Abstract

Whether in art or for QR codes, images have proven to be both powerful and efficient carriers of information. Spatial light modulators allow an unprecedented level of control over the generation of optical fields by using digital holograms. There is no unique way of obtaining a desired light pattern however, leaving many competing methods for hologram generation. In this paper, we test six hologram generation techniques in the creation of a variety of modes as well as a photographic image: rating the methods according to obtained mode quality and power. All techniques compensate for a non-uniform mode profile of the input laser and incorporate amplitude scaling. We find that all methods perform well and stress the importance of appropriate spatial filtering. We expect these results to be of interest to those working in the contexts of microscopy, optical trapping or quantum image creation.

© 2016 Optical Society of America

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References

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    [Crossref]

2015 (4)

C. Alpmann, C. Schöler, and C. Denz, “Elegant Gaussian beams for enhanced optical manipulation,” Appl. Phys. Lett. 106, 241102 (2015).
[Crossref]

D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
[Crossref]

R. Liu, D. B. Phillips, F. Li, M. D. Williams, D. L. Andrews, and M. J. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 45608 (2015).
[Crossref]

R. Liu, F. Li, M. J. Padgett, and D. B. Phillips, “Generalized photon sieves: fine control of complex fields with simple pinhole arrays,” Optica 2, 1028–1036 (2015).
[Crossref]

2014 (3)

2013 (6)

N. Radwell, G. Walker, and S. Franke-Arnold, “Cold-atom densities of more than 10 12 cm3 in a holographically shaped dark spontaneous-force optical trap,” Phys. Rev. A 88, 043409 (2013).
[Crossref]

J. Albero, P. García-Martínez, J. L. Martínez, and I. Moreno, “Second order diffractive optical elements in a spatial light modulator with large phase dynamic range,” Opt. Laser. Eng. 51, 111–115 (2013).
[Crossref]

T. Sarkadi, Á. Kettinger, and P. Koppa, “Spatial filters for complex wavefront modulation,” Appl. Optics 52, 5449–5454 (2013).
[Crossref]

A. S. Ostrovsky, C. Rickenstorff-Parrao, and V. Arrizón, “Generation of the perfect optical vortex using a liquid-crystal spatial light modulator,” Opt. Lett. 38, 534–536 (2013).
[Crossref] [PubMed]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38, 3546–3549 (2013).
[Crossref] [PubMed]

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21, 23068–23074 (2013).
[Crossref] [PubMed]

2011 (1)

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. 2011, 14008 (2011).
[Crossref]

2010 (2)

M. Mestre, F. Diry, B. V. de Lesegno, and L. Pruvost, “Cold atom guidance by a holographically-generated Laguerre-Gaussian laser mode,” Eur. Phys. J. D 57, 87–94 (2010).
[Crossref]

R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based Shack–Hartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt. 12, 124004 (2010).
[Crossref]

2009 (2)

2008 (1)

Q. Huynh-Thu and M. Ghanbari, “Scope of validity of PSNR in image/video quality assessment,” Electron. Lett. 44, 800–801 (2008).
[Crossref]

2007 (3)

2003 (1)

2000 (1)

L. Allen and M. J. Padgett, “The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
[Crossref]

1999 (1)

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Optics 38, 5004–5013 (1999).
[Crossref]

1997 (1)

G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Optics 36, 1517–1524 (1997).
[Crossref]

1996 (1)

1994 (1)

R. W. Cohn and M. Liang, “Approximating fully complex spatial modulation with pseudorandom phase-only modulation,” Appl. Optics 33, 4406–4415 (1994).
[Crossref]

1978 (1)

C. K. Hsueh and A. A. Sawchuk, “Computer-generated double-phase holograms,” Appl. Optics 17, 3874–3883 (1978).
[Crossref]

1971 (1)

J. P. Kirk and A. L. Jones, “Phase-only complex-valued spatial filter,” JOSA 61, 1023–1028 (1971).
[Crossref]

1967 (1)

M. P. Givens, “Introduction to holography,” Am. J. Phys 35, 1056–1064 (1967).
[Crossref]

Albero, J.

J. Albero, P. García-Martínez, J. L. Martínez, and I. Moreno, “Second order diffractive optical elements in a spatial light modulator with large phase dynamic range,” Opt. Laser. Eng. 51, 111–115 (2013).
[Crossref]

Allen, L.

L. Allen and M. J. Padgett, “The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
[Crossref]

Alpmann, C.

C. Alpmann, C. Schöler, and C. Denz, “Elegant Gaussian beams for enhanced optical manipulation,” Appl. Phys. Lett. 106, 241102 (2015).
[Crossref]

Ando, T.

Andrews, D. L.

R. Liu, D. B. Phillips, F. Li, M. D. Williams, D. L. Andrews, and M. J. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 45608 (2015).
[Crossref]

Apolinar-Iribe, A.

Arias, A.

J. Varga, A. Solís-Prosser, L. Rebón, A. Arias, L. Neves, C. Iemmi, and S. Ledesma, “Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator,” in Vol. 605 of Journal of Physics: Conference Series, (IOP Publishing, 2015), p. 012035.

Arnold, A. S.

Arrizón, V.

Bent, N.

Bolduc, E.

Bowman, R.

Bowman, R. W.

R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based Shack–Hartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt. 12, 124004 (2010).
[Crossref]

Boyd, R. W.

Bruce, G. D.

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. 2011, 14008 (2011).
[Crossref]

Campos, J.

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Optics 38, 5004–5013 (1999).
[Crossref]

Carrada, R.

V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A. 24, 3500–3507 (2007).
[Crossref]

Cassettari, D.

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. 2011, 14008 (2011).
[Crossref]

Cohn, R. W.

R. W. Cohn and M. Liang, “Approximating fully complex spatial modulation with pseudorandom phase-only modulation,” Appl. Optics 33, 4406–4415 (1994).
[Crossref]

Cottrell, D. M.

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Optics 38, 5004–5013 (1999).
[Crossref]

Davis, J. A.

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Optics 38, 5004–5013 (1999).
[Crossref]

de Lesegno, B. V.

M. Mestre, F. Diry, B. V. de Lesegno, and L. Pruvost, “Cold atom guidance by a holographically-generated Laguerre-Gaussian laser mode,” Eur. Phys. J. D 57, 87–94 (2010).
[Crossref]

Denz, C.

C. Alpmann, C. Schöler, and C. Denz, “Elegant Gaussian beams for enhanced optical manipulation,” Appl. Phys. Lett. 106, 241102 (2015).
[Crossref]

Ding, D.-S.

D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
[Crossref]

Diry, F.

M. Mestre, F. Diry, B. V. de Lesegno, and L. Pruvost, “Cold atom guidance by a holographically-generated Laguerre-Gaussian laser mode,” Eur. Phys. J. D 57, 87–94 (2010).
[Crossref]

Edgar, M. P.

Ellinas, D.

Erdei, G.

Franke-Arnold, S.

N. Radwell, G. Walker, and S. Franke-Arnold, “Cold-atom densities of more than 10 12 cm3 in a holographically shaped dark spontaneous-force optical trap,” Phys. Rev. A 88, 043409 (2013).
[Crossref]

S. Franke-Arnold, J. Leach, M. J. Padgett, V. E. Lembessis, D. Ellinas, A. J. Wright, J. M. Girkin, P. Ohberg, and A. S. Arnold, “Optical ferris wheel for ultracold atoms,” Opt. Express 15, 8619–8625 (2007).
[Crossref] [PubMed]

Fukuchi, N.

Gabor, D.

D. Gabor, “Microscopy by reconstructed wave-fronts,” in Vol. 197 of Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, (The Royal Society, 1949), pp. 454–487.

García-Martínez, P.

J. Albero, P. García-Martínez, J. L. Martínez, and I. Moreno, “Second order diffractive optical elements in a spatial light modulator with large phase dynamic range,” Opt. Laser. Eng. 51, 111–115 (2013).
[Crossref]

Ghanbari, M.

Q. Huynh-Thu and M. Ghanbari, “Scope of validity of PSNR in image/video quality assessment,” Electron. Lett. 44, 800–801 (2008).
[Crossref]

Giacobino, E.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photon. 8, 234–238 (2014).
[Crossref]

Gibson, G. M.

Giner, L.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photon. 8, 234–238 (2014).
[Crossref]

Girkin, J. M.

Givens, M. P.

M. P. Givens, “Introduction to holography,” Am. J. Phys 35, 1056–1064 (1967).
[Crossref]

González, L. A.

V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A. 24, 3500–3507 (2007).
[Crossref]

Göröcs, Z.

Guo, G.-C.

D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
[Crossref]

Hsueh, C. K.

C. K. Hsueh and A. A. Sawchuk, “Computer-generated double-phase holograms,” Appl. Optics 17, 3874–3883 (1978).
[Crossref]

Huynh-Thu, Q.

Q. Huynh-Thu and M. Ghanbari, “Scope of validity of PSNR in image/video quality assessment,” Electron. Lett. 44, 800–801 (2008).
[Crossref]

Iemmi, C.

J. Varga, A. Solís-Prosser, L. Rebón, A. Arias, L. Neves, C. Iemmi, and S. Ledesma, “Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator,” in Vol. 605 of Journal of Physics: Conference Series, (IOP Publishing, 2015), p. 012035.

Inoue, T.

Jiang, Y.-K.

D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
[Crossref]

Jonathan, P.

Jones, A. L.

J. P. Kirk and A. L. Jones, “Phase-only complex-valued spatial filter,” JOSA 61, 1023–1028 (1971).
[Crossref]

Karimi, E.

Kettinger, Á.

T. Sarkadi, Á. Kettinger, and P. Koppa, “Spatial filters for complex wavefront modulation,” Appl. Optics 52, 5449–5454 (2013).
[Crossref]

Kirk, J. P.

J. P. Kirk and A. L. Jones, “Phase-only complex-valued spatial filter,” JOSA 61, 1023–1028 (1971).
[Crossref]

Koppa, P.

Lancis, J.

Laurat, J.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photon. 8, 234–238 (2014).
[Crossref]

Leach, J.

Ledesma, S.

J. Varga, A. Solís-Prosser, L. Rebón, A. Arias, L. Neves, C. Iemmi, and S. Ledesma, “Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator,” in Vol. 605 of Journal of Physics: Conference Series, (IOP Publishing, 2015), p. 012035.

Lembessis, V. E.

Li, F.

R. Liu, F. Li, M. J. Padgett, and D. B. Phillips, “Generalized photon sieves: fine control of complex fields with simple pinhole arrays,” Optica 2, 1028–1036 (2015).
[Crossref]

R. Liu, D. B. Phillips, F. Li, M. D. Williams, D. L. Andrews, and M. J. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 45608 (2015).
[Crossref]

Liang, M.

R. W. Cohn and M. Liang, “Approximating fully complex spatial modulation with pseudorandom phase-only modulation,” Appl. Optics 33, 4406–4415 (1994).
[Crossref]

Liu, R.

R. Liu, D. B. Phillips, F. Li, M. D. Williams, D. L. Andrews, and M. J. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 45608 (2015).
[Crossref]

R. Liu, F. Li, M. J. Padgett, and D. B. Phillips, “Generalized photon sieves: fine control of complex fields with simple pinhole arrays,” Optica 2, 1028–1036 (2015).
[Crossref]

Lorincz, E.

Love, G. D.

G. D. Love, “Wave-front correction and production of Zernike modes with a liquid-crystal spatial light modulator,” Appl. Optics 36, 1517–1524 (1997).
[Crossref]

Martínez, J. L.

J. Albero, P. García-Martínez, J. L. Martínez, and I. Moreno, “Second order diffractive optical elements in a spatial light modulator with large phase dynamic range,” Opt. Laser. Eng. 51, 111–115 (2013).
[Crossref]

Matsumoto, N.

Maxein, D.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photon. 8, 234–238 (2014).
[Crossref]

Mayoh, J.

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. 2011, 14008 (2011).
[Crossref]

Mendez, G.

Mendoza-Yero, O.

Mestre, M.

M. Mestre, F. Diry, B. V. de Lesegno, and L. Pruvost, “Cold atom guidance by a holographically-generated Laguerre-Gaussian laser mode,” Eur. Phys. J. D 57, 87–94 (2010).
[Crossref]

Mínguez-Vega, G.

Mitchell, K. J.

Moreno, I.

J. Albero, P. García-Martínez, J. L. Martínez, and I. Moreno, “Second order diffractive optical elements in a spatial light modulator with large phase dynamic range,” Opt. Laser. Eng. 51, 111–115 (2013).
[Crossref]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Optics 38, 5004–5013 (1999).
[Crossref]

Neto, L. G.

Neves, L.

J. Varga, A. Solís-Prosser, L. Rebón, A. Arias, L. Neves, C. Iemmi, and S. Ledesma, “Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator,” in Vol. 605 of Journal of Physics: Conference Series, (IOP Publishing, 2015), p. 012035.

Nicolas, A.

A. Nicolas, L. Veissier, L. Giner, E. Giacobino, D. Maxein, and J. Laurat, “A quantum memory for orbital angular momentum photonic qubits,” Nat. Photon. 8, 234–238 (2014).
[Crossref]

Ohberg, P.

Ohtake, Y.

Ostrovsky, A. S.

Padgett, M. J.

Phillips, D. B.

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N. Radwell, G. Walker, and S. Franke-Arnold, “Cold-atom densities of more than 10 12 cm3 in a holographically shaped dark spontaneous-force optical trap,” Phys. Rev. A 88, 043409 (2013).
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J. Varga, A. Solís-Prosser, L. Rebón, A. Arias, L. Neves, C. Iemmi, and S. Ledesma, “Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator,” in Vol. 605 of Journal of Physics: Conference Series, (IOP Publishing, 2015), p. 012035.

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C. K. Hsueh and A. A. Sawchuk, “Computer-generated double-phase holograms,” Appl. Optics 17, 3874–3883 (1978).
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C. Alpmann, C. Schöler, and C. Denz, “Elegant Gaussian beams for enhanced optical manipulation,” Appl. Phys. Lett. 106, 241102 (2015).
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Shi, B.-S.

D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
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D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
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G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. 2011, 14008 (2011).
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D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
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R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based Shack–Hartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt. 12, 124004 (2010).
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D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
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D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
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L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep.4 (2014).
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C. K. Hsueh and A. A. Sawchuk, “Computer-generated double-phase holograms,” Appl. Optics 17, 3874–3883 (1978).
[Crossref]

Appl. Phys. Lett. (1)

C. Alpmann, C. Schöler, and C. Denz, “Elegant Gaussian beams for enhanced optical manipulation,” Appl. Phys. Lett. 106, 241102 (2015).
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Q. Huynh-Thu and M. Ghanbari, “Scope of validity of PSNR in image/video quality assessment,” Electron. Lett. 44, 800–801 (2008).
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M. Mestre, F. Diry, B. V. de Lesegno, and L. Pruvost, “Cold atom guidance by a holographically-generated Laguerre-Gaussian laser mode,” Eur. Phys. J. D 57, 87–94 (2010).
[Crossref]

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R. Liu, D. B. Phillips, F. Li, M. D. Williams, D. L. Andrews, and M. J. Padgett, “Discrete emitters as a source of orbital angular momentum,” J. Opt. 17, 45608 (2015).
[Crossref]

R. W. Bowman, A. J. Wright, and M. J. Padgett, “An SLM-based Shack–Hartmann wavefront sensor for aberration correction in optical tweezers,” J. Opt. 12, 124004 (2010).
[Crossref]

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V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A. 24, 3500–3507 (2007).
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Optica (2)

Phys. Rev. A (1)

N. Radwell, G. Walker, and S. Franke-Arnold, “Cold-atom densities of more than 10 12 cm3 in a holographically shaped dark spontaneous-force optical trap,” Phys. Rev. A 88, 043409 (2013).
[Crossref]

Phys. Rev. Lett. (1)

D.-S. Ding, W. Zhang, Z.-Y. Zhou, S. Shi, G.-Y. Xiang, X.-S. Wang, Y.-K. Jiang, B.-S. Shi, and G.-C. Guo, “Quantum storage of orbital angular momentum entanglement in an atomic ensemble,” Phys. Rev. Lett. 114, 50502 (2015).
[Crossref]

Phys. Scr. (1)

G. D. Bruce, J. Mayoh, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “A smooth, holographically generated ring trap for the investigation of superfluidity in ultracold atoms,” Phys. Scr. 2011, 14008 (2011).
[Crossref]

Other (3)

L. Zhu and J. Wang, “Arbitrary manipulation of spatial amplitude and phase using phase-only spatial light modulators,” Sci. Rep.4 (2014).
[Crossref]

D. Gabor, “Microscopy by reconstructed wave-fronts,” in Vol. 197 of Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, (The Royal Society, 1949), pp. 454–487.

J. Varga, A. Solís-Prosser, L. Rebón, A. Arias, L. Neves, C. Iemmi, and S. Ledesma, “Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator,” in Vol. 605 of Journal of Physics: Conference Series, (IOP Publishing, 2015), p. 012035.

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Figures (10)

Fig. 1
Fig. 1

A fibre-coupled 776 nm laser (with 4.9 µm 1/e2 mode field diameter) is first expanded to a waist of 4.65 mm before illuminating the centre of the SLM, where the inset highlights the axes and wavevectors of interest. The output beam is then Fourier filtered before being imaged at one of three propagation distances.

Fig. 2
Fig. 2

(a) Desired intensity of a Laguerre-Gaussian superposition mode. (b) Experimentally realised intensity after propagation by 1 Rayleigh range when only the phase is controlled.

Fig. 3
Fig. 3

(a) Intensity and phase (inset) of the input Gaussian beam. (b) Intensity and phase (inset) of the desired beam (here shown for an ’optical Ferris wheel’ beam). (c) Hologram generated using method A, where the 8-bit greyscale is converted to phase by the SLM. (d) Intensity and phase (inset) of the beam generated by the input beam in (a) and the hologram in (c). The phase insets use phase ranges from −π to π periodically (red to red on a standard colour wheel). (e) Numerical evalution of the mode quality for the six different hologram generation methods, shown for imaging plane (0.0zR) and further propagation by half (0.5zR) and a full Rayleigh range (1.0zR).

Fig. 4
Fig. 4

An overview of the measured beam intensities for an optical Ferris wheel shaped according to each hologram generation method (horizontal) and propagation distance (vertical) respectively. The first row shows the simulated prediction for each method and the first column indicates the desired field intensity for 0.0, 0.5 and 1.0 Rayleigh ranges.

Fig. 5
Fig. 5

An overview of the measured beam intensities for a fundamental Gaussian, an LG10 and an arbitrary image according to each hologram generation method. The first column indicates the desired pattern, the first and middle row show the measured beam after one Rayleigh range of propagation and the bottom row shows an arbitrary scene in the image plane of the SLM.

Fig. 6
Fig. 6

An estimation of the constructed field quality, as determined by the peak signal-to-noise ratio for the three propagating modes and the arbitrary pattern.

Fig. 7
Fig. 7

The variation in mode efficiency across the different hologram generation methods, as measured for different propagation distances of an optical Ferris wheel. The total power after the spatial filter for each method is scaled by the associated cross-correlation between each mode and its fit, before being expressed as a percentage of the measured input power of 26.4 mW.

Fig. 8
Fig. 8

(a) The Ferris wheel PSNR and total power as the size of the spatial filter is adjusted, where the red bars highlight the data points that have been visualised in (c). (b) The full far- and near-field intensity profiles associated with filter size 0.6 mm where the red dashed box indicates the sub-region used in the left column of (c). (c) Far- and near-field intensity profiles associated with the filter sizes marked in pink in (a), with the filter boundary marked with a white circle.

Fig. 9
Fig. 9

The intensity profile of the beam taken at the focus of a 750 mm focal length lens for (a) the beam before the SLM and (b) the beam after the SLM. (c) shows the beam after the SLM when a cylindrical lens of focal length 11 m at an angle of 96 degrees to the vertical is added to the hologram.

Fig. 10
Fig. 10

(a) The PSNR and associated beam power of the simulated Ferris wheels with respect to the intensity threshold level. Four key threshold levels are highlighted by a red bar, corresponding to the images in (b). (b) 2D intensity profiles and central cross sections of the assumed input beam (grey) and the generated beam (blue).

Equations (19)

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

E in ( x , y ) e i k in r ^ × e iH ( x , y ) = E des ( x , y ) e i k des r ^
e i H ( x , y ) = E des ( x , y ) E in ( x , y ) e i ( k des k in ) r ^ = A rel ( x , y ) e i Φ relg ( x , y )
Φ g ( x , y ) = Mod ( 2 π x Λ , 2 π ) ,
H ( x , y ) = Φ relg ( x , y ) .
H ( x , y ) = f ( A ( x , y ) ) Φ relg ( x , y ) .
H ( x , y ) = A rel ( x , y ) Φ relg ( x , y ) .
H ( x , y ) = arg ( N E dg ( x , y ) + E in ( x , y ) )
A = e i ( 1 f ( A ( x , y ) ) ) π sinc [ π ( 1 f ( A ( x , y ) ) ) ]
f ( A ( x , y ) ) = 1 1 π sinc 1 ( A )
H ( x , y ) = ( 1 1 π sinc 1 ( A rel ( x , y ) ) ) Φ relg ( x , y ) .
H ( x , y ) = M ( Φ relg ( x , y ) π M ) , where
M = 1 + 1 π sinc 1 ( A rel ( x , y ) ) .
H ( x , y ) = Φ relg ( x , y ) + f ( A rel ( x , y ) ) sin ( Φ relg ( x , y ) ) .
J 0 [ f ( A rel ( x , y ) ) ] = A rel ( x , y )
H ( x , y ) = f ( A rel ( x , y ) ) ] sin ( Φ relg ( x , y ) )
J 1 [ f ( A rel ( x , y ) ) ] = a A rel ( x , y ) .
E out ( x , y ) = E in ( x , y ) e i H ( x , y ) .
M S E = 1 m n i = 0 m 1 j = 0 n 1 [ I ( i , j ) K ( i , j ) ] 2
P S N R = 10 log 10 ( M A X I 2 M S E )

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