Joint estimation of point spread function and molecule positions in SMLM informed from multiple planes

The advent of single molecule localization microscopy (SMLM) has transformed our capacity to investigate biological structures at the nanoscale. While the research focus has long been on improving localization precision, systematic errors caused by optical aberrations are often overlooked. In the case of 3D SMLM, such errors have the potential to significantly impair the quality of the resulting images. In this paper, we present an imaging and data processing approach that jointly estimates both, molecule positions and optical aberrations in SMLM. Therefore, the method minimizes systematic errors in SMLM reconstructions without the necessity of additional experimental calibration steps, such as the recording of fluorescent bead z-stacks. We investigate the reliability of this approach, especially in situations where the joint retrieval can be expected to be ill-posed, i.e., whenever the sample is "flat" and provides little diversity among the captured single molecule images. To enhance the reliability of the inverse problem solution, we suggest utilizing small SMLM data sets acquired at one or more slightly defocused "auxiliary" planes. We investigate the effectiveness of our approach through numerical simulations and imaging experiments of a calibration probe and nuclear pore complexes. Our method is simple and integrates seamlessly into existing SMLM setups without necessitating modifications or added complexity to the system.