Use of a correlation chopper for time of flight neutron scattering. Part I: theory of the deconvolution

The principle of the correlation chopper is recalled and a matrix formalism changing the deconvolution into the resolution of a linear system of N equations with N unknown roots is developed. The case of an ideal rectangular signal function is considered and the system is solved when the number of analysing channels is equal to, or larger than the number of elements in the slot sequence. It is shown that, in practice, the correlation chopper improves the statistical accuracy with respect to a one slot chopper if the mean value of the diffraction function is smaller than one half the time independent background. It is also shown that an increase of the number of analysing channels, the experiment lasting the same time, improves the definition of the shape of the peaks, without modification of the relative accuracy of the measurement