Statistical Models for Averaging of the Pump–Probe Traces: Example of Denoising in Terahertz Time-Domain Spectroscopy

In this paper, we first discuss the main types of noise in a typical pump-probe system, and then focus specifically on terahertz time domain spectroscopy (THz-TDS) setups. We then introduce three statistical models for the noisy pulses obtained in such systems, and detail rigorous mathematical algorithms to denoise such traces, find the proper averages, and characterize various types of experimental noise. Finally, we perform a comparative analysis of the performance, advantages, and limitations of the algorithms by testing them on the experimental data collected using a particular THz-TDS system available in our laboratories. We conclude that using advanced statistical models for trace averaging results in fitting errors that are significantly smaller than those obtained with only a simple statistical average.