Iluminating and Imaging Edges

George Papanicolaou
Stanford University

ABSTRACT:
I will describe how reflectors can be imaged from echoes received at an
array of sensors. I will then describe ways in which the edges of the
reflectors can be imaged so that their shape can be visualized. It
turns out that the best way to image edges is by illuminating the
reflectors from the edges of the array. The mathematical framework for
analyzing this problem is the singular value decomposition, which in a
certain high frequency regime can be determined explicitly using
generalized prolate spheroidal functions. These functions have some
interesting properties that are particularly useful in assessing image
resolution. I will also show the results of extensive numerical
simulations. 

This is joint work with L. Borcea and F. Guevara Vasquez.