Temporal-multiplexing interferometry applied to co-phased profilometry

Abstract: Fringe-projection profilometry with 1 camera and 1 fringe-projector is a well-known and widely used technique in optical metrology. Spatial-frequency multiplexing interferometry with several spatial-carriers having non-overlapping spatial-spectra is also well known and productive in optical metrology. In this paper we propose temporal-multiplexing phase-shifting interferometry applied to profilometry. That is, instead of having fringe-patterns with well separated spatial-spectra, we propose instead to separate the fringe information in the temporal-spectra. In other words, we may have overlapping spatial-spectra, but separated in the temporal-spectra by frequency multiplexing. Using 1-camera and several fringe-projectors one minimizes the object shadows and specular reflections from the digitizing solid. Temporal multiplexing profilometry allows us to illuminate the object from several projectors turned-on simultaneously. In previous phase-shifting co-phased profilometry, the projectors were turned-on and off sequentially. As seen in this work temporal-multiplexing allow us to demodulate the several fringe-patterns without crosstalk from other simultaneously projected fringes. This is entirely analogous to having several television stations broadcasting simultaneously, each TV-transmitter having its own broadcasting frequency. A given TV-receiver tunes into a single TV-station and filter-out all other broadcasters. Following this analogy, each fringe-projector must have its own temporal broadcasting frequency to remain well separated from all other projectors in the time-spectra domain. In addition to the general theory presented, we assess its feasibility with experimental results.