Nanometer-scale height measurements in micromachined picoliter vials based on interference fringe analysis

Micromachined picoliter vials in silicon dioxide with a typical depth of 6.0 μm 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. On the other hand, when there are objects on the bottom of the vial, the height of these objects are observed as phase jumps in the fringes proportional to their height. First, this paper presents the underlying optical model. Secondly, an image processing method is described to retrieve 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. Finally, this algorithm is applied to measure height differences on the bottom in other micromachined vials with a precision of about five nanometer