## 1 Introduction  
Saffron, the dried red stigmas of _Crocus sativus_ L., is highly valued in the food industry for its aroma, taste, and color and is one of the world's most expensive spices. Approximately 150,000 flowers are required to produce a single kilogram of saffron, which is subsequently sold for $1400-2600 USD (price for export) and $2-12 USD per gram (retail price) [1; 2; 3]. It has been estimated that the global annual production of saffron is approximate 205 tons, 80 percent of which comes from Iran, while Spain and Greece export around 60 and 4.5 tons, respectively [4].  
Saffron releases its aroma after it has undergone a thermal process, with safranal being the main component [5; 6; 7]. Although various other components--and not only safranal--play a role in producing the saffron aroma, safranal is viewed as the key sensorial compound, and this suggests that the development of methods for the extraction and analysis of safranal would be extremely useful for categorizing and grading saffron's commercial quality [6; 8; 9]. Safranal is a highly rated antioxidant and acts as a protective agent against indomethacin-induced gastric ulcers, while in vitro tests have shown that it is also effective against certain cancer cells [10].  
In order to differentiate between different qualities of saffron, the sector uses a spectrophotometric method described at ISO Normative 3632-1:2011 [11] to categorize saffron according to the strength of its aroma (expressed as safranal), flavor (expressed as picro-crocin), and coloring (expressed as crocin). Nevertheless, this type of general analysis cannot tackle the issue of quality grading, which would make a positive contribution to the international market in saffron sales [8; 12; 13; 14; 15]. One further disadvantage to using this method is its inability to ensure the authenticity of saffron [16; 17; 18]. The safranal index used by ISO Normative cannot be harnessed to make distinctions between commercial samples, since safranal is not fully solubilized in water--the solvent used in the method for UV determination at \(\lambda\) = 330 nm [14; 15]. It has also been pointed out that the _cis_-crocetin ester isomers interfere at precisely the same wavelength [19; 20].  
One commonly used method for determining food aroma compounds is the combination of solid-phase microextraction (SPME) and gas chromatography-mass spectrometry (GC-MS). This approach has a number of advantages, namely the following: it precludes the co-extraction of less volatile compounds from real sample matrices and does away with the need to use toxic solvents and laborious sample preparations [21]. This method has been employed to quantify safranal in a range of saffron samples [22; 23; 24; 25; 26], saffron drink [9], for the detection of adulterants [18], and for the purpose of geographical discrimination of saffron [27; 28]. However, several factors that affect the SPME extraction of safranal such as the quantity of saffron and the volume of water added have not been yet evaluated and optimized. In particular, the quantity of saffron can be a very important factor, as it increases the cost of analysis.  
This study set out to examine the factors that affect the extraction of safranal by SPME and methods of upgrading and improving the SPME procedure through the optimization of the factors affecting the analysis in order to attain the highest possible concentration of safranal. GC-MS was used to analyze the aroma profile, and experimental design was based on a five-level rotatable central composite design (RCCD), combined with the application of response surface methodology (RSM).