## 2 Principles of PLIF Thermometry  
OH is usually in the thermal equilibrium state in a typical combustion environment, and the ground state energy-level distribution is subject to the Boltzmann distribution determined by temperature. Then the temperature of the flow field can be retrieved from the distribution of ground state energy-level. Generally there are two mechanisms used for PLIF thermometry: multi-line fitting and double-line calibration. The multi-line PLIF method can obtain temperature directly by Boltzmann fitting without additional calibration [10; 11], but the wavelength tuning process is time-consuming and only suitable for steady-state flow field. In transient process, the two color PLIF is preferred, in which two rotational energy levels with different temperature responses are used [12; 13]. In the short period between the two PLIF systems, the change of total particle number is ignored, and the temperature is obtained from the ratio of fluorescence intensity. Due to the influence of temperature and flow components on the transition process, the change in the fluorescence efficiency must be considered, especially in the flow field where the flow parameter varies widely. There have been two typical methods of eliminating the interference of fluorescence quenching. Cattolica excites different ground level to the Co-upper energy level and carries on the broadband measurement [12], which effectively eliminates the interference of fluorescence absorption and fluorescence quenching to the double-line temperature measurement, but the difference of ground state energy level is limited when the Co-upper energy level is excited, and the sensitivity range of this method is limited to the low temperature area of combustion field. [PERSON] discusses in detail the selection of excitation line and single point calibration method of double-line PLIF temperature measurement [19]. By comparing the results of temperature measurement of different excitation lines, the excitation line with less interference by quenching is obtained, but the selection result is limited to a certain parameter flow field. In the high temperature region of the combustion flow field, the fluorescence efficiency changes relatively little with the temperature, especially when the calibration environment is similar to the measured flow field. The ratio of fluorescence can be shown as Formula (1):  
\[R(T)=\frac{(IB\phi\eta)_{i}}{(IB\phi\eta)_{j}}\cdot\frac{2J_{i}+1}{2J_{j}+1} \cdot\exp(-\frac{E_{i}-E_{j}}{kT})=C\exp(\frac{-\Delta E_{ij}}{kT}) \tag{1}\]  
\(I\) is the energy of the excitation laser, \(B\) is the absorption coefficient of the transition level, \(\phi\) is the transition probability or the fluorescence yield of the excited states, \(\eta\) is the efficiency of the measurement system, \(J\) is the rotational quantum number of the energy states, \(E\) is the energy of the corresponding energy level, and \(k\) is the Boltzmann constant. Among them,  
\[C=\frac{(IB\phi\eta)_{i}}{(IB\phi\eta)_{j}}\cdot\frac{2J_{i}+1}{2J_{j}+1} \tag{2}\]the \(C\) is usually acquired from calibration. The fluorescence intensity ratio is \(R_{0}\) in a flame at temperature \(T_{0}\), which is similar to that of the measurement object's state. The calibration parameter can be written as  
\[C=\frac{R_{0}}{\exp\left(-\Delta E_{ij}/kT_{0}\right)} \tag{3}\]  
Then the temperature of the flow field to be measured can be obtained from the intensity ratio and calibration coefficient \(C\)  
\[T=\frac{\Delta E_{ij}}{k\ln(C/R)} \tag{4}\]  
However, when the temperature of the flow field changes in a large range, the variation of the fluorescence efficiency cannot be ignored. If the single point calibration method is used, the temperature results will deviate from the actual temperature at a region quite different from the calibrated temperature.