Ranking TEM cameras by their response to electron shot noise

We demonstrate two ways in which the Fourier transforms of images that consist solely of randomly distributed electrons (shot noise) can be used to compare the relative performance of different electronic cameras. The principle is to determine how closely the Fourier transform of a given image does, or does not, approach that of an image produced by an ideal camera, i.e. one for which single-electron events are modeled as Kronecker delta functions located at the same pixels where the electrons were incident on the camera. Experimentally, the average width of the single-electron response is characterized by fitting a single Lorentzian function to the azimuthally averaged amplitude of the Fourier transform. The reciprocal of the spatial frequency at which the Lorentzian function falls to a value of 0.5 provides an estimate of the number of pixels at which the corresponding line-spread function falls to a value of 1/e. In addition, the excess noise due to stochastic variations in the magnitude of the response of the camera (for single-electron events) is characterized by the amount to which the appropriately normalized power spectrum does, or does not, exceed the total number of electrons in the image. These simple measurements provide an easy way to evaluate the relative performance of different cameras. To illustrate this point we present data for three different types of scintillator-coupled camera plus a silicon-pixel (direct detection) camera.