Abstract

New optical implementations of the Radon–Wigner display for a one-dimensional signal are proposed based on the fractional Fourier transform. The setups involve only one varifocal lens. Furthermore, the same magnification can be realized simultaneously for all the fractional transform orders, which is quite convenient for practical applications.

© 1998 Optical Society of America

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References

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  1. J. C. Wood and D. T. Barry, IEEE Trans. Signal Process. 42, 2094 (1994).
    [CrossRef]
  2. J. C. Wood and D. T. Barry, IEEE Trans. Signal Process. 42, 2105 (1994).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. S. Liu, H. Ren, J. Zhang, and X. Zhang, Appl. Opt. 36, 5671 (1997).
    [CrossRef] [PubMed]
  8. T. Alieva and F. Agullo-Lopez, Opt. Commun. 125, 267 (1996).
    [CrossRef]

1997 (2)

1996 (2)

1994 (3)

A. W. Lohmann and B. H. Soffer, J. Opt. Soc. Am. 11, 1798 (1994).
[CrossRef]

J. C. Wood and D. T. Barry, IEEE Trans. Signal Process. 42, 2094 (1994).
[CrossRef]

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

1993 (1)

Agullo-Lopez, F.

T. Alieva and F. Agullo-Lopez, Opt. Commun. 125, 267 (1996).
[CrossRef]

Alieva, T.

T. Alieva and F. Agullo-Lopez, Opt. Commun. 125, 267 (1996).
[CrossRef]

Andres, P.

Barry, D. T.

J. C. Wood and D. T. Barry, IEEE Trans. Signal Process. 42, 2094 (1994).
[CrossRef]

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

Dorsh, R. G.

Ferreira, C.

Furlan, W. D.

Granieri, S.

Liu, S.

Lohmann, A. W.

Mendlovic, D.

Ren, H.

Saavddra, G.

Soffer, B. H.

A. W. Lohmann and B. H. Soffer, J. Opt. Soc. Am. 11, 1798 (1994).
[CrossRef]

Wood, J. C.

J. C. Wood and D. T. Barry, IEEE Trans. Signal Process. 42, 2094 (1994).
[CrossRef]

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

Zalevsky, Z.

Zhang, J.

Zhang, X.

Appl. Opt. (3)

IEEE Trans. Signal Process. (2)

J. C. Wood and D. T. Barry, IEEE Trans. Signal Process. 42, 2094 (1994).
[CrossRef]

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

J. Opt. Soc. Am. (1)

A. W. Lohmann and B. H. Soffer, J. Opt. Soc. Am. 11, 1798 (1994).
[CrossRef]

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

Opt. Commun. (1)

T. Alieva and F. Agullo-Lopez, Opt. Commun. 125, 267 (1996).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Classic type II Lohmann setup for achieving the FRFT.

Fig. 2
Fig. 2

Schematic of the optical setup for achieving the RWD for a one-dimensional signal.

Fig. 3
Fig. 3

Variances of P, fs, and zs with y for case (a), with c1=1.

Fig. 4
Fig. 4

Variances of P, fs, and zs with y for case (b), with c2=1.

Fig. 5
Fig. 5

Variances of P, fs, and zs with y for case (c), with c3=5.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

Ux=exp-iπλfx2FPsx0,
FPsx0=sx0expiπλFIx2+x02cot ϕ-2xx0 csc ϕdx0,
f=FI/tanϕ/2,
z=FI sinϕ,
fsy=1/tanπPy/4,
zsy=sinπPy/2.
Py=1-c1y,
fsy=1/tanπ1-c1y/4,
zsy=sinπ1-c1y/2,
zsy=1-c2y,
Py=2 arcsin1-c2y/π,
fsy=1/tanarcsin1-c2y/2.
fsy=1+c3y,
Py=4 arctan1+c3y/π,
zsy=sin2 arctan1+c3y.

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