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Tomographic systems have their performance deeply affected by the finite spatial resolution of the detectors equipping them. It is therefore very important to measure it, making thus possible to forecast-by using of a proper simulator-the potential improvement of the image quality achievable by a better detector resolution. Some techniques to measure the detector resolution require the determination of the Line Spread Function-LSF, but this function is somewhat difficult and cumbersome to be directly assessed. This paper presents a new method to determine the detector resolution, as a by-product of an image processing employing an unfolding of the position spectra, used as projections, with a Gaussian of variable width representing the detector's LSF. A narrow LSF does not correct properly the actual degradation caused by the detector, while a broad one overcorrect its spoiling effect, yielding images exhibiting an apparent better resolution. This illusive improvement is nevertheless achieved at the cost of a violation in the image aspect ratio. Therefore, a plot of the measured aspect ratio against the LSF width used in the unfolding furnishes the detector resolution at the known aspect ratio of a rectangular insert in the test-object. The algorithm developed to perform the unfolding has been written in Fortran IV language, being capable to deal with experimentally acquired position spectra, or generate similar ones in order to simulate detectors of different resolutions. It has been applied to measure the resolution of a position sensitive detector equipping a 2D neutron tomographic system, and the results were compared with other conventional techniques.