## 5 Discussion  
Three items of scientific interest emerge from the presented methods and data. The first is a novel method of investigating the temperature dependent variation of the dielectric parameters in samples in the THz range using continuous, non-polarised, synchrotron radiation. The method is shown to be useful over a range of sample types, and over a range of temperatures. The method relies on the use of ATR apparatus, and retains the advantage of minimal sample preparation, which is a feature of ATR methods. The ability for rapid measurement with a bright synchrotron source demonstrates a \"proof of concept\" of rapidly monitoring temperature dependent changes in reflectance whilst continuously heating or cooling the sample by using a temperature variable Thermal Stage.  
The second item is the novel method's ability to retain the ATR advantages with samples where the refractive index leaves the ATR apparatus to no longer act in a \"true\" attenuated total reflection mode, but in a reflection/transmission mode. The ability of an ATR apparatus to usefully act as a reflectance/transmission apparatus in the instances where the refractive index of the sample precludes attenuated total reflection study is demonstrated with the water reflectance experiments. The ATR can only return a refractive index in this mode and further modification of technique, such as a mirror reflector at a small distance [6] is required to extract the absorption coefficient in these circumstances. The reflected signal intensity of water in the experiments suggests that the reflection from the crystal/sample interface in the transmitted mode is non-polarised. Remarkably, reflected signal intensity changes of ice in the 1.70-2.25 THz band were recognisable between \(-\)25 \({}^{\circ}\)C and \(-\)15 \({}^{\circ}\)C. The changes of refractive index in ice are not well known in the THz frequency range and the techniques described in this paper open the possibility to accurately document these fundamental properties. The experimental results were in line with the predicted numbers from theoretical calculation and literature data.  
The third item is the demonstration of the a \"proof of concept\" of estimating temperature dependent ATR reflected signal intensity of lard and Lurpak(r) butter. Both are within the ATR range of the diamond crystal in a \"true\" ATR mode. Lard was studied in the range \(-\)15 \({}^{\circ}\)C and 24 \({}^{\circ}\)C with results showing no clear temperature related change at either the  
Figure 7: Spectral bands centered around 0.9 and 2.0 THz. There is a decline in reflected signal intensity with increasing temperature at both frequencies with a temperature dependent plateau over the 0 to 10 \({}^{\circ}\)C range at 2.0 THz.  
0.7 to 1.15 THz or the 1.70 to 2.25 THz range, with the variation staying in the error range of the air calibration (within +/\(-\)1.5% (0.70 to 1.15 THz) +/\(-\)0.46%). This suggests that lipids can be regarded as having invariable, constant, dielectric properties within mixtures when biological substances are being assessed for temperature dependent dielectric variation.  
Lurpak(r) butter has a water content of 14.7% (_w/w_), approximating adipose tissue (-15% bulk water). Lurpak(r) butter displays temperature dependent reflected signal intensity features, with a steady decline in reflectivity with increasing temperature. Given that Lurpak(r) butter has a refractive index within the \"true\" attenuated total reflectance of the diamond crystal equipped ATR, the result suggests an increase in the absorption coefficient with increasing temperature. There is no rapid change in reflected signal intensity which would suggest a change of state even at \(-\)20 \({}^{\circ}\)C. The contribution of the protein fraction of Lurpak(r) butter has not yet been determined.