  TEM images of strained crystals often exhibit symmetries, the source of which
is not always clear. To understand these symmetries we distinguish between
symmetries that occur from the imaging process itself and symmetries of the
inclusion that might affect the image. For the imaging process we prove
mathematically that the intensities are invariant under specific
transformations. A combination of these invariances with specific properties of
the strain profile can then explain symmetries observed in TEM images. We
demonstrate our approach to the study of symmetries in TEM images using
selected examples in the field of semiconductor nanostructures such as quantum
wells and quantum dots.
