Direct Phase Retrieval from the Diffraction Pattern of Separated Objects

Speaker: Ben Leshem
Affiliation: Ph.D. Student, Weizmann Institute of Science

Abstract: The phase retrieval problem arises in various fields ranging from physics and astronomy to biology and microscopy. Computational reconstruction of the Fourier phase from a single diffraction pattern can be achieved using iterative alternating projections algorithms imposing a non-convex computational challenge. A different approach is holography, in which a known reference field is used to directly infer the unknown field evading the non-convexity of the phase problem. Here we consider a scenario in which generating a known reference field is impossible or very difficult. This is the case, for example, in coherent diffraction imaging (CDI). We present a novel phase retrieval approach for the reconstruction of two (or more) sufficiently separated objects from their diffraction pattern [1]. In our approach we combine the constraint that the objects are finite as well as the information in the interference between them to construct an overdetermined set of linear equations. We show that this set of equations is guaranteed to yield the correct solution almost always and that it can be solved efficiently by standard numerical algebra tools.

Essentially, our method combines a commonly used constraint (that the object is finite) with a holographic-like approach (interference information). It differs from holographic methods in the fact that a known reference field is not required, instead the unknown objects serve as reference to one another. Our method can be applied in a single-shot for two (or more) separated objects or with several measurements with a single object. We demonstrated our method numerically, as well as experimentally in the optical regime. Furthermore, we performed a proof-of-principle demonstration in the X-ray regime using data from X-ray free electron laser experiment.

[1] Leshem, B. ,  Xu, R. , Dalla, Y. , Miao, J. , Nadler, B. , Oron, D. , Dudovich, N. & Raz. , O. (2015). “Direct single-shot phase retrieval from the diffraction pattern of two separated objects”. Accepted.  Nature Communications.

For more information, contact Prof. Aydogan Ozcan ()

Date/Time:
Date(s) - Feb 23, 2016
11:00 am - 1:00 pm

Location:
E-IV Tesla Room #53-125
420 Westwood Plaza - 5th Flr., Los Angeles CA 90095