Calculation, consequences and measurement of the point spread function for low-loss inelastic scattering

We have previously derived an analytical formula for the point spread function (PSF) that describes the delocalization of low-loss inelastic scattering. Here, we modify the formula to take account variation of scattered-electron phase. The exponentially attenuated Lorentzian form is retained but its halfwidth at half maximum is chosen to provide better agreement with measurements of the median delocalization distance. For low energy losses, the 1/r2 tails of the PSF extend beyond the region of energy deposition, allowing a small-diameter electron probe to provide energy-loss data from relatively undamaged regions of a beam-sensitive specimen. Alternatively, a core-loss or elastic image can be recorded with less damage by sparse scanning, as in scanned moiré imaging. A procedure is proposed for directly measuring the PSF, using a TEM with aberration-corrected lenses and an energy-filtered imaging system.