In many fields of science and engineering, one encounters the phase retrieval problem: given the magnitude of the complex-valued Fourier transform of a function, find the Fourier phase, and reconstruct the function (given some constraints on the function). Phase retrieval allows us to take multiple images of astronomical objects, blurred by the earth's atmosphere, and produce a sharp, fine-resolution image. Phase retrieval can be used to form 2-D and 3-D images, without any imaging optics, from the intensity of a laser beam scattered off an object. Phase retrieval allowed us to precisely determine the aberrations of the Hubble Space Telescope, which made possible its repair. It is also under development for the James Webb Space Telescope, to align its multiple hexagonal-shaped mirror segments after it is unfolded in space.
This seminar will describe the phase retrieval algorithms and show their application to these various problem areas
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