Data Analysis Example

We can analyze some simulated neutron scattering data to show how to use PAN in some detail.  If you are a non-neutron scatterer, don’t worry…this is just noisy, peaky data used to illustrate how to use PAN.  In particular, we will load in the test data set, fit an appropriate model to the data, and extract the group-dependence of some important parameters.

First launch PAN if it is not already running.  Next, select File/Load test data.  In a few moments a data set that contains a large central peak and two small satellite peaks corrupted by noise should appear.  Also, the GROUPS TO FIT text field should have been updated to read “1-20” indicating that there are now 20 groups (or Q-values for you neutron scatterers).  You can move the slider control labeled GROUP SELECTION and the data displayed in the window will change.  As you move to larger detector numbers, the central peak will be accompanied by two growing satellite peaks (this data simulates a rotational tunneling spectrum taken on a neutron backscattering instrument).  Move the slider control so that you are viewing group (detector) 7.  Click the right mouse button so that you autoscale.  If you wish, you can hold the left mouse button down and drag a rubberband-type zoom box across the plot to enlarge a particular portion of the data window.  A right mouse click will always result in zooming out all the way.

We will fit this group first and then fit the remaining groups automatically.  The data looks like it has 4 components.  The central peak looks approximately Gaussian, the two satellite peaks are approximately Lorentzian, and there is an underlying offset (a background level).  Choose background from the drop-menu called Select function.  Move the cursor into the plot window and hold down the left mouse button.  A dashed line should appear across the extents of the data plot.  As you move the cursor up and down in the data window while holding down the left mouse button, the dashed line should follow the cursor.  This action is used to specify the offset of the overall model function.  Once you are satisfied with the level, release the left mouse button.  Now hold down the left mouse button again and move the cursor around the data window.  You should see the slope of the line change and pivot about the midpoint of the x-axis.  Once you are satisfied with the slope, release the left mouse button.  For this function, the slope should be quite small.

Next we will add a Gaussian curve to model the central peak.  Choose Gaussian from the Select function menu.  Move the cursor over the plot window and hold down the left mouse button.  A Gaussian should follow your cursor movements both in location and in height.  Change the vertical position to change the Gaussian peak height and change the horizontal position to change the Gaussian peak center.  Once you are satisfied that the peak has the correct amplitude as that of the central data peak and is located at the correct position, release the left mouse button.  Next hold down the left mouse button and move the cursor horizontally, thus changing the width of the curve.  Once you are satisfied with the width release the left mouse button.

Next add a Lorentzian to fit the satellite peak to the left of the central peak.  The method to change the amplitude, center, and width of the Lorentzian is exactly the same as for the Gaussian.  Finally, add another Lorentzian to model the satellite peak to the right of the central peak.

You have just specified the initial guesses for the fit using the mouse and now it is time to fit the model to the data.  You can look at the actual guess values by pressing the Display fit parameters button and the values should appear in the text box on the right hand side of the main interface.  Next press the button named Fit current group.  In a moment you should see the result of a least-squares fit of the model to the data.  Your final answer may be different but mine is shown below in figure 1.  You can see the residuals plotted in the bottom window which, in addition to the chi-squared value, provide a visual goodness-of-fit.  If you have modeled the data well then the residuals should vary between ±1, as shown by the horizontal dashed lines.  It looks like we have a good fit in figure 1.

 Screen shot with completed fit
Figure 1 Fit of model to data for current group.

The model parameters with uncertainties are found in the text panel displayed to the right of the data window. 

The next part of the analysis we want to do is to fit all of the groups.  However we need to be careful at this stage.  Scroll the Group selection slider control down to group 1 and notice how small the satellite peaks have become.  There is a possibility that the least-squares routine will have trouble fitting this same model to this data.  Therefore we would like to impose a constraint on the area and width of the satellite peaks.  Move the Group selection slider control back to group 4 and press the Modify fit parameters button.  Set the lower limit for the areas and FWHM (full-width at half maximum) for the Lorentzians.  This means that you need to check the Set low boxes for the Lorentzians and make sure that the Lower limit boxes equal 0.0.

When you have finished this, press the button labeled Fit all groups.  You should see fits being performed for each group starting with group 1 and finishing with group 20.  Once it is finished you can change the Group selection slider to inspect each fit.  Whenever a new group is displayed with its fit, its fit parameters, uncertainties, and chi-squared value are also displayed in the text panel to the right of the data window for you to examine.

Now we would like to look at the dependence of the peak position of the Lorentzian to the right of the central peak on the group (i.e. the Q-dependence of the peak position).  First we should note which parameter and curve this corresponds to in terms of our notation discussed above.  Inspection of the parameters (see figure 1) indicates that this parameter is #6.  Press the Plot fit parameter button and type in 6 in the field labeled parameter #.  Press Accept and you should see data that looks similar to that shown in figure 2.  You can save these parameters and errors in a three-column formatted ASCII file (that can be read back into PAN for further analysis), print to a postscript or JPEG file, add plot to an HTML log file (if open), zoom into the window using the same mouse operations as in the main PAN application, and/or exit the plot utility.  You may choose to examine the group-dependence of any of the fit parameters by simply specifying the curve and parameter using the technique discussed above.

Parameter group dependence
Figure 2 Dependence of parameter #6 on the group

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