No abstract

The effect of primary aberrations on the focusing of an elliptical mirror based system is studied by using the Debye integral. Specifically, the apodization function for elliptical mirror is derived and expressed by the eccentricity of the elliptical mirror. For the elliptical mirror with low aperture, intensity distributions in the presence of aberrations near focus are presented based on the derived scalar theory, while for the high-aperture condition, vectorial theory is used to describe the electric field in the focal region. In particular, the effect of aberrations is studied under radially polarized illumination. Moreover, tolerance conditions are given based on the knowledge of focusing with aberrations. It is found that the elliptical mirror based system shares a similar level of tolerance conditions with that of the single lens, while both of them are more sensitive to the presence of astigmatism than other aberrations. It is believed that the results will theoretically support the application of the high-aperture elliptical mirror in scanning microscopy.

An analytical apodization function of an elliptical mirror with an aperture angle greater than π is derived for the analysis of the focusing properties. The distribution of electric field intensity near the focal region is given using vectorial Debye theory. Simulation results indicate that a bone-shaped focal spot is formed under linearly polarized illumination, and a tight-circularly symmetric spot is generated under radially polarized illumination. The change in eccentricity causes such a change in the focusing pattern under radially polarized illumination, that a greater eccentricity causes a spot tighter in transverse direction but wider in axial direction. Under radially polarized illumination, the transverse and axial fullwidth-at-half-maximum will be 0.382λ and 0.757λ, respectively, and the conversion efficiency of the longitudinal component can go beyond 99%, when the semi-aperture angle is 2π∕3 and the eccentricity is 0.6. It can, therefore, be concluded that the tight focusing pattern with strong and pure longitudinal field can be achieved under radially polarized illumination for particle acceleration, optical tweezers, and high-resolution scanning microscopy.