Date of Award

Spring 5-17-2019

Author's Department

Electrical & Systems Engineering

Degree Name

Master of Science (MS)

Degree Type



Three-dimensional super-resolution microscopy enables the 3D positions of single fluorescent molecules to be measured from the 2D images produced by a microscope with nanoscale precision. However, the point spread function (PSF) of a conventional microscope is ill-suited for 3D imaging, necessitating the design of engineered PSFs. Although numerous PSFs have been demonstrated, none of these obtain the so-called Quantum Cramer-Rao Lower Bound (CRLB). In this thesis, I aim to design 3D PSFs that perform close to this limit by utilizing two optimization approaches, using a Quasi-Newton algorithm in Matlab and a gradient descent algorithm in the TensorFlow framework, specifically seeking to relax unnecessary constraints that have compromised previous approaches. I optimize the performance, e.g. CRLB in z direction, of each design by testing various loss functions, constraints, and initial conditions. I show that the localization precision of existing PSFs, such as the Tetrapod and Double Helix, can be improved using our approach. Further, I design new PSFs, composed of photon distributions that rotate or translate, that are inspired by existing PSFs but contain superior Fisher information. I use our optimization framework to design corresponding optimized phase masks and quantify the performance of these new designs. Using these new approaches, my dumbbell PSF achieves an average localization precision along z of 12.7 nm for 1000 signal photons and 2 background photons/pixel over a depth range of 1000 nm, an improvement of 8.7% over the Tetrapod PSF.


English (en)


Matthew D. Lew

Committee Members

Joseph A. O'Sullivan, Umberto Villa

Included in

Engineering Commons