New results on the single molecule localization problem in two and three dimensions

Fluorescence microscopy is an optical microscopy technique which has been extensively used to study specifically- labeled subcellular objects, such as proteins, and their functions. The best possible accuracy with which an object of interest can be localized when imaged using a fluorescence microscope is typically calculated using the Cramer- Rao lower bound (CRLB). The calculation of the CRLB, however, so far relied on an analytical expression for the image of the object. This can pose challenges in practice since it is often difficult to find appropriate analytical models for the images of general objects. Even if an appropriate analytical model is available, the lack of knowledge about the precise values of imaging parameters might also impose difficulties in the calculation of the CRLB. To address these challenges, we have developed an approach that directly uses an experimentally collected image set to calculate the best possible localization accuracy for a general subcellular object in two and three dimensions. In this approach, we fit smoothly connected piecewise polynomials, known as splines, to the experimentally collected image set to provide a continuous model of the object. This continuous model can then be used for the calculation of the best possible localization accuracy.