The performance of a narrow-linewidth nanosecond pulsed deep-UV coherent light source consisting of a frequency-tripled nanosecond pulsed Ti:sapphire laser injection seeded by a frequency-scanning cw Ti:sapphire laser has been characterized by using optogalvanic spectroscopy of silicon atoms as a diagnostic. The envelope of the optogalvanic spectrum indicates the pure Doppler broadening of silicon atoms, which was estimated to be as broad as 4 GHz, without the broadening effect from the laser linewidth itself.