Abstract

We present a radically new class of optical setup working with white-light illumination, namely, a chromatically compensated processor operating in the Fresnel domain. The optical configuration is a hybrid (diffractive–refractive) three-lens system that exhibits an intermediate achromatic Fresnel plane and an output image plane without chromatic distortion. As a first application of this optical arrangement we develop a parallel space-variant color pattern-recognition experiment with white light.

© 2002 Optical Society of America

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    [CrossRef]

2002 (1)

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, and P. Andrés, Opt. Lett. 27, 944 (2002).
[CrossRef]

2000 (1)

1998 (1)

E. Tajahuerce, J. Lancis, V. Climent, and P. Andrés, Opt. Commun. 151, 86 (1998).
[CrossRef]

1997 (2)

Z. Zalevsky, I. Raveh, G. Shabtay, D. Mendlovic, and J. García, Opt. Eng. 36, 2127 (1997).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, and E. Tepichin, Opt. Commun. 136, 297 (1997).
[CrossRef]

1996 (1)

1992 (1)

1989 (1)

1972 (1)

Andrés, P.

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, and P. Andrés, Opt. Lett. 27, 944 (2002).
[CrossRef]

E. Tajahuerce, G. Saavedra, W. D. Furlan, E. E. Sicre, and P. Andrés, Appl. Opt. 39, 238 (2000).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, and P. Andrés, Opt. Commun. 151, 86 (1998).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, and E. Tepichin, Opt. Commun. 136, 297 (1997).
[CrossRef]

Climent, V.

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, and P. Andrés, Opt. Lett. 27, 944 (2002).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, and P. Andrés, Opt. Commun. 151, 86 (1998).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, and E. Tepichin, Opt. Commun. 136, 297 (1997).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Fernández-Alonso, M.

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, and P. Andrés, Opt. Lett. 27, 944 (2002).
[CrossRef]

Furlan, W. D.

García, J.

Z. Zalevsky, I. Raveh, G. Shabtay, D. Mendlovic, and J. García, Opt. Eng. 36, 2127 (1997).
[CrossRef]

Gregory, D. A.

Highnote, S. M.

Jin, Y.

Katyl, R. H.

Lancis, J.

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, and P. Andrés, Opt. Lett. 27, 944 (2002).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, and P. Andrés, Opt. Commun. 151, 86 (1998).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, and E. Tepichin, Opt. Commun. 136, 297 (1997).
[CrossRef]

Mendlovic, D.

Z. Zalevsky, I. Raveh, G. Shabtay, D. Mendlovic, and J. García, Opt. Eng. 36, 2127 (1997).
[CrossRef]

D. Mendlovic, Z. Zalevsky, and H. M. Ozaktas, in Optical Pattern Recognition, F. T. S. Yu and S. Jutamulia, eds. (Cambridge U. Press, New York, 1998), pp. 89–125.

Mínguez-Vega, G.

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, and P. Andrés, Opt. Lett. 27, 944 (2002).
[CrossRef]

Nestorovic, N.

O’Shea, D. C.

Ozaktas, H. M.

D. Mendlovic, Z. Zalevsky, and H. M. Ozaktas, in Optical Pattern Recognition, F. T. S. Yu and S. Jutamulia, eds. (Cambridge U. Press, New York, 1998), pp. 89–125.

Potous, M. K.

Raveh, I.

Z. Zalevsky, I. Raveh, G. Shabtay, D. Mendlovic, and J. García, Opt. Eng. 36, 2127 (1997).
[CrossRef]

Saavedra, G.

Shabtay, G.

Z. Zalevsky, I. Raveh, G. Shabtay, D. Mendlovic, and J. García, Opt. Eng. 36, 2127 (1997).
[CrossRef]

Sicre, E. E.

Tajahuerce, E.

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, and P. Andrés, Opt. Lett. 27, 944 (2002).
[CrossRef]

E. Tajahuerce, G. Saavedra, W. D. Furlan, E. E. Sicre, and P. Andrés, Appl. Opt. 39, 238 (2000).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, and P. Andrés, Opt. Commun. 151, 86 (1998).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, and E. Tepichin, Opt. Commun. 136, 297 (1997).
[CrossRef]

Tepichin, E.

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, and E. Tepichin, Opt. Commun. 136, 297 (1997).
[CrossRef]

Tiangco, R. P.

Yu, F. T. S.

Zalevsky, Z.

Z. Zalevsky, I. Raveh, G. Shabtay, D. Mendlovic, and J. García, Opt. Eng. 36, 2127 (1997).
[CrossRef]

D. Mendlovic, Z. Zalevsky, and H. M. Ozaktas, in Optical Pattern Recognition, F. T. S. Yu and S. Jutamulia, eds. (Cambridge U. Press, New York, 1998), pp. 89–125.

Zhang, C.

Appl. Opt. (4)

Opt. Commun. (2)

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, and E. Tepichin, Opt. Commun. 136, 297 (1997).
[CrossRef]

E. Tajahuerce, J. Lancis, V. Climent, and P. Andrés, Opt. Commun. 151, 86 (1998).
[CrossRef]

Opt. Eng. (1)

Z. Zalevsky, I. Raveh, G. Shabtay, D. Mendlovic, and J. García, Opt. Eng. 36, 2127 (1997).
[CrossRef]

Opt. Lett. (2)

J. Lancis, G. Mínguez-Vega, E. Tajahuerce, M. Fernández-Alonso, V. Climent, and P. Andrés, Opt. Lett. 27, 944 (2002).
[CrossRef]

F. T. S. Yu, C. Zhang, Y. Jin, and D. A. Gregory, Opt. Lett. 14, 922 (1989).
[CrossRef] [PubMed]

Other (1)

D. Mendlovic, Z. Zalevsky, and H. M. Ozaktas, in Optical Pattern Recognition, F. T. S. Yu and S. Jutamulia, eds. (Cambridge U. Press, New York, 1998), pp. 89–125.

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Figures (4)

Fig. 1
Fig. 1

Schematic of an achromatic Fourier processor.

Fig. 2
Fig. 2

Schematic of a dispersion-compensated space-variant Fresnel processor.

Fig. 3
Fig. 3

Pictures of the irradiance distribution of (a) the input transparency and (b) the reference target. The dominant colors at the input are green, blue, red, and yellow from left to right and from top to bottom. The reference target is white.

Fig. 4
Fig. 4

(a) Irradiance profile along the x axis at the output plane of the Fresnel processor in Fig. 2 for each chromatic component R, G, B. (b) Irradiance at the center of the output plane versus the displacement of the input.

Equations (5)

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

Ux,y=expiπσdσx2+y2-tx0,y0×exp-i2πβ0xx0+yy0dx0dy0,
Ux,y=txM0,yM0g˜xβ0,yβ0,
UFx,y;f0=expiπσdσx2+y2-tx0,y0×exp-iπσ0f0x02+y02×exp-i2πβ0xx0+yy0dx0dy0.
Fx,y;R0=-ax0,y0expiπσ0R0x02+y02×exp-i2πσ0R0xx0+yy0dx0dy0.
UFx,y=expiπσ0Z0M02x2+y2txM0,yM0expiπσ0β02/R0x2+y2axR0β0,yR0β0.

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