\begin{thebibliography}{1} \bibitem{Doucas_Theory_1998} J.~Walsh J.~H.~Brownell and G.~Doucas. \newblock Spontaneous smith-purcell radiation described through induced surface currents. \newblock {\em Phys. Rev}, 1998. \bibitem{delerue:in2p3-01020128} N.~Delerue et~al. \newblock Study of phase reconstruction techniques applied to smith-purcell radiation measurements. \newblock In {\em IPAC17}. \end{thebibliography}