To ensure the motion accuracy of a machine tool over its entire three-dimensional workspace, it is
important to evaluate all the volumetric errors associated with three linear axes including three linear
displacement errors, six straightness errors and three squareness errors. The laser step diagonal
measurement modifies the diagonal displacement measurement, described in the standard ISO 230-6,
by executing a diagonal as a sequence of single-axis motions. It has been claimed that the step diagonal
test enables the identification of all the volumetric error components by using a linear laser interferometer
only. This paper first shows that the conventional formulation of step diagonal measurements
is potentially subject to a significant estimation error caused by setup errors in mirror and laser directions.
We then propose a new formulation of laser step diagonal measurement, in order to accurately
identify three-dimensional volumetric errors even under the existence of setup errors. The effectiveness
of the modified identification scheme is experimentally investigated by an application example of
three-dimensional laser step diagonal measurements to a high-precision vertical machining center.