Nanometric depth resolution from multi-focal images in microscopy

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels.

[1]  H. Balci,et al.  Three-dimensional particle tracking via bifocal imaging. , 2007, Nano letters.

[2]  Three-dimensional particle imaging by wavefront sensing. , 2006, Optics letters.

[3]  A. Greenaway,et al.  Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy. , 2010, Optics express.

[4]  O. Mandula,et al.  t-SNARE Protein Conformations Patterned by the Lipid Microenvironment* , 2010, The Journal of Biological Chemistry.

[5]  H. I. Campbell,et al.  High-speed, 3-dimensional, telecentric imaging. , 2006, Optics express.

[6]  Joseph Rosen,et al.  Non-scanning motionless fluorescence three-dimensional holographic microscopy , 2008 .

[7]  W. Greenleaf,et al.  Direct observation of base-pair stepping by RNA polymerase , 2005, Nature.

[8]  A. Greenaway,et al.  Estimation of spatial power spectra in speckle interferometry , 1979 .

[9]  M. Unser,et al.  A maximum-likelihood formalism for sub-resolution axial localization of fluorescent nanoparticles. , 2005, Optics express.

[10]  S. Ram,et al.  High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells. , 2008, Biophysical journal.

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

[12]  Alexander Egner,et al.  Isotropic 3D Nanoscopy based on single emitter switching. , 2008, Optics express.

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

[14]  Yale E Goldman,et al.  Parallax: high accuracy three-dimensional single molecule tracking using split images. , 2009, Nano letters.

[15]  Monika Ritsch-Marte,et al.  Depth of field multiplexing in microscopy. , 2010, Optics express.

[16]  Hideo Higuchi,et al.  Three-dimensional nanometry of vesicle transport in living cells using dual-focus imaging optics. , 2007, Biochemical and biophysical research communications.

[17]  F. Helmchen,et al.  Imaging cellular network dynamics in three dimensions using fast 3D laser scanning , 2007, Nature Methods.

[18]  A H Greenaway,et al.  Simultaneous multiplane imaging with a distorted diffraction grating. , 1999, Applied optics.

[19]  Shuming Nie,et al.  Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes , 2008, Proceedings of the National Academy of Sciences.

[20]  S. Ram,et al.  Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions , 2004, IEEE Transactions on NanoBioscience.

[21]  A. Trubuil,et al.  Visualization and quantification of vesicle trafficking on a three‐dimensional cytoskeleton network in living cells , 2007, Journal of microscopy.

[22]  Y. Sergeev,et al.  Motion of tracer particles in He II , 2005 .

[23]  P. Koumoutsakos,et al.  Feature point tracking and trajectory analysis for video imaging in cell biology. , 2005, Journal of structural biology.

[24]  Glen L. Beane,et al.  Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy. , 2009, Optics express.

[25]  U. Szewzyk,et al.  Widefield deconvolution epifluorescence microscopy combined with fluorescence in situ hybridization reveals the spatial arrangement of bacteria in sponge tissue. , 2000, Journal of microbiological methods.

[26]  Gabriel Popescu,et al.  Hilbert phase microscopy for investigating fast dynamics in transparent systems. , 2005, Optics letters.

[27]  G. Toraldo di Francia,et al.  Super-gain antennas and optical resolving power , 1952 .

[28]  L. Mets,et al.  Nanometer-localized multiple single-molecule fluorescence microscopy. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[29]  J. Lippincott-Schwartz,et al.  Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure , 2009, Proceedings of the National Academy of Sciences.

[30]  Paul M. Blanchard,et al.  Broadband simultaneous multiplane imaging , 2000 .

[31]  S. Hess,et al.  Three-dimensional sub–100 nm resolution fluorescence microscopy of thick samples , 2008, Nature Methods.

[32]  S. Ram,et al.  Improved single particle localization accuracy with dual objective multifocal plane microscopy. , 2009, Optics express.

[33]  J. Katz,et al.  Digital holographic microscope for measuring three-dimensional particle distributions and motions. , 2006, Applied optics.

[34]  R. Muller,et al.  Real-time correction of atmospherically degraded telescope images through image sharpening , 1974 .

[35]  W. E. Moerner,et al.  Localizing and tracking single nanoscale emitters in three dimensions with high spatiotemporal resolution using a double-helix point spread function. , 2010, Nano letters.

[36]  A. C. Aitken,et al.  XV.—On the Estimation of Statistical Parameters , 1942, Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences.