The Precision Measurement of Roundness – M. Steadman

A roundness measuring system is being developed at the National
Physical Laboratory (NPL) for assessing X-ray mirrors and other axisymmetric
surfaces to an accuracy approaching 1 nm. Spindle error contributes
to measured radial displacement, and analyses in two and in three dimensions
show that three and all six respectively of the kinematic components
of error are involved. Experimental data obtained with a stylus transducer on
a sphere confirm predictions of the two-dimensional analysis, In general,
there is an axial plane for the transducer in which optimal performance of
the spindle is obtained. For surfaces of suitable smoothness the system of
laser autocollimation and slope integration developed at NPL for profilometry
can be applied to the non-contact measurement of roundness to nanometre
levels.