Study of Phase Reconstruction Techniques applied to Smith-Purcell   Radiation Measurements
  Measurements of coherent radiation at accelerators typically give the absolute value of the beam profile Fourier transform but not its phase. Phase reconstruction techniques such as Hilbert transform or Kramers Kronig reconstruction are used to recover such phase. We report a study of the performances of these methods and how to optimize the reconstructed profiles. 
Nicolas Delerue, Joanna Barros, M\'elissa Vieille-Grosjean, Oleg   Bezshyyko, Vitalii Khodnevych
physics.acc-ph