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Completed Project

Optimizing Image Reconstruction of Virtual C. elegans Diffraction Patterns Using Iterative Fourier Transform Algorithms

Elias Kim, Vassar College ’16, Brian Deer, Vassar College ’15 and Prof. Jenny Magnes and Kathleen M. Raley-Susman

Fourier transforms break a function down into magnitude components that represent the strengths of the function’s constituents and phase components that represent the positions of the constituents relative to each other. In the inverse process, it is possible to transform the magnitude and phase back into the original function. In the case of diffraction patterns, the shape and orientation of an object, for example a C. elegans worm, converts laser light into periodically spaced fringes resulting from wave interference. This diffraction pattern represents the magnitude of a Fourier transform, theoretically making it possible to retrieve the corresponding shape and orientation in image form. It is impossible, however, to complete such retrieval without the phase information, which the diffraction pattern does not contain. This “phase problem” has been present in many fields of optical imaging, and expanding it to the biological studies of microorganisms is an important step. In the current project, iterative algorithms have been tested and modified for use with C. elegans diffraction patterns. These algorithms perform hundreds of Fourier transforms per sequence, starting with a random or partially random phase matrix and iterating hundreds of times. The codes have been altered and tested hundreds of thousands of times. Magnitudes of C. elegans diffraction patterns were digitally acquired from microscope images and separated from their partner phase matrices. To track the impact of each modification, the error array and final produced image of every test was recorded and compared. At this point, at least two major factors have been identified as key components of the reconstructive process: the initial phase information and the support constraint. The results show that the optimization of both these factors yields extremely low error and high image quality. In the future it is hoped that these findings can be applied to diffraction patterns taken in the laboratory.