Vectorial combination of signals in Fourier transform spectroscopy

In an ideal Fourier transform spectrometer the measured spectrum is a scalar combination of two input sources, while, more generally, a vectorial combination occurs in a real instrument. The vectorial combination is caused by the absorption of the beamsplitter which introduces a deviation from π of the relative phase between the two input sources, as well as a third source. Moreover, the asymmetry of the beamsplitter can cause a frequency dependent phase delay adding complexity to the system. A general model of a Fourier transform spectrometer is presented and it is shown that such a complex behaviour can be characterized through the “composite phase parameter” of the beamsplitter. Furthermore, some general rules are identified that can be used to devise more efficient calibration procedures and strategies for the minimization of the distortions caused by the vectorial combination of the spectra.