Hilbert-Transform-Based Accurate Determination of Ultrashort-Time Delays in Terahertz Time-Domain Spectroscopy

Accurate determination of time delays is crucial for distinguishing a sample's different interfaces in terahertz time-domain spectroscopy (THz-TDS), especially for ultrathin samples or interfacial gaps. In this paper, Hilbert transform (HT) is invoked, along with posttransform signal spectral estimation of several varieties, including the conventional, that based on multiple-signal classification spectrum estimation (HT-MUSIC), and that based on autoregressive spectrum estimation using Yule-Walker law (HT-AR), to determine the sample's different interfaces. The results are compared with the traditional method of obtaining time delays in THz-TDS, along with analysis of the resolution and accuracy, as well as advantages and deficiencies of the various approaches. It is demonstrated that HT is an effective method for determining different interfaces of an ultrathin sample by simulation and experiments. The simulation results show that MUSIC-HT has the best resolution, at about 0.35 ps and AR-HT has the best accuracy, whose error is less than 0.075 ps. Experimental results for ultrathin air gaps and polymer films confirmed that MUSIC-HT can distinguish time delays as short as 0.44 ps from the THz time-domain spectra.