The instrument function of the High Resolution Thomson scattering (HRTS) diagnostic in the Joint European Torus (JET) has been calculated for use in improved pedestal profile analysis . The Full Width at Half Maximum (FWHM) of the spatial instrument response is (22±1)mm for the original HRTS system configuration and depends on the particular magnetic topology of the JET plasmas. An improvement to the optical design of the laser input system is presented. The spatial smearing across magnetic flux surfaces is reduced in this design. The new input system has been implemented (from JET Pulse No: 78742, July 2009) and the HRTS instrument function corresponding to the new configuration has improved to approximately FWHM = (9.8±0.8)mm. The reconstructed instrument kernels are used in combination with an ad-hoc forward deconvolution procedure for pedestal analysis as described in. This procedure produces good results for both the old and new set-ups, but the reliability of the deconvolved profiles is greatly reduced when the pedestal width is of the same order as, or less than the FWHM of the instrument kernel.