Electron track reconstruction and improved modulation for photoelectric X-ray polarimetry

The key to photoelectric X-ray polarimetry is the determination of the emission direction of photoelectrons. Because of the low mass of an electron, the ionisation trajectory is not straight and the useful information needed for polarimetry is stored mostly in the initial part of the track where less energy is deposited. We present a new algorithm, based on the shortest path problem in graph theory, to reconstruct the 2D electron track from the measured image that is blurred due to transversal diffusion along drift and multiplication in the gas chamber. Compared with previous methods based on moment analysis, this algorithm allows us to identify the photoelectric interaction point more accurately and precisely for complicated tracks resulting from high energy photons or low pressure chambers. This leads to a better position resolution and a higher degree of modulation toward high energy X-rays. The new algorithm is justified using simulations and measurements with the gas pixel detector (GPD), and it should also work for other polarimetric techniques such as a time projection chamber (TPC). As the improvement is restricted in the high energy band, this new algorithm shows limited improvement for the sensitivity of GPD polarimeters, but it may have a larger potential for low-pressure TPC polarimeters.