Channelling contrast analysis of lattice images: conditions for probe-insensitive STEM

Quantitative analysis of lattice resolved images generated by scanning transmission electron microscopy (STEM) requires specification of probe characteristics, such as defocus, aberration and source distribution. In this paper we show that knowledge of such characteristics is unnecessary for quantitative interpretation, if the signal is integrated over a unit cell. Such a condition, whether the result of experimental setup or post-processing of lattice resolved images, reduces the intensity distribution to that of channelling contrast, where the signal for plane wave incidence is averaged over the angular range of the probe, and the result is independent of the probe characteristics. We use a Bloch wave model to show analytically how this applies to all forms of STEM imaging, such as that formed by annular dark field or backscatter detection, as well as characteristic X-ray fluorescence or electron energy loss. As a specific example, we consider how the signal from an annular dark field detector can be used to determine specimen thickness via a transfer curve for the zone axis and scattering geometries employed. This method has advantages over matching lattice images with calculations since these are sensitive to probe coherence and aberration, and saturation of the on-column intensity is approached more rapidly.