A simple method for experimental spectral ratio calculation of CHG-FEL

Coherent harmonic generation free-electron laser (CHG-FEL) acts as a harmonic amplifier of the seed laser. The spectral ratio, which is defined as the ratio of coherent radiation intensity and incoherent radiation intensity in infinitesimal bandwidth and solid angle aperture, can evaluate the performance of the CHG-FEL. In the experiment, we can only get the experimental integral ratio integrated over the actual bandwidth and solid angle aperture of the radiation measurement system. Because the coherent radiation and incoherent radiation are very different in the spatial and spectral structure, the experimental integral ratio is greatly influenced by the measurement system and cannot be directly used to evaluate the performance of the CHG-FEL. So, we must calculate the experimental spectral ratio according to the experimental integral ratio, the bandwidth and solid angle aperture of the measurement system and the parameters of the CHG-FEL. Our work provides a simple method for the calculation of experimental spectral ratio.