Equivalence between 1D integrated data and 2D integrated data

[loichuder]

Sorry for the basic question. This is probably explained somewhere in the doc so feel free to answer with a link.

If I integrate an image with pyFAI in 2D and 1D, what is the relationship between the 2D intensity data and the 1D intensity data ?

For example, can I recover the 1D intensity by summing 2D intensity over the azimuth direction ?

What about errors then ?

[kif]

Hi Loic,

First of all one should understand how azimuthal integration is performed in pyFAI. For this, the best is to refer to the Eq. 2 and 4 in this document: https://arxiv.org/pdf/2411.09515 (the official paper will come out in February 2025).
Mean intensities and associated uncertainties (sem in the paper) are both ratio of sum of intensities, sum of partial variances and sum of normalizations.

The re-binning operation from 2d to 1d you are referring to are trivial to implement in numpy with a sum of the 2d array along the proper axis. The final ratio can be recalculated accordingly.

The result of an azimuthal integration looks like a tuple (https://github.com/silx-kit/pyFAI/blob/main/src/pyFAI/containers.py#L79), but in fact it is a much more complicated object, which hides in itself the properties: sum_signal, sum_variance and sum_normalization which can be used to re-bin from 2d to 1d those results.

I admit, coding a function doing this would have taken less time than explaining it ... so it is probably a good idea to implement it. Thanks for the suggestion

[loichuder]

Thanks for the references, Jérôme. These do answer my questions so I think I'll manage to code something based on this.

Thank you !