Abstract

Laboratory experiments are carried out to detect optical vortices in conditions typical of those experienced when a laser beam is propagated through the atmosphere. A Spatial Light Modulator (SLM) is used to mimic atmospheric turbulence and a Shack-Hartmann wavefront sensor is utilised to measure the slopes of the wavefront surface. A matched filter algorithm determines the positions of the Shack-Hartmann spot centroids more robustly than a centroiding algorithm. The slope discrepancy is then obtained by taking the slopes measured by the wavefront sensor away from the slopes calculated from a least squares reconstruction of the phase. The slope discrepancy field is used as an input to the branch point potential method to find if a vortex is present, and if so to give its position and sign. The use of the slope discrepancy technique greatly improves the detection rate of the branch point potential method. This work shows the first time the branch point potential method has been used to detect optical vortices in an experimental setup.

© 2010 Optical Society of America

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2010 (1)

2009 (4)

2008 (2)

R. Mackey and C. Dainty, “Adaptive optics correction over a 3km near horizontal path,” Proc. SPIE 7108, 1–9 (2008).

K. Murphy, R. Mackey, and C. Dainty, “Branch point detection and correction using the branch point potential method,” Proc. SPIE 695105, 1–9 (2008).

2007 (3)

M. Chen, F. S. Roux, and J. C. Olivier, “Detection of phase singularities with a Shack-Hartmann wavefront sensor,” J. Opt. Soc. Am. A 24, 1994–2002 (2007).
[CrossRef]

L. Caucci, H. H. Barrett, N. Devaney, and J. J. Rodríguez, “Application of the hotelling and ideal observers to detection and localization of exoplanets,” J. Opt. Soc. Am. A 24, B13–B24 (2007).
[CrossRef]

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

2006 (1)

2004 (1)

2003 (2)

2002 (1)

2001 (1)

D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2001).
[CrossRef]

2000 (3)

1999 (2)

1998 (4)

1995 (2)

1992 (1)

1990 (1)

1983 (1)

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 165–190 (1974).
[CrossRef]

Aksenov, V. P.

Aksenova, V. P.

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Atuchin, V. V.

Atuchind, V. V.

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Baranova, N. B.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

Barchers, J. D.

Barclay, H. T.

Barrett, H. H.

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 165–190 (1974).
[CrossRef]

Booth, M. J.

Burke, D.

D. Burke, S. Gladysz, L. Roberts, N. Devaney, and C. Dainty, “An Improved Technique for the Photometry and Astrometry of Faint Companions,” Publ. Astron. Soc. Pac. 121, 767–777 (2009).
[CrossRef]

Caucci, L.

Chen, M.

Courtial, J.

Dainty, C.

C. Leroux and C. Dainty, “Estimation of centroid positions with a matched-filter algorithm: relevance for aberrometry of the eye,” Opt. Express 18, 1197–1206 (2010).
[CrossRef] [PubMed]

K. Murphy, R. Mackey, and C. Dainty, “Experimental detection of phase singularities using a Shack-Hartmann wavefront sensor,” Proc. SPIE 74760O, 1–9 (2009).

D. Burke, S. Gladysz, L. Roberts, N. Devaney, and C. Dainty, “An Improved Technique for the Photometry and Astrometry of Faint Companions,” Publ. Astron. Soc. Pac. 121, 767–777 (2009).
[CrossRef]

R. Mackey and C. Dainty, “Adaptive optics correction over a 3km near horizontal path,” Proc. SPIE 7108, 1–9 (2008).

K. Murphy, R. Mackey, and C. Dainty, “Branch point detection and correction using the branch point potential method,” Proc. SPIE 695105, 1–9 (2008).

Dainty, J. C.

Devaney, M. N.

Devaney, N.

D. Burke, S. Gladysz, L. Roberts, N. Devaney, and C. Dainty, “An Improved Technique for the Photometry and Astrometry of Faint Companions,” Publ. Astron. Soc. Pac. 121, 767–777 (2009).
[CrossRef]

L. Caucci, H. H. Barrett, N. Devaney, and J. J. Rodríguez, “Application of the hotelling and ideal observers to detection and localization of exoplanets,” J. Opt. Soc. Am. A 24, B13–B24 (2007).
[CrossRef]

Flatte, S. M.

Fried, D. L.

Gibson, G.

Gladysz, S.

D. Burke, S. Gladysz, L. Roberts, N. Devaney, and C. Dainty, “An Improved Technique for the Photometry and Astrometry of Faint Companions,” Publ. Astron. Soc. Pac. 121, 767–777 (2009).
[CrossRef]

Grier, D. G.

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

Herrmann, J.

Humphreys, R. A.

Izmailov, I. V.

Izmailova, I. V.

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Johnston, R. A.

Juskaitis, R.

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
[CrossRef] [PubMed]

Kanev, F. Yu.

Kaneva, F. Y.

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Kibblewhite, E. J.

Kochemasov, G. G.

F. A. Starikov, G. G. Kochemasov, M. O. Koltygin, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Correction of vortex laser beam in a closed-loop adaptive system with bimorph mirror,” Opt. Lett. 34, 2264–2266 (2009).
[CrossRef] [PubMed]

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Koltygin, M. O.

Kudryashovb, A. V.

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Kulikov, S. M.

F. A. Starikov, G. G. Kochemasov, M. O. Koltygin, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Correction of vortex laser beam in a closed-loop adaptive system with bimorph mirror,” Opt. Lett. 34, 2264–2266 (2009).
[CrossRef] [PubMed]

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Lane, R. G.

Le Bigot, E. O.

Lee, D. J.

Leroux, C.

Link, D. J.

Mackey, R.

K. Murphy, R. Mackey, and C. Dainty, “Experimental detection of phase singularities using a Shack-Hartmann wavefront sensor,” Proc. SPIE 74760O, 1–9 (2009).

K. Murphy, R. Mackey, and C. Dainty, “Branch point detection and correction using the branch point potential method,” Proc. SPIE 695105, 1–9 (2008).

R. Mackey and C. Dainty, “Adaptive optics correction over a 3km near horizontal path,” Proc. SPIE 7108, 1–9 (2008).

Malakhovc, Y. I.

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Mamaev, A. V.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

Manachinsky, A. N.

F. A. Starikov, G. G. Kochemasov, M. O. Koltygin, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Correction of vortex laser beam in a closed-loop adaptive system with bimorph mirror,” Opt. Lett. 34, 2264–2266 (2009).
[CrossRef] [PubMed]

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Martin, J. M.

Maslov, N. V.

F. A. Starikov, G. G. Kochemasov, M. O. Koltygin, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Correction of vortex laser beam in a closed-loop adaptive system with bimorph mirror,” Opt. Lett. 34, 2264–2266 (2009).
[CrossRef] [PubMed]

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Murphy, K.

K. Murphy, R. Mackey, and C. Dainty, “Experimental detection of phase singularities using a Shack-Hartmann wavefront sensor,” Proc. SPIE 74760O, 1–9 (2009).

K. Murphy, R. Mackey, and C. Dainty, “Branch point detection and correction using the branch point potential method,” Proc. SPIE 695105, 1–9 (2008).

Myers, K. J.

Neil, M. A. A.

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
[CrossRef] [PubMed]

M. A. A. Neil, M. J. Booth, and T. Wilson, “Dynamic wave-front generation for the characterization and testing of optical systems,” Opt. Lett. 23, 1849–1851 (1998).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A 336, 165–190 (1974).
[CrossRef]

Ogorodnikov, A. V.

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Olivier, J. C.

Padgett, M. J.

Pilipetsky, N. F.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
[CrossRef]

Poyneer, L. A.

Price, T. R.

Primmerman, C. A.

Roberts, L.

D. Burke, S. Gladysz, L. Roberts, N. Devaney, and C. Dainty, “An Improved Technique for the Photometry and Astrometry of Faint Companions,” Publ. Astron. Soc. Pac. 121, 767–777 (2009).
[CrossRef]

Rodriguez, J. J.

Rodríguez, J. J.

Roggemann, M. C.

Roux, F. S.

Shkunov, V. V.

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, and B. Y. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. A 73, 525–528 (1983).
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F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Starikov, F. A.

F. A. Starikov, G. G. Kochemasov, M. O. Koltygin, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Correction of vortex laser beam in a closed-loop adaptive system with bimorph mirror,” Opt. Lett. 34, 2264–2266 (2009).
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F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

Sukharev, S. A.

F. A. Starikov, G. G. Kochemasov, M. O. Koltygin, S. M. Kulikov, A. N. Manachinsky, N. V. Maslov, S. A. Sukharev, V. P. Aksenov, I. V. Izmailov, F. Yu. Kanev, V. V. Atuchin, and I. S. Soldatenkov, “Correction of vortex laser beam in a closed-loop adaptive system with bimorph mirror,” Opt. Lett. 34, 2264–2266 (2009).
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Tyler, G. A.

Vaughn, J. L.

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[CrossRef]

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Appl. Opt. (6)

J. Microsc. (1)

M. A. A. Neil, T. Wilson, and R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (2000).
[CrossRef] [PubMed]

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K. Murphy, R. Mackey, and C. Dainty, “Experimental detection of phase singularities using a Shack-Hartmann wavefront sensor,” Proc. SPIE 74760O, 1–9 (2009).

F. A. Starikov, V. P. Aksenova, V. V. Atuchind, I. V. Izmailova, F. Y. Kaneva, G. G. Kochemasov, A. V. Kudryashovb, S. M. Kulikov, Y. I. Malakhovc, A. N. Manachinsky, N. V. Maslov, A. V. Ogorodnikov, I. S. Soldatenkovd, and S. A. Sukharev, “Wave front sensing of an optical vortex and its correction in the close-loop adaptive system with bimorph mirror,” Proc. SPIE 6747, 1–8 (2007).

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Figures (6)

Fig. 1.
Fig. 1.

A 2π radian vortex in an atmospherically distorted phasefunction, the vertical axis is the phase in radians and the xy plane is the space where the phase is measured. This shows the spiral phase around the centre of the vortex as well as the wavefront dislocation created by the vortex.

Fig. 2.
Fig. 2.

Plots of the LROC curves for: Hot MF , Hot ML and MF.

Fig. 3.
Fig. 3.

Schematic of experimental setup used in the laboratory.

Fig. 4.
Fig. 4.

Bar chart showing the ability of the branch point potential method to detect vortices using both the raw Shack-Hartmann slopes and the slopes discrepancy technique.

Fig. 5.
Fig. 5.

The interferometric fringes of a turbulent vortex beam for σ 2 I = 0.154 (a) and the detected vortex shown as a contour plot (b). The vortex is detected as it is the only peak/valley above/below the threshold used to separate a vortex from noise.

Fig. 6.
Fig. 6.

The interferometric fringes of a turbulent vortex beam for σ 2 I = 0.652 (a) and the detected vortex shown as a contour plot (b). The vortex is detected as it is the only peak/valley above/below the threshold used to separate a vortex from noise.

Tables (1)

Tables Icon

Table 1. Summary of testing the HotMF , HotML , MF and centroiding algorithms on ten thousand simulated spot images. The HotMF showed the lowest mean error in spot position estimation. This algorithm was also the most efficient spot detector having the highest AUC of the four tested observers.

Equations (21)

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Λ ( g r spot ) = pr ( g H 1 , r spot ) pr ( g H 0 ) ,
t Hot ( g r spot ) = w T g ,
K g = 1 2 [ K g H 1 + K g H 0 ] ,
t Hot ( g r spot ) = [ K g 1 s r spot ] g .
K g = 1 2 [ K g H 1 + K g H 0 ] ,
K g H 0 = [ σ m 2 + b m ] δ m , m ,
K g H 1 = [ A * h m ( r spot ) + σ m 2 + b m ] δ m , m .
SNR = I Peak I ¯ ring σ ( I ring ) ,
s = A ϕ ,
ϕ lmse = ( ( A A ) 1 A ) s .
ϕ = ϕ lmse + ϕ hid ,
ϕ hid = × H ( r ) ,
H ( r ) = [ 0 , 0 , h ( r ) ] ,
( i , j ) = Δ x ( i , j ) Δ y ( i + 1 , j ) + Δ x ( i , j + 1 ) + Δ y ( i , j ) ,
( R π 2 ) * ( s ) = ( 0 1 1 0 ) * ( s ) = ( s y s x ) ,
A = ( A A + m 2 ) 1 A ,
V = ( A ) ( R π 2 s ) .
ϕ slpdis = s ϕ lmse ,
Ψ = Π k = 1 K { ( X X k ) + m k i ( Y Y k ) } ,
Q = arctan ( Im { Ψ } Re { Ψ } ) ,
σ I 2 = I 2 I 2 I 2 ,

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