We find that a microcylindrical axilens with a closed boundary and with an f-number less than 1 still can achieve the properties of long focal depth and high transverse resolution, unlike a microcylindrical axilens with an open boundary, which fails to maintain those properties for low f-numbers. The focusing characteristics of the closed-boundary axilens and the open-boundary axilens are numerically investigated based on the boundary integral method. The numerical results show that the ratio of the extended focal depth of the closed-boundary axilens to the focal depth of the conventional microlens can reach up to 1.26 and 2.12 for the preset focal depths 3 and 5 microm, respectively, even though the f-number is reduced to 1/3.
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