Publications & technical resources

The double-helix point spread function microscope encodes the axial (z) position information of single emitters in wide-field (x,y) images, thus enabling localization in three dimensions (3D) inside extended volumes. We experimentally determine the statistical localization precision σ of this approach using single emitters in a cell under typical background conditions, demonstrating σ < 20 nm laterally and <30 nm axially for N ≈ 1180 photons per localization. Combined with light-induced blinking of single-molecule labels, we present proof-of-concept imaging beyond the optical diffraction limit of microtubule network structures in fixed mammalian cells over a large axial range in three dimensions.

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 demonstrate an integrated holographic optical tweezers system with double-helix point spread function (DH-PSF) imaging for high precision three-dimensional multi-particle tracking. The tweezers system allows for the creation and control of multiple optical traps in three-dimensions, while the DH-PSF allows for high precision, 3D, multiple-particle tracking in a wide field. The integrated system is suitable for particles emitting/scattering either coherent or incoherent light and is easily adaptable to existing holographic tweezers systems. We demonstrate simultaneous tracking of multiple micro-manipulated particles and perform quantitative estimation of the lateral and axial forces in an optical trap by measuring the fluid drag force exerted on the particles. The system is thus capable of unveiling complex 3D force landscapes that make it suitable for quantitative studies of interactions in colloidal systems, biological materials, and a variety of soft matter systems.

Optical imaging of single biomolecules and complexes in living cells provides a useful window into cellular processes. However, the three-dimensional dynamics of most important biomolecules in living cells remains essentially uncharacterized. The precise subcellular localization of mRNA-protein complexes plays a critical role in the spatial and temporal control of gene expression, and a full understanding of the control of gene expression requires precise characterization of mRNA transport dynamics beyond the optical diffraction limit. In this paper, we describe three-dimensional tracking of single mRNA particles with 25-nm precision in the x and y dimensions and 50-nm precision in the z dimension in live budding yeast cells using a microscope with a double-helix point spread function. Two statistical methods to detect intermittently confined and directed transport were used to quantify the three-dimensional trajectories of mRNA for the first time, using ARG3 mRNA as a model. Measurements and analysis show that the dynamics of ARG3 mRNA molecules are mostly diffusive, although periods of non-Brownian confinement and directed transport are observed. The quantitative methods detailed in this paper can be broadly applied to the study of mRNA localization and the dynamics of diverse other biomolecules in a wide variety of cell types.

Wide-field microscopy with a double-helix point spread function (DH-PSF) provides three-dimensional (3D) position information beyond the optical diffraction limit. We compare the theoretical localization precision for an unbiased estimator of the DH-PSF to that for 3D localization by astigmatic and biplane imaging using Fisher information analysis including pixelation and varying levels of background. The DH-PSF results in almost constant localization precision in all three dimensions for a 2 μm thick depth of field while astigmatism and biplane improve the axial localization precision over smaller axial ranges. For high signal-to-background ratio, the DH-PSF on average achieves better localization precision.

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 point spread function (PSF) of a widefield fluorescence microscope is not suitable for three-dimensional superresolution imaging. We characterize the localization precision of a unique method for 3D superresolution imaging featuring a double-helix point spread function (DH-PSF). The DH-PSF is designed to have two lobes that rotate about their midpoint in any transverse plane as a function of the axial position of the emitter. In effect, the PSF appears as a double helix in three dimensions. By comparing the Cramer-Rao bound of the DH-PSF with the standard PSF as a function of the axial position, we show that the DH-PSF has a higher and more uniform localization precision than the standard PSF throughout a 2 μm depth of field. Comparisons between the DH-PSF and other methods for 3D superresolution are briefly discussed. We also illustrate the applicability of the DH-PSF for imaging weak emitters in biological systems by tracking the movement of quantum dots in glycerol and in live cells.

Three-dimensional nanoscale localization and tracking of dim single emitters can be obtained with a widefield fluorescence microscope exhibiting a double-helix point spread function (DH-PSF). We describe in detail how the localization precision quantitatively depends upon the number of photons detected and the z position of the nanoscale emitter, thereby showing a ∼10 nm localization capability along x, y, and z in the limit of weak emitters. Experimental measurements are compared to Fisher information calculations of the ultimate localization precision inherent in the DH-PSF. The DH-PSF, for the first time, is used to track single quantum dots in aqueous solution and a quantum dot-labeled structure inside a living cell in three dimensions.

Accurate estimation of the three-dimensional (3D) position of particles is critical in applications like biological imaging, atom/particle-trapping, and nanomanufacturing. While it is well-known that localization accuracy better than the Rayleigh resolution limit is possible, it was recently shown that, for photon-limited cases, 3D point spread functions (PSFs) can be shaped to increase accuracies over a 3D volume [Pavani and Piestun, Opt. Express 16, 22048 (2008)]. Here, we show that in the detector-limited regime, the gain in accuracy occurs in all three dimensions throughout the axial range of interest. The PSF is shaped as a double helix, resulting in a system with fundamentally better 3D localization accuracies than standard PSF systems, capable of achieving single-image subnanometer accuracies.