definition of fitting function in m2.py

[SReich-EMI]

I like this module, as is makes analysis very easy. However, I wonder about the fitting for M2. Especially I refer to

def _beam_fit_fn_(z, d0, z0, Theta): """Fitting function for d0, z0, and Theta.""" return d0**2 + (Theta*(z-z0))**2

I understand the idea of fitting d(z)^2 = ... wwithout the sqrt. But if I change the input from d**2 to d and also the function from d0**2 + (Theta*(z-z0))**2 to np.sqrt(d0**2 + (Theta*(z-z0))**2), I get different results.

Has anyone an idea, where this change comes from and how to get the proper output? Which of the two versions is right?

[SReich-EMI]

I think I have opened this issue to early. The differences are not only related to the different fitting functions, they also depend on the data set himself and consequently on the proper definitions of starting values and bounds where the fit function ends up.
Therefore, the fitting by the sqrt-function seems to be all right and I close this issue again.

[scottprahl]

You bring up an interesting point though. Changing the fitting function changes how errors in data are weighted. I have to look more carefully, but the current code might be overweighting beam size measurement made farther away from the beam waist.

[scottprahl]

I changed the code to fit to d and not d**2. Not that much difference.