scholarly journals Accurate 4Pi single-molecule localization using an experimental PSF model

2020 ◽  
Author(s):  
Yiming Li ◽  
Elena Buglakova ◽  
Yongdeng Zhang ◽  
Jervis Vermal Thevathasan ◽  
Joerg Bewersdorf ◽  
...  
Keyword(s):  
Single Molecule ◽  
Simulated Data ◽  
Current Data ◽  
Localization Algorithm ◽  
Resolution Limit ◽  
Isotropic Resolution ◽  
Spread Function ◽  
Phase Images ◽  
Analysis Workflow ◽  
Single Molecule Localization Microscopy

Interferometric single-molecule localization microscopy (iPALM, 4Pi-SMS) uses multiphase interferometry to localize single fluorophores and achieves nanometer isotropic resolution in 3D. The current data analysis workflow, however, fails to reach the theoretical resolution limit due to the suboptimal localization algorithm. Here, we develop a method to fit an experimentally derived point spread function (PSF) model to the interference 4Pi-PSF. As the interference phase is not fixed with respect to the shape of the PSF, we decoupled the phase term in the model from the 3D position of the PSF. The fitter can reliably infer the interference period even without introducing astigmatism, reducing the complexity of the microscope. Using a spline-interpolated experimental PSF model and by fitting all phase images globally, we show on simulated data that we can achieve the theoretical limit of 3D resolution, the Cramer-Rao lower bound (CRLB), also for the 4Pi microscope.

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

2017 ◽  
Author(s):  
Koen J.A. Martens ◽  
Arjen N. Bader ◽  
Sander Baas ◽  
Bernd Rieger ◽  
Johannes Hohlbein
Keyword(s):  
Single Molecule ◽  
Iterative Algorithms ◽  
Region Of Interest ◽  
Depth Information ◽  
Localization Algorithm ◽  
Two Phase ◽  
Model Free ◽  
Spread Function ◽  
2D And 3D ◽  
Single Molecule Localization Microscopy

AbstractWe 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 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.

scholarly journals Quantifying accuracy and heterogeneity in single-molecule super-resolution microscopy

2019 ◽  
Author(s):  
Hesam Mazidi ◽  
Tianben Ding ◽  
Arye Nehorai ◽  
Matthew D. Lew
Keyword(s):  
Single Molecule ◽  
Computational Models ◽  
Amyloid Fibrils ◽  
Imaging System ◽  
Simulated Data ◽  
Super Resolution ◽  
Ground Truth ◽  
Localization Algorithm ◽  
Reconstruction Algorithms ◽  
Imaging Data

The resolution and accuracy of single-molecule localization micro-scopes (SMLMs) are routinely benchmarked using simulated data, calibration “rulers,” or comparisons to secondary imaging modalities. However, these methods cannot quantify the nanoscale accuracy of an arbitrary SMLM dataset. Here, we show that by computing localization stability under a well-chosen perturbation with accurate knowledge of the imaging system, we can robustly measure the confidence of individual localizations without ground-truth knowledge of the sample. We demonstrate that our method, termed Wasserstein-induced flux (WIF), measures the accuracy of various reconstruction algorithms directly on experimental 2D and 3D data of microtubules and amyloid fibrils. We further show that WIF confidences can be used to evaluate the mismatch between computational models and imaging data, enhance the accuracy and resolution of recon-structed structures, and discover hidden molecular heterogeneities. As a computational methodology, WIF is broadly applicable to any SMLM dataset, imaging system, and localization algorithm.

scholarly journals Photon count estimation in single-molecule localization microscopy

2018 ◽  
Author(s):  
Rasmus Ø. Thorsen ◽  
Christiaan N. Hulleman ◽  
Mathias Hammer ◽  
David Grünwald ◽  
Sjoerd Stallinga ◽  
...  
Keyword(s):  
Single Molecule ◽  
Axial Position ◽  
Optical Aberrations ◽  
Intensity Estimation ◽  
Localization Microscopy ◽  
Photon Count ◽  
Point Spread ◽  
Spread Function ◽  
Gaussian Point ◽  
Single Molecule Localization Microscopy

Recently, Franke, Sauer and van de Linde1 introduced a way to estimate the axial position of single-molecules (TRABI). To this end, they compared the detected photon count from a temporal radial-aperture-based intensity estimation to the estimated count from Gaussian point-spread function (PSF) fitting to the data. Empirically they found this photometric ratio to be around 0.7-0.8 close to focus and decreasing away from it. Here, we explain this reported but unexplained discrepancy and furthermore show that the photometric ratio as indicator for axial position is susceptible even to typical optical aberrations.

A literature review of localization methods and emergence of deep learning in single-molecule localization microscopy

2020 ◽  
Author(s):  
Anish Mukherjee
Keyword(s):  
Deep Learning ◽  
Single Molecule ◽  
Super Resolution ◽  
Point Sources ◽  
Learning Approaches ◽  
Localization Algorithm ◽  
Localization Microscopy ◽  
Trade Offs ◽  
Emitter Localization ◽  
Single Molecule Localization Microscopy

The quality of super-resolution images largely depends on the performance of the emitter localization algorithm used to localize point sources. In this article, an overview of the various techniques which are used to localize point sources in single-molecule localization microscopy are discussed and their performances are compared. This overview can help readers to select a localization technique for their application. Also, an overview is presented about the emergence of deep learning methods that are becoming popular in various stages of single-molecule localization microscopy. The state of the art deep learning approaches are compared to the traditional approaches and the trade-offs of selecting an algorithm for localization are discussed.

scholarly journals Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines

2016 ◽  
Author(s):  
Hazen P. Babcock ◽  
Xiaowei Zhuang
Keyword(s):  
Single Molecule ◽  
Super Resolution ◽  
Computation Time ◽  
Cubic Splines ◽  
Localization Algorithm ◽  
Localization Microscopy ◽  
Analytical Functions ◽  
Open Source Software Package ◽  
Microscopy Data ◽  
Single Molecule Localization Microscopy

AbstractThe resolution of super-resolution microscopy based on single molecule localization is in part determined by the accuracy of the localization algorithm. In most published approaches to date this localization is done by fitting an analytical function that approximates the point spread function (PSF) of the microscope. However, particularly for localization in 3D, analytical functions such as a Gaussian, which are computationally inexpensive, may not accurately capture the PSF shape leading to reduced fitting accuracy. On the other hand, analytical functions that can accurately capture the PSF shape, such as those based on pupil functions, can be computationally expensive. Here we investigate the use of cubic splines as an alternative fitting approach. We demonstrate that cubic splines can capture the shape of any PSF with high accuracy and that they can be used for fitting the PSF with only a 2-3x increase in computation time as compared to Gaussian fitting. We provide an open-source software package that measures the PSF of any microscope and uses the measured PSF to perform 3D single molecule localization microscopy analysis with reasonable accuracy and speed.

scholarly journals Minimizing Structural Bias in Single-Molecule Super-Resolution Microscopy

2018 ◽  
Author(s):  
Hesam Mazidi ◽  
Jin Lu ◽  
Arye Nehorai ◽  
Matthew D. Lew
Keyword(s):  
Single Molecule ◽  
Super Resolution ◽  
Estimation Algorithm ◽  
Image Resolution ◽  
Spread Function ◽  
Localization Errors ◽  
Imaging Artifacts ◽  
Detection And Localization ◽  
Super Resolution Microscopy ◽  
Single Molecule Localization Microscopy

ABSTRACTSingle-molecule localization microscopy (SMLM) depends on sequential detection and localization of individual molecular blinking events. Due to the stochasticity of single-molecule blinking and the desire to improve SMLM’s temporal resolution, algorithms capable of analyzing frames with a high density (HD) of active molecules, or molecules whose images overlap, are a prerequisite for accurate location measurements. Thus far, HD algorithms are evaluated using scalar metrics, such as root-mean-square error, that fail to quantify the structure of errors caused by the structure of the sample. Here, we show that the spatial distribution of localization errors within super-resolved images of biological structures are vectorial in nature, leading to systematic structural biases that severely degrade image resolution. We further demonstrate that the shape of the microscope’s point-spread function (PSF) fundamentally affects the characteristics of imaging artifacts. We built a Robust Statistical Estimation algorithm (RoSE) to minimize these biases for arbitrary structures and PSFs. RoSE accomplishes this minimization by estimating the likelihood of blinking events to localize molecules more accurately and eliminate false localizations. Using RoSE, we measure the distance between crossing microtubules, quantify the morphology of and separation between vesicles, and obtain robust recovery using diverse 3D PSFs with unmatched accuracy compared to state-of-the-art algorithms.

scholarly journals Enhanced 4Pi single-molecule localization microscopy with coherent pupil based localization

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Sheng Liu ◽  
Fang Huang
Keyword(s):  
Adaptive Optics ◽  
Single Molecule ◽  
Super Resolution ◽  
Resolving Power ◽  
Localization Algorithm ◽  
Whole Cells ◽  
4Pi Microscopy ◽  
Axial Dimension ◽  
Localization Precision ◽  
Single Molecule Localization Microscopy

AbstractOver the last decades, super-resolution techniques have revolutionized the field of fluorescence microscopy. Among them, interferometric or 4Pi microscopy methods exhibit supreme resolving power in the axial dimension. Combined with single-molecule detection/localization and adaptive optics, current 4Pi microscopy methods enabled 10–15 nm isotropic 3D resolution throughout whole cells. However, further improving the achieved 3D resolution poses challenges arising from the complexity of single-molecule emission patterns generated by these coherent single-molecule imaging systems. These complex emission patterns render a large portion of information carrying photons unusable. Here, we introduce a localization algorithm that achieves the theoretical precision limit for a 4Pi based single-molecule switching nanoscopy (4Pi-SMSN) system, and demonstrate improvements in localization precision, accuracy as well as stability comparing with state-of-the-art 4Pi-SMSN methods.

scholarly journals Depth-dependent PSF calibration and aberration correction for 3D single-molecule localization

2019 ◽  
Author(s):  
Yiming Li ◽  
Yu-Le Wu ◽  
Philipp Hoess ◽  
Markus Mund ◽  
Jonas Ries
Keyword(s):  
Single Molecule ◽  
Open Source Software ◽  
Software Tool ◽  
Calibration Procedure ◽  
Experimental Calibration ◽  
Point Spread ◽  
Processing Step ◽  
Spread Function ◽  
The Individual ◽  
Single Molecule Localization Microscopy

Abstract3D Single molecule localization microscopy relies on fitting of the individual molecules with a point spread function (PSF) model. The reconstructed images often show local squeezing or expansion in z. A common cause are depth-induced aberrations in conjunction with an imperfect PSF model calibrated from beads on a coverslip, resulting in a mismatch between measured PSF and real PSF. Here, we developed a strategy for accurate z-localization in which we use the imperfect PSF model for fitting, determine the fitting errors and correct for them in a post-processing step. We present an open-source software tool and a simple experimental calibration procedure that allow retrieving accurate z-positions in any PSF engineering approach or fitting modality, even at large imaging depths.

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