Abstract
Optical metrology using phase measurements has benefited significantly from the introduction of phase-shifting
methods, first in interferometry, then also in fringe projection and fringe reflection. As opposed to interferometry, the
latter two techniques generally use a spatiotemporal phase-shifting approach: A sequence of fringe patterns with varying
spacing is used, and a phase map of each is generated by temporal phase shifting, to allow unique assignments of
projector or screen pixels to camera pixels. One ubiquitous problem with phase-shifting structured-light techniques is
that phase artefacts appear near regions of the image where the modulation amplitude of the projected or reflected fringes
changes abruptly, e.g. near dirt/dust particles on the surface in deflectometry or bright-dark object colour transitions in
fringe projection. Near the bright-dark boundaries, responses in the phase maps appear that are not plausible as actual
surface features. The phenomenon has been known for a long time but is usually ignored because it does not compromise
the overall reliability of results. In deflectometry, however, often the objective is to find and classify small defects, and
of course it is then important to distinguish between bogus phase responses caused by fringe modulation changes, and
actual surface defects. We present, for what we believe is the first time, an analytical derivation of the error terms, study
the parameters influencing the phase artefacts (in particular the fringe period), and suggest some simple algorithms to
minimise them.
