Rigorous theory on elliptical mirror focusing for point scanning microscopy

Abstract

A rigorous elliptical mirror focusing formula based on spherical wave transformation is derived as a kind of imaging technique with high NA for potential applications in molecule imaging, spectroscopy and industrial artifact microscopy. An apodization factor is given and used to compare the energy conversation rules in lens transmission and parabolic and elliptical mirror reflections. Simulation results indicate that the axial HFWHM of elliptical and parabolic mirrors is about 80% of the corresponding HFWHM of lens in case of NA = 1 and φs = 0, and the side lobe noise is also slightly lower than that of lens, but the transverse HFWHM of mirrors is comparatively wider despite the width of main lobe is still smaller. In comparison with parabolic mirror based system, an elliptical mirror based system is potentially promising in aberration control of incident beam when the aperture of mirror is enlarged to adapt a large stage or specimen container at a small beam shading ratio.