The moral of the story that I'm getting from this plot: something funny is going on.
Yup, something funny was going on. Nic's MM code that I used, "a la mode", calls for the focal length of the optics, whereas the code that I wrote and used for ages called for the radius of curvature. f = R/2. Fixing that factor of 2 I get something more like:
So, what does it all mean? That I'm not sure of yet.
In an attempt to estimate the errors on the fit parameters I upgraded my Mathematica code to use the function 'NonlinearModelFit', which allows us to define weights and also reports the errors on the fit parameters. The plots have been upgraded to show the error bars and residuals.
The parameters determined are given below and compared to the earlier measurements of 06/18/2010
There is a significant change in the beam waist location (as compared to previous report) because I corrected a mistake in the sign convention that I was using in measuring the distances to the waist from the zero-reference.