  Strain and composition play a fundamental role in semiconductor physics,
since they are means to tune the electronic and optical properties of a
material and hence develop new devices. Today it is still a challenge to
measure strain in epitaxial systems in a non-destructive manner which becomes
especially important in strain-engineered devices that often are subjected to
intense stress. In this work, we demonstrate a microscopic mapping of the full
tensors of strain and lattice orientation by means of scanning X-ray
diffraction microscopy. We develope a formalism to extract all components of
strain and orientation from a set of scanning diffraction measurements and
apply the technique to a patterned In$_x$Ga$_{1-x}$N double layer to study
strain relaxation and indium incorporation phenomena. The contributions due to
varying indium content and threading dislocations are separated and analyzed.
