3-D PSF fitting for fluorescence microscopy: implementation and localization application

Localization microscopy relies on computationally efficient Gaussian approximations of the point spread function for the calculation of fluorophore positions. Theoretical predictions show that under specific experimental conditions, localization accuracy is significantly improved when the localization is performed using a more realistic model. Here, we show how this can be achieved by considering three-dimensional (3-D) point spread function models for the wide field microscope. We introduce a least-squares point spread function fitting framework that utilizes the Gibson and Lanni model and propose a computationally efficient way for evaluating its derivative functions. We demonstrate the usefulness of the proposed approach with algorithms for particle localization and defocus estimation, both implemented as plugins for ImageJ.

Super-resolution fluorescence microscopy based on physical models

François Aguet

This thesis introduces a collection of physics-based methods for super-resolution in optical microscopy. The core of these methods constitutes a framework for 3-D localization of single fluorescent molecules. Localization is formulated as a parameter estimation problem relying on a physically accurate model of the system's point spread function (PSF). In a similar approach, methods for fitting PSF models to experimental observations and for extended-depth-of-field imaging are proposed. Imaging of individual fluorophores within densely labeled samples has become possible with the discovery of dyes that can be photo-activated or switched between fluorescent and dark states. A fluorophore can be localized from its image with nanometer-scale accuracy, through fitting with an appropriate image function. This concept forms the basis of fluorescence localization microscopy (FLM) techniques such as photo-activated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM), which rely on Gaussian fitting to perform the localization. Whereas the image generated by a single fluorophore corresponds to a section of the microscope's point spread function, only the in-focus section of the latter is well approximated by a Gaussian. Consequently, applications of FLM have for the most part been limited to 2-D imaging of thin specimen layers. In the first section of the thesis, it is shown that localization can be extended to 3-D without loss in accuracy by relying on a physically accurate image formation model in place of a Gaussian approximation. A key aspect of physically realistic models lies in their incorporation of aberrations that arise either as a consequence of mismatched refractive indices between the layers of the sample setup, or as an effect of experimental settings that deviate from the design conditions of the system. Under typical experimental conditions, these aberrations change as a function of sample depth, inducing axial shift-variance in the PSF. This property is exploited in a maximum-likelihood framework for 3-D localization of single fluorophores. Due to the shift-variance of the PSF, the axial position of a fluorophore is uniquely encoded in its diffraction pattern, and can be estimated from a single acquisition with nanometer-scale accuracy. Fluroescent molecules that remain fixed during image acquisition produce a diffraction pattern that is highly characteristic of the orientation of the fluorophore's underlying electromagnetic dipole. The localization is thus extended to incorporate the estimation of this 3-D orientation. It is shown that image formation for dipoles can be represented through a combination of six functions, based on which a 3-D steerable filter for orientation estimation and localization is derived. Experimental results demonstrate the feasibility of joint position and orientation estimation with accuracies of the order of one nanometer and one degree, respectively. Theoretical limits on localization accuracy for these methods are established in a statistical analysis based on Cramér-Rao bounds. A noise model for fluorescence microscopy based on a shifted Poisson distribution is proposed. In these localization methods, the aberration parameters of the PSF are assumed to be known. However, state-of-the-art PSF models depend on a large number of parameters that are generally difficult to determine experimentally with sufficient accuracy, which may limit their use in localization and deconvolution applications. A fitting algorithm analogous to localization is proposed; it is based on a simplified PSF model and shown to accurately reproduce the behavior of shift-variant experimental PSFs. Finally, it is shown that these algorithms can be adapted to more complex experiments, such as imaging of thick samples in brightfield microscopy. An extended-depth-of-field algorithm for the fusion of in-focus information from frames acquired at different focal positions is presented; it relies on a spline representation of the sample surface and as a result yields a continuous and super-resolved topography of the specimen.

EPFL2009

Deconvolution of 3D fluorescence micrographs with automatic risk minimization

Sathish Ramani, Michaël Unser, Cédric René Jean Vonesch

We investigate the problem of automatic tuning of a deconvolution algorithm for three-dimensional (3D) fluorescence microscopy; specifically, the selection of the regularization parameter lambda. For this, we consider a realistic noise model for data obtained from a CCD detector: Poisson photon-counting noise plus Gaussian read-out noise. Based on this model, we develop a new risk measure which unbiasedly estimates the original mean-squared-error of the deconvolved signal estimate. We then show how to use this risk estimate to optimize the regularization parameter for Tikhonov-type deconvolution algorithms. We present experimental results on simulated data and numerically demonstrate the validity of the proposed risk measure. We also present results for real 3D microscopy data.

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Developing luminescent Brownian probes for near-field investigations of the intracellular environment

Flavio Maurizio Mor

Life sciences have a constantly growing need for novel methodological approaches suitable to investigate the intracellular environment with increased temporal and spatial resolutions. Recently, optical near-field probes, such as laser-irradiated pointed metal, uncoated/metal-coated tapered optical fibers, as well as nano-emitters, such as single molecules or nanoparticles, have attracted increasing attention as key components of high-resolution microscopes. In parallel, super-resolution fluorescence microscopy, operating in far-field regime and overcoming the light diffraction limit, has markedly improved imaging resolution. Although both near- and far-field optical approaches drastically improve image resolution, they still represent numerous drawbacks, such as, technical difficulties concerning probe preparation (near-field) or potential damaging through very high light intensities (far-field). The aforementioned shortcomings of high-resolution optical microscopy can be overcome to a great extent by photonic force microscopy (PFM). PFM employs a strongly focused near-infrared (NIR) laser light to hold a dielectric or metallic particle as a local probe. Such an optical trap enables one to ‘cage’ a mesoscopic particle and track its three-dimensional (3D) thermal fluctuations in the surrounding environment, e.g. a viscous liquid. Therefore, besides offering near-field 3D imaging, PFM reports also on other important quantities concerning local mechanical properties, including force and viscosity as well as dynamical properties of the surrounding medium. This additional information is derived from the careful analysis of the jittery motion (so-called Brownian motion) of the trapped single-particle probe that collides with thermally-activated surrounding molecules. In this thesis, we first study in detail the Brownian motion of a single spherical particle that is confined within the harmonic potential of the optical trap. To this end, we optimize the NIR light path and electronic noise floor of our custom-built PFM set-up for detecting and quantifying resonances in the Brownian motion. These resonances arise from the coupling between the hydrodynamic memory and strong strength of the optical trap. Due to the high sensitivity of the short-time dynamics, the size of the particle can be measured by simultaneous fitting of the velocity autocorrelation function and power spectral density of its thermal fluctuations. In order to choose the best-suitable spherical probe for a given experiment in PFM, computational modeling based on a Matlab toolbox is performed. The generalized Lorenz-Mie theory is computed using the T -matrix method for various experimental conditions, including changes in the size and refractive index of the sphere, as well as different laser polarization states. The axial equilibrium position is examined to predict its location compared with the position of the laser focus. Optical forces acting on the sphere are investigated in 3D to highlight, in particular, the limits of the perfectly harmonic potential assumption. These limits are quantified and discussed. Subsequently, we identify different types of inorganic nano/micro-sized particles that can be trapped by the NIR laser of the PFM and used simultaneously as mechanical and near-field light sources. To this end, we take advantage of the visible light emission from single probes confined in the optical trap and excited by the NIR laser light. The emphasis is on particles revealing nonlinear optical properties. In particular, nonlinear optical field enhancement resulting from excitation of surface plasmon resonance (SPR) on trapped gold particles of 200 nm is demonstrated by measuring the emission of that second-harmonic generation (SHG). Furthermore, we show, under optical trapping conditions, SHG emission from single potassium niobate (KNbO3) nano/micro-sized particles. We also report on the multicolor upconversion luminescence (UCL), at the single particle level, for randomly shaped crystals of sodium yttrium fluoride codoped with ytterbium and erbium, NaYF4:Yb,Er (UCC), when they are held in the optical trap. In parallel, 3D Brownian fluctuations of a single trapped particle are quantified. Moreover, luminescence resonance energy transfer (LRET) between a KNbO3 particle or an UCC and molecules of an organic dye (rose bengal) adsorbed on their surface is highlighted and analyzed. Finally, randomly shaped UCCs and hexagonal nanoplates are characterized in detail at the single particle level. The hexagonal β phase in the polycrystalline and monocrystalline crystals is identified, in both randomly and hexagonally shaped particles by electron microscopy. UCL emission from the trapped crystal is quantified in terms of power and found to be dependent on the laser power density, size and shape of the particle as well as its orientation within the trap. Most importantly, the different colors in the UCL spectrum do not vary with the same trend for different orientations of the randomly or hexagonally shaped crystal upon trapping. This suggests the existence of crystalline anisotropy-dependent UCL. Thereby, we should be able to design the best-suited particle probe for LRET experiments with subwavelength resolution.