Recently, single molecule-based superresolution fluorescence microscopy has surpassed the diffraction limit to improve resolution to the order of 20 nm or better. These methods typically use image fitting that assumes an isotropic emission pattern from the single emitters as well as control of the emitter concentration. However, anisotropic single-molecule emission patterns arise from the transition dipole when it is rotationally immobile, depending highly on the molecule's 3D orientation and z position. Failure to account for this fact can lead to significant lateral (x, y) mislocalizations (up to ∼50-200 nm). This systematic error can cause distortions in the reconstructed images, which can translate into degraded resolution. Using parameters uniquely inherent in the double-lobed nature of the Double-Helix Point Spread Function, we account for such mislocalizations and simultaneously measure 3D molecular orientation and 3D position. Mislocalizations during an axial scan of a single molecule manifest themselves as an apparent lateral shift in its position, which causes the standard deviation (SD) of its lateral position to appear larger than the SD expected from photon shot noise. By correcting each localization based on an estimated orientation, we are able to improve SDs in lateral localization from ∼2× worse than photon-limited precision (48 vs. 25 nm) to within 5 nm of photon-limited precision. Furthermore, by averaging many estimations of orientation over different depths, we are able to improve from a lateral SD of 116 (∼4× worse than the photonlimited precision; 28 nm) to 34 nm (within 6 nm of the photon limit).

We demonstrate quantitative multicolor 3D subdiffraction imaging of the structural arrangement of fluorescent protein fusions in living Caulobacter crescentus bacteria. Given single-molecule localization precisions of 20–40 nm, a flexible locally-weighted image registration algorithm is critical to accurately combine the super-resolution data with <10 nm error. Simple surface-relief dielectric phase masks implement a double-helix response at two wavelengths to distinguish two different fluorescent labels and to quantitatively and precisely localize them relative to each other in 3D.

Super-resolution imaging with photo-activatable or photoswitchable probes is a promising tool in biological applications to reveal previously unresolved intra-cellular details with visible light. This field benefits from developments in the areas of molecular probes, optical systems, and computational post-processing of the data. The joint design of optics and reconstruction processes using double-helix point spread functions (DH-PSF) provides high resolution three-dimensional (3D) imaging over a long depth-of-field. We demonstrate for the first time a method integrating a Fisher information efficient DH-PSF design, a surface relief optical phase mask, and an optimal 3D localization estimator. 3D super-resolution imaging using photo-switchable dyes reveals the 3D microtubule network in mammalian cells with localization precision approaching the information theoretical limit over a depth of 1.2 µm. Bewersdorf, "Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples," Nat. Methods 5(6), 527-529 (2008

When a single molecule is detected in a wide-field microscope, the image approximates the point spread function of the system. However, as the distribution of molecules becomes denser and their images begin to overlap, existing solutions to determine the number of molecules present and their precise three-dimensional locations can tolerate little to no overlap. We propose a localization scheme that can identify several overlapping molecule images while maintaining high localization precision. A solution to this problem involving matched optical and digital techniques, as here proposed, can substantially increase the allowable labeling density and accelerate the data collection time of single-molecule localization microscopy by more than one order of magnitude.

We present a double-helix point spread function (DH-PSF) based three-dimensional (3D) microscope with efficient photon collection using a phase mask fabricated by gray-level lithography. The system using the phase mask more than doubles the efficiency of current liquid crystal spatial light modulator implementations. We demonstrate the phase mask DH-PSF microscope for 3D photo-activation localization microscopy (PM-DH-PALM) over an extended axial range.

We present the performance limits on three-dimensional (3D) localization accuracy of currently used methods of wide-field superlocalization microscopy. The three methods investigated are double-helix microscopy, astigmatic imaging, and biplane detection. In the shot-noise limit, Cramer-Rao lower bound calculations show that, among these techniques, the double-helix microscope exhibits the best axial and 3D localization accuracy over short as well as long depth-of-field systems. The fundamental advantage of engineered point-spread function systems, like the double-helix, stems from the additional degrees of freedom available to control diffraction in three dimensions over variable regions of interest.

The 3D orientation and location of individual molecules is an important marker for the local environment and the state of a molecule. Therefore dipole localization and orientation estimation is important for biological sensing and imaging. Precise dipole localization is also critical for superresolution imaging. We propose and analyze wide field microscope configurations to simultaneously measure these parameters for multiple fixed dipole emitters. Examination of the images of radiating dipoles reveals how information transfer and precise detection can be improved. We use an information theoretic analysis to quantify the performance limits of position and orientation estimation through comparison of the Cramer-Rao lower bounds in a photon limited environment. We show that bi-focal and double-helix polarization-sensitive systems are attractive candidates for simultaneously estimating the 3D dipole location and orientation.

Super-resolution localization microscopy involves acquiring thousands of image frames of sparse collections of single molecules in the sample. The long acquisition time makes the imaging setup prone to drift, affecting accuracy and precision. Localization accuracy is generally improved by a posteriori drift correction. However, localization precision lost due to sample drifting out of focus cannot be recovered as the signal is originally detected at a lower peak signal. Here, we demonstrate a method of stabilizing a super-resolution localization microscope in three dimensions for extended periods of time with nanometer precision. Hence, no localization correction after the experiment is required to obtain super-resolved reconstructions. The method incorporates a closed-loop with a feedback signal generated from camera images and actuation on a 3D nanopositioning stage holding the sample.