  The basis for the application of Thomson scattering to the analysis of
coronagraph images has been laid decades ago.Even though the basic formulation
is undebated, a discussion has grown in recent years about the spatial
distribution of Thomson scatter sensitivity in the corona and the inner
heliosphere. These notes are an attempt to clarify the understanding of this
topic. We reformulate the classical scattering calculations in a more
transparent way using modern SI-compatible quantities extended to field
correlation matrices. The resulting concise formulation is easily extended to
the case of relativistic electrons. For relativistic electrons we calculate the
Stokes parameters of the scattered radiation and determine changes in degree
and orientation of its polarisation, blue-shift and radiant intensities
depending on the electron velocity magnitude and direction. We discuss the
probability to see these relativistic effects in white-light coronagraph
observations of the solar corona. Many mathematical and some basic physical
ingredients are made explicit in several chapters of the appendix.
