## Materials and Methods
### Analytical Method  
The analysis by headspace solid phase micro-extraction coupled to gas chromatography/mass spectrometry method (HS-SPME GC/MS) was performed according to [30] with slight modifications. In brief, for volatiles extraction, 50/30 \(\upmu\)m of DVB/CAR/PDMS fibers (Supelco St. Louis, MO, USA) were used. The HS-SPME was performed by CTC Combi-Pal auto-sampler (CTC Analytics AG, Zwingen, Switzerland). A Peltier temperature controller was used to control the temperature of incubation and extraction of the samples. Desorption of the volatiles from the SPME fiber was done in the GC injection port (split/splitless) at 230 \({}^{\circ}\)C for 1 min. The cleaning of the fiber was done after each analysis in a conditioning chamber for 20 min at 280 \({}^{\circ}\)C.  
The analysis was done using Trace-GC 2000 (Thermo-Scientific, Waltham, MA, USA) coupled to a PolarisQ ion-trap mass spectrometer (Thermo-Scientific, Waltham, MA, USA). The chromatographic separation was achieved using PoraBond-Q (25 m \(\times\) 0.32 mm \(\times\) 5 \(\upmu\)m) column (Varian, Palo Alto, CA, USA) at a constant flow rate of 1.7 mL/min He (alpha gas 2, Air Liquid, Belgium). The GC temperature program begins at 45 \({}^{\circ}\)C during 1 min, ramp at 120 \({}^{\circ}\)C/min to 120 \({}^{\circ}\)C, hold for 20 min, followed by another temperature ramp of 10 \({}^{\circ}\)C/min until 260 \({}^{\circ}\)C and hold for 2 min resulting in a total run time equal to 37 min. The mass spectral acquisition was recorded in selected ion monitoring (SIM) mode.  
To ensure the reliability of the results provided by this work, a validation plan was created prior to the analysis of the 1003 samples. In brief, this plan targeted mainly five food matrices mentioned in the EFSA report [17] including coffee, baby foods, chips and snacks, and cereal-based foods and beverages. The strategy of the validation was performed based on the European Commission decision n\({}^{\circ}\) 2002/657/EC [31] by evaluating the linearity of the calibration curves, the precision, the trueness, the specificity, and the limit of detection (LOD) and limit of quantification (LOQ). Then, the produced results were evaluated based on the criteria of the analytical performances recommended by the European commission for furan and methylfurans analysis [21]. The obtained LOQ for furan, 2-MeF, and 3-MeF is 1.8 \(\upmu\)g/kg in coffee and 0.5 \(\upmu\)g/kg in other food matrices. The LOQ of 2-EtF, 2,5-dMeF, and 2,3-dMeF is 4.5 \(\upmu\)g/kg in coffee and 2.5 \(\upmu\)g/kg in other foods. These values could slightly be changed depending on the nature of the analyzed food matrix.  
The performances of the analytical method were checked by participating in international proficiency tests (PT) organized by the European Reference Laboratory for Process Contaminants. Three PT were performed to measure the demanded furan compounds in coffee, in baby food, and in cereals. Satisfactory results were obtained with z-score within the \(\pm\)2 range. In addition, to ensure the daily performance of the method, in each injection sequence, one or two spiked samples with known amounts of native furans standards were added to ensure the recovery estimated by dividing the measured content to the fortification level.  
The methods and analyses were performed under an ISO17025 system and the used method was accredited by BELAC (the Belgian accreditation body).