Abstract

An improved first Rayleigh-Sommerfeld method (IRSM1) is proposed and applied to the analysis of cylindrical microlenses with small f-numbers. Numerical results obtained by both the IRSM1 and the original Rayleigh–Sommerfeld method (ORSM1) are compared with those obtained by the rigorous boundary element method (BEM). For both refractive and diffractive lenses, the results obtained by the IRSM1 are close to those obtained by the BEM even for small f-numbers; by contrast, the results by the ORSM1 differ significantly from those obtained by the BEM. Moreover, the IRSM1 uses much less time and computer memory in the computations than the BEM.

© 2004 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  6. M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds., Handbook of Optics, Vol. 2: Devices, Measurements, and Properties (McGraw-Hill, New York, 1995).

2002 (1)

1998 (1)

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Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calf., 1968), Chaps. 3 and 4.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, 1999), Chap. 1.
[Crossref]

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, eds., Handbook of Optics, Vol. 2: Devices, Measurements, and Properties (McGraw-Hill, New York, 1995).

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Figures (3)

Fig. 1
Fig. 1

Geometry of a continuous refractive microlens.

Fig. 2
Fig. 2

Normalized intensity distributions for continuous refractive lenses with two f-numbers. (a), (c) Transverse intensity distributions on the preset focal plane of y=-f for f/1.0 and f/0.5, (b), (d) axial intensity distributions on the plane x=0 for f/1.0 and f/0.5. Solid, dotted, and dashed curves correspond to the results calculated by the IRSM1, the BEM, and the ORSM1, respectively.

Fig. 3
Fig. 3

Normalized intensity distributions on the preset focal plane for the diffractive lenses with eight-level quantization depths for two f-numbers. The boundary profiles of the diffractive lenses are shown in the insets.

Tables (1)

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Table 1 Focal Performance of Continuous Refractive Lenses Calculated by Three Methods for TE Polarization

Equations (5)

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Er2=-ΓEΓrΓG2r2,rΓnˆ-G2r2,rΓEΓrΓnˆdl,
EORSM1r2=-ΓtEΓtincrΓtG2RS1r2,rΓtnˆtdl,
EIRSM1r2=-ΓEΓincrΓG2RS1r2,rΓnˆdl.
ASRD=-+I1x-I0BEMx2dx-+I0BEMx2dx1/2,
hx=n2n1-n2f2+x2-f,

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