Abstract

A novel vortex-transform is proposed. This transform allows for generating complex-valued functions from modulated intensity patterns, including high frequency components from modulation, without the generation of unstable phase singularities. From these complex-valued functions it is possible to obtain intensity and pseudo-phase maps to analyze the intensity recordings without the necessity of phase retrieval techniques. The intensity and pseudo-phase maps obtained by using this transform preserve the modulation structure onto the intensity and phase modulo 2π maps, including stable phase singularities.

© 2013 OSA

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2013 (2)

2012 (1)

2010 (2)

2009 (1)

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A, Pure Appl. Opt.11(9), 094021 (2009).
[CrossRef]

2008 (1)

2006 (3)

2005 (1)

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun.248(1-3), 59–68 (2005).
[CrossRef]

2000 (1)

1971 (1)

Almi, U.

Angel, L.

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, “Measuring optical vortices in a speckle pattern using a multi-pinhole interferometer,” Opt. Express18(13), 13836–13841 (2010).
[CrossRef] [PubMed]

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A, Pure Appl. Opt.11(9), 094021 (2009).
[CrossRef]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, “Measuring optical vortices in a speckle pattern using a multi-pinhole interferometer,” Opt. Express18(13), 13836–13841 (2010).
[CrossRef] [PubMed]

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A, Pure Appl. Opt.11(9), 094021 (2009).
[CrossRef]

Bolognini, N.

Chen, W.

Chen, X.

Cheng, C.

Da, F.

Ding, J.

Fienup, J. R.

Fu, Y.

Gai, S.

Gorthi, S. S.

Guo, C. S.

Han, Y. J.

Hanson, S. G.

Hu, S.

Ishii, N.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun.248(1-3), 59–68 (2005).
[CrossRef]

Ishijima, R.

Li, X.

Li, Z.

Liang, G.

Miyamoto, Y.

W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, M. Takeda, and S. G. Hanson, “Optical vortex metrology for nanometric speckle displacement measurement,” Opt. Express14(1), 120–127 (2006).
[CrossRef] [PubMed]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun.248(1-3), 59–68 (2005).
[CrossRef]

Rajshekhar, G.

Rastogi, P.

Takeda, M.

Tang, X.

Tebaldi, M.

Trivi, M.

Wada, A.

Wang, W.

Weinberger, H.

Xu, J. B.

Yang, Y.

Yokozeki, T.

Zhang, M.

Zhou, S.

Appl. Opt. (2)

J. Opt. A, Pure Appl. Opt. (1)

G. C. G. Berkhout and M. W. Beijersbergen, “Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics,” J. Opt. A, Pure Appl. Opt.11(9), 094021 (2009).
[CrossRef]

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

Opt. Commun. (1)

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun.248(1-3), 59–68 (2005).
[CrossRef]

Opt. Express (7)

Opt. Lett. (1)

Other (1)

W. Wang, S. G. Hanson, and M. Takeda, “Optical vortex metrology,” in Advances in Speckle Metrology and Related Techniques, G. H. Kaufmann, ed. (Wiley-VCH, 2011), pp. 207–238.

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Figures (4)

Fig. 1
Fig. 1

Doughnut-like amplitudes and spiral pure phase plate functions for the proposed filter when using Eq. (2) with a four pupil aperture mask: In (a) the amplitude and in (b) the phase modulo 2π.

Fig. 2
Fig. 2

Setups to generate modulated intensity patterns. (a) A plane wave impinges over a multi-aperture mask, and is diffracted through a distance z, where the observation plane is located. . (b) A diffuser is attached to the multi-aperture mask in the latter setup to generate modulated speckle patterns.

Fig. 3
Fig. 3

Superposition of the intensity map obtained by using VT-MP and Laguerre-Gauss. The coincident information is depicted in green

Fig. 4
Fig. 4

Experimental results for modulated speckle patterns, by using the VT-MP. In (a) the recorded speckle intensity, in (b) the VT-MP intensity distribution, and in (c) the respective pseudo-phase map.

Tables (2)

Tables Icon

Table 1 Simulated results for VT-MP applied to a plane wave diffracted by a multi-aperture mask

Tables Icon

Table 2 Simulated results for VT-MP and Laguerre-Gauss transform applied to the light diffracted by 12 multi-aperture mask

Equations (2)

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g ˜ (x,y)= H( f x , f y ) G( f x , f y )exp[ 2πi( f x x+ f y y ) ]d f x d f y
h(x,y)= j=i n ( i π 2 ω 4 )[ r j exp( π 2 r j 2 ω 2 )exp( i α j ) ]

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