error bars on calibration fitting

[ttortorici]

Hello,

As far as I can tell, there is no built in functionality for this, but I think it would be very helpful if the calibration process would not only spit out the sample-detector distance, but also the error of that result from the fitting procedure. This would be helpful in being able to determine accurate errorbars for fitting lattice parameters to reduced data.

Thanks,
Teddy

[kif]

Hi Teddy,

Thanks you for this very interesting question. I was asked the same
several years back (internally at ESRF) an I will try to summarize the
answer on how to determine the uncertainties on the refined parameters
in pyFAI-calib ?

First of all, the calibration process is a least-squares refinement of
a cost function based on experimental data with a parameter set.
The experimental data consists of a set of control-point associated
with the ring number of the calibrant. The parameter set consists of 3
translations, 3 rotations and the wavelength (i.e. 7 DoF).

The optimization is performed by SLSQP
which has proven to be the most robust algorithm ... but probably not
the best when it comes to the precision of the results. Improving this
is linked to the "pyFAI2" project.
In principle, minimize provides the hessian matrix which can be
inverted to provide the covariance matrix.
First problem: the cost function is invariant by a rotation along axis
3 (i.e along the incident beam), making this inversion impossible.
One has to fix the rot3 to any arbitrary value.

The obtained uncertainties I found on the couple of example I studied
(at that time) were just huge, on the order of 1e-2 along all 6
remaining dimensions. This was found to be related to some strong
coupling in the model:

• distance and wavelength
• rot1 and poni2
• rot2 and poni1
  If one fixes the wavelength and the 2 rotations, the uncertainties
  drops to 1e-4 which is on the order of what was expected. Moreover the
  calibration result depends on the set of control point chosen.
  To work around this issue, I recently worked on a quality of fit
  indicator which would be independent of the set of input points and of
  the cost-function. https://github.com/silx-kit/pyFAI/pull/2385/files
  This indicator is pretty slow for now and still under evaluation ...
  Moreover, a good QoF would be on no use for your initial issue which is
  about propagating those uncertainties.

Cheers,

Jérôme