Abstract
The computation of point spread functions, which are typically used to model the image profile of a single molecule, represents a central task in the analysis of single molecule microscopy data. To determine how the accuracy of the computation affects how well a single molecule can be localized, we investigate how the fineness with which the point spread function is integrated over an image pixel impacts the performance of the maximum likelihood location estimator. We consider both the Airy and the two-dimensional Gaussian point spread functions. Our results show that the point spread function needs to be adequately integrated over a pixel to ensure that the estimator closely recovers the true location of the single molecule with an accuracy that is comparable to the best possible accuracy as determined using the Fisher information formalism. Importantly, if integration with an insufficiently fine step size is carried out, the resulting estimates can be significantly different from the true location, particularly when the image data is acquired at relatively low magnifications. We also present a methodology for determining an adequate step size for integrating the point spread function.
Highlights
In single molecule microscopy, accurately determining the location of a single molecule is a central problem that has significant implications for the analysis of the acquired data [1, 2]
Both the difference d between the median of the estimates and the true value, and the percentage difference δ between the standard deviation of the estimates and the practical localization accuracy measure (PLAM), are plotted as a function of the pixel integration factor (PIF) used by the maximum likelihood (ML) estimator
The computation of image profiles represents an integral task in the analysis of single molecule microscopy data
Summary
Accurately determining the location of a single molecule is a central problem that has significant implications for the analysis of the acquired data [1, 2]. In localization microscopy the accuracy with which the position of a single molecule can be estimated influences the resolution of the reconstructed superresolution image, which in turn affects the interpretation of the results [3,4,5]. The localization algorithm typically consists of a curve fitting procedure wherein an appropriately chosen parametric image profile is fitted to a region of interest in the image to determine the position of the single molecule. The selected image profile is typically assumed to model the point spread function of the microscope. In many single molecule imaging applications, various research groups assume a two-dimensional (2D) Gaussian profile to model the point spread function of the microscope [7,8,9]
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