Procedures

# Loomis-Wood Plots

Loomis Wood style plots can be produced with PGOPHER; they work by plotting the same spectrum several times, with successive spectra horizontally displaced by an amount given by a function in terms of the plot number, m. With the correct choice of function (typically a polynomial), successive transitions in a branch will appear lined up.

This is done by adding a Loomis Wood object in the Overlays window (brought up with "View, Overlays"); they can be created at the top level (in which case multiple windows are created) or under a specific plot, in which case the plot is duplicated in a single window. Right click on the top level object or the specific plot as required, and select "Add New...", "Loomis Wood". The required function is given in the comment in terms of the running plot number, m. The default polynomial is:

b(m-mLowest) + d(m-mLowest)2
but any sensible function of m can be given. (See expressions for more on what is possible.) For a simple diatomic molecule b = 2B will line up all the lines in a P or R branch.

To determine the parameters of the function a built in fitting process can be used, similar to that used for calibrating spectra. A Loomis Wood window can be brought up by right clicking on the Loomis-Wood object, and selecting "View...". When this is visible, and selecting an active Loomis-Wood object, a series of peaks making up a branch can be measured. Right clicking and dragging over a peak will add the peak to the series for that object, with the m value set according to the spectrum the peak is measured in. Pressing "Fit" will do a least squares fit on the parameters in the function using the given peaks, and then update the display to reflect the new parameters. To avoid undesirable correlation in the parameters of the function, the values fitted to are offsets from the position of the peak with the lowest value of m. The mLowest parameter (and the corresponding variable in the expression) is set to this value of m at the start of the fit. Other operations in the Loomis-Wood window include:

• The up and down arrows increment and decrement by one all the m values in the peak list, to allow assignments to be adjusted.
• The polynomial setting can be used to change the function to a polynomial of the given order; to use a more general function or constrain parameters use the non-linear fit dialog obtained by pressing the adjacent button.
• Changing the moffset value sets the m offset for the Loomis Wood object, and also shifts the main display so that the peak for which m = mOffset is at the centre of the display. This can be used to walk backwards and forwards along a branch.
• Other..., Copy for BranchExpr copies the selected measurements to the clipboard, suitable for line list fitting using the BranchExpr directive. This allows the specification of the conversion of the running number, m, to branch labels to be specified in a general way.

## Settings

 Active True to produce a Loomis-Wood plot; there can be multiple Loomis-Wood objects, but only one should be active at a time. nDebug If non zero, write the values of all the variables and the value of the function on each evaluation to the log window. See debugging for options on the output. nPlots The number of plots to produce mOffset The m values used in the plots are displaced by this. The plots have m values of mOffset to mOffset+nPlots-1. ShrinkSimulation If false, the simulation occupies half the plot. If false, the simulation shrinks to 1/(nPlots+1) of the plot. ShowProduct For future functionality

## Parameters

 yOffset The vertical offset between plots, expressed as a fraction of the vertical height of one plot. Possible values are in the range -1.1 ... +1.1. mLowest This parameter is set to the lowest m value for the peaks included in the fit at the start of each fit. ... Parameters in the polynomial given in the comment are shown here.