A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking

Recent technological advances have rendered widefield fluorescence microscopy as an invaluable tool to image fast dynamics of trafficking events in two dimensions (i.e., in the plane of focus). Three-dimensional trafficking events are studied by sequentially imaging different planes within the specimen by moving the plane of focus with a focusing device. However, these devices are typically slow and hence when the cell is being imaged at one focal plane, important events could be missed at other focal planes. To overcome this limitation, we recently developed a novel imaging technique called multifocal plane microscopy that enables the simultaneous imaging of multiple focal planes within the sample. Here, by using tools of information theory, we present a quantitative evaluation of this technique in the context of 3D particle tracking. We calculate the Fisher information matrix for the problem of determining the 3D location of an object that is imaged on a multifocal plane setup. In this way, we derive a lower bound on the accuracy with which the object can be localized in 3D. We illustrate our results by considering the object of interest to be a single molecule. It is well known that a conventional widefield microscope has poor depth discrimination capability and therefore there exists significant uncertainty in determining the axial location of the object, especially when it is close to the plane of focus. Our results predict that the multifocal plane microscope setup offers improved accuracy in determining the axial location of objects than a conventional widefield microscope.