We show that in spatially resolved reflectance anisotropy (RA) spectrometers, off-axis optical rays introduce a spurious signal component that cannot be addressed by optical alignment. Such a component is associated with the difference between the reflectivities s and p of the sample and depends, in a complex manner, on the incidence position of the incident light on the surface of the sample. We report a data-reduction procedure to easily identify and remove spurious RA signals associated with the off-axis optical rays, based on the singular value decomposition analysis of spatially resolved RA spectra. We validated this approach by developing a spatially resolved RA spectrometer based on an 8 × 8 multi-anode photomultiplier (PMT). The PMT allowed the use of phase-sensitive detection techniques to enhance the signal-to-noise ratio, which is essential for the evaluation of the proposed data reduction procedure.