Focusing of an elliptical mirror based system with aberrations

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.