Ginni Grover

Simultaneous, accurate measurement of the 3D position and orientation of single molecules

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 photon-limited precision; 28 nm) to 34 nm (within 6 nm of the photon limit).

Quantitative multicolor subdiffraction imaging of bacterial protein ultrastructures in three dimensions.

We demonstrate quantitative multicolor three-dimensional (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. 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.

Performance limits on three-dimensional particle localization in photon-limited microscopy.

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.

Super-resolution photon-efficient imaging by nanometric double-helix point spread function localization of emitters (SPINDLE)

Super-resolution imaging with photo-activatable or photo-switchable 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.

Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging

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.

Three-dimensional super-resolution and localization of dense clusters of single molecules

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.

Limits of 3D dipole localization and orientation estimation for single-molecule imaging: towards Green’s tensor engineering

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.

Real-time adaptive drift correction for super-resolution localization microscopy.

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.

Effect of double-helix point-spread functions on 3D imaging in the presence of spherical aberrations

Double Helix point-spread functions (DH-PSFs), the result of PSF engineering, are used for super resolution microscopy. The DH-PSF design features two dominant lobes in the image plane which rotate with the change in axial (z) position of the light point source. The center of the DH-PSF gives the precise XY location of the point source, while the orientation of the lobes gives the axial location. In this paper we investigate the effect of spherical aberrations on the DH-PSF. Physical parameters such as the lens used, the size of the particle, refractive index of medium, and depth i.e., location within the underlying object, contribute to the amount of spherical aberration. DH-PSFs with spherical aberrations are computed for different imaging conditions. Three-dimensional images were generated of computer-generated objects using both space-invariant and depth-variant approach. Different approaches to estimate intensity and location of points from these images were investigated. Our results show that the DH-PSFs are susceptible to spherical aberration leading to an apparent shift in the location of the point source with increasing spherical aberrations which is comparable to the conventional PSF. Estimation algorithms like the depth variant expectation maximization (DVEM) can be used to obtain estimates of the true underlying object from the image obtained with DH-PSFs.

Double helix PSF engineering for computational fluorescence microscopy imaging

Point spread function engineering with a double helix (DH) phase mask has been recently used in a joint computationaloptical approach for the determination of depth and intensity information from fluorescence images. In this study, theoretically determined DH-PSFs computed from a model that incorporates different amounts of depth-induced spherical aberration (SA) due to refractive-index mismatch in the three-dimensional imaging layers, are evaluated through a comparison to empirically determined DH-PSFs measured from quantum dots. The theoretically-determined DH-PSFs show a trend that captures the main effects observed in the empirically-determined DH-PSFs. Calibration curves computed from these DH-PSFs show that SA slows down the rate of rotation observed in a DH-PSF which results in: 1) an extended range of rotation; and 2) asymmetric rotation ranges as the focus is moved in opposite directions. Thus, for accurate particle localization different calibration curves need to be known for different amounts of SA. Results also show that the DH-PSF is less sensitive to SA than the conventional PSF. Based on this result, it is expected that fewer depth-variant (DV) DH-PSFs will be required for 3D computational microscopy imaging in the presence of SA compared to the required number of conventional DV PSFs.