Noise-enhanced measurement of weak doublet spectra with a Fourier-transform spectrometer and a 1-bit analog-to-digital converter

We demonstrate an efficient noise dithering procedure for measuring the pow er spectrum of a weak spectral doublet with a Fourier-transform spectromete r in which the subthreshold interferogram is measured by a 1-bit analog-to- digital converter without oversampling. In the absence of noise, no informa tion is obtained regarding the doublet spectrum because the modulation term s(x) of its interferogram is below the instrumental detection Limit B, i.e ., \s(x)\ < B, for all path difference x values. Extensive numerical experi ments are carried out concerning the recovery of the doublet power spectrum that is represented by s(x) = (s(0)/2)exp(-<pi>(2)x(2)/beta)[cos(2 pif(1)x ) + cos(2 pif(2)x)], where s(0) is a constant, beta is the linewidth factor , and [f] = (f(1) + f(2))/2. Different values of [f], s(0), and beta are co nsidered to evaluate thoroughly the accuracy of the procedure to determine the unknown values of f(1) and f(2), the spectral Linewidth, and the peak v alues of the spectral profiles. Our experiments show that, even for short o bservation times, the resonant frequencies of s(x) could be located with hi gh accuracy over a wide range of [f] and beta values. Signal-to-noise ratio s as high as 50 are also gained for the recovered power spectra. The perfor mance of the procedure is also analyzed with respect to another method that recovers the amplitude values of s(x) directly. (C) 2001 Optical Society o f America.