Abstract

Different coding schemes for diffractive multilevel microlenses are compared. A simple method to code a lens to get the optimum diffraction efficiency is given. Furthermore, a straightforward way to estimate the achievable efficiency of a lens is presented.

© 1995 Optical Society of America

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References

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  1. H. Nishihara, T. Suhara, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, pp. 3–37.
    [CrossRef]
  2. J. Jahns, S. J. Walker, Appl. Opt. 29, 931 (1990).
    [CrossRef] [PubMed]
  3. W. H. Welch, J. E. Morris, M. R. Feldman, J. Opt. Soc. Am. 10, 1729 (1993).
    [CrossRef]
  4. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 361–390.
  5. E. Noponen, J. Turunen, A. Vasara, Appl. Opt. 31, 5910 (1992).
    [CrossRef] [PubMed]

1993 (1)

W. H. Welch, J. E. Morris, M. R. Feldman, J. Opt. Soc. Am. 10, 1729 (1993).
[CrossRef]

1992 (1)

1990 (1)

Feldman, M. R.

W. H. Welch, J. E. Morris, M. R. Feldman, J. Opt. Soc. Am. 10, 1729 (1993).
[CrossRef]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 361–390.

Jahns, J.

Morris, J. E.

W. H. Welch, J. E. Morris, M. R. Feldman, J. Opt. Soc. Am. 10, 1729 (1993).
[CrossRef]

Nishihara, H.

H. Nishihara, T. Suhara, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, pp. 3–37.
[CrossRef]

Noponen, E.

Suhara, T.

H. Nishihara, T. Suhara, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, pp. 3–37.
[CrossRef]

Turunen, J.

Vasara, A.

Walker, S. J.

Welch, W. H.

W. H. Welch, J. E. Morris, M. R. Feldman, J. Opt. Soc. Am. 10, 1729 (1993).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

W. H. Welch, J. E. Morris, M. R. Feldman, J. Opt. Soc. Am. 10, 1729 (1993).
[CrossRef]

Other (2)

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), pp. 361–390.

H. Nishihara, T. Suhara, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, pp. 3–37.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Relative binary area of multilevel diffractive lenses as a function of F/# for four different wavelengths. The minimum feature size is assumed to be 1 μm.

Fig. 2
Fig. 2

Optimum diffraction efficiency profile (solid curve) and efficiency profiles when eight, four, and two phase levels are used (dashed line) and when all phase levels are used (dashed–dotted line). The F/# of this lens is 1.5, and the operating wavelength is 632.8 nm.

Tables (2)

Tables Icon

Table 1 Comparison of the Estimated Efficiencies ηl [Eq. (6)], Which Correspond to the DS Coding with 16 Phase Levels and to RSIDO Codinga

Tables Icon

Table 2 Diffraction Efficiencies of Cylindrical Lenses Coded with the DS Method and Estimated Efficiencies ηl [Eq. (6)]a

Equations (7)

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ϕ ( ρ ) = ( 2 π / λ ) ( f - f 2 + ρ 2 ) - ϕ 0 ,
( A b / A ) = 1 - 4 ( F / # ) 2 tan 2 [ arcsin ( λ / 3 mfs ) ] .
η 1 , N = [ sin ( π / N ) π / N ] 2 .
N = λ sin  θ mfs .
η ( θ ) = { sin [ ( π mfs sin  θ ) / λ ] ( π mfs sin  θ ) / λ } 2 ,
η l = 0 θ max s ( θ ) η ( θ ) d θ ,
s ( θ ) = { 2 / d for a cylindrical lens 8 f tan  θ / d 2 for a spherical lens ,

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