## 4 Results and Discussions
### Measurement of the Frozen Skin Thickness Based on Backscattering Intensity Variations  
In living tissue there is only access to the skin's surface; therefore, only backscattered signals can be used for determining the frozen depth and the sensor architecture includes fiber array-A only. For these experiments, the sensor head, shown in Figure 2, was positioned in contact with the skin's surface. The signal fibers were placed behind a 2 mm window, while the illumination fiber was level with the front facet. To eliminate frozen dew, the fiber array was placed in contact with the tissue, and IPA was applied prior to data acquisition to minimize surface backscattering. Based on these results and the calibration procedure described previously (Figure 4b), the depth of thawing could be measured from the backscattering signal, from a maximum depth of 1.5 mm up to the surface of the skin. To further study the thawing process, the tissue was mounted in contact with a brass substrate, maintained at a constant 34 \({}^{\circ}\)C as shown schematically in Figure 6. Porcine ex vivo skin tissue samples, consisting of the epidermis/dermis and a thin subcutaneous fatty layer, approximately 3 mm thick, were cut in sections of 5 \(\times\) 4 cm. Three modified thermocouples (0.3 mm heads) were embedded at different vertical depths from the skin surface, as measured from the surface by a bespoke needle gauge micrometer, with Th\({}_{1}\) at a depth of 0.2 mm, Th\({}_{2}\) at 1.3 mm, and Th\({}_{3}\) at 2.1 mm being deepest and in close proximity to the brass plate. The lateral separation was 3 mm as shown in Figure 6. The fiber-array axis was vertical and positioned laterally about 2 mm away from the thermocouples, to avoid any optical interference or reflections from the embedded metallic wires. The experimental procedure involved retracting the fiber-array, to allow access of cryogen, and freezing an area of about 2.5 to 3 cm\({}^{2}\) of tissue, to about \(-\)80 \({}^{\circ}\)C. After applying IPA, the fiber array-sensor was re-positioned on the skin surface, and data from the signal-fibers and the embedded thermocouples were obtained. Thawing lasted about 85 to 100 s, with the skin's surface temperature, as measured by Th\({}_{1}\), changing from \(-\)80 \({}^{\circ}\)C to \(+\)10 \({}^{\circ}\)C. The process was repeated over ten times in different positions of the skin and different skin sections yielding near identical results. As in the previous experiments, the signals from the inner fibers gave higher intensities, dropping off with time as the sample thaws [10; 11]. However, the intensity timelines of the outer signal-fibers displayed decreasing signals as the tissue  
Figure 5: Calibration curve of freezing depth. freezes and increasing as the tissue thaws. This is attributed to increased backscattering, which reduces optical diffusion in frozen tissue with less light reaching the outer fibers. Figure 7 shows the timelines of the backscattering intensity together with the temperature variations ranging from about \(-50\)\({}^{\circ}\)C to \(+10\)\({}^{\circ}\)C.  
In all experiments, Th\({}_{1}\) reached the lowest temperature, which was expected, as it is virtually on the skin surface hence closer to the application point of the cryogen. Similarly, the temperature gradient around 0 \({}^{\circ}\)C was low and nearly constant, for all the thermocouples, which is attributed to the latent heat of ice melting, i.e., remained constant until the ice was melted. According to Figure 7, the intensity timelines for the two inner fibers (3,4) are higher and nearly constant when the tissue is frozen, temperature range \(-50\)\({}^{\circ}\)C to 0 \({}^{\circ}\)C as measured at near surface by T\({}_{1}\) (0-25 s), and lower and constant for the unfrozen (5 \({}^{\circ}\)C to 20 \({}^{\circ}\)C, 55-80 s) temperature range.