We demonstrate the feasibility of artifact-free measurements of Circularly Polarised Luminescence (CPL) spectra on an imaging spectrometer. The polarization is spatially separated on two measurement channels using an achromatic quarter-wave plate associated with a polarizing beam splitter. The two channels are then imaged on a spectrometer to give the left and right circularly polarized spectra. The artifacts have been highlighted via the Mueller formalism and verified experimentally. As they add spectral contributions from either the shape of the luminescence or its derivative, they are almost impossible to eliminate by pre-calibration. We show that, at the cost of a second measurement that reverses the role of the two measuring arms, these artifacts are reduced in proportion to the stability of the lamp. The experimental results show the ability of our setup to measure CPL spectra on different kind of molecules in an accurate way with a dramatic (3 orders of magnitude) reduction in the recording time compared to a standard step by step measurement.