A Temporal Phase Unwrapping Algorithm Applied to Dynamic Interferograms Generated in Evaporating Picoliter Liquid Samples

Micromachined picoliter vials in silicon dioxide with a typical depth of 6μm are filled with a liquid sample. Epi-illuminated microscopic imaging during evaporation of the liquid shows dynamic fringe patterns. These fringe patterns are caused by interference between the direct part and the reflected part of an incident plane wave (reflected from the bottom of the vial). The optical path difference (OPD) between the direct and the reflected wave is proportional to the distance to the reflecting bottom of the vial. Evaporation decreases the OPD at the meniscus level and causes alternating constructive and destructive interference of the incident light resulting in an interferogram. Imaging of the space-varying OPD yields a fringe pattern in which the isophotes correspond to isoheight curves of the meniscus. When the bottom is flat, the interference pattern allows monitoring of the liquid meniscus as a function of time during evaporation. First, this paper presents the underlying optical model. Secondly, a temporal phase unwrapping algorithm is described in detail that retrieves the meniscus profile from the interference pattern. This algorithm is based on estimating the wrapped (relative) phase of the fringe pattern in the recorded images.