Using splines for point spread function calibration atnon-uniform depths in localization microscopy

Single-molecule localization microscopy methods extensively leverage the microscope point spread function (PSF) for fitting the molecules. Calibrating an accurate PSF model is especially difficult in the presence of depth-dependent aberrations which alter the PSF shape depending on the imaging depth. The aberrations at depths of a few micrometers become substantial enough to considerably impoverish the conventional calibration methods performance. In our work, we propose a novel spline model which enables the depth-dependent PSF model calibration by interpolating between the beads at arbitrary depths. We show that diffspline reduces the PSF intensity overestimation by 67.8 percentage points and underestimation by 21.8 percentage points. Moreover, it eliminates the depth-dependent bias and improves the localization precision two-fold compared to previous approaches.