“…For an inelastic neutron spin echo experiment with a low signal, the key is to obtain the parameters precisely from the measured data points with sinusoidal oscillations, namely IðxÞ ¼ A sin ½ðx þ ÈÞ þ C. Here, C denotes the shim neutron intensity, which scales with the counting time, is the frequency of the oscillations, which is determined by the setup and neutron energy, x is the parameter of scanning, which is magnetic field intensity in this case, È is the phase of the oscillation and A is the amplitude of the oscillation. It is also helpful for us to understand how to perform the fit for other Larmor labeling techniques, like spin echo modulated smallangle neutron scattering (Li, Parnell, Bai et al, 2016) and spin echo small-angle neutron scattering (Parnell et al, 2015). So in the following section, for each point on a sinusoidal curve of [x, I(x)], a random number generator will be used to generate a number [x, I 0 (x)], where I 0 (x) follows a Poisson distribution, similar to a real neutron source.…”