Practical method to estimate the standard deviation in absorption coefficients measured with THz time-domain spectroscopy

Abstract

a b s t r a c tA model of standard deviation in the intensity spectrum of electric field observed with the terahertz timedomain spectroscopy (THz-TDS) is proposed to estimate the random error in the transmittance and absorption coefficients from a single or a few measurements of a sample. The proposed standard deviation which is derived on the basis of the statistical standard deviation and noise floor of intensity spectrum of reference fits well to the standard deviation of transmittance as well as absorption coefficient computed statistically. This study contributes the simple and computationally efficient method to demonstrate the accuracy in optical constants like imaginary part of refractive index and absorption coefficients measured using the THz-TDS.

Exploration of the origin of random error in spectrum intensity measured with THz-TDS

“…Figure 1 shows a mean intensity of spectrum and the standard deviation of sixteen reference data without a sample in transmission measurements obtained using our THz-TDS system. Recently, it has been found that the standard deviation is almost proportional to the signal intensity and approaches to the noise floor at the lowest intensity signal region [5] and such a feature is similarly seen in Fig. 1.…”

“…An interesting thing about the SNR is that the almost same maximum values have been obtained with different THz-TDS systems as shown in Ref. [5]. Therefore, a mechanism of occurrence of the random error may be identical between those systems.…”

“…Although a number of measurement results based on THz-TDS have been reported, it seems that the standard deviations and quantitative consideration of reliability in the measurement results have not been closely discussed. In a few papers, the signal-to-noise ratio (SNR) in intensity spectra measured with THz-TDS has been discussed based on the standard deviation of measurement data [4,5].…”

Metrology Issues and Solutions in THz Time-Domain Spectroscopy: Noise, Errors, Calibration

“…Based on the empirical observation that the standard deviation (SD) of the THz spectral amplitude is proportional to the amplitude itself ( see Fig. 2a), Tripathi et al [8] derive a simple and very useful method for estimating the standard deviation of absorption coefficients. The SD of measured amplitude is assumed to be approximately given by α max is larger for the thinner sample.…”

Highly sensitive terahertz measurement of layer thickness using a two-cylinder waveguide sensor

“…Delay lines, for instance, have mechanical specifications with an accuracy between 0.1 and 1 m. However, the largest influence is due to thermal drifts, 14 which requires frequent reference scans to minimize the accumulated error. 15 The reference zero delay of our system drifts by approximately 20 fs/h. This is reasonable, as the free-space optics is mounted on a stainless-steel table ͑thermal expansion coefficient 17.3 m / m°C͒.…”