Analytic evaluation of the intensity point spread function

Abstract

The intensity point spread function (PSF) for geometric imaging such as occurs in a projection electron system like SCALPEL is derived analytically from the ray aberration coefficients. The results show that, as expected, the PSF for ordinary aberrations has a finite radius and is not Gaussian. Hence blur estimates, which are often based on assuming a Gaussian PSF and computing the root-sum-square or “rss” of the separate blur radii will generally overestimate the true aberration blur. Global space charge acts like an electrostatic lens and hence its effects can be included in the PSF calculation as well. The net PSF can be convolved with an object to produce an accurate representation of the image. The convolution integral can also be performed first which yields the image intensity distribution directly in terms of the aberrations.