Abstract

We report the first experimental results, to our knowledge, with fractal zone plates implemented in a liquid-crystal display. Our results largely agree with theory for the axial irradiance distribution of these lenses. The dependence of the shape and size of the focus points on critical design parameters is discussed. Additional unpredicted features are also described.

© 2004 Optical Society of America

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References

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  1. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1982).
  2. J. Uozumi and T. Asakura, in Current Trends in Optics, J. C. Dainty, ed. (Academic, Cambridge, 1994), pp. 83–94.
  3. D. Rodriguez Merlo, J. A. Rodrigo Martín-Romo, T. Alieva, and M. L. Calvo, Opt. Spectrosc. 95, 131 (2003).
    [CrossRef]
  4. G. Saavedra, W. D. Furlan, and J. A. Monsoriu, Opt. Lett. 28, 971 (2003).
    [CrossRef] [PubMed]
  5. A. Boivin, J. Opt. Soc. Am. 42, 60 (1952).
  6. J. A. Davis, I. Moreno, and P. Tsai, Appl. Opt. 37, 937 (1998).
    [CrossRef]
  7. I. Moreno and J. A. Davis, Opt. Eng. 37, 3048 (1998).
    [CrossRef]
  8. J. A. Davis, K. O. Valadez, and D. M. Cottrell, Appl. Opt. 42, 2003 (2003).
    [CrossRef] [PubMed]

2003

1998

1952

Alieva, T.

D. Rodriguez Merlo, J. A. Rodrigo Martín-Romo, T. Alieva, and M. L. Calvo, Opt. Spectrosc. 95, 131 (2003).
[CrossRef]

Asakura, T.

J. Uozumi and T. Asakura, in Current Trends in Optics, J. C. Dainty, ed. (Academic, Cambridge, 1994), pp. 83–94.

Boivin, A.

Calvo, M. L.

D. Rodriguez Merlo, J. A. Rodrigo Martín-Romo, T. Alieva, and M. L. Calvo, Opt. Spectrosc. 95, 131 (2003).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Furlan, W. D.

Mandelbrot, B. B.

B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1982).

Monsoriu, J. A.

Moreno, I.

Rodrigo Martín-Romo, J. A.

D. Rodriguez Merlo, J. A. Rodrigo Martín-Romo, T. Alieva, and M. L. Calvo, Opt. Spectrosc. 95, 131 (2003).
[CrossRef]

Rodriguez Merlo, D.

D. Rodriguez Merlo, J. A. Rodrigo Martín-Romo, T. Alieva, and M. L. Calvo, Opt. Spectrosc. 95, 131 (2003).
[CrossRef]

Saavedra, G.

Tsai, P.

Uozumi, J.

J. Uozumi and T. Asakura, in Current Trends in Optics, J. C. Dainty, ed. (Academic, Cambridge, 1994), pp. 83–94.

Valadez, K. O.

Appl. Opt.

J. Opt. Soc. Am.

Opt. Eng.

I. Moreno and J. A. Davis, Opt. Eng. 37, 3048 (1998).
[CrossRef]

Opt. Lett.

Opt. Spectrosc.

D. Rodriguez Merlo, J. A. Rodrigo Martín-Romo, T. Alieva, and M. L. Calvo, Opt. Spectrosc. 95, 131 (2003).
[CrossRef]

Other

B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1982).

J. Uozumi and T. Asakura, in Current Trends in Optics, J. C. Dainty, ed. (Academic, Cambridge, 1994), pp. 83–94.

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Figures (4)

Fig. 1
Fig. 1

Intensity as a function of longitudinal coordinate z for a FZP with N=2 and S=2. For simplicity we display a region up to z=6f.

Fig. 2
Fig. 2

Ordinary FZPs with focal distances f (top left), 3f (top right), 9f (bottom left), and 27f (bottom right). These plates are used for experimental implementation of FZPs in a LCD.

Fig. 3
Fig. 3

FZPs with (a) N=2 and S=2 and (b) N=2 and S=3. See the text for details on the theoretical formulation for the intensity transmittance.

Fig. 4
Fig. 4

Series of five focal regions obtained with the FZP as in Fig. 3(a) implemented in a LCD display: (a) z=1335 mm (with a precision of ±2 cm), (b) z=1445 mm, (c) z=1700 mm, (d) z=2050 mm, (e) z=2370 mm (with a precision of ±2.5 cm).

Equations (2)

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IFZPu, N, S=4 sin2πu2N-1Si=1Ssin22πNu2N-1isin22πu2N-1i.
IZPu, N, S=sin22πMu2N-1Scos2πu2N-1S.

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