Development of novel experimental and computational methods for three-dimensional coherent and super-resolution microscopy

Optical microscopy is one widely used tool to study cell functions and the interaction of molecules at a sub-cellular level. Optical microscopy techniques can be broadly divided into two categories: partially coherent and incoherent. Coherent microscopy techniques are usually label-free and provide diffraction limited structural information about the sample refractive index distribution though the measurement of phase delay induced by the sample. Since they can be very conservative in the illumination power directed toward the sample, they exhibit very low photo-toxicity and are suitable for both high speed and time lapse imaging. Fluorescence microscopy is an incoherent microscopy method which uses biochemistry techniques to label cellular structures with fluorescent molecules which emit light when excited by a laser. Fluorescence microscopy provides diffraction limited high specificity imaging but is limited in time due to photo-bleaching and photo-toxicity. Super-resolution microscopy is a sub-category of fluorescence microscopy which manipulates and exploits some properties of the fluorescent molecules to achieve high specificity sub-diffraction imaging. Super-resolution comes however at the price of an increased total acquisition time, which limits the applications of super-resolution microscopy to relatively slow cellular processes. The ideal microscope however does not exist; due to the limited spatio-temporal bandwidth of far-field microscopy, there will always be unavoidable trade-offs. There is therefore a need to find new ways to ensure that the methods are reaching their optimal performances and a need to study how different methods can complement each others. I start by presenting a new method for three-dimensional quantitative phase retrieval. I derive a model for the image formation of three-dimensional bright field images and extrapolate a novel expression allowing to retrieve the phase distribution from a bright field image stack. Using a unique image-splitting multi-plane prism that allows to acquire 8 distinct focal planes in a single exposure, I demonstrate three-dimensional quantitative phase imaging at 200 Hz . Finally, I show the association of three-dimensional super-resolution SOFI with phase imaging. To improve the imaging speed and lower the illumination intensity, I combine the same prism platform with a high-speed structured illumination. Since the structured illumination presented is using a digital micro-mirror device, about 90 \% of the laser light is diffracted outside of the optical path. To improve the illumination efficiency but keep its speed and flexibility, I present a new approach for achromatic high power high speed SIM, based on a Michelson interferometer. With the access to high illumination power density, I also show the first experimental combination of SIM with SOFI using a self-blinking dye. Motivated by the absence of tools to objectively judge the performance of the microscopy methods I develop, I present a novel algorithm for image resolution estimation. The method estimate the resolution by correlating the image with several filtered version of itself without any external parameters. Finally, in the context of the AD-gut consortium, I show a practical application of deep neural networks used to assists the segmentation and mapping of the microscopy image of enzymatically labeled DNA molecules