Mathematical Sciences Colloquium - "Multifrequency interferometric imaging with intensity-only measurements" by Dr. Chrysoula Tsogka (Stanford University) - Washburn Shops 323

Thursday, November 02, 2017
3:00 pm to 4:00 pm

Location:

Floor/Room #: 
323

When: Thursday Nov. 2nd     3pm in SH306

Speaker: Dr. Chrysoula Tsogka  (Stanford University)

Title: Multifrequency interferometric imaging with intensity-only measurements

Abstract: We consider here the problem of coherent imaging using intensity-only measurements. The main challenge in intensity-only imaging is recovering phase information that is not directly available in the data, but is essential for coherent image reconstruction.  Imaging without phases arises in many applications such as crystallography, ptychography and optics where images are formed from the spectral intensities.

The  earliest and most widely used methods for imaging with intensity-only measurements are alternating projection algorithms. The basic idea is to project the iterates on the intensity data sequentially in both the real and the Fourier spaces. Although these algorithms are very efficient for reconstructing the missing phases in the data, and performance is often good in practice, they do not always converge to the true, missing phases. This is especially so if strong constrains or prior information about the object to be imaged, such as spatial support and non-negativity, are not reliably available.

Rather than using phase retrieval methods, we propose a different approach in which well-designed illumination strategies exploit the spatial and frequency diversity inherent in the problem. These illumination strategies allow for the recovery of  interferometric data that contain relative phase information which is all that is needed to reconstruct a so-called holographic image.  There is no need for phase reconstruction in this approach. Moreover, we show that this methodology leads to holographic images that suffer no loss of resolution compared with those that use full phase information. This is so when the background media through which the probing signals propagate are assumed known.

We also consider propagation media with fluctuations in the index of refraction which are unknown and therefore are modeled as a random process.

In such media the recovered relative phases fluctuate and this introduces noise and instability in the image formation process.  Using adequately designed filters (masks), the uncertainty in the recovered phases is reduced and statistically stable imaging results are obtained.

The robustness of our approach will be explored with numerical simulations carried out in an optical (digital) microscopy imaging regime.