## 3 System Characterization  
Figure 2 depicts the time-domain trace of a single-shot measurement acquired at maximum speed, i.e., completed within 625 \(\upmu\)s (green curve), together with an average of 1000 pulse traces (black). While the main pulses appear virtually indistinguishable, the averaged trace exhibits a significantly reduced noise floor, which is particularly evident in the pre-pulse background signal (inset). Terahertz-based thickness gauging almost always relies on an evaluation of time-domain traces. A crucial parameter to quantify system performance is thus the time-domain dynamic range (TD-DR), defined as the maximum peak-to-peak amplitude of the pulse trace divided by the root mean square (RMS) of the noise floor [30; 31; 32]:  
\[\text{TD-DR}=\frac{\text{maximum peak-to-peak of amplitude}}{\text{RMS of noise floor}}. \tag{1}\]  
Figure 3a shows the TD-DR of the ECOPS instrument at its maximum measurement speed (200 ps scan range @ 1600 Hz, blue triangles) and for the slowest setting (700 ps @ 200 Hz, red circles). As a benchmark, we have included values obtained with a state-of-the-art terahertz TDS system (\"TeraFlash pro\", TOPTICA Photonics AG), with its mechanical delay adjusted to a comparable scan range (200 ps @ 6 Hz, green squares). For each setting, we have evaluated both single-shot measurements as well  
Figure 2: Single-shot terahertz pulse trace (green) taken at a measurement speed of 1600 traces per second, and average of 1000 consecutive pulse traces (black). The inset shows a magnified cutout of the pre-pulse noise floor. as 10, 100 and 1000 trace averages. The single-shot TD-DR of the ECOPS system amounts to 61 dB (=20 \(\times\) log (TD-DR)), independent of the measurement speed. This agreement is expected, since the slower measurement covers a larger scan range (see below) and consequently, overall data rates and thus, electrical bandwidth requirements are comparable. By contrast, the TeraFlash pro achieves a TD-DR of 82 dB, significantly higher than that of the ECOPS system. We attribute this difference to two decisive characteristics of the design: First, the TeraFlash pro benefits from an extremely precise mechanical delay [15], the low timing jitter of which translates into an excellent signal quality. Even more important, the slower measurement speed of the TeraFlash pro permits the use of (comparatively) low-bandwidth--and hence, low-noise--electronics for signal readout. Both effects contribute to the high TD-DR, as evident from Figure 3a. Averaging multiple time traces, the TD-DR is expected to scale with the number of averages \(N_{\text{ave}}\) according to:  
\[\text{TD-DR (dB)}\propto 20\log\Bigl{(}\sqrt{N_{\text{ave}}}\Bigr{)}. \tag{2}\]  
Indeed, we find that averages of 10, 100, and 1000 terahertz pulse traces increase the TD-DR of the ECOPS system by approximately 10 dB, 20 dB and 30 dB, respectively. A similar signal gain is observed for the TeraFlash pro, too. Figure 3b rearranges the same data as a function of the measurement time. In this regard, the ECOPS setup actually outperforms the TeraFlash pro, achieving a TD-DR of 91 dB in less than one second. We will return to the trade-off between signal quality and measurement speed in Section 4. A complementary parameter in practical applications is the time-domain signal-to-noise ratio (TD-SNR), which characterizes the minimum signal change that can still be quantified. The TD-SNR is defined as the ratio of the mean peak-to-peak amplitude and its standard deviation [30; 31; 32]:  
\[\text{TD-SNR}=\frac{\text{mean peak-to-peak amplitude}}{\text{standard deviation of amplitude}}. \tag{3}\]  
Figure 3: **(a)** TD-DR as a function of the number of pulse-trace averages. The plot compares values obtained with ECOPS at measurement speeds of 1600 traces per second (blue triangles), 200 traces per second (red circles) and a conventional terahertz TDS system (TeraFlash pro) operating at 6 traces per second (green squares). **(b)** Same data, as a function of the measurement time.