Considerations on the proposed linear theory of surface measurement for coherence scanning interferometers

It was suggested in [Appl. Opt. 52, 3662 (2013)] that the result of a measurement via coherence scanning inter-ferometry could be viewed as the convolution of a point spread function of the instrument and an open surface in 3D space that lies at the air/material interface over a portion of the object's surface. Further, it was suggested that by measuring certain objects, such as ones that are very close to spherical, and whose surface is known to a sufficient level of accuracy, that a point spread function for the instrument could be determined from the measurement result. We conclude that the approximations used in this calculation do not give sufficient accuracy to allow this to be achieved, and that the truncation of the surface function from the closed surface surrounding the object is not defined sufficiently well in order to give a unique solution to the problem. The physical justification for the truncation of the surface in this manner is also questioned.