A grazing incidence interferometer using computer generated diffractiv
e axicon elements as beam splitter and recombiner can be applied for t
he testing of cylindrical surfaces. The interferometer provides a redu
ced sensitivity due to grazing incidence and allows the measurement of
deviations from the cylindrical form in a single step on the whole su
rface of the test piece. The evaluation of the fringe pattern can be c
arried out using phase shifting interferometry whereby the necessary p
hase shifts can be introduced by small axial shifts of one of the axic
ons. In order to extract pure surface deviations from the interferomet
er data. we give a theoretical analysis of phase terms belonging to th
e stale of adjustment of the test sample relative to the interferometr
ic setup. Finally, we discuss a method for the elimination of those ph
ase terms.