Abstract

We focus on the novelty of three elements in holographic data storage systems (HDSS): the data pager, where we introduce a parallel-aligned liquid crystal on silicon (PA-LCoS) microdisplay; the recording material, where we consider the highly versatile PVA/AA photopolymer; and also in the architecture of the object arm, where a convergent correlator system is introduced. We show that PA-LCoS devices cannot implement pure hybrid-ternary modulated (HTM) data pages but a rather close approximation. Validation of the HDSS expressions for the convergent correlator and comparison with the widespread 4-f system is performed. Experimental results with PVA/AA material showing bit-error rates (BER) in the range of 10−3, further show its potential application for HDSS, and also demonstrate the validity of the testing platform and PA-LCoS calibration and optimization.

© 2015 Optical Society of America

Full Article  |  PDF Article
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2015 (1)

2014 (5)

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

Z. Ushiyama, H. Kurata, Y. Tsukamoto, S. Yoshida, and M. Yamamoto, “Shift-peristrophic multiplexing for high density holographic data storage,” Appl. Sci. 4(2), 148–157 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53, 067104 (2014).
[Crossref]

K.-I. Shimada, T. Ide, T. Shimano, K. Anderson, and K. Curtis, “New optical architecture for holographic data storage system compatible with Blu-ray Disc™ system,” Opt. Eng. 53(2), 025102 (2014).
[Crossref]

2012 (1)

A. Márquez, E. Fernández, F. J. Martínez, S. Gallego, M. Ortuño, A. Beléndez, and I. Pascual, “Analysis of the geometry of a holographic memory setup,” Proc. SPIE 8429, 84291Y (2012).
[Crossref]

2010 (2)

A. Márquez, S. Gallego, M. Ortuño, E. Fernández, M. L. Álvarez, A. Beléndez, and I. Pascual, “Generation of diffractive optical elements onto a photopolymer using a liquid crystal display,” Proc. SPIE 7717, 77170D (2010).
[Crossref]

E. Fernandez, A. Marquez, S. Gallego, R. Fuentes, C. García, and I. Pascual, “Hybrid ternary modulation applied to multiplexing holograms in photopolymers for data page storage,” J. Lightwave Technol. 28(5), 776–783 (2010).
[Crossref]

2009 (4)

S. Gallego, A. Márquez, S. Marini, E. Fernández, M. Ortuño, and I. Pascual, “In dark analysis of PVA/AA materials at very low spatial frequencies: phase modulation evolution and diffusion estimation,” Opt. Express 17(20), 18279–18291 (2009).
[Crossref] [PubMed]

B. Das, J. Joseph, and K. Singh, “Phase modulated gray-scale data pages for digital holographic data storage,” Opt. Commun. 282(11), 2147–2154 (2009).
[Crossref]

B. Das, J. Joseph, and K. Singh, “Material saturation in photopolymer holographic data recording and its effects on bit-error-rate and content-addressable search,” Opt. Commun. 282(2), 177–184 (2009).
[Crossref]

E. Fernández, A. Márquez, M. Ortuño, R. Fuentes, C. García, and I. Pascual, “Optimization of twisted-nematic liquid crystal displays for holographic data storage,” Opt. Pura Apl. 42, 125–132 (2009).

2008 (1)

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

2007 (6)

2006 (1)

2005 (2)

A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
[Crossref] [PubMed]

H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, “Characterisation of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing,” J. Opt. A, Pure Appl. Opt. 7(5), 255–260 (2005).
[Crossref]

2004 (1)

M. J. O’Callaghan, “Sorting through the lore of phase mask options - performance measures and practical commercial designs,” Proc. SPIE 5362, 159 (2004).

2003 (2)

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

A. Márquez, C. Neipp, A. Beléndez, S. Gallego, M. Ortuño, and I. Pascual, “Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings,” Opt. Lett. 28(17), 1510–1512 (2003).
[Crossref] [PubMed]

2001 (1)

1994 (1)

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[Crossref]

1963 (1)

Alvarez, M. L.

Álvarez, M. L.

A. Márquez, S. Gallego, M. Ortuño, E. Fernández, M. L. Álvarez, A. Beléndez, and I. Pascual, “Generation of diffractive optical elements onto a photopolymer using a liquid crystal display,” Proc. SPIE 7717, 77170D (2010).
[Crossref]

A. Márquez, S. Gallego, D. Méndez, M. L. Álvarez, E. Fernández, M. Ortuño, A. Beléndez, and I. Pascual, “Characterization and optimization of liquid crystal displays for data storage applications,” Proc. SPIE 6587, 658715 (2007).
[Crossref]

Anderson, K.

K.-I. Shimada, T. Ide, T. Shimano, K. Anderson, and K. Curtis, “New optical architecture for holographic data storage system compatible with Blu-ray Disc™ system,” Opt. Eng. 53(2), 025102 (2014).
[Crossref]

Beléndez, A.

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53, 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

A. Márquez, E. Fernández, F. J. Martínez, S. Gallego, M. Ortuño, A. Beléndez, and I. Pascual, “Analysis of the geometry of a holographic memory setup,” Proc. SPIE 8429, 84291Y (2012).
[Crossref]

A. Márquez, S. Gallego, M. Ortuño, E. Fernández, M. L. Álvarez, A. Beléndez, and I. Pascual, “Generation of diffractive optical elements onto a photopolymer using a liquid crystal display,” Proc. SPIE 7717, 77170D (2010).
[Crossref]

A. Márquez, S. Gallego, D. Méndez, M. L. Álvarez, E. Fernández, M. Ortuño, A. Beléndez, and I. Pascual, “Characterization and optimization of liquid crystal displays for data storage applications,” Proc. SPIE 6587, 658715 (2007).
[Crossref]

E. Fernández, M. Ortuño, S. Gallego, C. García, A. Beléndez, and I. Pascual, “Comparison of peristrophic multiplexing and a combination of angular and peristrophic holographic multiplexing in a thick PVA/acrylamide photopolymer for data storage,” Appl. Opt. 46(22), 5368–5373 (2007).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Alvarez, E. Fernández, M. Ortuño, C. Neipp, A. Beléndez, and I. Pascual, “Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories,” Opt. Lett. 32(17), 2511–2513 (2007).
[Crossref] [PubMed]

A. Márquez, C. Neipp, A. Beléndez, S. Gallego, M. Ortuño, and I. Pascual, “Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings,” Opt. Lett. 28(17), 1510–1512 (2003).
[Crossref] [PubMed]

Blümel, T.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

Campos, J.

Collings, N.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Crossland, W. A.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Curtis, K.

K.-I. Shimada, T. Ide, T. Shimano, K. Anderson, and K. Curtis, “New optical architecture for holographic data storage system compatible with Blu-ray Disc™ system,” Opt. Eng. 53(2), 025102 (2014).
[Crossref]

Das, B.

B. Das, J. Joseph, and K. Singh, “Phase modulated gray-scale data pages for digital holographic data storage,” Opt. Commun. 282(11), 2147–2154 (2009).
[Crossref]

B. Das, J. Joseph, and K. Singh, “Material saturation in photopolymer holographic data recording and its effects on bit-error-rate and content-addressable search,” Opt. Commun. 282(2), 177–184 (2009).
[Crossref]

B. Das, J. Joseph, and K. Singh, “Performance analysis of content-addressable search and bit-error rate characteristics of a defocused volume holographic data storage system,” Appl. Opt. 46(22), 5461–5470 (2007).
[Crossref] [PubMed]

Davey, A. B.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Dhar, L.

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

Evans, M.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Fernandez, E.

Fernández, E.

A. Márquez, E. Fernández, F. J. Martínez, S. Gallego, M. Ortuño, A. Beléndez, and I. Pascual, “Analysis of the geometry of a holographic memory setup,” Proc. SPIE 8429, 84291Y (2012).
[Crossref]

A. Márquez, S. Gallego, M. Ortuño, E. Fernández, M. L. Álvarez, A. Beléndez, and I. Pascual, “Generation of diffractive optical elements onto a photopolymer using a liquid crystal display,” Proc. SPIE 7717, 77170D (2010).
[Crossref]

E. Fernández, A. Márquez, M. Ortuño, R. Fuentes, C. García, and I. Pascual, “Optimization of twisted-nematic liquid crystal displays for holographic data storage,” Opt. Pura Apl. 42, 125–132 (2009).

S. Gallego, A. Márquez, S. Marini, E. Fernández, M. Ortuño, and I. Pascual, “In dark analysis of PVA/AA materials at very low spatial frequencies: phase modulation evolution and diffusion estimation,” Opt. Express 17(20), 18279–18291 (2009).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Alvarez, E. Fernández, M. Ortuño, C. Neipp, A. Beléndez, and I. Pascual, “Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories,” Opt. Lett. 32(17), 2511–2513 (2007).
[Crossref] [PubMed]

E. Fernández, M. Ortuño, S. Gallego, C. García, A. Beléndez, and I. Pascual, “Comparison of peristrophic multiplexing and a combination of angular and peristrophic holographic multiplexing in a thick PVA/acrylamide photopolymer for data storage,” Appl. Opt. 46(22), 5368–5373 (2007).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Álvarez, E. Fernández, M. Ortuño, A. Beléndez, and I. Pascual, “Characterization and optimization of liquid crystal displays for data storage applications,” Proc. SPIE 6587, 658715 (2007).
[Crossref]

Francés, J.

Fuentes, R.

E. Fernandez, A. Marquez, S. Gallego, R. Fuentes, C. García, and I. Pascual, “Hybrid ternary modulation applied to multiplexing holograms in photopolymers for data page storage,” J. Lightwave Technol. 28(5), 776–783 (2010).
[Crossref]

E. Fernández, A. Márquez, M. Ortuño, R. Fuentes, C. García, and I. Pascual, “Optimization of twisted-nematic liquid crystal displays for holographic data storage,” Opt. Pura Apl. 42, 125–132 (2009).

Gallego, S.

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53, 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

A. Márquez, E. Fernández, F. J. Martínez, S. Gallego, M. Ortuño, A. Beléndez, and I. Pascual, “Analysis of the geometry of a holographic memory setup,” Proc. SPIE 8429, 84291Y (2012).
[Crossref]

E. Fernandez, A. Marquez, S. Gallego, R. Fuentes, C. García, and I. Pascual, “Hybrid ternary modulation applied to multiplexing holograms in photopolymers for data page storage,” J. Lightwave Technol. 28(5), 776–783 (2010).
[Crossref]

A. Márquez, S. Gallego, M. Ortuño, E. Fernández, M. L. Álvarez, A. Beléndez, and I. Pascual, “Generation of diffractive optical elements onto a photopolymer using a liquid crystal display,” Proc. SPIE 7717, 77170D (2010).
[Crossref]

S. Gallego, A. Márquez, S. Marini, E. Fernández, M. Ortuño, and I. Pascual, “In dark analysis of PVA/AA materials at very low spatial frequencies: phase modulation evolution and diffusion estimation,” Opt. Express 17(20), 18279–18291 (2009).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Alvarez, E. Fernández, M. Ortuño, C. Neipp, A. Beléndez, and I. Pascual, “Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories,” Opt. Lett. 32(17), 2511–2513 (2007).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Álvarez, E. Fernández, M. Ortuño, A. Beléndez, and I. Pascual, “Characterization and optimization of liquid crystal displays for data storage applications,” Proc. SPIE 6587, 658715 (2007).
[Crossref]

E. Fernández, M. Ortuño, S. Gallego, C. García, A. Beléndez, and I. Pascual, “Comparison of peristrophic multiplexing and a combination of angular and peristrophic holographic multiplexing in a thick PVA/acrylamide photopolymer for data storage,” Appl. Opt. 46(22), 5368–5373 (2007).
[Crossref] [PubMed]

A. Márquez, C. Neipp, A. Beléndez, S. Gallego, M. Ortuño, and I. Pascual, “Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings,” Opt. Lett. 28(17), 1510–1512 (2003).
[Crossref] [PubMed]

García, C.

Hermerschmidt, A.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

Hill, A.

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

Ide, T.

K.-I. Shimada, T. Ide, T. Shimano, K. Anderson, and K. Curtis, “New optical architecture for holographic data storage system compatible with Blu-ray Disc™ system,” Opt. Eng. 53(2), 025102 (2014).
[Crossref]

Iemmi, C.

Ihas, B.

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

Jang, J. S.

Jeziorska, A. M.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Joseph, J.

B. Das, J. Joseph, and K. Singh, “Material saturation in photopolymer holographic data recording and its effects on bit-error-rate and content-addressable search,” Opt. Commun. 282(2), 177–184 (2009).
[Crossref]

B. Das, J. Joseph, and K. Singh, “Phase modulated gray-scale data pages for digital holographic data storage,” Opt. Commun. 282(11), 2147–2154 (2009).
[Crossref]

B. Das, J. Joseph, and K. Singh, “Performance analysis of content-addressable search and bit-error rate characteristics of a defocused volume holographic data storage system,” Appl. Opt. 46(22), 5461–5470 (2007).
[Crossref] [PubMed]

J. Joseph and D. A. Waldman, “Homogenized Fourier transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image,” Appl. Opt. 45(25), 6374–6380 (2006).
[Crossref] [PubMed]

Komarcevic, M.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Krüger, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

Kurata, H.

Z. Ushiyama, H. Kurata, Y. Tsukamoto, S. Yoshida, and M. Yamamoto, “Shift-peristrophic multiplexing for high density holographic data storage,” Appl. Sci. 4(2), 148–157 (2014).
[Crossref]

Lu, G.

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[Crossref]

Marini, S.

Marquez, A.

Márquez, A.

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53, 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

A. Márquez, E. Fernández, F. J. Martínez, S. Gallego, M. Ortuño, A. Beléndez, and I. Pascual, “Analysis of the geometry of a holographic memory setup,” Proc. SPIE 8429, 84291Y (2012).
[Crossref]

A. Márquez, S. Gallego, M. Ortuño, E. Fernández, M. L. Álvarez, A. Beléndez, and I. Pascual, “Generation of diffractive optical elements onto a photopolymer using a liquid crystal display,” Proc. SPIE 7717, 77170D (2010).
[Crossref]

E. Fernández, A. Márquez, M. Ortuño, R. Fuentes, C. García, and I. Pascual, “Optimization of twisted-nematic liquid crystal displays for holographic data storage,” Opt. Pura Apl. 42, 125–132 (2009).

S. Gallego, A. Márquez, S. Marini, E. Fernández, M. Ortuño, and I. Pascual, “In dark analysis of PVA/AA materials at very low spatial frequencies: phase modulation evolution and diffusion estimation,” Opt. Express 17(20), 18279–18291 (2009).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Alvarez, E. Fernández, M. Ortuño, C. Neipp, A. Beléndez, and I. Pascual, “Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories,” Opt. Lett. 32(17), 2511–2513 (2007).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Álvarez, E. Fernández, M. Ortuño, A. Beléndez, and I. Pascual, “Characterization and optimization of liquid crystal displays for data storage applications,” Proc. SPIE 6587, 658715 (2007).
[Crossref]

A. Márquez, C. Iemmi, I. Moreno, J. Campos, and M. Yzuel, “Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency,” Opt. Express 13(6), 2111–2119 (2005).
[Crossref] [PubMed]

A. Márquez, C. Neipp, A. Beléndez, S. Gallego, M. Ortuño, and I. Pascual, “Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings,” Opt. Lett. 28(17), 1510–1512 (2003).
[Crossref] [PubMed]

Martin, S.

H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, “Characterisation of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing,” J. Opt. A, Pure Appl. Opt. 7(5), 255–260 (2005).
[Crossref]

Martínez, F. J.

McGinn, C.

H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, “Characterisation of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing,” J. Opt. A, Pure Appl. Opt. 7(5), 255–260 (2005).
[Crossref]

Méndez, D.

A. Márquez, S. Gallego, D. Méndez, M. L. Alvarez, E. Fernández, M. Ortuño, C. Neipp, A. Beléndez, and I. Pascual, “Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories,” Opt. Lett. 32(17), 2511–2513 (2007).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Álvarez, E. Fernández, M. Ortuño, A. Beléndez, and I. Pascual, “Characterization and optimization of liquid crystal displays for data storage applications,” Proc. SPIE 6587, 658715 (2007).
[Crossref]

Michaels, D.

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

Moore, J. R.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Moreno, I.

Naydenova, I.

H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, “Characterisation of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing,” J. Opt. A, Pure Appl. Opt. 7(5), 255–260 (2005).
[Crossref]

Neipp, C.

O’Callaghan, M. J.

M. J. O’Callaghan, “Sorting through the lore of phase mask options - performance measures and practical commercial designs,” Proc. SPIE 5362, 159 (2004).

Ortuño, M.

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53, 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

A. Márquez, E. Fernández, F. J. Martínez, S. Gallego, M. Ortuño, A. Beléndez, and I. Pascual, “Analysis of the geometry of a holographic memory setup,” Proc. SPIE 8429, 84291Y (2012).
[Crossref]

A. Márquez, S. Gallego, M. Ortuño, E. Fernández, M. L. Álvarez, A. Beléndez, and I. Pascual, “Generation of diffractive optical elements onto a photopolymer using a liquid crystal display,” Proc. SPIE 7717, 77170D (2010).
[Crossref]

E. Fernández, A. Márquez, M. Ortuño, R. Fuentes, C. García, and I. Pascual, “Optimization of twisted-nematic liquid crystal displays for holographic data storage,” Opt. Pura Apl. 42, 125–132 (2009).

S. Gallego, A. Márquez, S. Marini, E. Fernández, M. Ortuño, and I. Pascual, “In dark analysis of PVA/AA materials at very low spatial frequencies: phase modulation evolution and diffusion estimation,” Opt. Express 17(20), 18279–18291 (2009).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Alvarez, E. Fernández, M. Ortuño, C. Neipp, A. Beléndez, and I. Pascual, “Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories,” Opt. Lett. 32(17), 2511–2513 (2007).
[Crossref] [PubMed]

E. Fernández, M. Ortuño, S. Gallego, C. García, A. Beléndez, and I. Pascual, “Comparison of peristrophic multiplexing and a combination of angular and peristrophic holographic multiplexing in a thick PVA/acrylamide photopolymer for data storage,” Appl. Opt. 46(22), 5368–5373 (2007).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Álvarez, E. Fernández, M. Ortuño, A. Beléndez, and I. Pascual, “Characterization and optimization of liquid crystal displays for data storage applications,” Proc. SPIE 6587, 658715 (2007).
[Crossref]

A. Márquez, C. Neipp, A. Beléndez, S. Gallego, M. Ortuño, and I. Pascual, “Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings,” Opt. Lett. 28(17), 1510–1512 (2003).
[Crossref] [PubMed]

Osten, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

Parker, R. J.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Pascual, I.

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53, 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

A. Márquez, E. Fernández, F. J. Martínez, S. Gallego, M. Ortuño, A. Beléndez, and I. Pascual, “Analysis of the geometry of a holographic memory setup,” Proc. SPIE 8429, 84291Y (2012).
[Crossref]

E. Fernandez, A. Marquez, S. Gallego, R. Fuentes, C. García, and I. Pascual, “Hybrid ternary modulation applied to multiplexing holograms in photopolymers for data page storage,” J. Lightwave Technol. 28(5), 776–783 (2010).
[Crossref]

A. Márquez, S. Gallego, M. Ortuño, E. Fernández, M. L. Álvarez, A. Beléndez, and I. Pascual, “Generation of diffractive optical elements onto a photopolymer using a liquid crystal display,” Proc. SPIE 7717, 77170D (2010).
[Crossref]

E. Fernández, A. Márquez, M. Ortuño, R. Fuentes, C. García, and I. Pascual, “Optimization of twisted-nematic liquid crystal displays for holographic data storage,” Opt. Pura Apl. 42, 125–132 (2009).

S. Gallego, A. Márquez, S. Marini, E. Fernández, M. Ortuño, and I. Pascual, “In dark analysis of PVA/AA materials at very low spatial frequencies: phase modulation evolution and diffusion estimation,” Opt. Express 17(20), 18279–18291 (2009).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Alvarez, E. Fernández, M. Ortuño, C. Neipp, A. Beléndez, and I. Pascual, “Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories,” Opt. Lett. 32(17), 2511–2513 (2007).
[Crossref] [PubMed]

E. Fernández, M. Ortuño, S. Gallego, C. García, A. Beléndez, and I. Pascual, “Comparison of peristrophic multiplexing and a combination of angular and peristrophic holographic multiplexing in a thick PVA/acrylamide photopolymer for data storage,” Appl. Opt. 46(22), 5368–5373 (2007).
[Crossref] [PubMed]

A. Márquez, S. Gallego, D. Méndez, M. L. Álvarez, E. Fernández, M. Ortuño, A. Beléndez, and I. Pascual, “Characterization and optimization of liquid crystal displays for data storage applications,” Proc. SPIE 6587, 658715 (2007).
[Crossref]

A. Márquez, C. Neipp, A. Beléndez, S. Gallego, M. Ortuño, and I. Pascual, “Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings,” Opt. Lett. 28(17), 1510–1512 (2003).
[Crossref] [PubMed]

Sarid, D.

D. Sarid and B. H. Schechtman, “A roadmap for data storage applications,” Opt. Photonics News 18(5), 32–37 (2007).
[Crossref]

Schechtman, B. H.

D. Sarid and B. H. Schechtman, “A roadmap for data storage applications,” Opt. Photonics News 18(5), 32–37 (2007).
[Crossref]

Schnoes, M.

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

Schomberger, G.

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

Setthachayanon, S.

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

Sherif, H.

H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, “Characterisation of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing,” J. Opt. A, Pure Appl. Opt. 7(5), 255–260 (2005).
[Crossref]

Shimada, K.-I.

K.-I. Shimada, T. Ide, T. Shimano, K. Anderson, and K. Curtis, “New optical architecture for holographic data storage system compatible with Blu-ray Disc™ system,” Opt. Eng. 53(2), 025102 (2014).
[Crossref]

Shimano, T.

K.-I. Shimada, T. Ide, T. Shimano, K. Anderson, and K. Curtis, “New optical architecture for holographic data storage system compatible with Blu-ray Disc™ system,” Opt. Eng. 53(2), 025102 (2014).
[Crossref]

Shin, D. H.

Singh, K.

B. Das, J. Joseph, and K. Singh, “Material saturation in photopolymer holographic data recording and its effects on bit-error-rate and content-addressable search,” Opt. Commun. 282(2), 177–184 (2009).
[Crossref]

B. Das, J. Joseph, and K. Singh, “Phase modulated gray-scale data pages for digital holographic data storage,” Opt. Commun. 282(11), 2147–2154 (2009).
[Crossref]

B. Das, J. Joseph, and K. Singh, “Performance analysis of content-addressable search and bit-error rate characteristics of a defocused volume holographic data storage system,” Appl. Opt. 46(22), 5461–5470 (2007).
[Crossref] [PubMed]

Toal, V.

H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, “Characterisation of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing,” J. Opt. A, Pure Appl. Opt. 7(5), 255–260 (2005).
[Crossref]

Tsukamoto, Y.

Z. Ushiyama, H. Kurata, Y. Tsukamoto, S. Yoshida, and M. Yamamoto, “Shift-peristrophic multiplexing for high density holographic data storage,” Appl. Sci. 4(2), 148–157 (2014).
[Crossref]

Ushiyama, Z.

Z. Ushiyama, H. Kurata, Y. Tsukamoto, S. Yoshida, and M. Yamamoto, “Shift-peristrophic multiplexing for high density holographic data storage,” Appl. Sci. 4(2), 148–157 (2014).
[Crossref]

Van Heerden, P. J.

Waldman, D. A.

Wilkinson, T. D.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Wilson, W. L.

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

Xu, H.

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

Yamamoto, M.

Z. Ushiyama, H. Kurata, Y. Tsukamoto, S. Yoshida, and M. Yamamoto, “Shift-peristrophic multiplexing for high density holographic data storage,” Appl. Sci. 4(2), 148–157 (2014).
[Crossref]

Yoshida, S.

Z. Ushiyama, H. Kurata, Y. Tsukamoto, S. Yoshida, and M. Yamamoto, “Shift-peristrophic multiplexing for high density holographic data storage,” Appl. Sci. 4(2), 148–157 (2014).
[Crossref]

Yu, F. T. S.

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[Crossref]

Yzuel, M.

Zhang, Z.

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[Crossref]

Appl. Opt. (5)

Appl. Sci. (1)

Z. Ushiyama, H. Kurata, Y. Tsukamoto, S. Yoshida, and M. Yamamoto, “Shift-peristrophic multiplexing for high density holographic data storage,” Appl. Sci. 4(2), 148–157 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (1)

J. R. Moore, N. Collings, W. A. Crossland, A. B. Davey, M. Evans, A. M. Jeziorska, M. Komarčević, R. J. Parker, T. D. Wilkinson, and H. Xu, “The silicon backplane design for an LCOS polarization-insensitive phase hologram SLM,” IEEE Photonics Technol. Lett. 20(1), 60–62 (2008).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

H. Sherif, I. Naydenova, S. Martin, C. McGinn, and V. Toal, “Characterisation of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing,” J. Opt. A, Pure Appl. Opt. 7(5), 255–260 (2005).
[Crossref]

Opt. Commun. (2)

B. Das, J. Joseph, and K. Singh, “Phase modulated gray-scale data pages for digital holographic data storage,” Opt. Commun. 282(11), 2147–2154 (2009).
[Crossref]

B. Das, J. Joseph, and K. Singh, “Material saturation in photopolymer holographic data recording and its effects on bit-error-rate and content-addressable search,” Opt. Commun. 282(2), 177–184 (2009).
[Crossref]

Opt. Eng. (3)

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53, 067104 (2014).
[Crossref]

K.-I. Shimada, T. Ide, T. Shimano, K. Anderson, and K. Curtis, “New optical architecture for holographic data storage system compatible with Blu-ray Disc™ system,” Opt. Eng. 53(2), 025102 (2014).
[Crossref]

Z. Zhang, G. Lu, and F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal television,” Opt. Eng. 33(9), 3018–3022 (1994).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Opt. Photonics News (1)

D. Sarid and B. H. Schechtman, “A roadmap for data storage applications,” Opt. Photonics News 18(5), 32–37 (2007).
[Crossref]

Opt. Pura Apl. (1)

E. Fernández, A. Márquez, M. Ortuño, R. Fuentes, C. García, and I. Pascual, “Optimization of twisted-nematic liquid crystal displays for holographic data storage,” Opt. Pura Apl. 42, 125–132 (2009).

Proc. SPIE (6)

M. J. O’Callaghan, “Sorting through the lore of phase mask options - performance measures and practical commercial designs,” Proc. SPIE 5362, 159 (2004).

A. Márquez, E. Fernández, F. J. Martínez, S. Gallego, M. Ortuño, A. Beléndez, and I. Pascual, “Analysis of the geometry of a holographic memory setup,” Proc. SPIE 8429, 84291Y (2012).
[Crossref]

M. Schnoes, B. Ihas, A. Hill, L. Dhar, D. Michaels, S. Setthachayanon, G. Schomberger, and W. L. Wilson, “Holographic data storage media for practical systems,” Proc. SPIE 5005, 29–37 (2003).
[Crossref]

A. Márquez, S. Gallego, D. Méndez, M. L. Álvarez, E. Fernández, M. Ortuño, A. Beléndez, and I. Pascual, “Characterization and optimization of liquid crystal displays for data storage applications,” Proc. SPIE 6587, 658715 (2007).
[Crossref]

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystalbased micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

A. Márquez, S. Gallego, M. Ortuño, E. Fernández, M. L. Álvarez, A. Beléndez, and I. Pascual, “Generation of diffractive optical elements onto a photopolymer using a liquid crystal display,” Proc. SPIE 7717, 77170D (2010).
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K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, eds., Holographic Data Storage: From Theory to Practical Systems (John Wiley & Sons, Ltd., 2010).

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Figures (13)

Fig. 1
Fig. 1 Scheme for the experimental setup we model in this work where the various elements and also the names for the magnitudes and variables are introduced.
Fig. 2
Fig. 2 Calculated values for the average retardance and the fluctuation amplitude for λ = 532nm, at an angle of incidence of 11.5°, for sequence 5-5 with configuration voltages (Vbright = 2.02V, Vdark = 1.11V) for BIM (continuous) and (Vbright = 3.82V, Vdark = 0.03V) for HTM (dashed).
Fig. 3
Fig. 3 Simulation for BIM. (a) Intensity transmission and phase-shift; (b) Phasor evolution in the complex plane. Input and output polarizers at + 45° with respect to the X-axis (lab vertical).
Fig. 4
Fig. 4 Simulation for pHTM. (a) Intensity transmission and phase-shift; (b) Phasor evolution in the complex plane. Input and output polarizers at + 55° and −45° with respect to the X-axis.
Fig. 5
Fig. 5 Diagram for the experimental HDSS testing platform. System described in the text.
Fig. 6
Fig. 6 Fourier plane where the limiting stop is double the length of the Nyquist radius, which is 512 pixels. (a) Image plane; (b) Radial cut across a diameter crossing the center of the Fourier plane. The representation is logarithmic. We have considered a 128x128 bits BIM data page.
Fig. 7
Fig. 7 Simulation for BIM and for 128x128 bits data page. (a) Homogeneity in the recording plane; (b) Q-factor and (c) BER, to evaluate the quality of the reconstruction. In the legend, size of the Nyquist aperture in Nyquist radius units.
Fig. 8
Fig. 8 Simulation for ideal HTM and for 128x128 bits data page. (a) Homogeneity in the recording plane; (b) Q-factor and (c) BER, to evaluate the quality of the reconstruction. In the legend, size of the Nyquist aperture in Nyquist radius units.
Fig. 9
Fig. 9 Simulation for pHTM and for 128x128 bits data page. (a) Homogeneity in the recording plane; (b) Q-factor and (c) BER, to evaluate the quality of the reconstruction. In the legend, size of the Nyquist aperture in Nyquist radius units.
Fig. 10
Fig. 10 Experimental results BIM data page and no material. (a) Data page; (b) Histograms.
Fig. 11
Fig. 11 Experimental results BIM data page and PVA/AA. (a) Data page; (b) Histograms.
Fig. 12
Fig. 12 Experimental results pHTM data page and no material. (a) Data page; (b) Histogram.
Fig. 13
Fig. 13 Experimental results pHTM data page and PVA/AA. (a) Data page; (b) Histogram.

Equations (31)

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f 3 ( x 3 , y 3 )= ψ( x 1 , y 1 ; Z 1 ) ψ * ( x 1 , y 1 ; F 1 ) ( x 2 , y 2 ; Z 2 ) f( x 2 , y 2 ) ψ( x 3 , y 3 ; Z 3 ).
f 3 ( x 3 , y 3 )= ψ( x 3 , y 3 ;Z ' 3 ) P2 ψ( x 2 , y 2 ; Z 2 +Z ' 3 Z 2 2 Z 1 + Z 2 F 1 )f( x 2 , y 2 )exp( j2π λ( z 3 +Δz ) ( x 3 x 2 + y 3 y 2 ) )d x 2 d y 2
exp( j πΔz R 2 λ z 3 2 ( x N2 2 + y N2 2 ) )=exp( j2π W 20 ( x N2 2 + y N2 2 ) )
W 20 = Δz ( NA ) 2 / 2λ
f 3 ( x 3 , y 3 )=ψ( x 3 , y 3 ;Z ' 3 )FT [ exp( j2π W 20 ( x N2 2 + y N2 2 ) )f( R x N2 ,R y N2 ) ] u= R x 3 λ( z 3 +Δz ) ,v= R y 3 λ( z 3 +Δz )
f 5 ( x 5 , y 5 )= f 3 ( x 3 , y 3 ) P 3 ( x 3 , y 3 )ψ( x 4 , y 4 ; Z 4 ) ψ * ( x 4 , y 4 ; F 4 ) ψ( x 5 , y 5 ; Z 5 )
Z 3 + Z 4 ( Z 4 2 / ( Z 4 + Z 5 F 2 ) )=0
f 5 ( x 5 , y 5 )=ψ( x 5 , y 5 ; Z 5 Z 5 2 Z 4 + Z 5 F 2 ) { ψ * ( λu Z ' 3 , λv Z ' 3 ;Δz Z 3 2 )f( λu Z ' 3 , λv Z ' 3 ) P 3 ( u,v ) } u,v
u= Z 4 Z 5 x 5 λ( Z 4 + Z 5 F 2 ) ,v= Z 4 Z 5 y 5 λ( Z 4 + Z 5 F 2 )
f 5 ( x 5 , y 5 )=f ( λu Z ' 3 , λv Z ' 3 ) u,v
P X =( 1 0 0 0 )
W( ϕ )=( exp( jϕ/2 ) 0 0 exp( +jϕ/2 ) )
R( θ )=( cosθ sinθ sinθ cosθ )
E OUT = P X R( θ 2 )( 1 0 0 1 ) W PA ( Γ ¯ )( cos θ 1 sin θ 1 )
Q= | μ 1 μ 0 | σ 1 + σ 0
R DCterm =10 log 10 ( I DC / I avrg )
h(x,y) = e jkz jλz exp( j k 2z ( x 2 + y 2 ) ).
t L (x,y) = exp( j π λf ( x 2 + y 2 ) )
ψ( x,y;Z= 1 z )exp( j πZ λ ( x 2 + y 2 ) )
h(x,y) = e jkz jλ Zψ(x,y;Z)
t L (x,y)=ψ(x,y;F)
1 ) ψ(x,y;Z)= ψ * (x,y;Z)
2º) ψ(x,y;Z) = ψ(x,y;Z)
3º) ψ(x,y; Z 1 ) ψ(x,y; Z 2 ) = ψ(x,y; Z 1 + Z 2 )
4º) ψ(x,y; Z 1 ) ψ * (x,y; Z 2 ) = ψ(x,y; Z 1 Z 2 )= ψ * (x,y; Z 2 Z 1 )
5º) ψ(cx,cy;Z) = ψ(x,y; c 2 Z)
6º) ψ(xu,yv;Z) = ψ(u,v;Z)ψ(x,y;Z)exp( j 2π λz ( ux+vy ) )
7º) lim Z0 ψ * (x,y;Z) = 1
8º) lim Z Zψ(x,y;Z) = δ( x,y )
9º) + + ψ(x,y; Z 1 ) exp( j 2π λ z 2 ( ux+vy ) ) dxdy= jλ Z 1 ψ * (u,v; Z 2 2 Z 1 ) ,
+ + ψ * (x,y; Z 1 ) exp( j 2π λ z 2 ( ux+vy ) ) dxdy= jλ Z 1 ψ(u,v; Z 2 2 Z 1 )

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