Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions.

Photo-activation localization microscopy is a far-field superresolution imaging technique based on the localization of single molecules with subdiffraction limit precision. Known under acronyms such as PALM (photo-activated localization microscopy) or STORM (stochastic optical reconstruction microscopy), these techniques achieve superresolution by allowing only a sparse, random set of molecules to emit light at any given time and subsequently localizing each molecule with great precision. Recently, such techniques have been extended to three dimensions, opening up unprecedented possibilities to explore the structure and function of cells. Interestingly, proper engineering of the three-dimensional (3D) point spread function (PSF) through additional optics has been demonstrated to theoretically improve 3D position estimation and ultimately resolution. In this paper, an optimal 3D single-molecule localization estimator is presented in a general framework for noisy, aberrated and/or engineered PSF imaging. To find the position of each molecule, a phase-retrieval enabled maximum-likelihood estimator is implemented. This estimator is shown to be efficient, meaning it reaches the fundamental Cramer-Rao lower bound of x, y, and z localization precision. Experimental application of the phase-retrieval enabled maximum-likelihood estimator using a particular engineered PSF microscope demonstrates unmatched low-photon-count 3D wide-field single-molecule localization performance.

Three-dimensional parallel particle manipulation and tracking by integrating holographic optical tweezers and engineered point spread functions.

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.

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.

Polarization sensitive, three-dimensional, single-molecule imaging of cells with a double-helix system.

Double-helix point spread function photoactivation-localization microscopy allows three-dimensional (3D) superresolution imaging of objects smaller than the optical diffraction-limit. We demonstrate polarization sensitive detection with 3D super-localization of single-molecules and unveil 3D polarization specific characteristics of single-molecules within the intracellular structure of PtK1 cells expressing photoactivatable green fluorescent protein. The system modulates orthogonal polarization components of single-molecule emissions with a single spatial light modulator and detects them separately with a single detector. Information obtained from the two polarization channels demonstrates polarization based contrast in 3D superresolution imaging. Further, we show that the 3D information from the two channels can be optimally combined to yield up to 30% improvement in localization precision relative to a single polarization channel system.

Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function.

We demonstrate single-molecule fluorescence imaging beyond the optical diffraction limit in 3 dimensions with a wide-field microscope that exhibits a double-helix point spread function (DH-PSF). The DH-PSF design features high and uniform Fisher information and has 2 dominant lobes in the image plane whose angular orientation rotates with the axial (z) position of the emitter. Single fluorescent molecules in a thick polymer sample are localized in single 500-ms acquisitions with 10- to 20-nm precision over a large depth of field (2 microm) by finding the center of the 2 DH-PSF lobes. By using a photoactivatable fluorophore, repeated imaging of sparse subsets with a DH-PSF microscope provides superresolution imaging of high concentrations of molecules in all 3 dimensions. The combination of optical PSF design and digital postprocessing with photoactivatable fluorophores opens up avenues for improving 3D imaging resolution beyond the Rayleigh diffraction limit.

Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system.

We demonstrate three-dimensional tracking of fluorescent microparticles, with a computational optical system whose point spread function (PSF) has been engineered to have two twisting lobes along the optical axis, generating a three-dimensional (3D) double-helix (DH) PSF. An information theoretical comparison in photon limited systems shows that the DH-PSF delivers higher Fisher information for 3D localization than the standard PSF. Hence, DH-PSF systems provide better position estimation accuracy. Experiments demonstrate average position estimation accuracies under 14nm and 37nm in the transverse and axial dimensions respectively. The system determines the 3D position of multiple particles with a single image and tracks them over time while providing their velocities.

High-efficiency rotating point spread functions.

Rotating point spread functions (PSFs) present invariant features that continuously rotate with defocus and are important in diverse applications such as computational imaging and atom/particle trapping. However, their transfer function efficiency is typically very low. We generate highly efficient rotating PSFs by tailoring the range of invariant rotation to the specific application. The PSF design involves an optimization procedure that applies constraints in the Gauss-Laguerre modal plane, the spatial domain, and the Fourier domain. We observed over thirty times improvement in transfer function efficiency. Experiments with a phase-only spatial light modulator demonstrate the potential of high-efficiency rotating PSFs.

Quantitative structured-illumination phase microscopy.

We introduce a quantitative phase imaging method for homogeneous objects with a bright field transmission microscope by using an amplitude mask and a digital processing algorithm. A known amplitude pattern is imaged on the sample plane containing a thick phase object by placing an amplitude mask in the field diaphragm of the microscope. The phase object distorts the amplitude pattern according to its optical path length (OPL) profile, and the distorted pattern is recorded in a CCD detector. A digital processing algorithm then estimates the object's quantitative OPL profile based on a closed form analytical solution, which is derived using a ray optics model for objects with small OPL gradients.