Image quality in single-molecule localization microscopy depends largely on the accuracy and precision of the localizations. While under ideal imaging conditions, the theoretically obtainable precision and accuracy are achieved; in practice, this changes if (field-dependent) aberrations are present. Currently, there is no simple way to measure and incorporate these aberrations into the point-spread function (PSF) fitting; therefore, the aberrations are often taken as constant or neglected altogether. Here we introduce a model-based approach to estimate the field-dependent aberration directly from single-molecule data without a calibration step. This is made possible by using nodal aberration theory to incorporate the field dependency of aberrations into our fully vectorial PSF model. This results in a limited set of aberration fit parameters that can be extracted from the raw frames without a bead calibration measurement, also in retrospect. The software implementation is computationally efficient, enabling the fitting of a full 2D or 3D dataset within a few minutes. We demonstrate our method on 2D and 3D localization data of microtubuli, nuclear pore complexes, and nuclear lamina over fields of view of up to 180 µm and compare it with Gaussian fitting, spline-based fitting, and a deep-learning-based approach.

In volume fluorescence microscopy, refractive index matching is essential to minimize aberrations. There are, however, common imaging scenarios where a refractive index mismatch (RIM) between immersion and a sample medium cannot be avoided. This RIM leads to an axial deformation in the acquired image data. Over the years, different axial scaling factors have been proposed to correct for this deformation. While some reports have suggested a depth-dependent axial deformation, so far none of the scaling theories has accounted for a depth-dependent, non-linear scaling. Here, we derive an analytical theory based on determining the leading constructive interference band in the objective lens pupil under RIM. We then use this to calculate a depth-dependent re-scaling factor as a function of the numerical aperture (NA), the refractive indices n₁ and n₂, and the wavelength λ. We compare our theoretical results with wave-optics calculations and experimental results obtained using a measurement scheme for different values of NA and RIM. As a benchmark, we recorded multiple datasets in different RIM conditions, and corrected these using our depth-dependent axial scaling theory. Finally, we present an online web applet that visualizes the depth-dependent axial re-scaling for specific optical setups. In addition, we provide software that will help microscopists to correctly re-scale the axial dimension in their imaging data when working under RIM.