טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentZewi Oded
SubjectSparse Ptychography
DepartmentDepartment of Physics
Supervisor ? 18? Mordechai Segev


Abstract

In any practical microscopy measurement system, noise presents a limiting factor. Although improvement in signal to noise ratio is always desirable, in some cases it only comes at the expense of parameters such as acquisition time, or the radiation dose the system is exposed to, in a manner detrimental to successful application (e.g. real time applications, photo-toxicity). In these cases it is beneficial to tackle the problem from the post-processing perspective. Prior knowledge on the object of interest can be exploited to recover it from noisy measurements.

One form of prior information, which is considered in this work, is sparsity. Signals which are not fully random, tend to admit to sparse representation (i.e. representation with only a few non-zero coefficients) in a dictionary bearing their inner structure. The sparsity prior manifests as knowledge of the dictionary in which the sought signal is sparse. Knowledge of the representation itself is not required, and not even the exact degree of sparsity, for the utilization of sparsity.

In this research thesis, I present my work focused on ptychography - a lensless microscopy technique of growing interest in recent years. In ptychography the object of interest is illuminated with a collimated probe beam producing a measured far-field diffraction pattern. The probe beam is then translated over the object, and further diffraction patterns are measured. Scanning the object with overlapping probe beams enables its algorithmic reconstruction from the diffraction patterns.

There exists a tradeoff between robustness of the reconstruction to noise and the number of required measurements, limiting data acquisition time and sample radiation. In my work, I propose a solution to the tradeoff - a method, based on the common ptychographic reconstruction algorithm, PIE (Ptychographic Iterative Engine), harnessing sparsity to overcome the effects of noise. I lay out numerical results, suggesting significant improvement in robustness to noise.