Abstract

In this paper we compare experimentally two methods of detecting optical vortices from Shack-Hartmann wavefront sensor (SHWFS) data, the vortex potential and the contour sum methods. The experimental setup uses a spatial light modulator (SLM) to generate turbulent fields with vortices. In the experiment, many fields are generated and detected by a SHWFS, and data is analysed by the two vortex detection methods. We conclude that the vortex potential method is more successful in locating vortices in these fields.

© 2011 OSA

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2011

2010

2008

J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun. 281, 360–397 (2008).
[CrossRef]

G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A 25, 225–230 (2008).
[CrossRef]

2004

2001

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

2000

1999

1998

1997

1995

1992

1974

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

1953

H. Babcock, “The possibility of compensated astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229 (1953).
[CrossRef]

Babcock, H.

H. Babcock, “The possibility of compensated astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229 (1953).
[CrossRef]

Barnett, S. M.

Berry, M. V.

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

Burke, D.

Courtial, J.

Dainty, C.

Devaney, N.

Eliel, E. R.

Franke-Arnold, S.

Fried, D. L.

Gbur, G.

Gibson, G.

Harding, C. M.

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]

Kouznetsov, D.

Lane, R. G.

Law, C. T.

Le Bigot, E. O.

Monken, C. H.

Morozov, D. K.

Murphy, K.

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]

Notaras, J.

J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun. 281, 360–397 (2008).
[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]

J. F. Nye, Natural Focusing and Fine Structures of Light (Institute of Physics, London, 1999).

Padgett, M. J.

Pasko, V.

Paterson, C.

J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun. 281, 360–397 (2008).
[CrossRef]

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

Pors, B. J.

Roux, F. S.

Rozas, D.

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

Swartzlander, G. A.

Tyler, G. A.

Tyson, R. K.

Vasnetsov, M.

Vaughn, J. L.

Voitsekhovich, V. V.

Wild, W. J.

Wilson, T.

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]

Woerdman, J. P.

Appl. Opt.

J. Microsc.

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]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Refract. Surg.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

Opt. Commun.

J. Notaras and C. Paterson, “Point-diffraction interferometer for atmospheric adaptive optics in strong scintillation,” Opt. Commun. 281, 360–397 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. R. Soc. Lond. A

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

Publ. Astron. Soc. Pac.

H. Babcock, “The possibility of compensated astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229 (1953).
[CrossRef]

Other

R. K. Tyson, Principles of Adaptive Optics, 3rd ed, Optics and Optoelectronics (CRC Press, 2011).

J. F. Nye, Natural Focusing and Fine Structures of Light (Institute of Physics, London, 1999).

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Figures (8)

Fig. 1
Fig. 1

Differing representations of a phase singularity, showing the spiral phase pattern, (a), and the line of phase discontinuity in an otherwise flat wavefront, (b), the colour bar is in radians.

Fig. 2
Fig. 2

Schematic of the complete optical setup built and used experimentally in the laboratory, with the various beams shown.

Fig. 3
Fig. 3

The normalised intensity scintillation, σ I 2, plotted against the approximate coherence length, r0, for the wavefronts used in the experiments. The error bars on the σ I 2 values correspond to the maximum and minimum intensity scintillation for the various degrees of Shack-Hartmann sampling.

Fig. 4
Fig. 4

Graphs of the percentage of correct detection of vortices against the coherence length, r0, for the vortex potential (the blue line) and the contour sum (the red line), for the case of phase aberrations with uniform intensity. The SH sampling level is 1.68 cm/lenslet for (a), 0.83 cm/lenslet for (b), 0.55 cm/lenslet for (c) and 0.28 cm/lenslet for (d).

Fig. 5
Fig. 5

Percentage of correct detections against SH sampling levels for the contour sum method for six different r0 levels; 80, 32, 21, 11, 8 and 4.8 cms for (a) through to (f) respectively.

Fig. 6
Fig. 6

The percentage of correct detection of optical vortices against the coherence length, r0, and the intensity scintillation, σ I 2, for the vortex potential method (blue line) and the contour sum method (red line), for the case of the full optical field. The Shack-Hartmann sampling level for each of these graphs is; 1.68 cm/lenslet for (a), 0.83 cm/lenslet for (b), 0.55 cm/lenslet for (c) and 0.28 cm/lenslet for (d).

Fig. 7
Fig. 7

Percentage of correct detections against SH sampling levels for the contour sum method for six different coherence lengths, r0; 80 cm, 32 cm, 21 cm, 11 cm, 8 cm and 4.8 cm, and their associated intensity scintillations, σ I 2; for (a) through to (f) respectively.

Fig. 8
Fig. 8

The percentage of correct detection for the contour sum (red) and vortex potential methods (blue) against the spatial separation of vortices in terms of SH lenslets. The case of phase aberrations only, (a), and the case of the full optical field, (b), are shown for a coherence length r0 = 80 cm and an intensity scintillation σ I 2 = 0.04.

Tables (5)

Tables Icon

Table 1 The relationship between the range of values used for the coherence length, r0, and the intensity scintillation, σ I 2, in the experiments. The four separate SH lenslet samplings used are given.

Tables Icon

Table 2 The data used in Fig. 4 comparing how the contour sum method performs for the case of phase aberrations only over the four SH sampling levels shown against the vortex potential method. The data highlighted in grey is that for the vortex potential method, with the data in white is the detection rate for the contour sum method.

Tables Icon

Table 3 The data used in Fig. 4 comparing how the contour sum method performs for the full optical field case over four SH sampling levels to the vortex potential method. The data in grey is that for the vortex potential method, with the data in white is the detection rate for the contour sum method.

Tables Icon

Table 4 The data used in Fig. 8(a) for the case of phase aberrations only. It shows the percentage of correct detections of vortex pairs for various SH lenslet separations.

Tables Icon

Table 5 The data used in Fig. 8(b) for the case of the full optical field. The percentage of correct detections of vortex pairs for various SH lenslet separations is presented.

Equations (6)

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R π / 2 s = ( s y s x ) ,
M = ( M * M + m 2 ) 1 M * ,
V = M R π / 2 s .
C ϕ d l = ± m 2 π .
( i , j ) = s x ( i , j ) + s x ( i , j + 1 ) s x ( i + 1 , j + 1 ) s x ( i + 1 , j ) s y ( i , j ) + s y ( i , j + 1 ) + s y ( i + 1 , j + 1 ) s y ( i + 1 , j ) ,
ϕ total = ϕ lmse + ϕ sd ,

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