Improving the precision and accuracy of three-dimensional single-molecule localization microscopy
Keywords: Chemistry.

Knowledge of the point spread function (PSF) of a microscope allows point sources of light such as single molecules and particles to be localized in space with a precision on the order of tens of nanometers or better. Single-molecule localization microscopy (SMLM) leverages this to enable both tracking of single molecules to study their dynamics as well as super-resolution imaging of static objects labeled with fluorescent molecules to reveal their structure. Since localization entails estimating parameters of the molecule from its PSF, the precision and accuracy with which those parameters can be determined are of fundamental importance to the quality of the results in a localization experiment. The work presented in this Dissertation seeks to improve the precision and accuracy of single-molecule localization through developments in computational tools, optical design, and calibration methods. Special attention is paid to the localization of engineered PSFs, in which the PSF shape is deliberately altered to encode information such as three-dimensional (3D) molecular position or orientation of the molecular dipole. The first two Chapters in this Dissertation serve as introductions. Chapter 1 presents general background on a variety of topics relevant to single-molecule localization microscopy. In Chapter 2, the theory underlying image formation in single-molecule fluorescence microscopy is presented, with a special focus on aberrations and engineered PSFs, which play a crucial role throughout the Dissertation. Chapter 3 of this Dissertation reviews the experimental methods employed in this Dissertation. This includes the optical designs employed for illuminating molecules and detecting their fluorescence, as well as descriptions of the instrument control procedures and a detailed walkthrough of the image analysis and localization procedures employed throughout the remaining Chapters. The primary results presented in this Dissertation are the subject of Chapters 4-7. The first two of these focus on the improvement of localization precision. In Chapter 4, it is shown that models of the tetrapod PSF derived from diffraction theory calculations are not sufficient to enable precise 3D localization of single emitters. A method of phase retrieval is demonstrated which enables the determination of a more realistic PSF model, informed by experimental measurements, and allows for recovery of the localization precision to nearly its theoretical limit. Chapter 5 presents a complementary approach to improving localization precision based on illumination with a tilted light sheet excitation beam instead of conventional wide-field illumination to achieve optical sectioning of samples several microns thick. Combination of this illumination strategy with the double helix PSF is shown to improve the signal-to-background ratio and enable 3D single-molecule super-resolution imaging of large structures within mammalian cells with superior localization precision. In the final two Chapters of this Dissertation, the theme shifts from localization precision to localization accuracy. Chapter 6 describes an experimental study of the PSF near the interface between an aqueous sample medium and a glass coverslip. Refraction of collected fluorescence through this interface gives the PSF a depth-dependent shape leading to a distortion of axial position estimates as well as an apparent rescaling of the focal position, both of which limit the accuracy of 3D localization microscopy. These effects are carefully characterized using a calibration standard I developed which provides ground truth. Finally, Chapter 7 addresses an orientation-dependent lateral bias in the PSF which is induced by the anisotropy of the dipole radiation patterns of single molecules. An experimental approach based on polarization filtering is shown to remove the bias by rejecting the component of emitted light which is radially-polarized in the Fourier plane of the microscope, producing a PSF which enables unbiased estimation of the lateral position and azimuthal orientation of the molecule