Abstract

We propose a new method for realizing high-spatial-resolution detection of singularity points in optical vortex beams. The method uses a Shack–Hartmann wavefront sensor (SHWS) to record a Hartmanngram. A map of evaluation values related to phase slope is then calculated from the Hartmanngram. The position of an optical vortex is determined by comparing the map with reference maps that are calculated from numerically created spiral phases having various positions. Optical experiments were carried out to verify the method. We displayed various spiral phase distribution patterns on a phase-only spatial light modulator and measured the resulting singularity point using the proposed method. The results showed good linearity in detecting the position of singularity points. The RMS error of the measured position of the singularity point was approximately 0.056, in units normalized to the lens size of the lenslet array used in the SHWS.

© 2012 OSA

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2012 (1)

2010 (1)

2009 (1)

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

2008 (4)

2007 (5)

M. Chen, F. S. Roux, and J. C. Olivier, “Detection of phase singularities with a Shack-Hartmann wavefront sensor,” J. Opt. Soc. Am. A24(7), 1994–2002 (2007).
[CrossRef] [PubMed]

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

J. Wu, H. Li, and Y. Li, “Encoding information as orbital angular momentum states of light for wireless optical communications,” Opt. Eng.46(1), 019701 (2007).
[CrossRef]

2005 (1)

2004 (1)

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dandliker, “High-resolution measurement of phase singularities produced by computer-generated holograms,” Opt. Commun.242(1-3), 163–169 (2004).
[CrossRef]

2002 (2)

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann sensor precision and accuracy,” Proc. SPIE4779, 148–160 (2002).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

1998 (2)

E. O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE3381, 76–87 (1998).
[CrossRef]

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A15(10), 2759–2768 (1998).
[CrossRef]

1992 (1)

1970 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336, 165–190 (1970).

Aksenov, V. P.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Ando, T.

Atuchin, V. V.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Auksorius, E.

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336, 165–190 (1970).

Boruah, B. R.

Burke, D.

Chen, M.

Chernyshov, A.

Copland, J.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann sensor precision and accuracy,” Proc. SPIE4779, 148–160 (2002).
[CrossRef]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

Dainty, C.

Dandliker, R.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dandliker, “High-resolution measurement of phase singularities produced by computer-generated holograms,” Opt. Commun.242(1-3), 163–169 (2004).
[CrossRef]

Devaney, N.

Dunsby, C.

French, P. M. W.

Fried, D. L.

Fukuchi, N.

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25(7), 1642–1651 (2008).
[CrossRef]

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

Hanson, S. G.

Hara, T.

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25(7), 1642–1651 (2008).
[CrossRef]

H. Huang, T. Inoue, and T. Hara, “Adaptive aberration compensation system using a high-resolution liquid crystal on silicon spatial light modulator,” Proc. SPIE7156, 71560F, 71560F-10 (2008).
[CrossRef]

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

Helmcke, J.

Herzig, H. P.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dandliker, “High-resolution measurement of phase singularities produced by computer-generated holograms,” Opt. Commun.242(1-3), 163–169 (2004).
[CrossRef]

Honda, D.

Huang, H.

H. Huang, T. Inoue, and T. Hara, “Adaptive aberration compensation system using a high-resolution liquid crystal on silicon spatial light modulator,” Proc. SPIE7156, 71560F, 71560F-10 (2008).
[CrossRef]

Igasaki, Y.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

Inoue, T.

H. Huang, T. Inoue, and T. Hara, “Adaptive aberration compensation system using a high-resolution liquid crystal on silicon spatial light modulator,” Proc. SPIE7156, 71560F, 71560F-10 (2008).
[CrossRef]

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25(7), 1642–1651 (2008).
[CrossRef]

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

Ishijima, R.

Ivanovskyy, A. A.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dandliker, “High-resolution measurement of phase singularities produced by computer-generated holograms,” Opt. Commun.242(1-3), 163–169 (2004).
[CrossRef]

Izmailov, I. V.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Kanev, F. Y.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Kennedy, G.

Kibblewhite, E. J.

E. O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE3381, 76–87 (1998).
[CrossRef]

Kobayashi, Y.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

Kochemasov, G. G.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

Kudryashov, A. V.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

Kulikov, S. M.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Lanigan, P. M. P.

Le Bigot, E. O.

E. O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE3381, 76–87 (1998).
[CrossRef]

Li, H.

J. Wu, H. Li, and Y. Li, “Encoding information as orbital angular momentum states of light for wireless optical communications,” Opt. Eng.46(1), 019701 (2007).
[CrossRef]

Li, Y.

J. Wu, H. Li, and Y. Li, “Encoding information as orbital angular momentum states of light for wireless optical communications,” Opt. Eng.46(1), 019701 (2007).
[CrossRef]

Malakhov, Y. I.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

Manachinsky, A. N.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Maslov, N. V.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Matsuda, A.

Matsumoto, N.

N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, “Generation of high-quality higher-order Laguerre-Gaussian beams using liquid-crystal-on-silicon spatial light modulators,” J. Opt. Soc. Am. A25(7), 1642–1651 (2008).
[CrossRef]

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

Murphy, K.

Neal, D.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann sensor precision and accuracy,” Proc. SPIE4779, 148–160 (2002).
[CrossRef]

Neal, D. R.

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann sensor precision and accuracy,” Proc. SPIE4779, 148–160 (2002).
[CrossRef]

Neil, M. A. A.

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336, 165–190 (1970).

Ogorodnikov, A. V.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Ohtake, Y.

Olivier, J. C.

Pfund, J.

Qiao, Y.

Riehle, F.

Rockstuhl, C.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dandliker, “High-resolution measurement of phase singularities produced by computer-generated holograms,” Opt. Commun.242(1-3), 163–169 (2004).
[CrossRef]

Roux, F. S.

Salt, M. G.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dandliker, “High-resolution measurement of phase singularities produced by computer-generated holograms,” Opt. Commun.242(1-3), 163–169 (2004).
[CrossRef]

Soldatenkov, I. S.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Soskin, M. S.

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dandliker, “High-resolution measurement of phase singularities produced by computer-generated holograms,” Opt. Commun.242(1-3), 163–169 (2004).
[CrossRef]

Starikov, F. A.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Sterr, U.

Sukharev, S. A.

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Y. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Wavefront reconstruction of an optical vortex by a Hartmann-Shack sensor,” Opt. Lett.32(16), 2291–2293 (2007).
[CrossRef] [PubMed]

Takeda, M.

Takumi, M.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

Tanaka, H.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

Vaughn, J. L.

Wang, W.

Wild, W. J.

E. O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE3381, 76–87 (1998).
[CrossRef]

Wu, J.

J. Wu, H. Li, and Y. Li, “Encoding information as orbital angular momentum states of light for wireless optical communications,” Opt. Eng.46(1), 019701 (2007).
[CrossRef]

Yokozeki, T.

Yoshida, N.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

Appl. Opt. (2)

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

Opt. Commun. (2)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun.207(1-6), 169–175 (2002).
[CrossRef]

C. Rockstuhl, A. A. Ivanovskyy, M. S. Soskin, M. G. Salt, H. P. Herzig, and R. Dandliker, “High-resolution measurement of phase singularities produced by computer-generated holograms,” Opt. Commun.242(1-3), 163–169 (2004).
[CrossRef]

Opt. Eng. (1)

J. Wu, H. Li, and Y. Li, “Encoding information as orbital angular momentum states of light for wireless optical communications,” Opt. Eng.46(1), 019701 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Proc. R. Soc. Lond. A (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A336, 165–190 (1970).

Proc. SPIE (6)

E. O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, “Branch point reconstructors for discontinuous light phase functions,” Proc. SPIE3381, 76–87 (1998).
[CrossRef]

D. R. Neal, J. Copland, and D. Neal, “Shack-Hartmann sensor precision and accuracy,” Proc. SPIE4779, 148–160 (2002).
[CrossRef]

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, A. V. Kudryashov, S. M. Kulikov, Y. I. Malakhov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE6747, 67470P (2007).

F. A. Starikov, V. P. Aksenov, V. V. Atuchin, I. V. Izmailov, F. Y. Kanev, G. G. Kochemasov, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkov, and S. A. Sukharev, “Correction of vortex laser beams in a closed-loop adaptive system with bimorph mirror,” Proc. SPIE7131, 71311G (2009).

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulator,” Proc. SPIE6487, 64870Y, 64870Y-11 (2007).
[CrossRef]

H. Huang, T. Inoue, and T. Hara, “Adaptive aberration compensation system using a high-resolution liquid crystal on silicon spatial light modulator,” Proc. SPIE7156, 71560F, 71560F-10 (2008).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Concept of circulation calculation. Sx and Sy represents phase slopes in x-axis (horizontal) and y-axis (vertical) directions, and i, j denotes the lenslet index. The solid circles are the centers of lenslets, the open circles indicate crosspoints of neighboring 2 × 2 lenslets. The dashed line indicates a contour connecting the centers of the four neighboring lenslets. The symbol “” denotes the position of phase singularity point.

Fig. 2
Fig. 2

A model for calculation of reference maps.

Fig. 3
Fig. 3

Diagram of the correlation matching method.

Fig. 4
Fig. 4

Schematic of experimental setup used in verification tests

Fig. 5
Fig. 5

Spiral phase patterns for generating optical vortex beam of topological charge (a) n = 1, (b) n = 2, and (c) n = 3.

Fig. 6
Fig. 6

Images of optical vortex beams of topological charge (a) n = 1, (b) n = 2, and (c) n = 3, detected in far field. The scale bar is 0.1mm.

Fig. 7
Fig. 7

An experimental result shows the process for vortex position determination using proposed method.

Fig. 8
Fig. 8

Plots of measured positions of horizontal component of singularity point versus the horizontal displacements of spiral phase pattern displayed on LCOS-SLM for topological charge (a) n = 1, (b) n = 2, and (c) n = 3, respectively, and plot of averages of horizontal component measured versus the horizontal displacements assigned (d).

Fig. 9
Fig. 9

Plots of measured positions of vertical components of singularity point versus the horizontal displacements of spiral phase pattern for topological charge (a) n = 1, (b) n = 2, and (c) n = 3, respectively, and plot of the averages of vertical component measured versus the vertical displacements assigned (d).

Equations (7)

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C θd l =2πn,
C( p,q )= w 2 ( S x i,j + S x i,j+1 + S y i,j+1 + S y i+1,j+1 S x i+1,j+1 S x i+1,j S y i+1,j S y i,j ),
( p max , q max )=maxpos(C(p,q)),
CMM( u 0 ,v ) 0 = k=1 1 l=1 1 (C( p max +k, q max +l) C max ¯ )( C R (k,l;u , 0 v 0 ) C R ( u 0 , v 0 ) ¯ ) k=1 1 l=1 1 (C( p max +k, q max +l) C max ¯ ) 2 k=1 1 l=1 1 ( C R (k,l;u , 0 v 0 ) C R ( u 0 , v 0 ) ¯ ) 2 ,
( u max , v max )=maxpos(CMM( u 0 , v 0 )),
P= p max + u max ,
Q= q max + v max .

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