## 4 Results and Discussions
### Verification of Optical Method Using Ultra-Sound Measurements  
To verify the measurements obtained with the optical backscattering technique an independent measurement was implemented, using a dermatological ultrasound unit in conjunction with the fiber optical sensor. In a similar experimental arrangement, as the one distributed is Section 3, a tissue consisting of the epidermis and a fatty layer with a combined thickness of about 3.1 mm, and held tight on a frame, allowing access from both sides. The fiber array sensor was positioned in contact with the tissue, on side-A, while an ultrasonic sensor (model SonoScape S2, ShenZhen Sonoscape Co. Ltd., Shenzhen, China), was positioned directly opposite on side-B of the tissue, as shown schematically in Figure 9. Coupling gel on side-B, bridged the small gap of the acoustic sensor, transmitting the ultrasound in the tissue. As in the previous experiments, the tissue was frozen by cryogen spray, applied on side-A. During freezing, the fiber sensor was retracted and repositioned on the frozen tissue after the application of IPA which eliminated frozen dew on the surface. The temperature was monitored by a thermocouple, mounted on side-B, in contact with the skin and inside the gel between the tissue and the ultrasound head as shown in Figure 9.  
As before, the optical data from the fiber array sensor were detected by the data acquisition system stored in a computer. However, due to the limited memory of the ultrasound unit, the screen of the unit was continuously recorded by a digital video camera which also recorded the temperature of the thermometer. By synchronizing the optical signals with the video from the ultrasound unit, it was possible to correlate the results from the two systems and measure the depth of freezing. Specifically, by isolating sequential screen shots, taken every 10 s, we measured the frozen structures of the tissue with ImageJ ([[https://imagej.nih.gov/ij/](https://imagej.nih.gov/ij/)]([https://imagej.nih.gov/ij/](https://imagej.nih.gov/ij/)), v.1.52, U.S. National Institutes of Health, Bethesda, Maryland,  
Figure 8: (**a**) Backscattering intensity variation with depth of freezing for the fiber array sensor. (**b**) Optical diffusion in mm. USA). The resolution of this ultrasound system was about 0.1 mm to 0.2 mm with typical results shown in Figure 10a-f. Specifically, Figure 10a-f shows distinct frames of the video taken before freezing (Figure 10a) and during thawing (Figure 10b-f). Furthermore, in Figure 10a, the two red markers designate the unfrozen tissue which was about 3.2 mm thick (also indicated by the vertical trace). The white dense layer is the epidermis while the less dense region above is the fatty layer of the porcine specimen. The faint  
Figure 10: (**a–f**) Distinct sequential frames of the video taken during thawing. Figure 9: Verification setup with ultrasound. white structures below the epidermis are artifacts related to ultrasound reflections. The temperature behind the specimen was measured by a radio sparer (RS) digital dual thermometer measuring both Infrared (IR) radiation, (large digits) and temperature from the K-type thermocouple (small digits), used in these experiments. The ultrasound detector was placed on the upper side of the tissue and the fiber optic sensor on the lower side. Figure 10b shows the same specimen after it was frozen and the fiber optic sensor was repositioned in contact with the tissue having reached front (side-A) and back (side-B) temperatures of about -7 \({}^{\circ}\)C and a -110 \({}^{\circ}\)C, respectively. There are several observations to be noted in these frames: (a) as the tissue freezes, ultrasound does not reflect back to the sensor and the frozen tissue appears dark thus designating the depth of freezing; (b) to avoid freezing the gel, which is water based, cooling was terminated when the temperature on the back facet reached -5 \({}^{\circ}\)C to -7 \({}^{\circ}\)C; (c) as the tissue thawed it reappeared on the ultrasound screen (Figure 10c-f).