Using Attenuated Total Reﬂection (ATR) Apparatus to Investigate the Temperature Dependent Dielectric Properties of Water, Ice, and Tissue-Representative Fats

(ATR) Apparatus to Investigate the Temperature Dependent Abstract: A novel method of investigating the temperature dependent variation of aspects of the complex refractive index n * in samples in the THz range using continuous, non-polarised, synchrotron radiation is presented. The method relies on the use of ATR apparatus, and retains the advantage of minimal sample preparation, which is a feature of ATR techniques. The method demonstrates a “proof of concept” of monitoring temperature reﬂectance whilst continuously heating or cooling samples by using a temperature variable Thermal Sample Stage. The method remains useful when the refractive index of the sample precludes attenuated total reﬂection study. This is demonstrated with the water reﬂectance experiments. The temperature dependent ATR reﬂectance of tissue-representative fats (lard and Lurpak ® butter) was investigated with the novel approach. Both are within the ATR range of the diamond crystal in a “true” ATR mode. Lard showed no clear temperature variation between − 15 ◦ C and 24 ◦ C at 0.7 to 1.15 THz or 1.70 to 2.25 THz. Lard can be regarded as having invariable, constant, dielectric properties within mixtures when biological substances are being assessed for temperature dependent dielectric variation within the stated THz ranges. Lurpak ® butter (water content 14.7%) displayed temperature dependent reﬂected signal intensity features with a steady decline in reﬂectivity with increasing temperature. This is in line with the temperature-dependent behaviour of liquid water. There is no rapid change in reﬂected signal intensity even at − 20 ◦ C, suggesting that emulsiﬁed water retains liquid-water-like THz properties at freezing temperatures. This paper examines the viability of investigating biological tissues by employing the temperature dependent variation of THz dielectric parameters using an attenuated total reﬂection (ATR) apparatus, in both the “true” attenuated total reﬂection mode and in a novel “reﬂection/transmission” mode. The Australian Synchrotron’s THz-far infrared beamline provides a high brightness source, which results in rapid evaluation, enhanced spectral quality and superior spatial resolution when compared to a conventional source. Useful data can be obtained in spectral scan blocks of 30 sec or less, with the beam running 24 h per day. The Synchrotron’s beam is continuous which makes it unsuitable for time domain spectroscopy, thus novel approaches are needed to maximise its utility. The synchrotron ATR apparatus is equipped with a diamond crystal, which has a refractive index ( n ) of 2.40, and since n of water at THz frequencies is in the order of 1.95 to 2.15, the setup is ideal to determine the dielectric properties of water-based compounds by using the novel “reﬂection/transmission” technique [6].


Introduction Overview
Terahertz radiation (THz) is highly absorbed by liquid water and this presents the possibility to image biological materials using the difference in water content between normal and pathological lesions [1]. Efforts have been made in the past to evaluate THz properties of biological tissues with a view to devising diagnostic imaging techniques [2][3][4]. The small-scale variability of biological tissue produces large "normal" ranges for THz dielectric parameters, which have substantial overlaps with the dielectric parameters of diseased tissue [5]. THz examination can also be time consuming and involves highly specialised expertise. These problems have resulted in difficulties in devising a diagnostic test which is both clinically relevant and practical. 3 of 12 apparatus is coupled with a temperature variation apparatus, the tissue characterisation does not depend on interpretation, but simply a comparison to an established dataset. The ATR/temperature variation apparatus thus offers the ability for rapid characterisation of the tissues with minimal preparation and minimal operator training. The Synchrotron's high brightness source facilitates the systematic application of this method by offering rapid evaluation, high spectral quality and excellent spatial resolution.

Attenuated Total Reflection
The technique of attenuated total reflection (ATR) spectroscopy has become a popular method to evaluate the dielectric properties of materials. It relies on the reduction in the reflected signal intensity at an angle of incidence where total reflection occurs at the crystal/sample interface. The technique relies on some of the incident energy being absorbed when an evanescent wave is generated in the sample.
The advantage of the method lies in the fact that solid and liquid samples can be studied with minimal preparation, since the only requirement is that a sample comes into secure contact with the crystal. The equations governing the reflection of an incident wave in ATR are outlined in Hansen, [19].
The Hansen equations take account of the angle of incidence and the complex refractive index of the sample (n 2 *) and the crystal (n 1 *). The complex refractive index (n*) is defined as n* = n + ik, where n and k are the real and imaginary part of the refractive index, respectively. The term k is related to the absorption coefficient (α) via the equation k = αλ/4π, where λ is the wavelength of the radiation. It is apparent from the equations that there is a set of refractive index/absorption coefficient combinations which can satisfy a given reflectance; no unique pair of n and α can be deduced from reflectance alone if a synchrotron-like continuous, non-polarised beam is used.
The combinations are dependent on frequency and angle of incidence. Examples of the combinations of sample refractive index n 1 and sample α at 0.3 THz and 1.0 THz, at 45 • angle of incidence and a diamond crystal (n 2 = 2.40) are set out in Table 1. Table 1. A sample of the n and α combinations at 0.3 THz and 1.0 THz which deliver the same reflected signal intensity at 45 • incidence. The example of the change from n 2 = 1.1 to n 2 = 1.65 with a change in the absorption coefficient from α = 5 cm −1 to α = 65 cm −1 to deliver a constant normalised reflected signal intensity of 0.79 at 1.0 THz is illustrated in Figure 1.
The changes in reflected signal intensity can come about with changes in either parameter, n 2 or α. Furthermore, changes in n 2 and α can either act to produce a synergistic reflectance change (when both n 2 and α are simultaneously increasing or decreasing) or negate any reflectance change when one parameter is increasing and the other decreasing.
Attenuated total reflection produces an evanescent wave in the sample. The penetration depth (d p ) of the evanescent wave is given by [20]: where λ is the wavelength of the incident radiation in air, n 1 and n 2 are the real parts of the refractive index of the ATR crystal and sample, respectively, and θ is the angle of incidence of the incoming radiation beam. A limit to the refractive index of the sample is evident from the equation. Since the expression sin 2 θ − (n 2 /n 1 ) 2 has to be a real number, sin θ needs to be >(n 2 /n 1 ). This property sets the limit on the refractive index of the sample that can be examined with attenuated total reflectance. Since it is dependent on θ and n 1 such limits are specific for a given ATR crystal at a given incident beam angle. When sin 2 θ < (n 2 /n 1 ), Equation (1) breaks down, and the incoming radiation is partially reflected and partially admitted to the sample at the crystal/sample interface as a traveling wave, i.e., there is no longer "total reflection". The changes in reflected signal intensity can come about with changes in either parameter, n2 or α. Furthermore, changes in n2 and α can either act to produce a synergistic reflectance change (when both n2 and α are simultaneously increasing or decreasing) or negate any reflectance change when one parameter is increasing and the other decreasing.
Attenuated total reflection produces an evanescent wave in the sample. The penetration depth (dp) of the evanescent wave is given by [20]: (1) where λ is the wavelength of the incident radiation in air, n1 and n2 are the real parts of the refractive index of the ATR crystal and sample, respectively, and θ is the angle of incidence of the incoming radiation beam. A limit to the refractive index of the sample is evident from the equation. Since the expression sin 2 θ − (n2/n1) 2 has to be a real number, sin θ needs to be > (n2/n1). This property sets the limit on the refractive index of the sample that can be examined with attenuated total reflectance. Since it is dependent on θ and n1 such limits are specific for a given ATR crystal at a given incident beam angle. When sin 2 θ < (n2/n1), Equation (1) breaks down, and the incoming radiation is partially reflected and partially admitted to the sample at the crystal/sample interface as a traveling wave, i.e., there is no longer "total reflection".
The practical result is a reduction in the signal reaching the ATR detector, and the reflected signal is now solely dependent on the Fresnel reflection equations. The ATR apparatus in this instance, i.e., where sin 2 θ < (n2/n1) 2 , is now acting in a reflection/transmission mode, where total reflection no longer occurs. This mode is not useless. Rather than delivering a possible set of sample n and α, it now delivers the real part of the refractive index n of the sample.
There are two common choices for an ATR crystal available for the lower end of the THz spectrum-silicon and diamond. Silicon crystal has an n of 3.42 [21] at THz frequencies. Using the Equation (1), the maximum n2 is 2.42. This results in most biological materials being in the "true" ATR range with an incident angle of 45°, since typical biological tissues at THz frequencies have an n < 2.3. Intuitively, it seems that silicon crystal is a good choice, however, contrast becomes a problem. dp = The practical result is a reduction in the signal reaching the ATR detector, and the reflected signal is now solely dependent on the Fresnel reflection equations. The ATR apparatus in this instance, i.e., where sin 2 θ < (n 2 /n 1 ) 2 , is now acting in a reflection/transmission mode, where total reflection no longer occurs. This mode is not useless. Rather than delivering a possible set of sample n and α, it now delivers the real part of the refractive index n of the sample.
There are two common choices for an ATR crystal available for the lower end of the THz spectrum-silicon and diamond. Silicon crystal has an n of 3.42 [21] at THz frequencies.
Using the Equation (1), the maximum n 2 is 2.42. This results in most biological materials being in the "true" ATR range with an incident angle of 45 • , since typical biological tissues at THz frequencies have an n < 2.3. Intuitively, it seems that silicon crystal is a good choice, however, contrast becomes a problem. Table 2 notes the reflectance of liquid water and ice (as a proxy for water containing biological tissues), using the Hansen equations. Silicon crystal delivers only modest contrast at 0.90 THz and very poor contrast at 2.0 THz. Diamond crystal has an n of 2.38 to 2.40 at THz frequencies, [22,23]. In the case of a diamond crystal and an incident angle of 45 • , sin 2 θ = 0.5. Thus, (n 2 /n 1 ) 2 needs to be <0.5, hence n 2 /n 1 < 0.707, or n 2 < 1.70, for the diamond crystal equipped ATR apparatus to function in "true" attenuated total reflectance mode. It follows that substrates with n > 1.70 cannot be examined in attenuated total reflectance mode with the described setup.
With n 2 > 1.70, the diamond crystal ATR apparatus becomes a partial reflectancepartial transmission device. In this instance, the reflected portion of the incident radiation is only dependent on the relative refractive indices on either side of the reflective surface.
The reflectance can be calculated by using the Fresnel equations, and these are silent about α. According to the Fresnel equations, the reflectance declines rapidly as n 2 approaches n 1 . Given the n of diamond crystal is~2.40, small changes in n 2 in the region of 1.72 to 1.90 will produce large changes in reflection giving good contrast. The relationship of contrast and n 2 with diamond crystal are presented in Figure 2. Diamond crystal has an n of 2.38 to 2.40 at THz frequencies, [22,23]. In the case of a diamond crystal and an incident angle of 45°, sin 2 θ = 0.5. Thus, (n2/n1) 2 needs to be < 0.5, hence n2/n1 < 0.707, or n2 < 1.70, for the diamond crystal equipped ATR apparatus to function in "true" attenuated total reflectance mode. It follows that substrates with n > 1.70 cannot be examined in attenuated total reflectance mode with the described setup.
With n2 > 1.70, the diamond crystal ATR apparatus becomes a partial reflectancepartial transmission device. In this instance, the reflected portion of the incident radiation is only dependent on the relative refractive indices on either side of the reflective surface.
The reflectance can be calculated by using the Fresnel equations, and these are silent about α. According to the Fresnel equations, the reflectance declines rapidly as n2 approaches n1. Given the n of diamond crystal is ~2.40, small changes in n2 in the region of 1.72 to 1.90 will produce large changes in reflection giving good contrast. The relationship of contrast and n2 with diamond crystal are presented in Figure 2. When using water and ice THz dielectric properties derived from literature, the Fresnel equations predict an ice to water reflectivity contrast of ~300%, i.e., ice is ~3× more reflective than water when using a diamond crystal. The estimated Fresnel equation based reflectivity is outlined in Table 3. The refractive index of ice is not well established at 2.0 THz, and two values were used in the calculations, n = 1.78 and n = 1.82 at this frequency. Using the ATR as a reflectance apparatus with a diamond promises better contrast compared to silicon crystal, particularly at 2.0 THz, thus it becomes a more attractive option.  When using water and ice THz dielectric properties derived from literature, the Fresnel equations predict an ice to water reflectivity contrast of~300%, i.e., ice is~3× more reflective than water when using a diamond crystal. The estimated Fresnel equation based reflectivity is outlined in Table 3. The refractive index of ice is not well established at 2.0 THz, and two values were used in the calculations, n = 1.78 and n = 1.82 at this frequency. Using the ATR as a reflectance apparatus with a diamond promises better contrast compared to silicon crystal, particularly at 2.0 THz, thus it becomes a more attractive option. There is a dichotomy with a diamond crystal ATR. At THz frequencies, biological fats and oils have an n of 1.4 to 1.6. Using an ATR diamond crystal with n of 2.40 results in "true" attenuated total reflection at 45 • incident beam with these substances. Reflectance measurements mainly deliver information regarding changes in α. Water based biological compounds have typical n in the order of 1.9 to 2.2, thus a diamond equipped ATR is acting as a partial reflection-partial transmission apparatus, delivering changes in n. The advantage of minimal sample preparation, and no requirement for thickness measurement (as would be needed for transmission studies), is retained by using the ATR apparatus in both modes.
In both cases, only a partial description of the dielectric properties is achieved. If the aim is to characterise the biological sample for the purpose of diagnosis by monitoring temperature dependent variation, then there may only be a need to find a characteristic reflected signal intensity change, rather than the full complex refractive index parameters.

Materials and Methods
The THz/Far-IR Beamline at the Australian Synchrotron, Melbourne, Australia, was used for the experiments. The Beamline was equipped with an attenuated total reflection (ATR) apparatus, a Bruker IFS 125/HR Fourier Transform spectrometer (Bremen, Germany), an Si Bolometer and a diamond prism stage (n = 2.40), and a 45 • incoming beam angle. OPUS 8.0 software (Bruker Optik GmbH, Ettlingen, Germany) was used for the initial data analysis. Air humidity was not more than 50%.
The viability of monitoring temperature related changes with the ATR apparatus, both in "true" ATR mode and in partial reflection-partial transmission mode, was explored with samples with bio-medical relevance. The materials were chosen for their different hydration levels, to offer varying insights into the possible temperature related changes. The temperature dependent variation of absorbance of air, water, ice, porcine rendered lard, and Lurpak ® (unsalted) butter was explored. Lurpak ® butter is homogeneous, and has water, lipid and protein components. It has an additional advantage of having established dielectric properties in the THz range [24].
The samples were applied through a spacer to define 2 mm thickness (water, lard, butter). At 2 mm, the path length of any returning signal from samples with absorption coefficients of >20 cm −1 become negligible.
A mirrored cooling bath was placed on top of the sample and fixed by a standard ATR mounting clip onto the ATR diamond prism window. In partial reflection-partial transmission mode, with a path length of >4 mm (2 × 2 mm sample thickness), any reflected signal from the mirror returning through the samples with absorption coefficients of >10 cm −1 becomes negligible. Similarly, in "true" ATR mode, lard and Lurpak ® butter have an n~1.5 to 1.6 in the 0.9 to 1.0 THz spectral window [24,25], which would, under ideal attenuated total refection circumstances of a negligible α, deliver a d p of <0.01 mm. Thus, any interference from the mirror reflection back through the sample is similarly negligible.
Polarisation of synchrotron radiation is a combination of linear (along the extraction mirror slit) and circular polarisations [26]. These two components arise due to the bending magnet caused dipole-emission inside the magnet and the edge-emission at the entrance/exit of the magnet edge. The THz and IR microscopy beamlines share the synchrotron radiation extracted from the magnet. The THz/Far-IR beamline receives a larger portion of the edge-emission compared to the dipole-emission. Polarisation is defined in the plane of incidence as Es and Ep, which are perpendicular (⊥) and parallel (k) to the plane (or TE and TM modes), respectively.
The reflected radiation at the 45 • incidence usually does not experience phase change upon reflection at the sample-prism interface for low refractive index (n 2 < 1.6) samples, which is typical for low "bulk water" biological samples. However, the P-polarised (TM; Ez) radiation, which probes the absorbance in the direction perpendicular to the prism-sample interface, has a strong dependence of the reflected phase on n 2 . At θi = 45 • incidence, a phase change of π occurs when θ B < θ i < θc (θ B and θc are the Brewster and critical angle, respectively) and the reflected Ez component becomes Ey.
The consequence of the phase dependence of the TM mode makes polarisation analysis of ATR signals complicated, and most of the published data do not discriminate polarisation. This approach was adopted in the current study. Future experiments will include a defined incident polarisation combined with polarisation analysis at the exit after the sample.
The ATR unit had a Thermal Stage fitted, with a capability to control the temperature of the sample and the crystal. The diamond ATR prism and the sample compartment were made suitable for cooling by using a bath from above the sample and also by a cooling/heating apparatus attached to the ATR bowl ( Figure 3). The temperature variation was monitored with a thermocouple probe placed in contact with the sample next to the diamond crystal.
sample interface, has a strong dependence of the reflected phase on n2. At θi = 45° incidence, a phase change of π occurs when θB < θi < θc (θB and θc are the Brewster and critical angle, respectively) and the reflected Ez component becomes Ey.
The consequence of the phase dependence of the TM mode makes polarisation analysis of ATR signals complicated, and most of the published data do not discriminate polarisation. This approach was adopted in the current study. Future experiments will include a defined incident polarisation combined with polarisation analysis at the exit after the sample.
The ATR unit had a Thermal Stage fitted, with a capability to control the temperature of the sample and the crystal. The diamond ATR prism and the sample compartment were made suitable for cooling by using a bath from above the sample and also by a cooling/heating apparatus attached to the ATR bowl ( Figure 3). The temperature variation was monitored with a thermocouple probe placed in contact with the sample next to the diamond crystal.

Air
The reflected signal intensity of air was measured at 20 °C, and also in 10 serial increasing increment outputs from −24 °C to 5 °C. The outputs showed no particular pattern and were within +/−1.5% (0.70 to 1.15 THz) +/− 0.46% (1.70 to 2.25 THz) of the median value for the entire group. The air reflectivity was used to normalise the other reflectivity data.

Water and Ice
The reflected signal intensity of water was measured at 5 °C to 10 °C in 10 serial outputs, averaging 50 scans per individual output, using the Thermal Stage. Ice was monitored in 10 serial outputs, also averaging 50 scans per individual output using the Thermal Stage. The temperature of the ice was allowed to rise from −25 °C to −15 °C. The water

Air
The reflected signal intensity of air was measured at 20 • C, and also in 10 serial increasing increment outputs from −24 • C to 5 • C. The outputs showed no particular pattern and were within +/−1.5% (0.70 to 1.15 THz) +/− 0.46% (1.70 to 2.25 THz) of the median value for the entire group. The air reflectivity was used to normalise the other reflectivity data.

Water and Ice
The reflected signal intensity of water was measured at 5 • C to 10 • C in 10 serial outputs, averaging 50 scans per individual output, using the Thermal Stage. Ice was monitored in 10 serial outputs, also averaging 50 scans per individual output using the Thermal Stage. The temperature of the ice was allowed to rise from −25 • C to −15 • C. The water and ice reflected signal intensity data are presented in Figure 4. Normalised water reflectivity (compared to air) was in the order 0.03 to 0.07 for wavenumber 23 to 38 (~0.70 to 1.15 THz) and~0.04 for wavenumber 56.5 to 75.0 (~1.70 to 2.25 THz). and ice reflected signal intensity data are presented in Figure 4. Normalised water reflectivity (compared to air) was in the order 0.03 to 0.07 for wavenumber 23 to 38 (~0.70 to 1.15 THz) and ~0.04 for wavenumber 56.5 to 75.0 (~1.70 to 2.25 THz).
Ice reflectivity showed a tighter grouping at 1.7 to 2.25 THz and a reduction in reflectivity with increasing frequency. There was much greater consistency of data in the 1.70 to 2.25 THz range when compared to the 0.70 to 1.15 THz range. The results at the most reliable point of 0.9 THz in the lower data set and at 2.0 THz are presented in Table 4.  The measured contrast between liquid water and ice reflected signal intensity at both ranges is broadly in line with the dielectric properties data from [14][15][16][17][18]. The reflected signal intensity of water and ice show a decline over the 0.70 to 1.15 THz range, but the experimental values are erratic. At 2.0 THz, the reflected signal intensity of water is flat over the measured range and does not change with temperature. The reflectance of ice declines with both frequency and temperature over the 1.70 to 2.25 THz range. The measured reflected signal intensity of ice at 2.0 THz is consistent with a refractive index of 1.83, which is at the upper boundary of the literature derived data.

Rendered Porcine Lard
Commercially obtained rendered porcine lard was used as a sample. Rendered lard contains chiefly triacylglycerides and fatty acids, with the water, protein and fibrous tissue components of adipose tissue being removed by the production process [27]. Lard has an n of 1.48 and α of 8 cm −1 in the 0.9 to 1.0 THz spectral window, [25], making lard within the "true" ATR range of the diamond crystal. Lard was studied between −15 °C and 24 °C with 42 individual serial outputs, each an average of 50 individual scans. The temperature was varied over a total time of 16 min with 21 discrete scanning episodes of 2 × 50 scans. The lard reflected signal intensity data are presented in Figure 5. Ice reflectivity showed a tighter grouping at 1.7 to 2.25 THz and a reduction in reflectivity with increasing frequency. There was much greater consistency of data in the 1.70 to 2.25 THz range when compared to the 0.70 to 1.15 THz range. The results at the most reliable point of 0.9 THz in the lower data set and at 2.0 THz are presented in Table 4. Table 4. Comparison of reflected signal intensity of the experimental data from water and ice to theoretical predictions *. The measured contrast between liquid water and ice reflected signal intensity at both ranges is broadly in line with the dielectric properties data from [14][15][16][17][18]. The reflected signal intensity of water and ice show a decline over the 0.70 to 1.15 THz range, but the experimental values are erratic. At 2.0 THz, the reflected signal intensity of water is flat over the measured range and does not change with temperature. The reflectance of ice declines with both frequency and temperature over the 1.70 to 2.25 THz range. The measured reflected signal intensity of ice at 2.0 THz is consistent with a refractive index of 1.83, which is at the upper boundary of the literature derived data.

Rendered Porcine Lard
Commercially obtained rendered porcine lard was used as a sample. Rendered lard contains chiefly triacylglycerides and fatty acids, with the water, protein and fibrous tissue components of adipose tissue being removed by the production process [27]. Lard has an n of 1.48 and α of 8 cm −1 in the 0.9 to 1.0 THz spectral window, [25], making lard within the "true" ATR range of the diamond crystal. Lard was studied between −15 • C and 24 • C with 42 individual serial outputs, each an average of 50 individual scans. The temperature was varied over a total time of 16 min with 21 discrete scanning episodes of 2 × 50 scans. The lard reflected signal intensity data are presented in Figure 5.
The thermal dependence of the dielectric properties of Lurpak ® butter were investigated with a total of 140 individual serial spectral outputs between −20 °C and 24 °C. Each output was an average of 50 scans. The temperature was varied over a total time frame of 24 min with continual scanning during the temperature variation. The raw spectral data for Lurpak ® butter are presented in Figure 6. Spectral bands centred around 0.9 THz and 2.0 THz are shown in Figure 7.
The thermal dependence of the dielectric properties of Lurpak ® butter were investigated with a total of 140 individual serial spectral outputs between −20 • C and 24 • C. Each output was an average of 50 scans. The temperature was varied over a total time frame of 24 min with continual scanning during the temperature variation. The raw spectral data for Lurpak ® butter are presented in Figure 6. Spectral bands centred around 0.9 THz and 2.0 THz are shown in Figure 7.
The thermal dependence of the dielectric properties of Lurpak ® butter were investigated with a total of 140 individual serial spectral outputs between −20 °C and 24 °C. Each output was an average of 50 scans. The temperature was varied over a total time frame of 24 min with continual scanning during the temperature variation. The raw spectral data for Lurpak ® butter are presented in Figure 6. Spectral bands centred around 0.9 THz and 2.0 THz are shown in Figure 7.   There is a temperature dependent reduction in the, reflected signal intensity of Lurpak ® butter in the frequency range of 0.7 to 1.15 THz. There is a temperature dependent plateau over the 0 °C to 10 °C range at 1.7 to 2.2 THz, which becomes more evident with increasing frequency. Lurpak ® butter shows a ~13% decrease in, reflected signal intensity between −20 °C and 24 °C, at 0.9 THz, and a 3.5% decrease in, reflected signal intensity between −20 °C and 24 °C, at 2.0 THz.
Lurpak ® butter displays temperature dependent reflected signal intensity which is not the featureless reflected signal intensity of lard. There is a steady decline in reflectivity with increasing temperature suggesting an increase in α in line with the temperature dependent behaviour of liquid water (the temperature dependent α changes in ice are not well documented). There is no sudden change in reflected signal intensity which would suggest a change of state of the constituent water, even at −20 °C, but, as noted, there is a plateau in the 0 °C to 10 °C range at ~2.0 THz, suggestive of some phase related transformation.

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 °C and −15 °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 ® butter. Both are within the ATR range of the diamond crystal in a "true" ATR mode. Lard was studied in the range −15 °C and 24 °C with results showing no clear temperature related change at either There is a temperature dependent reduction in the, reflected signal intensity of Lurpak ® butter in the frequency range of 0.7 to 1.15 THz. There is a temperature dependent plateau over the 0 • C to 10 • C range at 1.7 to 2.2 THz, which becomes more evident with increasing frequency. Lurpak ® butter shows a~13% decrease in, reflected signal intensity between −20 • C and 24 • C, at 0.9 THz, and a 3.5% decrease in, reflected signal intensity between −20 • C and 24 • C, at 2.0 THz.
Lurpak ® butter displays temperature dependent reflected signal intensity which is not the featureless reflected signal intensity of lard. There is a steady decline in reflectivity with increasing temperature suggesting an increase in α in line with the temperature dependent behaviour of liquid water (the temperature dependent α changes in ice are not well documented). There is no sudden change in reflected signal intensity which would suggest a change of state of the constituent water, even at −20 • C, but, as noted, there is a plateau in the 0 • C to 10 • C range at~2.0 THz, suggestive of some phase related transformation.

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 • C and −15 • 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 ® butter. Both are within the ATR range of the diamond crystal in a "true" ATR mode. Lard was studied in the range −15 • C and 24 • C with results showing no clear temperature related change at either the 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 ® butter has a water content of 14.7% (w/w), approximating adipose tissue (~15% bulk water). Lurpak ® butter displays temperature dependent reflected signal intensity features, with a steady decline in reflectivity with increasing temperature. Given that Lurpak ® 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 • C. The contribution of the protein fraction of Lurpak ® butter has not yet been determined.

Conclusions and Outlook
The flexibility and capacity of ATR apparatus, when coupled with a bright THz source such as the Australian Synchrotron, offers a range of possibilities which are beyond its strict capacity as an apparatus for measuring attenuated total reflection. This paper has demonstrated the use of the ATR as a reflectance/transmission apparatus and the capacity for apparatus to study temperature related changes in samples. Both novel functions can be performed quickly and reliably. This raises the possibility of finding "signatures" for clinically relevant biological tissues and disease states. In turn, this can lead to rapid diagnostic applications which rely on tissue properties which are not being assessed by other means. Since the reflectance of ice and water with the diamond crystal in the reflection/transmission mode is solely dependent on the refractive index, the outlined method can be used to accurately map the temperature and frequency variation of the refractive index of ice to a high degree of precision.
The next challenge is to provide methods to "fill in the gaps", with the need to evolve a rapid and reliable way to extract the complex refractive index with the ATR apparatus whilst using an incoherent bright THz source, and similarly the absorption coefficient in the instance when the ATR apparatus is performing in reflectance/transmission mode. There is also the pressing need to produce more background temperature variability data on biological tissues.  Data Availability Statement: Upon reasonable request, the corresponding author is ready to share.