Abstract

A novel focusing structure with fractal properties is presented. It is a photon sieve in which the pinholes are appropriately distributed over the zones of a fractal zone plate. The focusing properties of the fractal photon sieve are analyzed. The good performance of our proposal is demonstrated experimentally with a series of images obtained under white light illumination. It is shown that compared with a conventional photon sieve, the fractal photon sieve exhibits an extended depth of field and a reduced chromatic aberration.

© 2006 Optical Society of America

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References

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  1. S. Wang and X. Zhang, "Terahertz tomographic imaging with a Fresnel lens," Opt. Photonics News 13, 59 (2002).
    [CrossRef]
  2. Y Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
    [CrossRef] [PubMed]
  3. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
    [CrossRef] [PubMed]
  4. R. Hyde, "Eyeglass. 1. Very large aperture diffractive telescopes," Appl. Opt. 38, 4198-4212 (1999).
    [CrossRef]
  5. G. Andersen, "Large optical photon sieve," Opt. Lett. 30, 2976-2978 (2005).
    [CrossRef] [PubMed]
  6. R. Menon, D. Gil, G. Barbastathis, and H. Smith, "Photon sieve lithography," J. Opt. Soc. Am. A 22, 342-345 (2005).
    [CrossRef]
  7. G. Saavedra, W. D. Furlan, and J. A. Monsoriu, "Fractal zone plates," Opt. Lett. 28, 971-973 (2003).
    [CrossRef] [PubMed]
  8. W. D. Furlan, G. Saavedra, and J. A. Monsoriu, "Fractal zone plates produce axial irradiance with fractal profile," Opt. and Photon. News 14, 31 (2003).
    [CrossRef]
  9. J. A. Monsoriu, G. Saavedra, and W. D. Furlan, "Fractal zone plates with variable lacunarity," Opt. Express 12, 4227-4234 (2004).
    [CrossRef] [PubMed]
  10. W. D. Furlan, G. Saavedra and J. A. Monsoriu are preparing a paper to be called "Imaging with fractal zone plates."
  11. Q. Cao and J. Jahns, "Focusing analysis of the pinhole photon sieve: individual far field model," J. Opt. Soc. Am. A 19, 2387-2393 (2002).
    [CrossRef]
  12. Q. Cao and J. Jahns, "Non paraxial model for the focusing of high-numerical-aperture- photon sieves," J. Opt. Soc. Am. A 20, 1005-1012 (2003).
    [CrossRef]
  13. The spectral sensitivity of the camera used in the experiment can be looked up at the site http://astrosurf.com/buil/350d/350d.htm.
  14. M. J. Simpson and A. G. Michette, "Imaging properties of modified Fresnel zone plates," Opt. Acta 31, 403-413 (1984).
    [CrossRef]

2005 (2)

2004 (1)

2003 (4)

Y Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, "Fractal zone plates produce axial irradiance with fractal profile," Opt. and Photon. News 14, 31 (2003).
[CrossRef]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, "Fractal zone plates," Opt. Lett. 28, 971-973 (2003).
[CrossRef] [PubMed]

Q. Cao and J. Jahns, "Non paraxial model for the focusing of high-numerical-aperture- photon sieves," J. Opt. Soc. Am. A 20, 1005-1012 (2003).
[CrossRef]

2002 (2)

S. Wang and X. Zhang, "Terahertz tomographic imaging with a Fresnel lens," Opt. Photonics News 13, 59 (2002).
[CrossRef]

Q. Cao and J. Jahns, "Focusing analysis of the pinhole photon sieve: individual far field model," J. Opt. Soc. Am. A 19, 2387-2393 (2002).
[CrossRef]

2001 (1)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

1999 (1)

1984 (1)

M. J. Simpson and A. G. Michette, "Imaging properties of modified Fresnel zone plates," Opt. Acta 31, 403-413 (1984).
[CrossRef]

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Andersen, G.

Barbastathis, G.

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Cao, Q.

Furlan, W. D.

Gil, D.

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Hyde, R.

Jacobsen, C.

Y Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Jahns, J.

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Menon, R.

Michette, A. G.

M. J. Simpson and A. G. Michette, "Imaging properties of modified Fresnel zone plates," Opt. Acta 31, 403-413 (1984).
[CrossRef]

Monsoriu, J. A.

Saavedra, G.

Seemann, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Simpson, M. J.

M. J. Simpson and A. G. Michette, "Imaging properties of modified Fresnel zone plates," Opt. Acta 31, 403-413 (1984).
[CrossRef]

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Smith, H.

Wang, S.

S. Wang and X. Zhang, "Terahertz tomographic imaging with a Fresnel lens," Opt. Photonics News 13, 59 (2002).
[CrossRef]

Wang, Y

Y Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Yun, W.

Y Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

Zhang, X.

S. Wang and X. Zhang, "Terahertz tomographic imaging with a Fresnel lens," Opt. Photonics News 13, 59 (2002).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. A (3)

Nature (2)

Y Wang, W. Yun, and C. Jacobsen, "Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging," Nature 424, 50-53 (2003).
[CrossRef] [PubMed]

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, "Sharper images by focusing soft x-rays with photon sieves," Nature 414, 184-188 (2001).
[CrossRef] [PubMed]

Opt. Acta (1)

M. J. Simpson and A. G. Michette, "Imaging properties of modified Fresnel zone plates," Opt. Acta 31, 403-413 (1984).
[CrossRef]

Opt. and Photon. News (1)

W. D. Furlan, G. Saavedra, and J. A. Monsoriu, "Fractal zone plates produce axial irradiance with fractal profile," Opt. and Photon. News 14, 31 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Photonics News (1)

S. Wang and X. Zhang, "Terahertz tomographic imaging with a Fresnel lens," Opt. Photonics News 13, 59 (2002).
[CrossRef]

Other (2)

The spectral sensitivity of the camera used in the experiment can be looked up at the site http://astrosurf.com/buil/350d/350d.htm.

W. D. Furlan, G. Saavedra and J. A. Monsoriu are preparing a paper to be called "Imaging with fractal zone plates."

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Figures (5)

Fig. 1.
Fig. 1.

Periodic and fractal 1-D structures to be used to generate zone plates.

Fig. 2.
Fig. 2.

Comparison between (a) Fresnel zone plate, (b) FZP, and (c) FPS.

Fig. 3.
Fig. 3.

Normalized irradiance distributions along the optical axis produced by the zone plates in Figs. 2(b) and 2(c), (a) FZP, (b) and FPS (both computed for S=3).

Fig. 4.
Fig. 4.

Images obtained with FPS (left) and with Fresnel photon sieve (right) in a 4 f setup (λ=568nm). Images (a) and (b) were obtained at the green image plane. In (c) and (d) the object-image distance was kept constant and the defocus was obtained by moving the photon sieve 45 mm towards the CCD.

Fig. 5.
Fig. 5.

Axial irradiances computed for (a) the Fresnel photon sieve and (b) the FPS used in Fig. 4 for λ=647nm (red line, R), 568nm (green line, G), and 488nm (blue line, B).

Equations (3)

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I ( z ) = ( 2 π λ z ) 2 0 a 0 2 π p ( r o , ϕ ) exp ( i π λ z r o 2 ) r o d r o d ϕ 2
p o ( r o ) = 1 2 π 0 a p ( r o , ϕ ) d ϕ .
I ( z ) = ( 2 π λ z ) 2 0 a p o ( r o ) exp ( i π λ z r o 2 ) r o d r o 2 .

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