Large-FOV 3D localization microscopy by spatially variant point spread function generation.

Accurate characterization of the microscopic point spread function (PSF) is crucial for achieving high-performance localization microscopy (LM). Traditionally, LM assumes a spatially invariant PSF to simplify the modeling of the imaging system. However, for large fields of view (FOV) imaging, it becomes important to account for the spatially variant nature of the PSF. Here, we propose an accurate and fast principal components analysis-based field-dependent 3D PSF generator (PPG3D) and localizer for LM. Through simulations and experimental three-dimensional (3D) single-molecule localization microscopy (SMLM), we demonstrate the effectiveness of PPG3D, enabling super-resolution imaging of mitochondria and microtubules with high fidelity over a large FOV. A comparison of PPG3D with a shift-variant PSF generator for 3D LM reveals a threefold improvement in accuracy. Moreover, PPG3D is approximately 100 times faster than existing PSF generators, when used in image plane-based interpolation mode. Given its user-friendliness, we believe that PPG3D holds great potential for widespread application in SMLM and other imaging modalities.

Publisher Correction: DeepSTORM3D: dense 3D localization microscopy and PSF design by deep learning.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

DeepSTORM3D: dense 3D localization microscopy and PSF design by deep learning.

An outstanding challenge in single-molecule localization microscopy is the accurate and precise localization of individual point emitters in three dimensions in densely labeled samples. One established approach for three-dimensional single-molecule localization is point-spread-function (PSF) engineering, in which the PSF is engineered to vary distinctively with emitter depth using additional optical elements. However, images of dense emitters, which are desirable for improving temporal resolution, pose a challenge for algorithmic localization of engineered PSFs, due to lateral overlap of the emitter PSFs. Here we train a neural network to localize multiple emitters with densely overlapping Tetrapod PSFs over a large axial range. We then use the network to design the optimal PSF for the multi-emitter case. We demonstrate our approach experimentally with super-resolution reconstructions of mitochondria and volumetric imaging of fluorescently labeled telomeres in cells. Our approach, DeepSTORM3D, enables the study of biological processes in whole cells at timescales that are rarely explored in localization microscopy.

VIPR: vectorial implementation of phase retrieval for fast and accurate microscopic pixel-wise pupil estimation.

In microscopy, proper modeling of the image formation has a substantial effect on the precision and accuracy in localization experiments and facilitates the correction of aberrations in adaptive optics experiments. The observed images are subject to polarization effects, refractive index variations, and system specific constraints. Previously reported techniques have addressed these challenges by using complicated calibration samples, computationally heavy numerical algorithms, and various mathematical simplifications. In this work, we present a phase retrieval approach based on an analytical derivation of the vectorial diffraction model. Our method produces an accurate estimate of the system's phase information, without any prior knowledge about the aberrations, in under a minute.