The determination of the geometry of the experimental setup for the diffraction pattern of a reference sample is called calibration in pyFAI. A geometry setup is composed of a detector, the six refined parameters like the distance and fixed parameters like the wavelength (or the energy of the beam), they are all saved together into a text files named ”.poni” (as a reference to the point of normal incidence) which is subsequently used for processing the experiment.

> The program pyFAI-calib helps calibrating

the experimental setup using a constrained least squares optimization on the Debye-Scherrer rings of a reference sample (\(LaB_6\), silver behenate, …) and saves the results into a .poni file. Alternatively, geometries calibrated using fit2d can be imported into pyFAI, including geometric distortions (i.e. optical-fiber tapers distortion) described as spline-files.

By storing all parameters together in a single small file, the risk of mixing two parameters is highly reduced and we believe this helps performing better science with fewer mistakes.

While entering the geometry of the experiment in a poni-file is possible it is easier to perform a calibration, using the Debye-Sherrer rings of a reference sample called calibrant. About 10 calibrant description files are shipped with the default installation of pyFAI, like LaB6, silicon, ceria, corrundum or silver behenate. The user can choose to provide their own calibrant description files which are simple text-file containing the largest d-spacing (in Angstrom) for a set of Miller plans. A useful reference is the American Mineralogist database [AMD] or the Crystallographic Open database [COD].

The calibration is divided into 4 major steps:

# Pre-processing of images:

The typical pre-processing consists of the averaging (or median filter) of darks images. Dark current images are then subtracted from data and corrected for flat.

If saturated pixels exists, the are likely to be treated like peaks but their positions will be wrong. It is advised to either mask them out or to desaturate them (pyFAI provides an option, but it is expensive in calculation time)

# Peak-picking

The Peak-picking consists in the identification of peaks and groups of peaks belonging to same ring. It can be performed by two methods : blob detection or massif detection.

## Massif detection

This method consists in making the difference of the original image and a blurred image. Then we look for a chain of positives values, corresponding to a single group of peak. The blurring parameter can be adjusted using the “-g” option in pyFAI-calib.

## Blob detection

The approach is based on difference of gaussians (DoGs) as described in the blob_detection article of wikipedia.

It consists in blurring the image by convolution with a 2D gaussian kernel and making differences between two successive blurs (called Difference Of Gaussian). In theses DoGs, keypoints are defined as the maxima in the 3D space (y,x,size of the gaussian). After their localization, keypoints are refined by Savitzky Golay algorithm or by an interpolation at the second order which is equivalent but uses less points. At this step, if the estimation of the maximum is too far from the maximum, the keypoint will be considered as a fake maximum and removed.

## Steepest ascent

This is very naive implementation which looks for the nearest local maximum. Subsequently a sub-pixel optimization is performed based on the local gradient and hessian.

## Monte-Carlo sampling

Series of peaks can be extracted using the Steepest Ascent on randomly selected seeds.

# Refinement of the parameters

After grouping of peaks, groups of peak are assigned to a Debye-Scherrer ring and to a d-spacing. PyFAI uses a least-squares refinement of the geometry parameters on peak position.

The optimization procedure is the Sequential Least SQuares Programming implemented in scipy.optimize.slsqp. The cost function is the sum of the square of the difference between the expected and calculated 2theta values for the various peaks. This sum is dependent on the number of control-points.

# Validation of the calibration

Validation by an human being of the geometry is an essential step: pyFAI will overlay to the diffraction image, the lines corresponding to the various diffraction rings expected from the calibrant. Those lines should be in pretty good agreement with the rings of the scattering image.

Once the calibration is finished, one can use the validate option to check the offset between the input image and the generated on from the diffraction pattern.