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"Iterative algorithm for the design of diffractive phase elements for laser beam shaping", by Jinsong Liu and M. R. Taghizadeh, Optics Letters, 27(16): 1463-1465, 2002.

An improved iterative algorithm for designing diffractive phase elements for laser beam shaping in free space is presented. The algorithm begins with the Gerchberg¨CSaxton approach to obtain a stable solution. This is followed by several new iterations, in which modified constraining functions are imposed in the Fourier domain while the phase distribution of each iteration remains unchanged. For super-Gaussian beam shaping suitable for inertial confinement fusion applications the mean-square errors of the amplitude and the intensity profile of the entire beam fitted to the corresponding parameters of the 12th-power super-Gaussian beam are approximately 0.035 and 9.75x10-3, respectively. Approximately 97.4% of the incident energy is converged into the desired region.

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