Abstract

We recognize that one can adapt any dispersion-compensated broadband optical Fourier transformer to achieve wavelength compensation in the Fresnel diffraction region just by inserting a diffractive lens at the input plane and vice versa. This unification procedure is employed in a second stage in the design of a novel hybrid (diffractive–refractive) optical setup that provides, in a sequential way, nearly wavelength-independent Fresnel diffraction patterns in the irradiance of the object transmittance.

© 2002 Optical Society of America

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References

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2001 (3)

2000 (2)

D. Wang, A. Pe’er, A. W. Lohmann, and A. A. Friesem, Opt. Eng. 39, 3014 (2000).
[CrossRef]

A. Pe’er, D. Wang, A. W. Lohmann, and A. A. Friesem, Opt. Lett. 25, 776 (2000).
[CrossRef]

1999 (2)

P. Andrés, V. Climent, J. Lancis, G. Mínguez-Vega, E. Tajahuerce, and A. W. Lohmann, Opt. Lett. 24, 1331 (1999).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, and V. Climent, Opt. Commun. 172, 153 (1999).
[CrossRef]

1998 (1)

1997 (1)

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

1995 (1)

1993 (1)

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, Opt. Commun. 104, 39 (1993).
[CrossRef]

1985 (1)

1984 (1)

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

1981 (1)

1972 (1)

Amitai, Y.

Andrés, P.

Arias, I.

Bonet, E.

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, Opt. Commun. 104, 39 (1993).
[CrossRef]

Bryngdahl, O.

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

Climent, V.

Domingo, M.

Eschbach, R.

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

Fernández-Alonso, M.

Friesem, A. A.

García, A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Javidi, B.

Katyl, R. H.

Lancis, J.

Leith, E. N.

Leon, S.

Lindlein, N.

Lohmann, A. W.

Mínguez-Vega, G.

Morris, G. M.

Packross, B.

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

Pe’er, A.

D. Wang, A. Pe’er, A. W. Lohmann, and A. A. Friesem, Opt. Eng. 39, 3014 (2000).
[CrossRef]

A. Pe’er, D. Wang, A. W. Lohmann, and A. A. Friesem, Opt. Lett. 25, 776 (2000).
[CrossRef]

Pons, A.

Reinhorn, S.

Schwab, M.

Schwider, J.

Sicre, E. E.

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, Opt. Commun. 104, 39 (1993).
[CrossRef]

Tajahuerce, E.

Tepichin, E.

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

Wang, D.

A. Pe’er, D. Wang, A. W. Lohmann, and A. A. Friesem, Opt. Lett. 25, 776 (2000).
[CrossRef]

D. Wang, A. Pe’er, A. W. Lohmann, and A. A. Friesem, Opt. Eng. 39, 3014 (2000).
[CrossRef]

Appl. Opt. (6)

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

Opt. Commun. (4)

J. Lancis, E. Tajahuerce, P. Andrés, G. Mínguez-Vega, M. Fernández-Alonso, and V. Climent, Opt. Commun. 172, 153 (1999).
[CrossRef]

B. Packross, R. Eschbach, and O. Bryngdahl, Opt. Commun. 50, 205 (1984).
[CrossRef]

P. Andrés, J. Lancis, E. E. Sicre, and E. Bonet, Opt. Commun. 104, 39 (1993).
[CrossRef]

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

Opt. Eng. (1)

D. Wang, A. Pe’er, A. W. Lohmann, and A. A. Friesem, Opt. Eng. 39, 3014 (2000).
[CrossRef]

Opt. Lett. (3)

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

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Figures (4)

Fig. 1
Fig. 1

Illustration of an optical Fourier transformer.

Fig. 2
Fig. 2

Diagram of a dispersion-compensated broadband Fourier transformer.

Fig. 3
Fig. 3

Hybrid (diffractive–refractive) lens configuration producing a nearly wavelength-independent Fresnel irradiance profile. See text for definitions. As the axial distance, d, is negative in this arrangement, achieving a final real image requires an additional focusing lens.

Fig. 4
Fig. 4

Achromatic diffraction patterns of a one-dimensional grating: (a) Fraunhofer pattern provided by the DCFT in Ref. 6, (b) first self-image provided by the DCFDS shown in Fig. 3. The originals were color pictures recorded with white light.

Equations (5)

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

Ux,y=expiπσzx2+y2-tx0,y0×exp-i2πσfexx0+yy0dx0dy0,
ULx,y=expiπσzx2+y2-tx0,y0×exp-iπσfx02+y02×exp-i2πσfexx0+yy0dx0dy0.
Uαx,y=expiπαx2+y2-tx0,y0×expiπαx02+y02×exp-i2παxx0+yy0dx0dy0,
Ux,y=expiπσzx2+y2-tx0,y0×exp-i2πSxx0+yy0dx0dy0,
UDLx,y=expiπσzx2+y2-tx0,y0×exp-iπσ0f0x02+y02×exp-i2πSxx0+yy0dx0dy0.

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