Entering an Initial Model and Model Optimisation

Fit models may be defined using the INITIALISE sub-menu. A fit model may be constructed from an arbitrary number of peak functions (Gaussian, Lorentzian, and Voigt) and trigonometric or exponential decay functions, and a polynomial function of specified order. The INITIALISE sub-menu is shown in Figure 30, Page .

Figure 30: The INITIALISE Sub-Menu

A model is built up by successfully selecting a function type to add to the model. e.g. To add a Gaussian peak function to the model:

1. Select the GAUSSIAN button.

2. The message CLICK ON PEAK TOP appears, and the graphics cursor is active. You should click reasonable accurately on the estimated top of the peak. This position is used for the initial peak position, and as part of the initial peak height calculation.

3. The message CLICK ON PEAK AT HALF HEIGHT appears, and the graphics cursor is active. You should click reasonable accurately on the estimated side of the peak at half height. Either side will do. This position together with the peak top position is used to calculate the initial standard deviation width of the peak, and it's maximum height.

As functions are added they are drawn on the diagram in blue.

For a general background function, the POLYNOMIAL button allows an user specified polynomial to be added to the model. The user is prompted for the order of the polynomial to add, and the order of the initial polynomial function to be fitted. The initial polynomial is automatically fitted to the residuals between the data and the currently input function values. Therefore, generally it is best to add any polynomial background function to the model last.

The SET-UP form allows the control parameters to be varied e.g. Weighted fitting or not (provided variance arrays exist). The CONSTRAINTS form allows individual model parameters to be constrained, or set to freely vary.

The OPTIMISE button optimises the model to the data, according to the current control parameters. The fitted data is output in the ``memory''. If the current region of interest contains more than one row, the subsequent rows of data will also be fitted using the fitted parameters of the previous fit, as their initial parameters.

The display of the fitted model and the data is shown in the upper X/Y graph in Figure 29, Page , and beneath is a display of the residuals. If error estimates are available for the data values, these too will be displayed. This graphical display of the results may be saved as a PostScript file using the PRINT button (while this is displayed in the graphics window).