## 2 Spectroscopy and Data Analytics  
A wide range of analytical techniques and methods have been proposed or utilized to characterize the chemical composition, nutritive value, and other characteristics of insects, including BSFL [34; 35]. Considering the principles behind the circular economy, the group of techniques based on IR spectroscopy seems to better fit as an analytical method due to properties that include being non-destructive, rapid, easy-to-use and reagent-free [30; 31; 32; 33; 34; 36; 37; 38; 39].  
Vibrational spectroscopy encompasses different methods that utilize energy in the electromagnetic spectrum [30; 31; 32; 33; 34; 36; 37]. The infrared (IR) region is divided into the mid infrared (MIR) (400 to 4000 cm\({}^{-1}\)) and near infrared (NIR) region (12,820 to 4000 cm\({}^{-1}\)) [31; 32]. This technique measures the combination and overtone bands of vibrations of important bonds (aliphatic C-H, aromatic or alkene groups, C-H, amine groups, N-H and O-H) that absorb in the NIR range [30; 31; 32; 33; 34; 36; 37; 38; 39]. The different molecules and chemical components present in a sample contribute to a characteristic position, shape, and size of the analyte's absorption bands [30; 31; 32; 33; 34; 36; 37; 38; 39]. MIR spectroscopy is characterized by the measurement of the fundamental absorption of molecules present in the sample [30; 31; 32; 33; 34; 36; 37; 38; 39]. In MIR spectroscopy, different techniques are available, including the Fourier transform (FT) IR techniques, which include sampling systems such as internal reflection spectroscopy, attenuated total reflection (ATR), diffuse reflection spectroscopy, or specular reflection, as well as the combination of internal and external reflection called diffuse reflection (DRIFT) [30; 31; 32; 33; 36; 37; 38; 39].  
The combination of the MIR or NIR spectra with chemometric methods has been utilized to determine different parameters in a wide range of samples, including insects [24; 34]. Advances in miniaturization and portability has contributed to the increase in the usage of these instruments, with them being able to move from the laboratory into the field, where on-site and in-field applications have been developed and implemented in the agriculture and food industries, including insects [35; 40; 41; 42]. These instruments also provide the same precision and performance as the laboratory bench instruments [40; 41; 42; 43]. More recently, hyperspectral imaging systems using wavelengths in the VIS (400 to 750 nm) or NIR spectral regions have been utilized to analyze different types of samples, including insects [24; 34].  
The chemometric techniques utilized can be distinguished as targeted and untargeted depending on their ability to identify constituents, composition, or other properties, such as origin, process characteristics, and traceability monitoring [43; 44]. Techniques such as principal components analysis (PCA) [45] and partial least squares (PLS) regression are usually applied to reduce dimensionality in the data set and to develop calibration models for a specific chemical constituent or property [45; 46; 47; 48]. Other algorithms are also explored, such as support vector machines (SVM), interval PLS (iPLS), and genetic algorithms (GA) [47]. The interpretation of the models or calibrations is usually achieved by the interpretation of statistics, such as the coefficient of determination in either calibration or cross-validation (R\({}^{2}\)), the standard error of the cross validation (SECV) or prediction (SEP), root mean square of standard error of prediction (RMSEP), and the residual predictive deviation value (RPD) [49].  
The developments in instrumentation and computational power have resulted in IR spectroscopy being evaluated to predict proximate composition and functional properties, as well as functioning as a tool for traceability in the production of BSFL. The following sections discuss some of the applications reported in the scientific literature.