Resolution matching between energy and momentum in position-sensitive detector on chopper spectrometer

We derived analytical expressions of energy (E) and momentum (Q) resolutions on a chopper spectrometer, including timing and geometrical parameters, such as a pulse width at a moderator, an opening time of a chopper, spectrometer lengths, sizes of a moderator, of a sample and of a position-sensitive detector (PSD) and pixel sizes in a PSD. For a long linear PSD, resolutions change for pixels dependently on their positions inside the PSD, because of the change in the flight path lengths. Controlling the pixel sizes can reduce such nonuniformity in resolutions. However, in order to diminish the nonuniformity in both of the E and Q resolutions simultaneously, the PSD length was found to be limited.