Using Etalons

If an etalon trace is available as one of the channels in experimental data, then it can be used to generate a linear frequency scale in a semi-automatic way. In particular, the etalon peaks can be measured automatically, provided they are reasonably equally spaced. The basic logic is to use the etalon trace first, to generate a linear frequency scale, and then calibrate the resulting scale (which should at most be a shift and linear scale factor) using the standard calibration procedure. The basic procedure is this:

1. Measure the first two etalon peaks by right clicking and dragging across each peak.
   
2. Right click on the etalon trace and select calibrate.
3. If you have an approximate (or exact) position for either or both peaks, set the corresponding actual values. Alternatively, a shift can be applied later.
   
4. Select Other, Etalon, and enter the etalon spacing if you know it. Alternatively accept the default (1) and fix later.
   
5. The remaining etalon peaks should be measured, and assigned "Actual" values based on the numbers entered so far. If the process goes astray, around a mode hop for example, delete the affected peaks in the calibration window. The process can normally be re-started by measuring a few peaks manually, and then using the automatic process as in step 4.
   
6. To check that the peaks have been found correctly try the fit button with the polynomial order set to 1. If this reveals any problems, delete the affected peaks. You can repeat from step 4 if necessary after deleting some peaks; the automatic process only uses the last two measured peaks.
   
7. To produce a linearized scale use one of:
   • An appropriate order of polynomial. Note that higher orders can give fitting problems as polynomials are often numerically unstable.
   • A spline fit - recommended if there are many etalon fringes. To do this, select "Other...", "Spline fit...", and normally check "Update immediately". The number of spline points used can be set in three ways:
   1. "Through Every Point" - a standard cubic spline through each of the calibration points
   2. "For Average error of" - a smoothed cubic spline through each of the calibration points adjusted to minimize the second derivative and give the average error input.
   3. "Through equally spaced points" - a cubic spline through the input number of equally spaced points, with the spline fitted to give the minimum average error.
   If many fringes are present, 3 is recommended, with the number of points rather less than the number of etalon fringes.
8. Give a good fit, "Other", "Apply to All" copies the new frequency scale to all your traces.

This process will generate a linear frequency scale starting around 0. You can then use the standard calibration process to complete the calibration. Alternatively, if you are confident of the etalon spacing entered, a simple offset set in the overlay properties may be sufficient.