Phasor based single-molecule localization microscopy in 3D (pSMLM-3D): an algorithm for MHz localization rates using standard CPUs

Abstract

We present a fast and model-free 2D and 3D single-molecule localization algorithm that allows more than 3 million localizations per second on a standard multi-core CPU with localization accuracies in line with the most accurate algorithms currently available. Our algorithm converts the region of interest around a point spread function (PSF) to two phase vectors (phasors) by calculating the first Fourier . CC-BY-NC 4.0 International license not peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was . http://dx.doi.org/10.1101/191957 doi: bioRxiv preprint first posted online 2 coefficients in both x-and y-direction. The angles of these phasors are used to localize the center of the single fluorescent emitter, and the ratio of the magnitudes of the two phasors is a measure for astigmatism, which can be used to obtain depth information (z-direction). Our approach can be used both as a stand-alone algorithm for maximizing localization speed and as a first estimator for more time consuming iterative algorithms.

Accelerating single molecule localization microscopy through parallel processing on a high‐performance computing cluster

“…For manual SMLM experiments, the overheads associated with transferring the data to an HPC cluster may outweigh the advantage gained by parallelizing the processing and this decision will depend on the local network infrastructure as well as the processing power of the local laboratory computer. The phasor-based approach of Martens et al (2018) is interesting since it is already available as a plug-in to ThunderSTORM and could provide useful preview images, particularly if it can be implemented on the laboratory computer to which the SMLM data are acquired.…”

“…Betzig et al, 2006;Rust et al, 2006) to algorithms able to fit higher densities of emitters with overlapping point spread functions (Holden et al, 2011;Wang et al, 2012;Zhu et al, 2012) to noniterative localization techniques (e.g. Henriques et al, 2010;Yu et al, 2011;Parthasarathy, 2012;Liu et al, 2013;Ma et al, 2015;Martens et al, 2018). After trying a number of different SMLM software tools to analyse our large (120 × 120 µm) field of view dSTORM data sets (often > 50 GB), we found ThunderSTORM (Ovesný et al, 2014) with iterative fitting of SMLM data to Gaussian point spread function (PSF) to provide the most useful combination of functionality and processing speed, noting that the benchmarking in Sage et al (2015) supported this choice.…”

“…We were also interested to compare the processing speed of SMLM data processing using iterative fitting of emitters to Gaussian profiles with a noniterative localization technique and have taken advantage of the recent availability of the ThunderSTORM plug-in providing noniterative phasor-based localization (Martens et al, 2018) for SMLM to provide such a comparison. Although the resulting super-resolved images are not the same as those generated by iterative fitting, the phasor localization approach provides images relatively rapidly for both 2D and 3D SMLM data when implemented on a reasonably fast desktop computer -even for large data sets.…”

Analyzing engineered point spread functions using phasor-based single-molecule localization microscopy

“…This approach has been the basis of the earliest localization algorithms [13,16,28], which allow for determination of the emitter locations [16] as long as overlapping of PSFs is negligible. Besides Gaussian-based methods, these symmetrical PSFs have been analyzed via other mathematical frameworks, such as radial symmetry [29], cubic splines [30], or phasor (Fourier) analysis [31]. The shape of the PSF quickly deteriorates, however, if the emitter is out of focus (~100s of nm), leading to both a limited available axial range and inaccessibility of the absolute axial position [32].…”

“…Historically, the first method (astigmatism; AS) introduced a cylindrical lens in the emission pathway to create ellipsoid PSFs if the emitters are out of focus [34,35]. The extent of the deformation along with its orientation allows for determination of the axial position after a calibration procedure, and fitting of these PSFs could usually be performed by derivatized localization algorithms as the ones used for 2D PSFs [28,31,36]. However, the available axial range of astigmatism is limited to less than ~1 µm, which lead to the development of more advanced PSF shaping procedures that involve modulating the light in the pupil (Fourier) plane.…”