To control the laser parameters and meet the requirements of precise physical experiments, it is necessary to accurately obtain the spectral width of the frequency-modulated (FM) light. The FM light has complex comb distribution that the morphological characteristics are different from the typical continuous spectrum. In this paper, we define the spectral width of the FM pulse according to the nature of the phase modulation and develop a correlation traversal algorithm based on spectral morphology matching. Then, we establish the relationship between the measured spectrum of the medium-precision spectrometer and the simulated spectrum and complete the spectral width calibration. The correlation of the measured spectrum and the simulated spectrum in 2.5 GHz frequency modulation, within the spectral width range of 0.05 nm ~ 0.30 nm is calculated. The correlation traversal algorithm can obtain a strongly correlated theoretical spectrum with an R-value greater than 0.9 for any measured spectrum. Through linear fitting of all data, we obtain the relationship curve between the -3dB spectral width measured by the medium-precision spectrometer and the calibrated spectral width. And the determination coefficient of the relationship curve is 0.9989. The results show that the spectral width calibration method has the advantages of strong correlation and high linearity. The spectral width calibration method completes the spectral width calibration of FM light for the first time, which lays a foundation for precise control of spectral parameters in inertial confinement fusion precision physics experiments.
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