A method to compute the covariance matrix of wavevector-energy transfer for neutron time-of-flight spectrometers

We present a method to calculate the covariance matrix of wavevector-energy transfer for neutron time-of-flight direct geometry spectrometers, with both pulse shaping and monochromating choppers. As the definition of the wavevector transfer and of its components depends on the detector geometry and on the instrumental parameters, three different geometries have been analyzed: spherical, cylindrical with horizontal and vertical axis. The specific dependence of the matrix elements on the instrumental parameters is explicitly given. The results of example calculations are also presented and discussed.