## 4 Result and Discussion
The extracted phase map of the corresponding area is displayed in Figure 7 (right), while the phase difference map between the hologram with and without the flame is presented in Figure 7 (left). The phase difference wraps more quickly than the phase difference shown in Figure 5. Consequently, according to Equation (9), the refractive index changes more quickly. Similarly, a cross-sectional profile plot of the phase difference map at pixel row number 1500 (red line) was chosen and plotted in Figure 8. The wrapped phase was unwrapped and shown in Figure 2.0 The corresponding refractive index difference was calculated and plotted in Figure 9 (centre). As expected from Equation (9), the phase changes and the refractive index follow the same trend. The temperature changes are shown in Figure 9 (right). Figure 2.1 Unwrapped phase change (**left**), refractive index difference (**centre**), and the calculated temperature (**right**), corresponding to the rectangular area indicated at the bottom of the flame (Figure 1, right). Figure 2.2 Extracted phase (**left**) and phase difference maps (**right**) for the rectangular area indicated at the top of the flame (Figure 1, right). The red line indicates the pixels chosen for the cross-sectional profile. In this region, the temperature exhibits two maxima around the flame's center. Specifically, in the surrounding areas of the flame's center, the temperature increases. As we move from the center towards the outer region of the flame, the temperature first increases and reaches a maximum. Then, it sharply decreases until reaching the outer region of the flame. The temperature distribution of a candle flame is influenced by various parameters, including the type of oil wax and wick thickness [28; 29]. Previous studies have reported peak temperatures ranging from 600 \({}^{\circ}\)C to 2000 \({}^{\circ}\)C for candle flames [23; 24; 28; 29; 46; 47; 48]. Additionally, temperature profiles along the radial distance at different heights have shown variations in temperature. The literature consistently demonstrates that the hottest zone of the candle flame is located around the flame's center, with the hottest location gradually shifting closer to the center as the height increases. Moreover, an interesting observation is the existence of a local minimum at the center of the flame, accompanied by two peaks of temperature [23; 24; 28; 29]. In our experimental investigation, as shown in Figures 6 and 9, we have observed patterns that support the aforementioned findings similar to those in [23; 24; 28; 29; 46; 47; 48]. Specifically, in Figure 6 (right) and Figure 9 (right), we present our measured temperature profiles, where the peak temperature is located around the flame's center. Notably, the left part of Figure 6 (right), corresponding to the position near the central position of the flame,  
Figure 2.3 A cross-sectional profile plot of the phase difference map (Figure 7, right) at pixel row number 1500 (the red line). Figure 2.4 Unwrapped phase change (**left**), refractive index difference (**centre**), and the calculated temperature (**right**) for the rectangular area indicated at the top of the flame (Figure 1, right). exhibits the closest proximity of the peak temperature to the flame's center. In Figure 9 (right), we observe a temperature profile with a local minimum at the center of the flame, flanked by two peaks of temperature. These experimental observations are in accordance with the reported measurements documented in [23; 24; 28; 29; 46; 47; 48]. From Equation (11), the estimation of temperature measurement uncertainty can be derived by considering the uncertainties associated with individual parameters involved in the measurement process.