Analysis of a cylindrical microlens array with long focal depth by a rigorous boundary-element method and scalar approximations

We investigated the focal characteristics of open-regional cylindrical microlens arrays with long focal depth by using a rigorous boundary-element method (BEM) and three scalar methods, i.e., a Kirchhoff and two Rayleigh-Sommerfeld diffraction integral forms. Numerical analysis clearly shows that the model cylindrical microlens arrays with different f-numbers can generate focusing beams with both long focal depth and high transverse resolution. The performance of the cylindrical microlens arrays, such as extended focal depth, relative extended focal depth, diffraction efficiency, and focal spot size, is appraised and analyzed. From a comparison of the results obtained by the rigorous BEM and by scalar approximations, we found that the results are quite similar when the f-number equals f/1.6; however, they are quite different for f/0.8. We conclude that the BEM should be adopted to analyze the performance of a microlens array system whose f-number is less than f/1.0.