Opt. Express (2)

Opt. Lett. (1)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

Signal Process. Image Commun. (1)

C. Desset, B. Macq, and L. Vandendorpe, “Block error-correcting codes for systems with a very high BER: Theoretical analysis and application to the protection of watermarks,” Signal Process. Image Commun. 17(5), 409–421 (2002).

Ultramicroscopy (1)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[PubMed]

Other (1)

B. S. Gurevich, S. B. Gurevich, K. M. Zhumaliev, S. A. Alymkulov, S. A. Sagymbaev, and I. A. Akkoziev, “Comparative evaluation of the volume holographic memory information capacity limits caused by different limitation factors,” in International Symposium on Optical Science & Technology 2000 (Society of Photo-Optical Instrumentation Engineers, 2000), p. 167–176.

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Figures (11)

Fig. 1
Fig. 1 The diagram of non-interferometric system for phase retrieval.
Fig. 2
Fig. 2 Convergent curves with different proportions of embedded phase data with threshold ɛ of 5 × 10−4.
Fig. 3
Fig. 3 Phase retrieval results using cameras with different dynamic ranges (8-bit, 10-bit, 12-bit) in the simulation.
Fig. 4
Fig. 4 Different embedded phase patterns and their intensity distribution in the Fourier plane. (a) Regular pattern. (b) Random pattern. (c) Intensity in the Fourier plane of regular pattern. (d) Intensity in the Fourier plane of random pattern.
Fig. 5
Fig. 5 The diagram of optical setup. SF: spatial filter, HWP: half wave plate, BS: beam splitter, L 1 ~ L 6 : lens ( L 1 =300mm, L 2 ~ L 5 =150mm, L 6 =75mm), SLM: spatial light modulator. The media is Irgacure 784-doped PMMA photopolymer which thickness is 1.5mm.
Fig. 6
Fig. 6 Test image to be recorded with size of 128 × 128 pixels.
Fig. 7
Fig. 7 Illustration of the process of encoding gray image to phase patterns to be recorded. Image of 128 × 128 pixels is divided into sub-blocks of 32 × 16 pixels first. Then encoding phase data with 64 × 32 pixels are generated as 4 phase pixels are used to encode a single image gray value. A fixed known embedded phase data page with 64 × 32 pixels is combined with the encoding phase data to form the 64 × 64 phase pattern. Then every pixel of the 64 × 64 phase pattern is enlarged by a 8 × 8 block to form the final 512 × 512 phase pattern uploaded on the SLM. Combination rules of the encoding phase and embedded phase is illustrated in the dashed line rectangular. (Pixels with north-east direction texture represent embedded phase data positions and pixels with north-west direction texture represent encoding phase data positions.)
Fig. 8
Fig. 8 Intensity distribution at the Fourier plane of the reconstructed beam.
Fig. 9
Fig. 9 Initial guess of phase pattern.
Fig. 10
Fig. 10 Phase pattern and corresponding gray image: (a) Original phase and gray image, (b) Resolved phase and gray image after 10 iterations, (c) Phase error distribution between original phase pattern and resolved phase pattern.
Fig. 11
Fig. 11 Image reconstruction comparison: (a) Original image, (b) Reconstructed image based on initial guess, (c) Reconstructed image based on resolved phase after 10 iterations.

Tables (1)

Tables Icon

Table 1 Simulation results for 4-level phase and 8-level phase encoding for different proportions of embedded data

Equations (10)

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

U n =exp( i φ n )
V n =F{ U n }=| A n |exp( i ϕ n )
V n ' =| I 0 |exp( i ϕ n )
U n ' = F 1 { V n ' }=| A n ' |exp( i ϕ n ' )
U n '' =exp( i ϕ n '' )
V n '' =F{ U n '' }
I n = V n '' V n ''
E n = ( | I 0 I n | ) I 0
ΔE= E n E n1
CR=( 1p ) log 2 N

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