Femtosecond x-ray free electron laser pulse duration measurement from spectral correlation function

We present a novel method for measuring the duration of femtosecond x-ray pulses from self-amplified spontaneous emission free electron lasers by performing statistical analysis in the spectral domain. Analytical expressions of the spectral correlation function were derived in the linear regime to extract both the pulse duration and the spectrometer resolution. Numerical simulations confirmed that the method can be also used in the nonlinear regime. The method was demonstrated experimentally at the Linac Coherent Light Source by measuring pulse durations down to 13 fs FWHM.