An improved phase retrieval algorithm for coherent beams

Summary form only given. We have developed a frequency quadrupled Nd:YLF laser as a source of photons to Compton backscatter from a beam of electrons circulating in a storage ring. The laser beam must be transported 22 meters to the interaction region in the synchrotron and the mode at that point must be matched to the electron beam. Unfortunately, the laser is non-Gaussian, so that both the phase and intensity must be known to calculate the beam propagation. The Gerchberg-Saxton phase retrieval procedure deduces the phase of an image from intensity measurements in the image plane and the diffraction plane. For a freely propagating non-TEM/sub 00/ beam it is generally difficult to locate the waist. Also, if the Rayleigh range of the beam is too small, high spatial resolution of the beam profiling device is necessary; conversely, if the Rayleigh range is too large, it may be difficult to make a measurement at a great enough distance to achieve the far field condition. To overcome these limitations, we have developed a generalization of the Gerchberg-Saxton procedure to include intensity measurements in multiple planes of the propagating beam. We have tested the algorithm with "synthetic" data generated computationally by propagating multimode Hermite-Gaussian beams, extracting intensity profiles at a series of planes and adding normally distributed noise. To test the procedure with data, we have measured the profile of the laser beam in several planes after an optical transport system, retrieved the phase, propagated the retrieved beam back to a location near the laser exit and compared this reconstructed beam profile to a measurement at that location.