Superresolution fluorescence microscopy consists of localizing single particles—one at a time. This, in turn, provides the means for overcoming Abbe's diffraction limit which considered the simultaneous, rather than separate, excitation of two neighboring fluorophores. There are currently several methods such as STED, PALM, FPALM, or STORM which achieve single-particle excitation. They all have been successfully utilized in a vast number of biological applications.
PSF models play a key role in superresolution techniques. The excitation and depletion beams in STED, for example, create defocus patterns in the specimen, originating from the limited aperture of the objective lens. The reduced excited volume is then determined by the superposition of these two PSF patterns. In PALM, FPALM, and STORM every point-source fluorophore gives rise to a PSF pattern in the image domain, and a localization procedure is applied to the individual patterns. Particle localization results in an approximate 3D location in the object domain, and the PSF model that is being used for this task determines the final accuracy.
In practice, the PSF models that are often being used are based on the Gaussian function. The advantage of using the Gaussian function is twofold: it can approximate the main lobe of the PSF pattern of the microscope and it introduces a relatively low computational complexity. Nevertheless, it is the side-lobe pattern that conveys most of the information about the particle location, and it is the maximum-likelihood criterion, rather than least-squares, that gives the best performance. Additionally, 3D Gaussian models result in poor approximation to the 3D PSF of a microscope, providing further motivation for using more realistic models instead.
There seems to be a gap between theoretical results on achievable localization accuracy and performance of currently available algorithms. In this project, we try to fill this gap by introducing several 3D PSF models that could be used for analyzing superresolution images at high accuracy. 3D reconstruction plays an important role in this project, and we shall try to incorporate PSF models to multiplane microscopic imaging. We also plan to investigate sampling theory aspects of the superresolution techniques, for instance the relation between the density of the fluorophores, the resolution of the acquisition device, and the accuracy of the reconstructed structure.