Errors due to demodulation in measurements of laser beam envelope and phase

The propagation of a laser beam through the atmosphere leads to spectral widening, which has a detrimental effect on information transmission. In literature the study of laser beam envelope and phase was achieved through demodulation. In this paper we explain that amplitude demodulation in the baseband leads to changes in analytic signals. We give a formula which allows this drawback to be overcome, achieving two demodulations with same frequency and different phases. Examples are given in the Gaussian framework and in the case of random propagation times.