Sri Rama Prasanna Pavani

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.

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.

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.

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.

Three-dimensional localization with nanometer accuracy using a detector-limited double-helix point spread function system

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.

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.

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 objects quantitative OPL profile based on a closed form analytical solution, which is derived using a ray optics model for objects with small OPL gradients.

3D microscopy with a double-helix point spread function

Double-helix point spread function (DH-PSF) is an engineered three-dimensional (3D) PSF specifically designed for 3D position estimation and imaging. It exhibits two lobes that rotate continuously around the optical axis with propagation. An information theoretical analysis shows that the DH-PSF carries higher and more uniform Fisher Information than the standard PSF through the 3D volume of interest. Experiments with DH-PSF demonstrate nanometer scale position localization accuracies in all three dimensions. Further, a variety of microscopy techniques such as bright-field, dark-field, and fluorescence can be directly transformed into their DH-PSF counterparts by placing an appropriate phase mask in the imaging path. The flexibility and performance make the DH-PSF attractive for 3D position localization in both photon-limited and photon-unlimited regimes.

QSIP: phase imaging made possible in a bright field microscope

Quantitative structured-illumination phase microscopy (QSIP) uses a conventional bright field microscope to quantitatively measure the optical path length profiles of homogenous phase-only objects. The illumination in QSIP is structured with a predetermined pattern by placing an amplitude mask in the field diaphragm of the microscope. From the image of the amplitude mask, a numerical algorithm implementing a closed form analytical solution calculates the objects optical path length profile. In this paper, we investigate the accuracy of the numerical algorithm used and show that it can be made arbitrarily accurate by using numerical optimization. We then analyze the effect of the systems numerical aperture (NA), and show that QSIP can be used with a wide range of NAs for objects with small phase gradients, and can be used with relatively lower NAs for objects with large phase gradients.