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We analyse the performance of a gas time projection chamber (TPC) as ahigh-performance gamma-ray telescope and polarimeter in the e$^+$e$^-$ paircreation regime. We use data collected at a gamma-ray beam of knownpolarisation. The TPC provides two orthogonal projections $(x,z)$ and $(y,z)$of the tracks induced by each conversion in the gas volume. We use a simplevertex finder in which vertices and pseudo-tracks exiting from them areidentified.  We study the various contributions to the single-photon angular resolutionusing Monte Carlo simulations and compare them with the experimental data andfind that they are in excellent agreement. The distribution of the azimutalangle of pair conversions shows a bias due to the non-cylindrical-symmetricstructure of the detector. This bias would average out for a long durationexposure on a space mission, but for this pencil-beam characterisation we haveensured its accurate simulation by a double systematics control scheme, datataking with the detector rotated at several angles with respect to the beampolarisation direction and systematics control with a non-polarised beam.  We measure, for the first time, the polarisation asymmetry of a linearlypolarised gamma-ray beam in the low energy pair creation regime. This sub-GeVenergy range is critical for cosmic sources as their spectra are power lawswhich fall quickly as a function of increasing energy.  This work could pave the way to extending polarised gamma-ray astronomybeyond the MeV energy regime.

Performance measurement of HARPO: a Time Projection Chamber as a gamma-ray telescope and polarimeter