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D. R. Scherer, C. N. Weiler, T. W. Neely, and B. P. Anderson, “Vortex formation by merging of multiple trapped Bose-Einstein condensates,” Phys. Rev. Lett. 98, 110402 (2007).

[CrossRef]
[PubMed]

T. Inoue, N. Matsumoto, N. Fukuchia, Y. Kobayashi, and T. Hara, “Highly stable wavefront control using a hybrid liquid-crystal spatial light modulator,” Proc. SPIE 6306, 630603 (2006).

[CrossRef]
[PubMed]

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]
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J. Sebby-Strabley, R. T. R. Newell, J. O. Day, E. Brekke, and T. G. Walker, “High-density mesoscopic atom clouds in a holographic atom trap,” Phys. Rev. A 71, 021401 (2005).

[CrossRef]
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B. DeMarco, C. Lannert, S. Vishveshwara, and T.-C. Wei, “Structure and stability of Mott-insulator shells of bosons trapped in an optical lattice,” Phys. Rev. A 71, 063601 (2005).

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[CrossRef]
[PubMed]

A. E. Leanhardt, Y. Shin, A. P. Chikkatur, D. Kielpinski, W. Ketterle, and D. E. Pritchard, “Bose-Einstein condensates near a microfabricated surface,” Phys. Rev. Lett. 90, 100404 (2003).

[CrossRef]
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[CrossRef]
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[CrossRef]
[PubMed]

A. E. Leanhardt, A. P. Chikkatur, D. Kielpinski, Y. Shin, T. L. Gustavson, W. Ketterle, and D. E. Pritchard, “Propagation of Bose-Einstein condensates in a magnetic waveguide,” Phys. Rev. Lett. 89, 040401 (2002).

[CrossRef]
[PubMed]

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S. Bühling and F. Wyrowski, “Improved transmission design algorithms by utilizing variable-strength projections,” J. Mod. Opt. 49, 1871–1892 (2002).

[CrossRef]
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An IFTA is most generically described using the block-projection algorithm formalism, which is not necessary for the relatively simple MRAF algorithm. For a description of the block-projection formalism as applied to IFTAs, see R. Piestun and J. Shamir, “Synthesis of Three-Dimensional Light Fields and Applications,” Proc. IEEE 90, 222–244 (2002).

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[CrossRef]

H. Akahori, “Spectrum leveling by an iterative algorithm with a dummy area for synthesizing the kinoform,” App. Opt. 25, 802–811 (1986).

[CrossRef]

D. R. Scherer, C. N. Weiler, T. W. Neely, and B. P. Anderson, “Vortex formation by merging of multiple trapped Bose-Einstein condensates,” Phys. Rev. Lett. 98, 110402 (2007).

[CrossRef]
[PubMed]

B. T. Seaman, M. Krämer, D. Z. Anderson, and M. J. Holland, “Atomtronics: Ultracold-atom analogs of electronic devices,” Phys. Rev. A 75, 023615 (2007).

[CrossRef]
[PubMed]

J. Estève, C. Aussibal, T. Schumm, C. Figl, D. Mailly, I. Bouchoule, C. I. Westbrook, and A. Aspect, “Role of wire imperfections in micromagnetic traps for atoms,” Phys. Rev. A 70, 043629 (2004).

[CrossRef]
[PubMed]

J. Estève, C. Aussibal, T. Schumm, C. Figl, D. Mailly, I. Bouchoule, C. I. Westbrook, and A. Aspect, “Role of wire imperfections in micromagnetic traps for atoms,” Phys. Rev. A 70, 043629 (2004).

[CrossRef]
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H. Aagedal, M. Schmid, T. Beth, S. Tiewes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).

[CrossRef]

A. Bezryadin, C. N. Lau, and M. Tinkham, “Quantum suppression of superconductivity in ultrathin nanowires”, Nature 404, 971–974 (2000).

[CrossRef]
[PubMed]

J. Estève, C. Aussibal, T. Schumm, C. Figl, D. Mailly, I. Bouchoule, C. I. Westbrook, and A. Aspect, “Role of wire imperfections in micromagnetic traps for atoms,” Phys. Rev. A 70, 043629 (2004).

[CrossRef]
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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]
[PubMed]

J. Sebby-Strabley, R. T. R. Newell, J. O. Day, E. Brekke, and T. G. Walker, “High-density mesoscopic atom clouds in a holographic atom trap,” Phys. Rev. A 71, 021401 (2005).

[CrossRef]
[PubMed]

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).

[CrossRef]
[PubMed]

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[CrossRef]
[PubMed]

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]
[PubMed]

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]
[PubMed]

A. E. Leanhardt, Y. Shin, A. P. Chikkatur, D. Kielpinski, W. Ketterle, and D. E. Pritchard, “Bose-Einstein condensates near a microfabricated surface,” Phys. Rev. Lett. 90, 100404 (2003).

[CrossRef]
[PubMed]

A. E. Leanhardt, A. P. Chikkatur, D. Kielpinski, Y. Shin, T. L. Gustavson, W. Ketterle, and D. E. Pritchard, “Propagation of Bose-Einstein condensates in a magnetic waveguide,” Phys. Rev. Lett. 89, 040401 (2002).

[CrossRef]
[PubMed]

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).

[CrossRef]
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[PubMed]

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, “Atomic Bose and Anderson glasses in optical lattices,” Phys. Rev. Lett. 91, 080403 (2003).

[CrossRef]
[PubMed]

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).

[CrossRef]
[PubMed]

J. Sebby-Strabley, R. T. R. Newell, J. O. Day, E. Brekke, and T. G. Walker, “High-density mesoscopic atom clouds in a holographic atom trap,” Phys. Rev. A 71, 021401 (2005).

[CrossRef]
[PubMed]

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]
[PubMed]

B. DeMarco, C. Lannert, S. Vishveshwara, and T.-C. Wei, “Structure and stability of Mott-insulator shells of bosons trapped in an optical lattice,” Phys. Rev. A 71, 063601 (2005).

[CrossRef]
[PubMed]

G. C. Spalding, J. Courtial, and R. DiLeonardo, “Holographic Optical Trapping,” in Structured Light and its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L. Andrews ed., (Elsevier Press) (to be published).

[PubMed]

J. Estève, C. Aussibal, T. Schumm, C. Figl, D. Mailly, I. Bouchoule, C. I. Westbrook, and A. Aspect, “Role of wire imperfections in micromagnetic traps for atoms,” Phys. Rev. A 70, 043629 (2004).

[CrossRef]
[PubMed]

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

[PubMed]

J. Estève, C. Aussibal, T. Schumm, C. Figl, D. Mailly, I. Bouchoule, C. I. Westbrook, and A. Aspect, “Role of wire imperfections in micromagnetic traps for atoms,” Phys. Rev. A 70, 043629 (2004).

[CrossRef]
[PubMed]

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]
[PubMed]

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

[CrossRef]
[PubMed]

T. Inoue, N. Matsumoto, N. Fukuchia, Y. Kobayashi, and T. Hara, “Highly stable wavefront control using a hybrid liquid-crystal spatial light modulator,” Proc. SPIE 6306, 630603 (2006).

[CrossRef]
[PubMed]

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).

[CrossRef]
[PubMed]

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).

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[CrossRef]
[PubMed]

A. E. Leanhardt, A. P. Chikkatur, D. Kielpinski, Y. Shin, T. L. Gustavson, W. Ketterle, and D. E. Pritchard, “Propagation of Bose-Einstein condensates in a magnetic waveguide,” Phys. Rev. Lett. 89, 040401 (2002).

[CrossRef]
[PubMed]

T. Inoue, N. Matsumoto, N. Fukuchia, Y. Kobayashi, and T. Hara, “Highly stable wavefront control using a hybrid liquid-crystal spatial light modulator,” Proc. SPIE 6306, 630603 (2006).

[CrossRef]
[PubMed]

O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43, 2549–2556 (2004).

[CrossRef]
[PubMed]

B. T. Seaman, M. Krämer, D. Z. Anderson, and M. J. Holland, “Atomtronics: Ultracold-atom analogs of electronic devices,” Phys. Rev. A 75, 023615 (2007).

[CrossRef]
[PubMed]

T. Inoue, N. Matsumoto, N. Fukuchia, Y. Kobayashi, and T. Hara, “Highly stable wavefront control using a hybrid liquid-crystal spatial light modulator,” Proc. SPIE 6306, 630603 (2006).

[CrossRef]
[PubMed]

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, “Cold bosonic atoms in optical lattices,” Phys. Rev. Lett. 81, 3108–3111 (1998).

[CrossRef]
[PubMed]

A. E. Leanhardt, Y. Shin, A. P. Chikkatur, D. Kielpinski, W. Ketterle, and D. E. Pritchard, “Bose-Einstein condensates near a microfabricated surface,” Phys. Rev. Lett. 90, 100404 (2003).

[CrossRef]
[PubMed]

A. E. Leanhardt, A. P. Chikkatur, D. Kielpinski, Y. Shin, T. L. Gustavson, W. Ketterle, and D. E. Pritchard, “Propagation of Bose-Einstein condensates in a magnetic waveguide,” Phys. Rev. Lett. 89, 040401 (2002).

[CrossRef]
[PubMed]

O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43, 2549–2556 (2004).

[CrossRef]
[PubMed]

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).

[CrossRef]
[PubMed]

A. E. Leanhardt, Y. Shin, A. P. Chikkatur, D. Kielpinski, W. Ketterle, and D. E. Pritchard, “Bose-Einstein condensates near a microfabricated surface,” Phys. Rev. Lett. 90, 100404 (2003).

[CrossRef]
[PubMed]

A. E. Leanhardt, A. P. Chikkatur, D. Kielpinski, Y. Shin, T. L. Gustavson, W. Ketterle, and D. E. Pritchard, “Propagation of Bose-Einstein condensates in a magnetic waveguide,” Phys. Rev. Lett. 89, 040401 (2002).

[CrossRef]
[PubMed]

T. Inoue, N. Matsumoto, N. Fukuchia, Y. Kobayashi, and T. Hara, “Highly stable wavefront control using a hybrid liquid-crystal spatial light modulator,” Proc. SPIE 6306, 630603 (2006).

[CrossRef]
[PubMed]

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative algorithm for designing diffractive optical elements with regularization,” Opt. Laser Eng. 29, 261–268 (1998).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

B. T. Seaman, M. Krämer, D. Z. Anderson, and M. J. Holland, “Atomtronics: Ultracold-atom analogs of electronic devices,” Phys. Rev. A 75, 023615 (2007).

[CrossRef]
[PubMed]

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]
[PubMed]

B. DeMarco, C. Lannert, S. Vishveshwara, and T.-C. Wei, “Structure and stability of Mott-insulator shells of bosons trapped in an optical lattice,” Phys. Rev. A 71, 063601 (2005).

[CrossRef]
[PubMed]

A. Bezryadin, C. N. Lau, and M. Tinkham, “Quantum suppression of superconductivity in ultrathin nanowires”, Nature 404, 971–974 (2000).

[CrossRef]
[PubMed]

A. E. Leanhardt, Y. Shin, A. P. Chikkatur, D. Kielpinski, W. Ketterle, and D. E. Pritchard, “Bose-Einstein condensates near a microfabricated surface,” Phys. Rev. Lett. 90, 100404 (2003).

[CrossRef]
[PubMed]

A. E. Leanhardt, A. P. Chikkatur, D. Kielpinski, Y. Shin, T. L. Gustavson, W. Ketterle, and D. E. Pritchard, “Propagation of Bose-Einstein condensates in a magnetic waveguide,” Phys. Rev. Lett. 89, 040401 (2002).

[CrossRef]
[PubMed]

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, “Atomic Bose and Anderson glasses in optical lattices,” Phys. Rev. Lett. 91, 080403 (2003).

[CrossRef]
[PubMed]

J. Estève, C. Aussibal, T. Schumm, C. Figl, D. Mailly, I. Bouchoule, C. I. Westbrook, and A. Aspect, “Role of wire imperfections in micromagnetic traps for atoms,” Phys. Rev. A 70, 043629 (2004).

[CrossRef]
[PubMed]

T. Inoue, N. Matsumoto, N. Fukuchia, Y. Kobayashi, and T. Hara, “Highly stable wavefront control using a hybrid liquid-crystal spatial light modulator,” Proc. SPIE 6306, 630603 (2006).

[CrossRef]
[PubMed]

D. R. Scherer, C. N. Weiler, T. W. Neely, and B. P. Anderson, “Vortex formation by merging of multiple trapped Bose-Einstein condensates,” Phys. Rev. Lett. 98, 110402 (2007).

[CrossRef]
[PubMed]

J. Sebby-Strabley, R. T. R. Newell, J. O. Day, E. Brekke, and T. G. Walker, “High-density mesoscopic atom clouds in a holographic atom trap,” Phys. Rev. A 71, 021401 (2005).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

R. Ozeri, L. Khaykovich, and N. Davidson, “Long spin relaxation times in a single-beam blue-detuned optical trap,” Phys. Rev. A 59, R1750–R1753 (1999).

[CrossRef]
[PubMed]

An IFTA is most generically described using the block-projection algorithm formalism, which is not necessary for the relatively simple MRAF algorithm. For a description of the block-projection formalism as applied to IFTAs, see R. Piestun and J. Shamir, “Synthesis of Three-Dimensional Light Fields and Applications,” Proc. IEEE 90, 222–244 (2002).

[CrossRef]
[PubMed]

A. E. Leanhardt, Y. Shin, A. P. Chikkatur, D. Kielpinski, W. Ketterle, and D. E. Pritchard, “Bose-Einstein condensates near a microfabricated surface,” Phys. Rev. Lett. 90, 100404 (2003).

[CrossRef]
[PubMed]

A. E. Leanhardt, A. P. Chikkatur, D. Kielpinski, Y. Shin, T. L. Gustavson, W. Ketterle, and D. E. Pritchard, “Propagation of Bose-Einstein condensates in a magnetic waveguide,” Phys. Rev. Lett. 89, 040401 (2002).

[CrossRef]
[PubMed]

N. Bertaux, Y. Frauel, P. Réfrégier, and B. Javidi, “Speckle removal using a maximum-likelihood technique with isoline gray-level regularization,” J. Opt. Soc. Am. A 21, 2283–2291 (2004).

[CrossRef]
[PubMed]

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[CrossRef]

O. Ripoll, V. Kettunen, and H. P. Herzig, “Review of iterative Fourier-transform algorithms for beam shaping applications,” Opt. Eng. 43, 2549–2556 (2004).

[CrossRef]
[PubMed]

B. Damski, J. Zakrzewski, L. Santos, P. Zoller, and M. Lewenstein, “Atomic Bose and Anderson glasses in optical lattices,” Phys. Rev. Lett. 91, 080403 (2003).

[CrossRef]
[PubMed]

D. R. Scherer, C. N. Weiler, T. W. Neely, and B. P. Anderson, “Vortex formation by merging of multiple trapped Bose-Einstein condensates,” Phys. Rev. Lett. 98, 110402 (2007).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

H. Aagedal, M. Schmid, T. Beth, S. Tiewes, and F. Wyrowski, “Theory of speckles in diffractive optics and its application to beam shaping,” J. Mod. Opt. 43, 1409–1421 (1996).

[CrossRef]

J. Estève, C. Aussibal, T. Schumm, C. Figl, D. Mailly, I. Bouchoule, C. I. Westbrook, and A. Aspect, “Role of wire imperfections in micromagnetic traps for atoms,” Phys. Rev. A 70, 043629 (2004).

[CrossRef]
[PubMed]

B. T. Seaman, M. Krämer, D. Z. Anderson, and M. J. Holland, “Atomtronics: Ultracold-atom analogs of electronic devices,” Phys. Rev. A 75, 023615 (2007).

[CrossRef]
[PubMed]

J. Sebby-Strabley, R. T. R. Newell, J. O. Day, E. Brekke, and T. G. Walker, “High-density mesoscopic atom clouds in a holographic atom trap,” Phys. Rev. A 71, 021401 (2005).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

P. Senthilkumaran and F. Wyrowski, “Phase synthesis in wave-optical engineering: mapping- and diffuser-type approaches,” J. Mod. Opt. 49, 1831–1850 (2002).

[CrossRef]
[PubMed]

V. V. Kotlyar, P. G. Seraphimovich, and V. A. Soifer, “An iterative algorithm for designing diffractive optical elements with regularization,” Opt. Laser Eng. 29, 261–268 (1998).

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We introduce several quantities in this manuscript which are functions of the input and output plane coordinates. For notational simplicty, we indicate this functional dependence only for the first use and when quantitites are explicitly written as functions of the coordinates.

We assume in this paper that only the center of a Gaussian beam interacts with the CGH, making the effect of intrinsic phase curvature negligible. Any effect of the intrisic phase curvature can be removed in the final kinoform using a compensating phase profile.

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