## 4 Results and Discussions  
### Depth and Temperature Calibrations of Samples  
The calibration procedure, described previously, correlates backscattered and transmitted light detected by fiber arrays A and B for different skin depths of the illumination fiber. Initially the illumination fiber was in contact with detection fiber (T4 in array-B), i.e., to a distance of \(x=0\). The tissue was frozen measuring backscattered and transmitted intensities from arrays-A and -B. When the tissue thawed, the illumination fiber was retracted in steps by 0.1 to 0.2 mm, and the process was repeated until the fiber reached the surface of the tissue. Typical results for successive freeze/thaw cycles of a 3.0 mm thick tissue sample are shown in Figure 3a,c, with the transmitted signals from fiber-T4 in array-B and BS4 in array-A, are plotted as a function of time (timeline) for different tissue depths. Generally, the traces in Figure 3a exhibiting an initial rapid reduction in intensity, due to the ice formation in the tissue which reduce the transmitted light, followed by a near constant low transmission,  
Figure 3: (**a**) Typical transmission and (**c**) backscattering through 0.0 mm, 3.2 mm embedded fiber in skin tissue; (**b**) collective transmission; and (**d**) collective backscattering in frozen and unfrozen tissue. which is dependent on the skin separation \(x\), between the two fibers. Thawing takes several minutes, with tissue gradually returning from pale white to its original color, and the transmitted intensity gradually returns to its initial value. The transmitted intensities as a function of skin thicknesses \(x\) for frozen and unfrozen tissue are plotted in Figure 3b, with the red trace being that of the unfrozen skin, while the black trace is for the frozen one. Based on the results in Figure 3b, it can be seen that light diffused much further in unfrozen tissue (red trace) in contrast to the optical diffusion in frozen tissue, which was greatly reduced reaching near zero when the depth was about 1.4 mm to 1.5 mm (black trace). Similarly, the graphs in Figure 3c show the backscattering timelines for the different depths \(x\). Figure 3d shows the backscattered intensities for frozen (black) and unfrozen tissue (red) as a function of distances \(x\). Here, the variation in intensities was reciprocal to those of transmitted signals, which is to be expected as light cannot be transmitted through frozen tissue, and therefore is backscattered. When the illumination fiber is fully retracted, \(x=3.0\) mm and in contact with the skin surface, the timeline for transmitted, backscattered intensities and temperature variation for a freeze/thaw cycle is shown in Figure 4a. When cryogen is applied, the temperature drops rapidly to about \(-80\)\({}^{\circ}\)C followed by a rapid increase up to \(0\)\({}^{\circ}\)C, increasing slowly (around 0.05 deg/s) thereafter which attributed to the latent heat of freezing of the frozen tissue (blue trace Figure 4a). The backscattered intensity variations, (in black), can be roughly divided in three regions related to the temperatures of the tissue, ignoring the first 100 s where temperature equalization happens. It is high and nearly constant when the tissue is frozen in the temperature range of \(-70\)\({}^{\circ}\)C to \(-3\)\({}^{\circ}\)C (100-300 s), lower and constant for the unfrozen in the 5 \({}^{\circ}\)C to 20 \({}^{\circ}\)C temperature range (450-700 s) and finally, in the region of \(-2\)\({}^{\circ}\)C to 3 \({}^{\circ}\)C, the optical signals exhibit a progressive drop (300-450 s). Conversely, the transmitted timeline signal (red trace) is, as expected, the reciprocal of the backscattered signal. This is attributed to the shrinking ice-hemisphere \"ice ball\" under the fiber sensor, as shown schematically in Figure 4b, which leads to a corresponding gradual reduction in scattering.