Abstract
We report the use of a phase retrieval procedure based on maximum likelihood estimation (MLE) to produce an improved, experimentally calibrated model of a point spread function (PSF) for use in three-dimensional (3D) localization microscopy experiments. The method estimates a global pupil phase function (which includes both the PSF and system aberrations) over the full axial range from a simple calibration scan. The pupil function is used to refine the PSF model and hence enable superior localizations from experimental data. To demonstrate the utility of the procedure, we apply it to experimental data acquired with a microscope employing a tetrapod PSF with a 6 µm axial range. The phase-retrieved model demonstrates significant improvements in both accuracy and precision of 3D localizations relative to the model based on scalar diffraction theory. The localization precision of the phase-retrieved model is shown to be near the limits imposed by estimation theory, and the reproducibility of the procedure is characterized and discussed. Code which performs the phase retrieval algorithm is provided.
Highlights
High-precision localization of nanoscale fluorescent emitters such as quantum dots, nanoparticles, fluorescent beads, and single molecules has enabled optical imaging techniques to track single particles [1,2,3] and visualize sub-diffraction structures in great detail and with molecular specificity via superresolution imaging [4,5,6,7]. Such localization microscopy has been widely used to acquire two-dimensional position data, in which the lateral (x, y) coordinates of an emitter are determined from its point spread function (PSF), namely, the image a point source creates on the camera, via a centroid calculation or a twodimensional fit to a model function (e.g. Gaussian) [8]
All three PSFs look similar since the total phase aberration in our microscope is small, especially in comparison to the contribution of the tetrapod phase pattern, M(ρ,φ)
A simple, global phase retrieval method has been presented to estimate the optical aberrations in a microscope and incorporate them into the imaging model in order to perform singleemitter localization for complex PSF designs
Summary
High-precision localization of nanoscale fluorescent emitters such as quantum dots, nanoparticles, fluorescent beads, and single molecules has enabled optical imaging techniques to track single particles [1,2,3] and visualize sub-diffraction structures in great detail and with molecular specificity via superresolution imaging [4,5,6,7] Such localization microscopy has been widely used to acquire two-dimensional position data, in which the lateral (x, y) coordinates of an emitter are determined from its point spread function (PSF), namely, the image a point source creates on the camera, via a centroid calculation or a twodimensional fit to a model function (e.g. Gaussian) [8]. Our lab demonstrated another family of PSFs called tetrapods, which extend the axial range over which localizations can be achieved to as much as 20 μm, but are able to deliver optimal 3D localization precision over a chosen axial range by encoding the maximum amount of position information in their shape [14,15]
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