Fit parameters, sliders and 'fit on a grid'

In the main window of SCOUT, switch with F7 to the treeview level and right-click the branch Fit parameters to open the list of fit parameters. At program start the list is empty. New parameters can be added using a dialog or by drag&drop from other lists of SCOUT.

The New command (or the button labeled '+') of the fit parameter list opens a dialog with a list of all possible fit parameters from which you have to select. Dielectric function parameters (like resonance frequencies of oscillators or volume fractions of effective medium models), layer parameters such as thicknesses, fit parameters of the computed optical spectra (angle of incidence or constants that appear in modification formula) and master parameters are listed as follows:

As indicated, you can select many parameters simultaneously by pressing the Ctrl-key while clicking on the various lines. Clicking an already selected line 'unselects' it. Only those lines beginning with '>' represent fit parameters. The other lines contain guiding information only.

Instead of using the fit parameter selection dialog, you can also select fit parameters by drag and drop operations. You have the following possibilities:

The chosen parameters are added at the end of the fit parameter list. This may look like this:

The name column gives the fit parameter's name. Since the names of fit parameters assigned automatically by SCOUT are sometimes quite lengthy you can overwrite the current name with your own. Just type in the new name. However, be sure to remember which parameter it really is. At present, there is no way to get back to the automaticly assigned name. In case you forgot what the parameter means, you have to delete it and create it new.

The Value column displays the current value of the parameter. If you would like to set bounds for the fit parameter value you can set an interval of allowed values using the Low limit and High limit values.

As Factor you can enter a number which is used to multiply the original value of the parameter: You can use this factor to scale up or down a parameter. If, for example, a thickness is given in micrometer you can multiply it by 1000 in order to see the value of the thickness in nm. If you change the factor, the current values of Low limit and High limit are multiplied by the factor as well.

Finally Digits specifies the number decimals used to display the current value of the parameter.

The Variation column allows to switch between different optimization options. In order to change the current option place the cursor on the cell and press the F5 key on your keyboard several times. By this action, you cycle through the available options. Stop where you want to stop. Pressing F4 you cycle backwards. At present, the following options are implemented in SCOUT:

Downhill simplex	The parameter is optimized in the automatic fit according to the downhill simplexscheme which is used at present as optimization technique in SCOUT.
Frozen	The parameter is not varied at all. This can be used, if you want to keep the parameter's value fixed for the moment but you may need it soon again. In this case, you don't delete the parameter but set is variation option to 'Frozen'.
Grid (100 points	If the variation option of a parameter is set to 'Grid (x points)' SCOUT will try x values of the parameter equally distributed in the range between Low limit and High limit before the automatic fit applying the downhill method is performed. For each value the model is re-computed, and the parameter value with the lowest deviation (i.e. difference between model and measurement) is taken as starting value for the automatic fit. If several fit parameters are to be varied on a grid of test values, the option 'Multidimensional grid fit' (please check or uncheck this option using the menu command 'File\|Options\|Fit\|Multidimensional grid fit' in the main window) determines how the computations are performed. Multidimensional grid fit switched off: SCOUT will do one-dimensional grid variations in the sequence given by the fit parameter list, starting at the top. Note, that the result for the parameters' starting values will depend on the sequence. Hence, the choice of the grid variation must be done carefully. Multidimensional grid fit switched on: SCOUT will collect all fit parameters for which a grid variation is set in the variation column, and do a multidimensional grid fit taking into account all possible combinations of parameter values. Note that the amount of computational work can be huge: If you select 4 parameters with 100 grid values for each of them, there are 100000000 re-computations of the optical model to be done.
Grid (50 points)	see above
Grid (20 points)	see above
Grid (10 points)	see above
Empty cell	Here you can enter a formula to compute the value of the fit parameter. In the formula, you can refer to the values of the master parameters (see below). This way you can introduce relations between parameters, or control several parameters of the model by one master parameter. If you know, for example, how the parameters of your optical constant models depend on temperature, you could introduce the temperature as master parameter and update the optical constants while the temperature is fitted.

The following example shows a frozen fit parameter and a factor different from 1.0:

You can do a 'manual fit' by typing new values for the fit parameters and selecting Update in the menu. This activates a new computation of the dielectric functions and all computed spectra as well as an update of all windows. This way you can immediately inspect how your changes influence the results.

A much more elegant way to visualize the parameter influence on the spectra is the use of sliders. Select a fit parameter in the list and click on the Slider menu item. This way a new window is created and displayed on the screen that allows you to 'move' a parameter value with the mouse and see instant updates of the model spectra:

In the top of the window there are three values: The left and the right define the interval of the slider, the center one (in blue) is the actual value of the fit parameter. When the slider window is created the first time the slider range is the fit parameter interval Low limit ... High limit if you defined one. If you did not set a fixed interval for a fit parameter the initial range of the slider is 80 ... 120% of the current parameter value.

At any time you can overwrite the slider range by typing in new values for the left and right limit. If the slider position reaches the left limit, for example, you can also press the arrow labeled '<' to the left. This centers the limits around the actual parameter value. This operation can be used to work in a large parameter space without switching between mouse and keyboard. It works in the analogous way on the right side of the parameter range.

Pressing the button labeled '<>' expands the current parameter range by a factor of 2 and centers around the current value. The '><' button reduces the range to 50% and centers around the current parameter value.

In addition to the Slider menu command you can also click on the fit parameter with the right mouse button to create the corresponding slider. You can open as many slider windows as you like if you want to investigate many parameters at a time. You can create regular blocks of slider windows by Drag&Drop: Create the first slider the regular way (as described above). To place a second slider window below the first one, 'drag' a fit parameter from the fit parameter list to the already existing slider and release the mouse cursor in the left half of the slider window. A new slider is created and placed directly below the first one:

If you release the mouse button in the right half of an existing slider the new slider window is created to the right of the existing one:

The command Fit on grid can be used to optimize one of the fit parameters on a grid of test values. To do so, select the fit parameter that you want to optimize in the list. Specify a parameter range by setting the low limit and the high limit for this fit parameter appropriately. Then apply one of the commands Fit on grid|with 10 points, Fit on grid|with 20 points, Fit on grid|with 50 points or Fit on grid|with 100 points. Now SCOUT scans the parameter range using the given number of points and returns the best value of the fit parameter on that grid.

The command Fit on grid|Do all grid fits will start the grid optimization taking into account all fit parameters for which a grid fit has been selected in the variation column.

This 'fit on a grid' is good for a rough parameter pre-selection, for example for finding film thicknesses in the case of interference patterns. Afterwards you should use the automatic fit for further optimization of the model.