Abstract
The localization of fluorescent microspheres is often employed for drift correction and image registration in single molecule microscopy, and is commonly carried out by fitting a point spread function to the image of the given microsphere. The mismatch between the point spread function and the image of the microsphere, however, calls into question the suitability of this localization approach. To investigate this issue, we subject both simulated and experimental microsphere image data to a maximum likelihood estimator that localizes a microsphere by fitting an Airy pattern to its image, and assess the suitability of the approach by evaluating the ability of the estimator to recover the true location of the microsphere with the best possible accuracy as determined based on the Cramér-Rao lower bound. Assessing against criteria based on the standard errors of the mean and the variance for an ideal estimator of the microsphere’s location, we find that microspheres up to 100 nm in diameter can in general be localized using a fixed width Airy pattern, and that microspheres as large as 1 μm in diameter can in general be localized using a floated width Airy pattern.
Highlights
In single molecule microscopy, fluorescent microspheres are commonly used as fiducial markers for the correction of sample drift [1,2,3,4] and the registration of spatially misaligned images, such as those detected by different cameras [2] or acquired in different colors [4,5,6,7]
We assess the suitability of using an Airy pattern to localize a microsphere by interpreting the results of maximum likelihood localizations carried out on both simulated and experimental data sets generated for and under conditions typical of single molecule microscopy
As specified in the section Standard error-based threshold criteria, for a given data set consisting of repeat images of a microsphere, the use of an Airy pattern for localization is determined to be suitable if, for each positional coordinate, the distance between the mean of the estimates and the true value is within some multiple of the standard error of the mean for an ideal estimator, and the distance between the variance of the estimates and the square of the limit of the localization accuracy is within some multiple of the standard error of the variance for an ideal estimator
Summary
Fluorescent microspheres are commonly used as fiducial markers for the correction of sample drift [1,2,3,4] and the registration of spatially misaligned images, such as those detected by different cameras [2] or acquired in different colors [4,5,6,7]. In these applications, the underlying idea is to localize the microspheres and use the estimated positions to determine the spatial adjustments necessary for the proper interpretation of the image data and of the results of analyses. In localization-based super-resolution microscopy [1, 3, 4, 6, 7], for example, the quality of the sub-diffraction-limit reconstruction of subcellular structures is highly sensitive to the accuracy with which drift correction and image registration have been carried out.
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