We explore dual-ended read out of LSO arrays with two position sensitive avalanche photodiodes (PSAPDs) as a high resolution, high efficiency depth-encoding detector for PET applications. Flood histograms, energy resolution and depth of interaction (DOI) resolution were measured for unpolished LSO arrays with individual crystal sizes of 1.0, 1.3 and 1.5 mm, and for a polished LSO array with 1.3 mm pixels. The thickness of the crystal arrays was 20 mm. Good flood histograms were obtained for all four arrays, and crystals in all four arrays can be clearly resolved. Although the amplitude of each PSAPD signal decreases as the interaction depth moves further from the PSAPD, the sum of the two PSAPD signals is essentially constant with irradiation depth for all four arrays. The energy resolutions were similar for all four arrays, ranging from 14.7% to 15.4%. A DOI resolution of 3-4 mm (including the width of the irradiation band which is approximately 2 mm) was obtained for all the unpolished arrays. The best DOI resolution was achieved with the unpolished 1 mm array (average 3.5 mm). The DOI resolution for the 1.3 mm and 1.5 mm unpolished arrays was 3.7 and 4.0 mm respectively. For the polished array, the DOI resolution was only 16.5 mm. Summing the DOI profiles across all crystals for the 1 mm array only degraded the DOI resolution from 3.5 mm to 3.9 mm, indicating that it may not be necessary to calibrate the DOI response separately for each crystal within an array. The DOI response of individual crystals in the array confirms this finding. These results provide a detailed characterization of the DOI response of these PSAPD-based PET detectors which will be important in the design and calibration of a PET scanner making use of this detector approach.