Transfer Functions for Direct Temporal Structure Measurement of Femtosecond Soft X-Ray

Under cross correlation between linearly polarized short duration laser and narrow bandwidth soft x-ray, the temporal structure of femtosecond soft x-ray can be directly reconstructed via the presented transfer functions from energy derivative of the excited photoelectron energy spectrum measured in the direction of or perpendicular to the laser polarization. The method has a broader temporal measurement range. The energy resolution of a photoelectron spectrometer and the size of energy bin are two important parameters for both measurement and calculation. The methods can be used for ultra-fast measurements and pump--probe detections on the femtosecond time scale.