Abstract

Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex formation during hologram calculation. We demonstrate the implementation of the conjugate gradient method for both discrete and continuous intensity distributions and discuss its applicability to optical trapping of ultracold atoms.

© 2014 Optical Society of America

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References

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2014 (1)

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

2013 (1)

2012 (3)

C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, and A. Kuhn, “Control and manipulation of cold atoms in optical tweezers,” New J. Phys. 14, 073051 (2012).
[Crossref]

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[Crossref]

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep. 2, 721 (2012).
[Crossref] [PubMed]

2011 (4)

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A 84, 053410 (2011).
[Crossref]

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. T143, 014008 (2011).
[Crossref]

B. Zimmermann, T. Müller, J. Meineke, T. Esslinger, and H. Moritz, “High-resolution imaging of ultracold fermions in microscopically tailored optical potentials,” New J. Phys. 13, 043007 (2011).
[Crossref]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

2009 (2)

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys. 11, 043030 (2009).
[Crossref]

2008 (2)

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B 41, 211001 (2008).
[Crossref]

M. Pasienski and B. DeMarco, “A high-accuracy algorithm for designing arbitrary holographic atom traps,” Opt. Express 16, 2176–2190 (2008).
[Crossref] [PubMed]

2006 (3)

N. Masuda, T. Ito, T. Tanaka, A. Shiraki, and T. Sugie, “Computer generated holography using a graphics processing unit,” Opt. Express 14, 603–608 (2006).
[Crossref] [PubMed]

M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[Crossref]

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

2005 (1)

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser Eng. 43, 43–56 (2005).
[Crossref]

2004 (3)

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z. J. Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51, 2235–2240 (2004).
[Crossref]

J. R. Hui, X. Wu, and C. Warde, “Addressing large arrays of electrostatic actuators for adaptive optics applications,” Proc. SPIE 5553, 17–27 (2004).
[Crossref]

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B 21, 1889–1894 (2004).
[Crossref]

2003 (2)

2002 (1)

J. Fortágh, H. Ott, S. Kraft, A. Günther, and C. Zimmermann, “Surface effects in magnetic microtraps,” Phys. Rev. A 66, 041604 (2002).
[Crossref]

2001 (1)

2000 (2)

G. Zhou, X. Yuan, P. Dowd, Y.-L. Lam, and Y.-C. Chan, “Efficient method for evaluation of the diffraction efficiency upper bound of diffractive phase elements,” Opt. Lett. 25, 1288–1290 (2000).
[Crossref]

M. Johansson and J. Bengtsson, “Robust design method for highly efficient beam-shaping diffractive optical elements using an iterative-fourier-transform algorithm with soft operations,” J. Mod. Opt. 47, 1385–1398 (2000).
[Crossref]

1998 (3)

1996 (1)

M. Clark and R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150–164 (1996).
[Crossref]

1992 (1)

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]

Allan, D. C.

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]

Arias, T. A.

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]

Arnold, A. S.

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B 41, 211001 (2008).
[Crossref]

Barredo, D.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

Béguin, L.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

Bengtsson, J.

M. Johansson and J. Bengtsson, “Robust design method for highly efficient beam-shaping diffractive optical elements using an iterative-fourier-transform algorithm with soft operations,” J. Mod. Opt. 47, 1385–1398 (2000).
[Crossref]

Bergamini, S.

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Bloch, I.

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[Crossref]

Bonnin, A.

Boshier, M. G.

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys. 11, 043030 (2009).
[Crossref]

Boyer, V.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z. J. Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51, 2235–2240 (2004).
[Crossref]

Brainis, E.

C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, and A. Kuhn, “Control and manipulation of cold atoms in optical tweezers,” New J. Phys. 14, 073051 (2012).
[Crossref]

Brandt, L.

C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, and A. Kuhn, “Control and manipulation of cold atoms in optical tweezers,” New J. Phys. 14, 073051 (2012).
[Crossref]

Bromley, S. L.

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A 84, 053410 (2011).
[Crossref]

Browaeys, A.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

S. Bergamini, B. Darquié, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B 21, 1889–1894 (2004).
[Crossref]

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. T143, 014008 (2011).
[Crossref]

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A 84, 053410 (2011).
[Crossref]

Cassettari, D.

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A 84, 053410 (2011).
[Crossref]

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. T143, 014008 (2011).
[Crossref]

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

Chan, Y.-C.

Chandrashekar, C. M.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z. J. Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51, 2235–2240 (2004).
[Crossref]

Clark, M.

M. Clark and R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150–164 (1996).
[Crossref]

Cronin, A. D.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

Dalibard, J.

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[Crossref]

Darquié, B.

Deb, A. B.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

DeMarco, B.

Dholakia, K.

Dong, B.-Z.

Dong, J.

C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, and A. Kuhn, “Control and manipulation of cold atoms in optical tweezers,” New J. Phys. 14, 073051 (2012).
[Crossref]

Dowd, P.

Esslinger, T.

B. Zimmermann, T. Müller, J. Meineke, T. Esslinger, and H. Moritz, “High-resolution imaging of ultracold fermions in microscopically tailored optical potentials,” New J. Phys. 13, 043007 (2011).
[Crossref]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1987).

Foot, C.

Foot, C. J.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z. J. Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51, 2235–2240 (2004).
[Crossref]

Fortágh, J.

J. Fortágh, H. Ott, S. Kraft, A. Günther, and C. Zimmermann, “Surface effects in magnetic microtraps,” Phys. Rev. A 66, 041604 (2002).
[Crossref]

Gaunt, A. L.

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep. 2, 721 (2012).
[Crossref] [PubMed]

Godun, R. M.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

Grangier, P.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

Gu, B.-Y.

Günther, A.

J. Fortágh, H. Ott, S. Kraft, A. Günther, and C. Zimmermann, “Surface effects in magnetic microtraps,” Phys. Rev. A 66, 041604 (2002).
[Crossref]

Hadzibabic, Z.

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep. 2, 721 (2012).
[Crossref] [PubMed]

Harte, T.

Henderson, K.

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys. 11, 043030 (2009).
[Crossref]

Himsworth, M.

C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, and A. Kuhn, “Control and manipulation of cold atoms in optical tweezers,” New J. Phys. 14, 073051 (2012).
[Crossref]

Houston, N.

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B 41, 211001 (2008).
[Crossref]

Hui, J. R.

J. R. Hui, X. Wu, and C. Warde, “Addressing large arrays of electrostatic actuators for adaptive optics applications,” Proc. SPIE 5553, 17–27 (2004).
[Crossref]

Ito, T.

Jacubowiez, L.

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Joannopoulos, J. D.

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]

Johansson, M.

M. Johansson and J. Bengtsson, “Robust design method for highly efficient beam-shaping diffractive optical elements using an iterative-fourier-transform algorithm with soft operations,” J. Mod. Opt. 47, 1385–1398 (2000).
[Crossref]

Jones, M.

Kraft, S.

J. Fortágh, H. Ott, S. Kraft, A. Günther, and C. Zimmermann, “Surface effects in magnetic microtraps,” Phys. Rev. A 66, 041604 (2002).
[Crossref]

Kuhn, A.

C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, and A. Kuhn, “Control and manipulation of cold atoms in optical tweezers,” New J. Phys. 14, 073051 (2012).
[Crossref]

Labuhn, H.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

Laczik, Z. J.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z. J. Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51, 2235–2240 (2004).
[Crossref]

Lahaye, T.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

Lam, Y.-L.

Liu, R.

MacCormick, C.

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys. 11, 043030 (2009).
[Crossref]

Masuda, N.

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[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. T143, 014008 (2011).
[Crossref]

McGloin, D.

Meineke, J.

B. Zimmermann, T. Müller, J. Meineke, T. Esslinger, and H. Moritz, “High-resolution imaging of ultracold fermions in microscopically tailored optical potentials,” New J. Phys. 13, 043007 (2011).
[Crossref]

Melville, H.

Mitchell, M.

M. Mitchell, An Introduction to Genetic Algorithms (MIT, 1998).

Moritz, H.

B. Zimmermann, T. Müller, J. Meineke, T. Esslinger, and H. Moritz, “High-resolution imaging of ultracold fermions in microscopically tailored optical potentials,” New J. Phys. 13, 043007 (2011).
[Crossref]

Muldoon, C.

C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, and A. Kuhn, “Control and manipulation of cold atoms in optical tweezers,” New J. Phys. 14, 073051 (2012).
[Crossref]

Müller, T.

B. Zimmermann, T. Müller, J. Meineke, T. Esslinger, and H. Moritz, “High-resolution imaging of ultracold fermions in microscopically tailored optical potentials,” New J. Phys. 13, 043007 (2011).
[Crossref]

Nascimbene, S.

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[Crossref]

Nogrette, F.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

Ott, H.

J. Fortágh, H. Ott, S. Kraft, A. Günther, and C. Zimmermann, “Surface effects in magnetic microtraps,” Phys. Rev. A 66, 041604 (2002).
[Crossref]

Pasienski, M.

Payne, M. C.

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1987).

Pritchard, D. E.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

Ravets, S.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

Reicherter, M.

M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[Crossref]

Riis, E.

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B 41, 211001 (2008).
[Crossref]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Ryu, C.

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys. 11, 043030 (2009).
[Crossref]

Schimmel, H.

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser Eng. 43, 43–56 (2005).
[Crossref]

Schmiedmayer, J.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

Seifert, L.

M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[Crossref]

Senthilkumaran, P.

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser Eng. 43, 43–56 (2005).
[Crossref]

Shiraki, A.

Sibbett, W.

Smirne, G.

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. T143, 014008 (2011).
[Crossref]

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A 84, 053410 (2011).
[Crossref]

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

Smith, R.

M. Clark and R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150–164 (1996).
[Crossref]

Spalding, G.

Stuart, D.

C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, and A. Kuhn, “Control and manipulation of cold atoms in optical tweezers,” New J. Phys. 14, 073051 (2012).
[Crossref]

Sugie, T.

Tanaka, T.

Teter, M. P.

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1987).

Torralbo-Campo, L.

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A 84, 053410 (2011).
[Crossref]

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. T143, 014008 (2011).
[Crossref]

Trypogeorgos, D.

Vernier, A.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1987).

Warde, C.

J. R. Hui, X. Wu, and C. Warde, “Addressing large arrays of electrostatic actuators for adaptive optics applications,” Proc. SPIE 5553, 17–27 (2004).
[Crossref]

Wu, M.

M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[Crossref]

Wu, X.

J. R. Hui, X. Wu, and C. Warde, “Addressing large arrays of electrostatic actuators for adaptive optics applications,” Proc. SPIE 5553, 17–27 (2004).
[Crossref]

Wyrowski, F.

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser Eng. 43, 43–56 (2005).
[Crossref]

Yang, G.-Z.

Yuan, X.

Zhou, G.

Zimmermann, B.

B. Zimmermann, T. Müller, J. Meineke, T. Esslinger, and H. Moritz, “High-resolution imaging of ultracold fermions in microscopically tailored optical potentials,” New J. Phys. 13, 043007 (2011).
[Crossref]

Zimmermann, C.

J. Fortágh, H. Ott, S. Kraft, A. Günther, and C. Zimmermann, “Surface effects in magnetic microtraps,” Phys. Rev. A 66, 041604 (2002).
[Crossref]

Comput. Sci. Eng. (1)

M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[Crossref]

J. Mod. Opt. (2)

V. Boyer, C. M. Chandrashekar, C. J. Foot, and Z. J. Laczik, “Dynamic optical trap generation using FLC SLMs for the manipulation of cold atoms,” J. Mod. Opt. 51, 2235–2240 (2004).
[Crossref]

M. Johansson and J. Bengtsson, “Robust design method for highly efficient beam-shaping diffractive optical elements using an iterative-fourier-transform algorithm with soft operations,” J. Mod. Opt. 47, 1385–1398 (2000).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

N. Houston, E. Riis, and A. S. Arnold, “Reproducible dynamic dark ring lattices for ultracold atoms,” J. Phys. B 41, 211001 (2008).
[Crossref]

Laser Photon. Rev. (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Nat. Phys. (1)

I. Bloch, J. Dalibard, and S. Nascimbene, “Quantum simulations with ultracold quantum gases,” Nat. Phys. 8, 267–276 (2012).
[Crossref]

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

New J. Phys. (3)

K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, “Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates,” New J. Phys. 11, 043030 (2009).
[Crossref]

C. Muldoon, L. Brandt, J. Dong, D. Stuart, E. Brainis, M. Himsworth, and A. Kuhn, “Control and manipulation of cold atoms in optical tweezers,” New J. Phys. 14, 073051 (2012).
[Crossref]

B. Zimmermann, T. Müller, J. Meineke, T. Esslinger, and H. Moritz, “High-resolution imaging of ultracold fermions in microscopically tailored optical potentials,” New J. Phys. 13, 043007 (2011).
[Crossref]

Opt. Commun. (1)

M. Clark and R. Smith, “A direct-search method for the computer design of holograms,” Opt. Commun. 124, 150–164 (1996).
[Crossref]

Opt. Express (4)

Opt. Laser Eng. (1)

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Laser Eng. 43, 43–56 (2005).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (3)

J. Fortágh, H. Ott, S. Kraft, A. Günther, and C. Zimmermann, “Surface effects in magnetic microtraps,” Phys. Rev. A 66, 041604 (2002).
[Crossref]

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402 (2006).
[Crossref]

G. D. Bruce, S. L. Bromley, G. Smirne, L. Torralbo-Campo, and D. Cassettari, “Holographic power-law traps for the efficient production of Bose-Einstein condensates,” Phys. Rev. A 84, 053410 (2011).
[Crossref]

Phys. Rev. X (1)

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

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. T143, 014008 (2011).
[Crossref]

Proc. SPIE (1)

J. R. Hui, X. Wu, and C. Warde, “Addressing large arrays of electrostatic actuators for adaptive optics applications,” Proc. SPIE 5553, 17–27 (2004).
[Crossref]

Rev. Mod. Phys. (2)

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, “Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients,” Rev. Mod. Phys. 64, 1045–1097 (1992).
[Crossref]

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009).
[Crossref]

Sci. Rep. (1)

A. L. Gaunt and Z. Hadzibabic, “Robust digital holography for ultracold atom trapping,” Sci. Rep. 2, 721 (2012).
[Crossref] [PubMed]

Other (6)

J. G. Lee and W. T. Hill, “Spatial shaping for generating arbitrary optical dipoles traps for ultracold degenerate gases,” (2014), http://arxiv.org/abs/1406.4084 .

G. D. Bruce, M. Y. H. Johnson, E. Cormack, D. Richards, J. Mayoh, and D. Cassettari, “Feedback-enhanced algorithm for aberration correction of holographic atom traps,” (2014), http://arxiv.org/abs/1409.3151 .

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 1987).

J. R. Shewchuk, “An introduction to the conjugate gradient method without the agonizing pain,” (1994), http://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf .

A. Bartok-Partay, S. Cereda, G. Csanyi, J. Kermode, I. Solt, W. Szlachta, C. Varnai, and S. Winfield, http://www.libatoms.org .

M. Mitchell, An Introduction to Genetic Algorithms (MIT, 1998).

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Figures (4)

Fig. 1
Fig. 1

Block diagram illustrating the conjugate gradient minimisation approach to hologram solution.

Fig. 2
Fig. 2

Second-order power-law trapping potential calculated using the cost function in Eq. (6). (left) Two-dimensional profiles and vertical line profiles taken through the centre of the pattern for target (upper inset and cyan line) and calculated output (lower inset and red points). The colorbar applies to the insets and to all subsequent figures. The predicted output is distorted by deep optical vortices. These vortices inhibit further improvements in accuracy, resulting in a poor fit to the target intensity. The root-mean square (RMS) fractional error between target and predicted output is 26%. (right) Vortex locations on the output plane, with red pixels indicating 2π phase windings and blue pixels −2π. The black circle indicates the trapping region. While the vortex density is reduced within this region in comparison to the remainder of the output plane, 232 are established within the trapping region with an insignificant fraction removed with further iterations due to the tangled phase contours.

Fig. 3
Fig. 3

Second-order power-law trapping potentials calculated with more sophisticated cost functions, starting with an educated guess phase. (left) Line profiles through pattern centre and two-dimensional profiles as insets. Calculated intensity patterns are denoted by points while the target profile is indicated with a cyan line. (right) output plane vortex map with the trapping region indicated by the black circle. (a) Ct=4 (purple, upper inset) and subsequent Ct=2 application (red, lower inset). Applying Ct=4 generates an approximate fit to the target while suppressing the initial vortex number. Subsequent smoothing using Ct=2 improves the accuracy and smoothness, and clears residual vortices from the trapping region. (b) A combination of Ct=2 and Cs achieves both direct smoothing and high reproduction accuracy.

Fig. 4
Fig. 4

Target (i) and calculated output intensity (ii) for the square lattice (a) and stirring ring pattern (b). Both are generated from a random initial phase and have RMS errors of 0.58% and 3.0% respectively.

Equations (15)

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

E in = A 0 S p q exp ( i ϕ p q ) .
E out = A 0 N p q S p q exp ( i ϕ p q ) exp ( 2 π i N ( p n + q m ) ) ,
d i H C d j = 0 ,
d i = g i + γ i d i 1
γ i = g i g i g i 1 g i 1 .
C = n m ( T n m | E out , n m | 2 ) 2 = n m ( T n m | A 0 ψ ˜ n m | 2 ) 2
ψ ˜ n m = 1 N p q ψ p q exp ( 2 π i N ( p n + q m ) )
C ϕ r s = 4 A 0 2 Re ( i ψ r s * X r s )
X r s = 1 N n m [ ( T n m | A 0 ψ ˜ n m | 2 ) ψ ˜ n m * exp ( 2 π i N ( r n + s m ) ) ] .
C t = n m ( T n m | A 0 ψ ˜ n m | 2 ) t .
C t ϕ r s = 2 t A 0 2 Re ( i ψ r s * X r s ) .
C s = n m [ ( | ψ ˜ n m | 2 | ψ ˜ n ( m 1 ) | 2 ) 2 + ( | ψ ˜ n m | 2 | ψ ˜ n ( m + 1 ) | 2 ) 2 + ( | ψ ˜ n m | 2 | ψ ˜ ( n 1 ) m | 2 ) 2 + ( | ψ ˜ n m | 2 | ψ ˜ ( n + 1 ) m | 2 ) 2 ] .
C s ( 1 ) ϕ r s = 4 N Re ( i ψ r s ( X 1 r s * X 2 r s * ) )
X 1 r s = 1 N n m [ ( | ψ ˜ n m | 2 | ψ ˜ n ( m 1 ) | 2 ) ψ ˜ n m exp ( 2 π i N ( r n + s m ) ) ]
X 2 r s = 1 N n m [ ( | ψ ˜ n m | 2 | ψ ˜ n ( m 1 ) | 2 ) ψ ˜ n ( m 1 ) exp ( 2 π i N ( r n + s m ) ) ] .

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