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"Automatic symmetrical iterative Fourier transform algorithm for the design of diffractive phase elements for highly precise laser beam shaping", by Jinsong Liu, Martin. J. Thomson and M. R. Taghizadeh, Journal of Modern Optics, 53, 2006.

A symmetrical iterative Fourier-transform algorithm (IFTA) using a combination of phase and amplitude freedom for the design of diffractive optical elements for highly precise laser beam shaping is presented. We compare this method with the basic IFTA and the symmetrical IFTA exclusively using phase freedom, and the basic IFTA using both phase and amplitude freedom, by employing these methods for super-Gaussian beam shaping. While the latter three methods fail to produce satisfactory solutions, the first method results in a beam non-uniformity error of 0.44% and a theoretical efficiency of 97.2%. Moreover, the new approach avoids the use of the trial-and-error method for finding the appropriate modified Fourier-domain constraints during the iteration, which can be difficult for some beam-shaping problems.

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