Resonance ionization mass spectrometry is an ultra-sensitive and highly element selective tool for spectroscopy, ionization and detection of atoms and thus enables rare isotope determination. In combination with spatially resolved sputtering of neutrals by an initial ion beam, e.g. within a commercial secondary ion mass spectrometer, an isotope and isobar selective analysis technique with resolution on the micrometer scale for particles and surfaces is realized. Detection of minuscule amounts of specific actinides, e.g. of plutonium, in environmental and technical samples by this ultra-trace analysis technique requires detailed knowledge about the atomic physics of the element. Identification and characterization of the specific resonance ionization scheme applied within the particular geometry of the apparatus in use is needed. An analysis of the dependence of the specifications, specifically regarding the influence of the relative laser beam polarizations is presented here as an aspect, that could have a severe impact on isotope ratio precision and overall efficiency in the resulting ion signal.