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A three-dimensional Positron Annihilation Spectroscopy System (3DPASS) capable to simultaneously measure three-dimensional electron-positron (e--e+) momentum densities measuring photons derived from e--e+ annihilation events was designed and characterized. 3DPASS simultaneously collects a single data set of correlated energies and positions for two coincident annihilation photons using solid-state double-sided strip detectors (DSSD). Positions of photons were determined using an interpolation method which measures a figure-of-merit proportional to the areas of transient charges induced on both charge collection strips directly adjacent to the charge collection strips interacting with the annihilation photons. The subpixel resolution was measured for both double-sided strip detectors (DSSD) and quantified using a new method modeled after a Gaussian point-spread function with a circular aperture.