Abstract

We propose a method for designing a two-dimensional random Dirichlet surface that, when it is illuminated at normal incidence by a scalar plane wave, scatters the wave with a circularly symmetric distribution of intensity. The method is applied to the design of a surface that acts as a Lambertian diffuser. The method is tested by computer simulations, and a procedure for fabricating such surfaces on photoresist is described.

© 2003 Optical Society of America

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References

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  1. J. C. Stover, Optical Scattering (SPIE, Bellingham, Wash., 1995).
    [CrossRef]
  2. F. Grum and G. W. Luckey, Appl. Opt. 7, 2295 (1968).
    [CrossRef]
  3. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), p. 281.

1968

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), p. 281.

Grum, F.

Luckey, G. W.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), p. 281.

Stover, J. C.

J. C. Stover, Optical Scattering (SPIE, Bellingham, Wash., 1995).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), p. 281.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), p. 281.

Appl. Opt.

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, New York, 1992), p. 281.

J. C. Stover, Optical Scattering (SPIE, Bellingham, Wash., 1995).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Segment of a single realization of (a) a numerically generated surface profile function Hr and (b) its derivative for a two-dimensional surface that acts as a Lambertian diffuser. The parameters are b=200λ and b0=0.

Fig. 2
Fig. 2

Mean differential reflection coefficient for scattering from a two-dimensional Lambertian diffuser estimated from Np=15,000 realizations of the surface profile function for normal incidence. The parameters are b=200λ, b0=0, and N=200. The dashed curve is a plot of the function given by Eq. (6).

Fig. 3
Fig. 3

Schematic diagram of the setup proposed for the fabrication of a circularly symmetric random surface.

Equations (9)

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RΩs=1Sω2πc2d2u exp-iq·u×d2xexpiau·ζx,
Hr=anr+bn, nbrn+1b, n=0,1,2,,
bn=b0+a0+a1++an-1-nanb, n1.
RΩs=2πaω2πc21qfqa.
fγ=8πγ1+γ22RΩsγ, γ0.
RΩs=1πcos θs, 0θsπ/2.
fγ=8γ1-γ21+γ23θ1-γθγ,
RΩs=1Sω2πc2rq2,
rq=2πn=0N-1exp-iabn×nbn+1bdrrJ0qrexp-iaanr,

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