An improved first Rayleigh-Sommerfeld method (IRSM1) is proposed and applied to the analysis of cylindrical microlenses with small -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 -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.
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