Delay compensation: its effect in reducing sampling errors in Fourier spectroscopy

An approximate formula is derived for the spectrum ghosts caused by periodic drive speed variations in a Michelson interferometer. The solution represents the case of fringe-controlled sampling and is applicable when the reference fringes are delayed to compensate for the delay introduced by the electrical filter in the signal channel. Numerical results are worked out for several common low-pass filters. It is shown that the maximum relative ghost amplitude over the range of frequencies corresponding to the lower half of the filter band is typically 20 times smaller than the relative zero-to-peak velocity error, when delayed sampling is used. In the lowest quarter of the filter band it is more than 100 times smaller than the relative velocity error. These values are ten and forty times smaller, respectively, than they would be without delay compensation if the filter is a 6-pole Butterworth.