Signal and noise in two-beam interferometry.

We assume the iterferogram is measured at equidistant optical path difference points, x = xo(=0), X, x2 ... L, where L is the maximum optical path difference attained, and furthermore each point is measured for the same amount of time. In general, the intensity of the interferogram measured at each x,, will have a noise contribution and this noise will be propagated into the spectrum obtained by Fourier cosine transformation of the interferogram. The noise is assumed to be independent of the signal and x. Let Ns and N, be the standard deviation of the noise in the spectrum and interferogram, respectively. Then