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A LiNbO3-based integrated optical network analyser for polarisation-resolved longitudinal structure characterisation of optical fibre Bragg gratings is reported. The frequency-dependent complete reflectance Jones matrix is measured by interferometry and transformed into the time-domain impulse response. From the impulse response matrix the vectorial grating structure is determined by inverse scattering. Local dichroic reflectivity and birefringence were derived from this data. Knowledge of the vectorial nature of refractive index modulation depth and phase should allow an improvement of the ultraviolet (UV) illumination process and an effective correction of phase mask errors by longitudinally selective UV light post-processing, in order to fabricate chirped and/or apodised gratings which require the highest fabrication accuracy.