Three-dimensional multiple-particle tracking with nanometric precision over tunable axial ranges

The precise localization of nanometric objects in three dimensions is essential to identify functional diffusion mechanisms in complex systems at the cellular or molecular level. However, most optical methods can achieve high temporal resolution and high localization precision only in two dimensions or over a limited axial (z) range. Here we develop a novel wide-field detection system based on an electrically tunable lens that can track multiple individual nanoscale emitters in three dimensions over a tunable axial range with nanometric localization precision. The optical principle of the technique is based on the simultaneous acquisition of two images with an extended depth of field while encoding the z position of the emitters via a lateral shift between images. We provide a theoretical framework for this approach and demonstrate tracking of free diffusing beads and GABAA receptors in live neurons. This approach allows getting nanometric localization precision up to an axial range above 10 µm with a high numerical aperture lens-quadruple that of a typical 3D tracking system. Synchronization or complex fitting procedures are not requested here, which leads to a suitable architecture for localizing single molecules in four dimensions, namely, three dimensions in real-time.