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

2012

2010

2009

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

2006

2005

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

1971

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.

J. Opt. A, Pure Appl. Opt.

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

Opt. Commun.

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

Opt. Lett.

Other

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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