Comparison of aplanatic and real lens focused spots in the framework of the local plane interface approximation

Tight focusing of various beams is widely used for microscopy, optical tweezers, lithography, optical storage, etc. In literature, the investigation of the tightly focused spot is very often based on an ideal lens, which is aplanatic, by the Debye-Wolf integral. In this work, we formulate the aplanatic lens by interpreting the Gaussian reference sphere as a fictitious surface. In this manner, the formulation of an ideal lens is analogous to the one of a real lens by local plane interface approximation, which is well known. It is straightforward to interpret. And furthermore, we compare the tight focusing of differently polarized beams via ideal and real lenses with circular and annular apertures. We find the focal spot by a well-designed real lens is in good agreement with that of the ideal lens in the case of perfect alignment. But the appearance of misalignment distorts the focal spot. The deformed focal spot is more sensitive in the case of the annular aperture compared with the circular aperture. It is in good agreement with the experimental results in literature. An investigation of the tolerance of misalignment of a specific lens system is also performed.