3D particle tracking and localization provide direct means to monitor biomolecular processes within nano-scale environments. However, optical aberrations due to inhomogeneous refractive indices are a major shortcoming in probing these processes in situ. In particular, point spread functions (PSF) may be distorted resulting in poor localization and linking across frames. This issue is particularly important when using pre-calibrated PSFs that do not take into account sample induced aberrations. The sample induced aberrations are often removed using experimental techniques such as adaptive optics (AO) by introducing new optical components to microscope setups. Here, we propose a computational method, leveraging a Bayesian framework, as an alternative to the AO techniques. Our Bayesian method is capable of simultaneous particle tracking, phase retrieval and PSF reconstruction directly from a given data set, without adding any new hardware to the optical setup. Moreover, our method is data efficient by rigorously propagating uncertainty from all existing sources in the problem, such as the uncertainty in the shape of PSF, often ignored. We benchmark our method using a wide range of synthetic and experimental data.
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