Temporal phase-unwrapping algorithm for dynamic interference pattern analysis in interference-contrast microscopy.

A temporal phase-unwrapping algorithm has been developed for the analysis of dynamic interference patterns generated with interference-contrast microscopy in micromachined picoliter vials. These vials are etched in silicon dioxide, have a typical depth of 6 mum, and are filled with a liquid sample. In this kind of microscopy, fringe patterns are observed at the air-liquid interface. These fringe patterns are caused by interference between the directly reflected part of an incident plane wave and the part of that wave that is reflected on the bottom of the vial. The optical path difference (OPD) between both parts 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 for monitoring of the meniscus as a function of time during evaporation. However, when there are objects on the bottom of the vial, the heights of these objects are observed as phase jumps in the fringes proportional to their heights. First, we present a classical electromagnetic description of interference-contrast microscopy. Second, a temporal phase-unwrapping algorithm is described that retrieves the meniscus profile from the interference pattern. Finally, this algorithm is applied to measure height differences of objects on the bottom in other micromachined vials with a precision of ~5 nm.