electronics Article Correction of Optical Delay Line Errors in Terahertz Time-Domain Spectroscopy Alexander Mamrashev 1, * , Fedor Minakov 1,2 , Lev Maximov 1,2 , Nazar Nikolaev 1 and Pavel Chapovsky 2,3 1 Laboratory of Information Optics, Institute of Automation and Electrometry SB RAS, 630090 Novosibirsk, Russia; minakovfa95@gmail.com (F.M.); lev.maximov@gmail.com (L.M.); nazar@iae.nsk.su (N.N.) 2 Physics Department, Novosibirsk State University, 630090 Novosibirsk, Russia 3 Laboratory of Nonlinear Spectroscopy of Gases, Institute of Automation and Electrometry SB RAS, 630090 Novosibirsk, Russia; chapovsky@iae.nsk.su * Correspondence: mamrashev@iae.nsk.su; Tel.: +7-383-330-8378 Received: 24 October 2019; Accepted: 22 November 2019; Published: 26 November 2019   Abstract: One of the key elements of terahertz time-domain spectrometers is the optical delay line. Usually it consists of a motorized translation stage and a corner reflector mounted on its top. Errors in the positioning of the translation stage lead to various distortions of the measured waveform of terahertz pulses and, therefore, terahertz spectra. In this paper, the accuracy of position measurements is improved by using an optical encoder. Three types of systematic errors are found: Increasing and periodic offsets of the translation stage position, as well as a drift of its initial position in a series of consecutive measurements. The influence of the detected errors on the measured terahertz spectra is studied and correction methods are proposed. Keywords: terahertz spectroscopy; optical delay line; correction; optical encoder; terahertz spectra; terahertz metrology 1. Introduction Terahertz time-domain spectroscopy (THz-TDS) has become one of the most common methods for studying optical and dielectric properties of materials in the frequency range of 0.1–10 THz with the development of femtosecond laser technology [1,2]. This method is used to study nonlinear optical crystals [3,4], nuclear spin isomers [5], complex biomolecules [6], and charge carriers in solids [7,8]. The principle of operation of terahertz time-domain spectrometers is based on the generation of terahertz pulses and measurement of their electric field waveform. An optical delay line allows changing of the path difference between generation and detection optical channels of the spectrometer. This enables point-by-point sampling of the terahertz pulse waveform. Digital Fourier transform is used to calculate the spectra of the measured signal that contain information on the absorption coefficient and the refractive index of the media under study. Details of the spectrometer operation will be discussed later. Various elements of spectrometers exhibit random and systematic errors, leading to distortion of terahertz pulses and, therefore, terahertz spectra [9–13]. The errors in the amplitude of terahertz pulses are mainly determined by random fluctuations and the long-term drift of the THz generation system, which consists of a femtosecond pump laser and an optical-to-terahertz converter. Errors in the positioning of the optical delay line lead to more complex distortions. In [14], the effect of a drift of the initial position of the delay line in a series of sequentially measured terahertz pulses was considered. It was shown that it led to error proportional to the THz signal shifted by a quarter cycle. Spectroscopy of thin films and attenuated total internal reflection spectroscopy are especially sensitive Electronics 2019, 8, 1408; doi:10.3390/electronics8121408 www.mdpi.com/journal/electronics