  The Gas Pixel Detector is a gas detector, sensitive to the polarization of
X-rays, currently flying on-board IXPE - the first observatory dedicated to
X-ray polarimetry. It detects X-rays and their polarization by imaging the
ionization tracks generated by photoelectrons absorbed in the sensitive volume,
and then reconstructing the initial direction of the photoelectrons. The
primary ionization charge is multiplied and ultimately collected on a
finely-pixellated ASIC specifically developed for X-ray polarimetry. The signal
of individual pixels is processed independently and gain variations can be
substantial, of the order of 20%. Such variations need to be equalized to
correctly reconstruct the track shape, and therefore its polarization
direction. The method to do such equalization is presented here and is based on
the comparison between the mean charge of a pixel with respect to the other
pixels for equivalent events. The method is shown to finely equalize the
response of the detectors on board IXPE, allowing a better track reconstruction
and energy resolution, and can in principle be applied to any imaging detector
based on tracks.
