Localization precision for imaging single molecules with elliptical point spread functions
Authors:Wesley Baxter, Davon Webb
Mentor:Alexander Small, Associate Professor of Physics, Cal Poly Pomona
The Diffraction limit has placed an upper bound on how finely an image can be resolved. Recently, computational techniques have been combined with single-molecule imaging to enable high resolution imaging of fluorescently-labeled biological structures. A few notable examples are STORM and PALM. We seek to apply a mathematical/computational technique in order to find the limit to how finely a fluorophore’s position can be resolved when the microscope produces single-molecule images that are elliptical rather than spherical. The elliptical images are used to obtain 3D information, whereas circular images carry less 3D information. We developed software in Python that finds the Cramer-Rao Lower Bound (CRLB) for the parameters of an image that was generated from a Gaussian PSF. We then simulated a large number of images with the same elliptical PSF that we used in our CRLB calculations. Using the PSF we determined the log likelihood of the data in each pixel of the image. We then used the Newton-Raphson method to find the parameters that maximized the log likelihood. From a large set of measurements we determined the standard deviations of the parameter estimates, both in best cases and more realistic cases. The resolution still scales as 1 over the square root of the photon count. The simulation results show a variance very close to the CRLB predictions. Our MLE approach to estimating ellipticity yields results slightly better than simpler second moment calculations.