A comparative study of high resolution microscopy imaging modalities using a three-dimensional resolution measure

From an acquired image, single molecule microscopy makes possible the determination of the distance separating two closely spaced biomolecules in three-dimensional (3D) space. Such distance information can be an important indicator of the nature of the biomolecular interaction. Distance determination, however, is especially difficult when, for example, the imaged point sources are very close to each other or are located near the focal plane of the imaging setup. In the context of such challenges, we compare the limits of the distance estimation accuracy for several high resolution 3D imaging modalities. The comparisons are made using a Cramer-Rao lower bound-based 3D resolution measure which predicts the best possible accuracy with which a given distance can be estimated. Modalities which separate the detection of individual point sources (e.g., using photoactivatable fluorophores) are shown to provide the best accuracy limits when the two point sources are very close to each other and/or are oriented near parallel to the optical axis. Meanwhile, modalities which implement the simultaneous imaging of the point sources from multiple focal planes perform best when given a near-focus point source pair. We also demonstrate that the maximum likelihood estimator is capable of attaining the limit of the accuracy predicted for each modality.