Hybrid algorithm based on radial symmetry and weighted least-square ellipse fitting for three-dimensional nanometer particle localization

Abstract. Choosing the localization algorithm in superresolution microscopy is an important factor in determining the resolution in such a modality. The point spread function (PSF) in defocused images has ring structures that can be used to localize the three-dimensional (3-D) position of single particles by calculating the ring center (x and y) and radius (z). As there is no well-developed mathematical model for a defocused PSF, it is difficult to perform a fitting-based algorithm in such images. A particle localization algorithm based on radial symmetry and ellipse fitting is developed to localize the centers and radii of defocused PSFs. Our method can localize the 3-D position of a fluorophore within 20-nm precision in three-dimensions in a range of 40  μm in z-dimension from defocused two-dimensional (2-D) images.

[1]  Andrew W. Fitzgibbon,et al.  Direct Least Square Fitting of Ellipses , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  S. Gibson,et al.  Diffraction by a circular aperture as a model for three-dimensional optical microscopy. , 1989, Journal of the Optical Society of America. A, Optics and image science.

[3]  Lucien E. Weiss,et al.  Multicolour localization microscopy by point-spread-function engineering , 2016, Nature Photonics.

[4]  S. Hess,et al.  Precisely and accurately localizing single emitters in fluorescence microscopy , 2014, Nature Methods.

[5]  Mark Bates,et al.  Three-Dimensional Super-Resolution Imaging by Stochastic Optical Reconstruction Microscopy , 2008, Science.

[6]  Samuel J. Lord,et al.  Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function , 2009, Proceedings of the National Academy of Sciences.

[7]  Alexandr Jonás,et al.  Three-dimensional tracking of fluorescent nanoparticles with subnanometer precision by use of off-focus imaging. , 2003, Optics letters.

[8]  Michael D. Mason,et al.  Ultra-high resolution imaging by fluorescence photoactivation localization microscopy. , 2006, Biophysical journal.

[9]  Lucien E. Weiss,et al.  Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions , 2015, Nano letters.

[10]  J. Lippincott-Schwartz,et al.  Imaging Intracellular Fluorescent Proteins at Nanometer Resolution , 2006, Science.

[11]  A. Savitzky,et al.  Smoothing and Differentiation of Data by Simplified Least Squares Procedures. , 1964 .

[12]  Michael J Rust,et al.  Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM) , 2006, Nature Methods.

[13]  Peter Daldrop,et al.  Camera-based three-dimensional real-time particle tracking at kHz rates and Ångström accuracy , 2014, Nature Communications.

[14]  W. Zipfel,et al.  Simultaneous spatial and temporal focusing of femtosecond pulses , 2005, (CLEO). Conference on Lasers and Electro-Optics, 2005..

[15]  Y. Silberberg,et al.  Scanningless depth-resolved microscopy. , 2005, Optics express.

[16]  Kai Virtanen,et al.  Direct Least Square Fitting of Hyperellipsoids , 2018, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  R. Parthasarathy.  Rapid, accurate particle tracking by calculation of radial symmetry centers , 2012, Nature Methods.

[18]  Pengfei Li,et al.  Real-time infrared gas detection based on an adaptive Savitzky–Golay algorithm , 2015 .

[19]  Yu Ding,et al.  Dual-color multiple-particle tracking at 50-nm localization and over 100-µm range in 3D with temporal focusing two-photon microscopy. , 2016, Biomedical optics express.

[20]  A. Small,et al.  Fluorophore localization algorithms for super-resolution microscopy , 2014, Nature Methods.