Abstract

We show the adaptation of a multifunctional optical system consisting of two spatial light modulators for the optimal measurement of the Radon–Wigner transform of one-dimensional signals. The proposed Radon–Wigner display allows reconstructing the Wigner distribution and the phase or the mutual intensity of fully or partially coherent fields, respectively. It is also suitable for the analysis of two-dimensional rotationally symmetric or separable in Cartesian coordinates optical fields. The feasibility of the proposed scheme is experimentally demonstrated in several examples.

© 2011 Optical Society of America

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References

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  1. J. Wood and D. Barry, IEEE Trans. Signal Process. 42, 2105 (1994).
    [CrossRef]
  2. M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
    [CrossRef] [PubMed]
  3. D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, Appl. Opt. 35, 3925 (1996).
    [CrossRef] [PubMed]
  4. Y. Zhang, B.-Y. Gu, B.-Z. Dong, and G.-Z. Yang, Opt. Lett. 23, 1126 (1998).
    [CrossRef]
  5. W. D. Furlan, C. Soriano, and G. Saavedra, Appl. Opt. 47, E63 (2008).
    [CrossRef] [PubMed]
  6. J. A. Rodrigo, T. Alieva, and M. L. Calvo, Opt. Express 17, 4976 (2009).
    [CrossRef] [PubMed]
  7. J. A. Rodrigo, T. Alieva, and M. J. Bastiaans, in Optical and Digital Image Processing, G.Cristóbal, P.Schelkens, and H.Thienpont, eds. (Wiley, 2011), pp. 251.
    [CrossRef]
  8. G. S. Agarwal and R. Simon, Opt. Lett. 25, 1379 (2000).
    [CrossRef]
  9. J. Davis, D. Cottrell, J. Campos, M. Yzuel, and I. Moreno, Appl. Opt. 38, 5004 (1999).
    [CrossRef]
  10. A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, J. Opt. Soc. Am. A 26, 1301 (2009).
    [CrossRef]

2011 (1)

J. A. Rodrigo, T. Alieva, and M. J. Bastiaans, in Optical and Digital Image Processing, G.Cristóbal, P.Schelkens, and H.Thienpont, eds. (Wiley, 2011), pp. 251.
[CrossRef]

2009 (2)

2008 (1)

2000 (1)

1999 (1)

1998 (1)

1996 (1)

1994 (2)

J. Wood and D. Barry, IEEE Trans. Signal Process. 42, 2105 (1994).
[CrossRef]

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Agarwal, G. S.

Alieva, T.

J. A. Rodrigo, T. Alieva, and M. J. Bastiaans, in Optical and Digital Image Processing, G.Cristóbal, P.Schelkens, and H.Thienpont, eds. (Wiley, 2011), pp. 251.
[CrossRef]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, J. Opt. Soc. Am. A 26, 1301 (2009).
[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, Opt. Express 17, 4976 (2009).
[CrossRef] [PubMed]

Barry, D.

J. Wood and D. Barry, IEEE Trans. Signal Process. 42, 2105 (1994).
[CrossRef]

Bastiaans, M. J.

J. A. Rodrigo, T. Alieva, and M. J. Bastiaans, in Optical and Digital Image Processing, G.Cristóbal, P.Schelkens, and H.Thienpont, eds. (Wiley, 2011), pp. 251.
[CrossRef]

Beck, M.

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Calvo, M. L.

Cámara, A.

Campos, J.

Cottrell, D.

Davis, J.

Dong, B.-Z.

Dorsch, R. G.

Ferreira, C.

Furlan, W. D.

Gu, B.-Y.

Lohmann, A. W.

McAlister, D. F.

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Mendlovic, D.

Moreno, I.

Raymer, M. G.

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Rodrigo, J. A.

J. A. Rodrigo, T. Alieva, and M. J. Bastiaans, in Optical and Digital Image Processing, G.Cristóbal, P.Schelkens, and H.Thienpont, eds. (Wiley, 2011), pp. 251.
[CrossRef]

A. Cámara, T. Alieva, J. A. Rodrigo, and M. L. Calvo, J. Opt. Soc. Am. A 26, 1301 (2009).
[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, Opt. Express 17, 4976 (2009).
[CrossRef] [PubMed]

Saavedra, G.

Simon, R.

Soriano, C.

Wood, J.

J. Wood and D. Barry, IEEE Trans. Signal Process. 42, 2105 (1994).
[CrossRef]

Yang, G.-Z.

Yzuel, M.

Zalevsky, Z.

Zhang, Y.

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Figures (5)

Fig. 1
Fig. 1

Radon–Wigner display scheme.

Fig. 2
Fig. 2

(a) Experimental and (c) numerically simulated RWT of a window signal. WD reconstructed from the (b) experimental and (d) simulated RWT.

Fig. 3
Fig. 3

(a) Experimental RWT of a windowed chirp signal and its WD recovered from (b) single- and (c) double-shot measurements. (d) Simulated WD.

Fig. 4
Fig. 4

Theoretical (solid black line) and experimental phase profiles retrieved from single- and double-shot measurements of the RWT of a windowed chirp signal with parameter f c = 0.93 m .

Fig. 5
Fig. 5

(a), (c) Experimental and (b), (d) simulated WD of the radial profile of the LG 0 , 0 + 2 LG 2 , 0 beam and of the HG 4 signal, respectively.

Equations (4)

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P ( α , x ) = d q W ( x cos α s 2 q sin α , q cos α + s 2 x sin α ) ,
K α ( x , u ) = exp { i π s 2 sin α [ ( x 2 + u 2 ) cos α 2 x u ] } s i sin α .
t ( 1 ) ( x ; j ) = exp [ i π s 2 x 2 ( 2 cot α j 2 ) ] ,
t ( 2 ) ( x ; j ) = exp [ i π s 2 x 2 4 ( 1 sin α N j + 1 ) ] ,

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