We demonstrate frequency domain spectroscopy of free-space terahertz (THz) radiation by using a vibrating optical delay and a rf spectrum analyzer. When the timing of the pump pulses is repeatedly varied at several Hz and an optical chopper at a frequency of several kHz simultaneously modulates the pump pulse, the spectrum analyzer directly obtains the THz spectrum as a sideband of the chopping frequency. This method can be used to measure in real time the transient change in the THz spectrum at a specific frequency corresponding to the water absorption.

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