## 2 Materials and Methods
### Experimental Setups
#### 2.2.2 Quasi-Optical THz Beam Delivery Setups
However, for the lowest frequency, \(\sim\)0.1 THz, corresponding to the longest wavelength, \(\lambda\sim\) 3.00 mm, \(Z_{R}\) is only a fraction of \(l\) and \(Z_{R}\)/\(l\)\(\sim\)0.6. This pushes the paraxial beam approximation to the limit. One cannot a priori neglect additional errors related to the unequal optical paths  
Figure 2: Performance of the THz-TDS system during measurements. Pulses were transmitted through ambient air without any sample. A 1.00 mm-long empty quartz cuvette was used, as well as the same cuvette filled with pure gasoline and isopropanol. **(a)** Time-profiles of the pulses with an artificially added horizontal offset of approx. 2.5 ps. **(b)** Power spectra of the pulses; a vertical offset \(\sim\)10 dB was added to visualize spectral features without overlapping. The noise floor level is representative for all spectra; however, it corresponds to the “true” noise line of the spectrum registered in ambient air. The reduction of the dynamic range and bandwidth is caused by the absorptive properties of substances. of the spectral components of the pulse. For the two shorter quartz cuvettes (\(l\) = 1.00 and 2.00 mm), the Rayleigh lengths are at least 1.5x longer than \(l\). Therefore, one should not expect the measured TOFs to be significantly biased by non-paraxial beam propagation. The second of the optical setups, the \(2f\) quasi-optical setup (Figure 1b), exploited a different approach to the issue of unequal optical paths. Here, the cuvette with gasoline samples was exposed to a collimated THz beam, occupying a midpoint between the two off-axis parabolic mirrors. The cuvette was situated at the Fourier plane, shifted by one focal length distance from the coupling mirror (first mirror on the left-hand side in Figure 1b). Smaller diameter mirrors, 25.4 mm (1-inch), with equal focal lengths,\(f_{trans}\) = 50.8 mm, were used in the \(2f\) configuration. The Rayleigh lengths of the spectral components of the THz pulse were estimated using the method described in the second part of Appendix A. They differ at most by only \(\sim\)1 mm for the whole bandwidth of the pulse, i.e., form 0.1-6.0 THz. More precisely, \(Z_{R}\) = 400 mm for the frequency of 0.1 THz and \(Z_{R}\) = 399 mm for the frequency of 6.0 THz. This is not surprising since, from a geometrical optics point of view, the \(2f\) system forms a bunch of ideally parallel rays between the two mirrors. The \(2f\) quasi-optical setup is best suited for sensitive TOF measurements when the optical path in the cuvette is long. Small changes in the refractive index can be detected in this way, which, in turn, assures extremely low detection limits for the TDS time-of-flight method. The main limitations of this configuration are unequal beam diameters of the spectral components of the pulse; this means that only samples that are uniform over a large area can be investigated using the \(2f\) setups. Gasoline solutions fulfill this requirement to a large extent, providing the saturation pressure of volatile fuel components inside a closed cuvette has been attained. This explains why the \(2f\) optical arrangement could be used together with the longest quartz cuvette as well as the TPX cuvette providing an optical path of \(l\) = 10.00 mm. As schematically indicated in Figure 2b, the size of the THz beam was intentionally larger than the transversal size of the cuvette. In this way, the part of the beam that passed freely through the air provided the \"zero delay\" time reference for pulses transmitted through gasoline samples. Any inaccuracy of the delay line position readout or temporal drift of a laser pulse could be corrected in this way. The THz waveforms were brought to the common starting point after their registration and before data analysis so that unbiased time of flights resulting exclusively from the compositional change of a mixture change could be measured. Figure 3a depicts a digital camera photograph of the \(2f\) setup.