Evaluation of disturbing effect of mesh holes in wide-acceptance-angle electrostatic mesh lenses

A curved mesh electrode introduced into an electrostatic lens enables spherical aberration correction over a wide acceptance angle. This technique has great advantages in X-ray photoelectron spectroscopy and related techniques, allowing considerable increase in photoelectron intensity and efficient measurement of photoelectron angular distribution. However, the use of meshes severely limits spatial resolution, as the image produced through each mesh hole is blurred by the lens action of the hole. This feature is studied in detail in this paper, in order to determine the best possible resolution that can be attained in electrostatic mesh lenses with wide acceptance angles. A simple way to evaluate the mesh-hole effect is to use the Davisson-Calbick formula, which expresses the focal length of a single-aperture lens. To make this approach more feasible, we take into account the influence of the angle of incidence to a mesh hole. We characterize the image blur due to each mesh hole in two orthogonal directions, considering the discrepancy in focal length in tangential and sagittal planes. After the demonstration of the validity of our approach in a simple example, the mesh-hole effect of a wide-acceptance-angle electrostatic mesh lens is evaluated.