Abstract

Holographic data storage (HDS), in which both the amplitude and the phase of a signal beam are modulated, has been extensively studied with the goal of increasing its storage capacity. To detect such modulation during data retrieval, it is necessary to acquire the complex amplitude of the signal beam. In this study, we focus on the transport of intensity equation (TIE) method, which allows us to detect the phase distribution of the light wave quantitatively without using interferometry, contributing to miniaturization of the optical system and improvement of the vibration tolerance of HDS. We discuss the conditions of the modulation phase distribution of the signal beam required for accurate phase detection and propose a method to estimate and eliminate the noise that frequently appears in the phase distribution detected by the TIE method.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

2017 (3)

2016 (3)

2014 (4)

2013 (6)

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
[Crossref]

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38, 3538–3541 (2013).
[Crossref] [PubMed]

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “High-speed transport-of-intensity phase microscopy with an electrically tunable lens,” Opt. Express 21, 24060–24075 (2013).
[Crossref] [PubMed]

M. Bunsen, S. Umetsu, M. Takabayashi, and A. Okamoto, “Method of phase and amplitude modulation/demodulation using datapages with embedded phase-shift for holographic data storage,” Jpn. J. Appl. Phys. 52, 09LD04 (2013).
[Crossref]

K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, and A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52, 09LD13 (2013).
[Crossref]

G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10, 115305 (2013).

2012 (3)

2011 (2)

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).
[Crossref]

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19, 13436–13444 (2011).
[Crossref] [PubMed]

2010 (2)

2007 (1)

2005 (1)

2004 (1)

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).
[Crossref] [PubMed]

2001 (1)

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
[Crossref]

1998 (1)

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[Crossref]

1996 (1)

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

1995 (1)

1992 (1)

1983 (1)

1982 (1)

Acosta, E.

Allen, L. J.

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
[Crossref]

Alonso, J. R.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
[Crossref]

Asundi, A.

Ayres, M.

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

Ayubi, G. A.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
[Crossref]

Bai, X.

Banerjee, P. P.

Barbastathis, G.

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Barty, A.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).
[Crossref] [PubMed]

Berger, G.

G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10, 115305 (2013).

Bie, R.

Bunsen, M.

M. Bunsen, S. Umetsu, M. Takabayashi, and A. Okamoto, “Method of phase and amplitude modulation/demodulation using datapages with embedded phase-shift for holographic data storage,” Jpn. J. Appl. Phys. 52, 09LD04 (2013).
[Crossref]

Chen, Q.

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Curtis, K.

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

Dalchiele, E. A.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
[Crossref]

Denz, C.

G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10, 115305 (2013).

Dhar, L.

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

Dietz, M.

G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10, 115305 (2013).

Endo, M.

Falaggis, K.

Fernández, A.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
[Crossref]

Ferrari, J. A.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
[Crossref]

Flores, J. L.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
[Crossref]

Fujimura, R.

Fujita, K.

T. Hoshizawa, K. Shimada, K. Fujita, and Y. Tada, “Practical angular-multiplexing holographic data storage system with 2 terabyte capacity and 1 gigabit transfer rate,” Jpn. J. Appl. Phys. 55, 09SA06 (2016).
[Crossref]

Fütterer, G.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gregory, D. A.

Guan, X.

Gureyev, T. E.

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

T. E. Gureyev, A. Roberts, and K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A 12, 1942–1946 (1995).
[Crossref]

Häussler, R.

Hill, A.

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

Honma, S.

S. Honma and T. Sekiguchi, “Multilevel phase and amplitude modulation method for holographic memories with programmable phase modulator,” Opt. Rev. 21, 597–598 (2014).
[Crossref]

Horimai, H.

Hoshizawa, T.

T. Hoshizawa, K. Shimada, K. Fujita, and Y. Tada, “Practical angular-multiplexing holographic data storage system with 2 terabyte capacity and 1 gigabit transfer rate,” Jpn. J. Appl. Phys. 55, 09SA06 (2016).
[Crossref]

Huang, Y.

Ina, H.

Ishii, N.

Y. Katano, T. Muroi, N. Kinoshita, and N. Ishii, “Prototype holographic data storage drive with wavefront compensation for playback of 8k video data,” IEEE Transactions on Consumer Electron. 63, 243–250 (2017).
[Crossref]

Kanbayashi, Y.

Katano, Y.

Y. Katano, T. Muroi, N. Kinoshita, and N. Ishii, “Prototype holographic data storage drive with wavefront compensation for playback of 8k video data,” IEEE Transactions on Consumer Electron. 63, 243–250 (2017).
[Crossref]

Kato, H.

Kinoshita, N.

Y. Katano, T. Muroi, N. Kinoshita, and N. Ishii, “Prototype holographic data storage drive with wavefront compensation for playback of 8k video data,” IEEE Transactions on Consumer Electron. 63, 243–250 (2017).
[Crossref]

Kirsch, J. C.

Kobayashi, S.

Komuro, K.

Kozacki, T.

Kunori, K.

Leister, N.

Li, J.

Li, Y.

Lin, X.

Liu, F.

Liu, J.

Liu, Y.

Luo, Y.

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).
[Crossref]

Martinez-Carranza, J.

Martino, J. M. Di

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
[Crossref]

McMahon, P. J.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).
[Crossref] [PubMed]

Muroi, T.

Y. Katano, T. Muroi, N. Kinoshita, and N. Ishii, “Prototype holographic data storage drive with wavefront compensation for playback of 8k video data,” IEEE Transactions on Consumer Electron. 63, 243–250 (2017).
[Crossref]

Nishimoto, H.

Nobukawa, T.

Nomura, T.

Nugent, K. A.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).
[Crossref] [PubMed]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

T. E. Gureyev, A. Roberts, and K. A. Nugent, “Partially coherent fields, the transport-of-intensity equation, and phase uniqueness,” J. Opt. Soc. Am. A 12, 1942–1946 (1995).
[Crossref]

Okamoto, A.

A. Shibukawa, A. Okamoto, M. Takabayashi, and A. Tomita, “Spatial cross modulation method using a random diffuser and phase-only spatial light modulator for constructing arbitrary complex fields,” Opt. Express 22, 3968–3982 (2014).
[Crossref] [PubMed]

M. Bunsen, S. Umetsu, M. Takabayashi, and A. Okamoto, “Method of phase and amplitude modulation/demodulation using datapages with embedded phase-shift for holographic data storage,” Jpn. J. Appl. Phys. 52, 09LD04 (2013).
[Crossref]

K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, and A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52, 09LD13 (2013).
[Crossref]

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19, 13436–13444 (2011).
[Crossref] [PubMed]

Oxley, M. P.

L. J. Allen and M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
[Crossref]

Paganin, D.

D. Paganin, A. Barty, P. J. McMahon, and K. A. Nugent, “Quantitative phase-amplitude microscopy. III. The effects of noise,” J. Microsc. 214, 51–61 (2004).
[Crossref] [PubMed]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80, 2586–2589 (1998).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Paganin, D. M.

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).
[Crossref]

Pavlov, K. M.

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).
[Crossref]

Perciante, C. D.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
[Crossref]

Poon, T.-C.

Qu, W.

Reichelt, S.

Roberts, A.

Saita, Y.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).

Sato, K.

K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, and A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52, 09LD13 (2013).
[Crossref]

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19, 13436–13444 (2011).
[Crossref] [PubMed]

Schmalz, J. A.

J. A. Schmalz, T. E. Gureyev, D. M. Paganin, and K. M. Pavlov, “Phase retrieval using radiation and matter-wave fields: Validity of Teague’s method for solution of the transport-of-intensity equation,” Phys. Rev. A 84, 023808 (2011).
[Crossref]

Sekiguchi, T.

S. Honma and T. Sekiguchi, “Multilevel phase and amplitude modulation method for holographic memories with programmable phase modulator,” Opt. Rev. 21, 597–598 (2014).
[Crossref]

Shanker, A.

Shibukawa, A.

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Figures (8)

Fig. 1
Fig. 1 Conceptual diagrams of HDS with SQAM and detection of the SQAM signal beam using the TIE method. (a) Generation and holographic recording of the SQAM signal beam. (b) Reconstruction of the SQAM signal beam from holographic material and its detection with the TIE method.
Fig. 2
Fig. 2 Simulation results of the detection of a SQAM signal beam with the TIE method in the case of discretely modulated spatial phase distribution. (a) Modulation intensity distribution. (b) Modulation phase distribution. (c) Detected phase distribution by the TIE method (α = 90°). (d) Detected phase distribution by the TIE method (α = 360°). (e) Phase distribution on the red line in (c). (f) Phase distribution on the red line in (d). (g) Constellation diagram of symbols in (d).
Fig. 3
Fig. 3 Simulation results of the detection of a SQAM signal beam with continuously modulated spatial phase distribution by the TIE method ((a), (b), (c), and (g): pyramidal phase modulation; (d), (e), (f), and (h): sinusoidal phase modulation). (a) and (d) Modulation phase distribution (α = 360°). (b) and (e) Detected phase distribution by the TIE method. (c) and (f) Phase distribution on the red line in (b) and (e); (g) and (h) constellation diagram of the symbols in (b) and (e), respectively.
Fig. 4
Fig. 4 RMSE of the detected phase as a function of the maximum phase modulation depth (α) for discrete, pyramidal, and sinusoidal phase modulations.
Fig. 5
Fig. 5 Simulation results with 2.5% Gaussian noise added to three diffracted intensity distribution images of the SQAM signal beam used in the TIE method. (a) Example of the phase detected by the TIE method (left) and phase distribution on the red line (right). (b) Constellation diagram of symbols in (a). (c) Noise distribution estimated by spatial linear interpolation (left) and phase distribution on the red line (right). (d) Detected phase distribution by the TIE method for the case of a 32 × 32 SQAM symbol arrangement. (e) Phase distribution after noise elimination. (f) Constellation diagram of symbols in (e). (g) Constellation diagram in the case of 8SQAM after noise elimination.
Fig. 6
Fig. 6 Experimental setup. S: Shutter, HWP: Half wave plate, BS: Beam splitter, PBS: Polarizing beam splitter, L: Lens.
Fig. 7
Fig. 7 Experimental results of the detection of the complex amplitude distribution of a holographically recorded and reconstructed SQAM signal beam with the TIE method where pyramidal phase modulation is used as continuous phase modulation. (a) Modulation phase. Intensity distributions of the signal beam captured by camera at (b) z = −5 mm, (c) z = 0 mm, and (d) z = 5 mm. (e) Detected phase distribution by the TIE method. (f) Noise distribution estimated by spatial linear interpolation. (g) Phase distribution after noise elimination. (h) Constellation diagram of symbols in (g).
Fig. 8
Fig. 8 Experimental results of the detection of the complex amplitude distribution of the holographically recorded and reconstructed SQAM signal beam with the TIE method where sinusoidal phase modulation is used as continuous phase modulation. (a) Modulation phase. Intensity distributions of the signal beam captured by camera at (b) z = −5 mm, (c) z = 0 mm, and (d) z = 5 mm. (e) Detected phase distribution by the TIE method. (f) Noise distribution estimated by spatial linear interpolation. (g) Phase distribution after noise elimination. (h) Constellation diagram of symbols in (g).

Equations (3)

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2 π λ z I ( x , y , z ) = I ( x , y , z )   ϕ ( x , y , z ) ,
ϕ ( x , y , 0 ) = 2 π λ F 1 [ q 2 F [ I ( x , y , 0 ) 1 F 1 [ q 2 F [ I ( x , y , 0 ) z ] ] ] ] ,
RMSE = 1 N x N y i = 1 N x j = 1 N y ( D i , j o f f s e t M i , j ) 2 .

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