Phase measurement profilometry (PMP) is primarily employed to analyze the morphology of a functional surface with precision. Historically, one of the most complex and persistent challenges in PMP has been reducing errors stemming from inconsistent indicators at the edges of a surface. In response to this challenge, we propose an optimized error compensation methodology specifically designed to handle edge artefacts. This methodology introduces the Hilbert transform and object surface albedo as tools to detect the edges of the artefact region that need to be compensated. Moreover, we analyze the characteristics of the sinusoidal fringe waveform propagation direction and investigate the reconstruction results of the fringe vertical to the current directions to compensate for edge artefacts. The experimental results for various objects show that the optimized approach can compensate for edge artefacts by projecting in two directions and reducing the projection by half. The compensated root mean square error (RMSE) for planar objects can be reduced by over 45%.