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Completed Project

Characteristics of Virtual and Experimentally Recorded Diffraction Patterns Affecting Iterative Image Reconstruction

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

Diffraction patterns are created when a beam of light interacts with an object of similar size to its wavelength. Fourier transforms convert an image of an object into two sets of information about the intensity of its pixels: magnitude and phase.  Inverse Fourier transforms convert these components back into the original image.  The intensity of the light in diffraction patterns is directly related to the magnitude of the Fourier transform but does not contain any phase information, hence the “phase problem;” the phase is missing when trying to reconstruct an image from it’s diffraction pattern.  One solution is to “retrieve” the phase information from magnitude data using iterative algorithms. The Vassar Applied Optics Lab uses dynamic diffraction analysis to study C. elegans locomotion and behavior, a technique that would be enhanced by image reconstruction. The current project seeks to find ideal conditions to record diffraction patterns that may then be reconstructed into images of worms. In virtual experiments, images of C. elegans were altered to have different color maps (gray, black and white, and edge), which were then used to determine effectiveness in different conditions. Additionally, the worm’s position and size relative to the image frame were altered to test how the position and size of the worm relative to the laser beam affects the recorded diffraction pattern. In the laboratory, an experimental setup was created to record diffraction patterns while reducing scattering and increasing image resolution. Virtual results showed a stark difference in quality based on the color map. The worm’s position was shown to be irrelevant, whereas the size proved to be a key factor. The edged color map is the most chaotic, while the gray is the most consistent. In the future we hope to continue to improve the quality and resolution of experimental diffraction patterns and successfully reconstruct a worm image from a diffraction pattern captured in the lab.