Three-dimensional nanoscopy with a double-helix microscope

Optical microscopy has evolved into a powerful tool for modern scientific investigations. It has enabled biologists to study cells; physicists to analyze forces on microparticles; chemists to examine molecular dynamics; and engineers to fabricate microstructures. The so-called optical diffraction limit, however, prohibits conventional optical microscopes from resolving nanometer scale structures such as intricate intracellular features in three dimensions. This thesis introduces a three-dimensional (3D) nanoscopy paradigm that breaks the diffraction limit by resolving nanometer scale structures in all three dimensions with a far-field optical microscope exhibiting a double-helix point spread function (DH-PSF).;Optical microscopy has evolved into a powerful tool for modern scientific investigations. It has enabled biologists to study cells; physicists to analyze forces on microparticles; chemists to examine molecular dynamics; and engineers to fabricate microstructures. The so-called optical diffraction limit, however, prohibits conventional optical microscopes from resolving nanometer scale structures such as intricate intracellular features in three dimensions. This thesis introduces a three-dimensional (3D) nanoscopy paradigm that breaks the diffraction limit by resolving nanometer scale structures in all three dimensions with a far-field optical microscope exhibiting a double-helix point spread function (DH-PSF), position localization, 3D tracking, and 3D velocimetry of multiple scattering and fluorescent particles.;Single fluorescent molecules are localized in 3D with nanometer scale precisions using a DH-PSF fluorescent microscope. By photoactivating (turning on) different sparse subsets of fluorophores at different times, molecules separated by a few nanometers are resolved, thereby breaking the optical diffraction limit by over an order of magnitude in all three dimensions.;A polarization specific DH-PSF nanoscope is also introduced. Light emitted by individual fluorescent protein molecules is decomposed into orthogonal polarization channels, phase modulated, and separately detected to resolve polarization-specific structures of a biological cell with nanometer scale 3D resolution.