Abstract

We report the achievement of the first images to our knowledge obtained with a fractal zone plates (FraZPs). FraZPs are diffractive lenses characterized by the fractal structure of their foci. This property predicts an improved performance of FraZPs as image forming devices with an extended depth of field and predicts a reduced chromatic aberration under white-light illumination. These theoretical predictions are confirmed experimentally in this work. We show that the polychromatic modulation transfer function of a FraZP affected by defocus is about two times better than one corresponding to a Fresnel zone plate.

© 2007 Optical Society of America

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References

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2006 (2)

S. H. Tao, X.-C. Yuan, J. Lin, and R. E. Burge, Appl. Phys. Lett. 89, 31105 (2006).
[CrossRef]

J. A. Monsoriu, W. D. Furlan, P. Andrés, and J. Lancis, Opt. Express 14, 9077 (2006).
[CrossRef] [PubMed]

2004 (2)

2003 (2)

2002 (1)

1999 (2)

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, and R. Barrett, Nature 401, 895 (1999).
[CrossRef]

R. A. Hyde, Appl. Opt. 38, 4198 (1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

FraZP design. The same procedure can be followed in designing fractal and Fresnel zone plates. It consists of three steps. (a) A Fresnel zone plate starts from a binary 1D compact supported function q ( ζ ) . After the change of variables ζ = ( r a ) 2 , the resulting function, which is periodic in the new coordinate, is rotated around the origin. The result is the zone plate represented in (b). (c) The originating function for the FraZP is a fractal binary 1D function f ( ζ ) . In this case it is a triadic Cantor set for stage 3 (see Ref. [5] for details). (d) The change of variables and rotation performed to obtain (b) now results in a FraZP.

Fig. 2
Fig. 2

Point spread functions for different wavelengths. The axial irradiances were computed by using Eq. (1) for a = 2.52 mm and λ = 647 nm (red or medium gray), λ = 568 nm (green or light gray), and λ = 488 nm (blue or dark gray). (a) Fresnel zone plate of 81 zones. (b) FraZP of the same focal distance. The FraZP in this case was obtained for a triadic Cantor set like the one in Fig. 1d but developed up to stage 4.

Fig. 3
Fig. 3

Images obtained with a FraZP and with a Fresnel zone plate. Three different locations for the image plane were considered: in front of the paraxial image plane ( d = 44.0 cm ) , at the paraxial image plane ( d = 39.4 cm ) , and behind the paraxial image plane ( d = 34.5 cm ) .

Fig. 4
Fig. 4

Modulation transfer functions for defocused planes. The MTFs correspond to the three locations of the image planes in Fig. 3.

Equations (1)

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I ( z ) = ( 2 π λ z ) 2 0 a p ( r ) exp ( i π λ z r 2 ) r d r 2 ,

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