fitting

Fitting for M²

Fitter ┬─> ODRFitter (scipy.odr):                optimizes x and y-error
       ├─> OCFFitter (scipy.optimize.curve_fit): optimizes y-error
       │
    ┌──┴───> MsqODRFitter / MsqOCFFitter: Provides all functionalities
    │                                     and fitting using the selected 
    │                                     fitting method
    │
MsqFitter: Provides functionalities common to all fitting methods

On top of the 2 fitting methods there are 3 fitting modes to fit for M²:

1. M²λ mode. In this mode, the function that is fitted combines the M²λ term as these 2 are heavily correlated (this means that that M² and λ cannot be fitted individually as fit parameters). Using Gaussian error propagation methods, the error in the wavelength can then be taken into account. The fit equation is:

   

   where .

2. M² mode. In this mode, a temporary function is created from the original beam equation with the wavelength hard-coded. The data is then fitted to this temporary function. This allows M² to be fitted directly as a fit-parameter. Due to the hard-coded nature of the wavelength, the error in the wavelength cannot be taken into account. The fit equation is:

3. ISO mode. In this mode, the fit is done according to the method described in ISO 11146-1:2021 Section 9, and Gaussian error propagation is used to find the error of M². Here we assume that the beam is either stigmatic or simple astigmatic. This method somehow creates really big errors with the data that I have tested on. The fit-equation is:

   

   Note: the ISO standard says that "It is common to perform the fit by minimizing the sum of the squared relative deviations of the diameters." → i.e. only y-error is minimized.

In the program, the modes are 0-indexed (i.e. Mode 0 is M²λ, etc.). Constants are provided in the class MsqFitter that map to each of these modes.

Under /tests/ there are parallelized code that runs on the LMU Physics CIP Pool Cluster for parameter-sweep purposes. These jobs are to be sent using the command:

sbatch slurm_proc.sh

In the script, it is important to not use srun, as this launches the same script in all the available nodes. Since we are using mpi here, we should ask mpi to do the distribution to ensure communication.

Outstanding matters:

1. Does the ISO fitting use d4σ-diameter or the d2√2σ-diameter? (Ref: BS EN ISO 11145:2018 or equivalent -- Beam Diameter vs Beam Width)
2. Adding a function to obtain the z_0 and w_0 from the fitted parameters depending on the mode.
3. Testing the ISO Method on more data and compare between all the methods.
4. Adding a flag to allow for small variation to the start parameters should the fit not converge. In this case, the function .fit() should not return until the fit has converged.
5. Ensure that the d4σ determination has background removed to increase its accuracy.