Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms

J. S. Liu, A. J. Caley, M. R. Taghizadeh

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


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. © 2006 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)347-355
Number of pages9
JournalOptics Communications
Issue number2
Publication statusPublished - 15 Nov 2006


  • Beam shaping
  • Diffractive optics
  • Gerchberg-Saxton algorithm
  • Image reconstruction
  • Iterative Fourier transform algorithm
  • Phase retrieval
  • Pulse shaping


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