## 3 Results and Discussion
### Headspace Linearity and Its Impact on Analyte Relative Distribution  
Volatile fraction profiling [45], can be run for effective cross-sample comparison, as in the case of a selection of olive oils that differ in origin, extraction technology, and storage time, so analytes and/or informative markers can be compared using chromatographic quantitative indicators that are based on peak areas (raw areas, percentage area), and peak-volume percentage in the case of GC \(\times\) GC (raw volume, percentage volume), or IS normalization (normalized area, normalized volume). These methods, which are based on relative/normalized responses, have been accepted by the scientific community for several application fields [46], despite being inaccurate and misleading if treated as absolute concentration indicators. They do not take into consideration several concurring effects, such as the effect exerted by the condensed phase (i.e., matrix effect) on the release of an analyte into the HS or the displacement and multiple-equilibria that occur with adsorption polymers (carboxen--CAR and divinylbenzene--DVB). Procedures that compensate, or model, the matrix effect are those known as quantitation approaches, and these are based on either external or internal calibration with authentic standards or stable isotopologues of the target analytes. Those suitable for liquid samples are: (a) External calibration in matrix-matched blank samples; (b) standard addition (SA) by spiking the sample with known incremental amounts of analyte(s); (c) stable isotope dilution assays (SIDA), which are a specific application of SA; and (d) multiple headspace extraction (MHE). HS linearity must be accomplished for an accurate quantitation of targeted analytes, whichever approach is applied. [44] This condition is verified when, under pre-determined sampling conditions (e.g., temperature, time, and phase-ratio), the condensed phase (liquid or solid sample) releases a minimal analyte amount into the HS without saturation and, in addition, a linear function can be established between the analyte concentration in the sample (C\({}_{0}\)) and its concentration in the gas phase (C\({}_{\text{g}}\)). Linearity is easily achievable for trace and sub-trace components, but becomes challenging in multi-analyte quantitation with complex volatile fractions. The linear range depends on analyte partition (K\({}_{\text{hs}}\)) and activity coefficients. It generally ranges between 0.1% and 1% of actual concentration in the sample and can be tuned by modifying the sampling extraction phase (adsorption/sorption mechanisms), the amount of extraction polymers, the sampling temperature and time, as well as by modifying the phase ratio between HS (V\({}_{h}\)) and the condensed phase volume (V\({}_{s}\)). In this study, HS linearity by SPME-TRIF sampling, which was taken as the reference technique, was explored, for the analytes listed in Table 2, by analyzing different amounts of EV olive oil, between 1.500 and 0.100 g, chosen on the basis of previous studies [3; 47; 48; 49; 50]. Results for normalized peak volumes and percentage responses are reported in Supplementary Table S2 (ST2), while they are summarized in Table 3 for a selection of potent odorants. Responses, obtained from three analytical replicates randomly distributed within a uniform sampling batch, were normalized over the IS (i.e., \(\alpha\)-tujone) and refer to 1.500 g of sample (the amount adopted for sampling-device screening) or to 0.100 g. At 0.100 g, at least 50% of the analytes failed to reach HS saturation for the applied sampling conditions (20 mL sampling vial, 40 \({}^{\circ}\)C, 60 min). Normalized volume ratios, calculated between 0.1 and 1.5 g of sampling amount, differ widely within the group of analytes considered. A histogram of Figure 6 summarizes the results. In particular, an average value of 1 (highlighted by a red line) was obtained for (\(Z\))-2-penten-1-ol, hexanal, (\(E\))-2-hexenal, ethyl acetate, and 2-pentanol.