A new method of finding the DOE for the PET/PEM device is proposed. The idea behind this is based on the conventional position finding method utilizing the light attenuation in a piece of scintillator. Stronger dependence of the signal pulse height along the scintillator length is more favorable without much degrading the energy resolution, and this can be realized by the present idea. To verify the expected performance, a number of scintillator samples of the recent advent, Pr:LuAG, were prepared: These were processed with 3 lateral grooves on their surfaces, whose depths were chosen preliminarily from 0.2, 0.4 and 0.6 mm. The tests were performed with LED or RI source such as Cs-137, using a UV-sensitive PMT or a SiPM as the photo-sensor. A discrete attenuation behavior of the signal amplitudes was observed in each section separated by the groove(s), and this seemed to indicate the possibility of efficient detection of the DOE in any thickness of the scintillator used. The conventional dual-ends read out scheme is much simplified by reducing the number of scintillators. The single-end read out also will be promising if the material is heavy enough to dominate the total absorption over the scatter events.