Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms |
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Authors: | JS Liu AJ Caley MR Taghizadeh |
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Institution: | School of Engineering and Physical Sciences - Physics, Heriot-Watt University, David Brewster Building, Riccarton, Edinburgh EH14 4AS, UK |
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Abstract: | A modified Gerchberg-Saxton algorithm, which we call symmetrical iterative Fourier transform algorithm, is presented and employed to a series of super-Gaussian beam shaping problems and arbitrary beam shaping problems. The main features of this algorithm include (1) using an amplitude-symmetric function of the failed result about the Fourier-domain constraint; (2) using both phase and amplitude freedoms in the iteration process, i.e. the noise produced outside the signal window by each iteration is kept. A formula is given to determine a critical constant in the search for the amplitude-symmetric function. The new method results in highly efficient solutions with highly precise beam profiles in the signal window for all the test problems. |
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Keywords: | Gerchberg-Saxton algorithm Iterative Fourier transform algorithm Diffractive optics Beam shaping Pulse shaping Phase retrieval Image reconstruction |
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