Coherent diffraction imaging
Coherent Diffraction Imaging
Contact Dr. K.M. Pavlov
The non-crystallographic phase problem of coherent diffractive imaging, namely the reconstruction of a two-dimensional aperiodic complex scalar wavefield from the known squared modulus of its Fourier transform, has been subject to intensive research in recent years. With historical roots that date back at least as far as the “Pauli problem” of determining a complex spatial wavefunction given knowledge of its probability density in both real-space and momentum-space, the CDI problem continues to be attacked using iterative algorithms.
These algorithms iterate between real and momentum space, imposing known constraints in each of these spaces. However, given that the CDI phase retrieval algorithms are iterative, the question naturally arises as to whether the problem of CDI is amenable to a closed-form analytic solution. It is important to pursue deterministic solutions to the CDI problem, both for (i) the foundational and conceptual clarity that deterministic algorithms provide, and (ii) the possibility of enhanced speed of reconstruction, afforded by eschewing iteration and thereby realizing “single shot” phase–amplitude retrieval. In Podorov et al we reported a particular analytical solution of the inverse problem of CDI (see Fig.5), for a uniformly illuminated object placed within a rectangular hole with transverse dimensions at least two times larger than the object. The solution employs a modified Fourier transform of the far-field diffracted intensity.
Figure 5.
Setup for non-iterative Coherent Diffractive Imaging.(from S.G. Podorov, K.M. Pavlov and D.M. Paganin. A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging. (2007) Optics Express 15(16), 9954-9962.)
PhD Project :
A project will develop the methodology of non-iterative CDI with emphasis on its experimental realisation using synchrotron sources.