  Nanoparticles (NPs) have proven their applicability in biosensing, drug
delivery, and photo-thermal therapy, but their performance depends critically
on the distribution and number of functional groups on their surface. When
studying surface functionalization using super-resolution microscopy, the NP
modifies the fluorophores point-spread function (PSF). This leads to systematic
mislocalizations in conventional analyses employing Gaussian PSFs. Here, we
address this shortcoming by deriving the first-ever analytical PSF model for a
fluorophore near a spherical NP. Its calculation is four orders of magnitude
faster than numerical approaches and thus feasible for direct use in
localization algorithms. We fit this model to individual 2D images from
DNA-PAINT experiments on DNA-coated gold NPs and demonstrate extraction of the
3D positions of functional groups with <5 nm precision, revealing inhomogeneous
surface coverage. Our method is exact, fast, accessible, and poised to become
the standard in super-resolution imaging of NPs for biosensing and drug
delivery applications.
