Analysis of microlens array with long focal depth and small f-number by improved first Rayleigh-Sommerfeld method

The improved first Rayleigh-Sommerfeld method (IRSM1) is applied to analyse the focusing performance of dual-and tri-cylindrical microlens arrays with long focal depth and small f-number for the TE polarization. The real extended focal depth, the diffraction efficiency, the spot size, and the real position of the focal plane of the microlens array with different f-numbers and the preset extended focal depths are calculated by the IRSM1, rigorous boundary element method (BEM), and original Rayleigh-Sommerfeld method (ORSM1), respectively. The accuracies of the IRSM1 and the ORSM1 are evaluated along the longitudinal direction. The results indicate that the IRSM1 can be used for analysing the cylindrical microlens array with long focal depth and small f-number, but the ORSM1 completely fails for those microlens arrays with small f-number. It is expected that this investigation will provide useful information in the design of the micro-optical elements for realizing longitudinal optical field modulation.