# Global Fit /全局拟合

Make sure the following are performed:

- The A(l,t) data matrix is corrected for the chirp of the super-continuum probe pulse. See the chirp correction section for more details.
- The time zero is adjusted for the real time zero using the coherent signal from the solvent. See the Time Zero Correction section for more details.
- The resulting matrix is decomposed into its principal spectral and kinetic components via SVD (singular value decomposition). See the
**Principal components**for more details. - The selected principal kinetic traces are globally fitted to a multi-exponential decay law convoluted with the Gaussian instrument response function using the nonlinear Marquardt algorithm.
- The pre-exponential coefficients as functions of the wavelength are calculated by the linear fit of the data obtained after step 1 to the exponentials obtained in step 3. Refer to the literature reference at the end of this chapter for more specific information on the employed methodology.

Prior to starting the **Global Fit** procedure make sure that you have the PrincipalSpectra.csv and PrincipalKinetics.csv (files acquired as a result of the SVD procedure) saved in the same directory as the main 3D surface data file. Select Global Fit from the upper drop down menu (Figure 38) to start the fitting procedure. The new window will open and its upper right panel will display the principal kinetic traces produced during the SVD operation (Figure 37).

You need to specify the following fit parameters (if you are unsure about the feasible values, several resonant kinetics fits at different wavelengths may help (see the ** Fit Resonant Kinetics section**)):

** Number of exponentials** – total number of expected lifetimes except infinite lifetime (Ainf);

**–check this option if the signal does not decay all the way to zero amplitude (adds an infinite exponential).**

*Use Ainf*You can fix one or more parameters. This feature is similar to the one described in Fit Resonant Kinetics section.

Click the Fit button to start the global fitting procedure. A window with a progress bar appears for the duration of the fitting. Upon completion:

- The computed parameters are displayed in the middle column titled
**Best Fit Coeff**. In the right column confidence intervals for the Coefficients are displayed; - The solid curves representing the best fits for the kinetic traces (squares) of same color will be added to the upper right panel (Figure 39);
- The bottom left panel will display the spectral distributions of the pre-exponential coefficients or amplitudes of each of the calculated lifetimes (specified in the legend with corresponding intervals). These lifetimes are the best result of the global fitting for the number of exponentials specified previously.

The quality of the 3D surface fit is represented by c2 on the top left panel. If the results of the fitting procedure are found satisfactory, save the data by clicking the Save button.

**Reference**

"Calculation Of Equilibrium Constants From Multiwavelength Spectroscopic Data - I, Mathematical Considerations", HaraldGampp, Marcel Maeder, Charles J. Meyer, and Andreas D. Zuberbühler, Talanta, 1985, 32, 95-101.