We demonstrate an efficient noise dithering procedure for measuring the power spectrum of a weak spectral doublet with a Fourier-transform spectrometer in which the subthreshold interferogram is measured by a 1-bit analog-to-digital converter without oversampling. In the absence of noise, no information is obtained regarding the doublet spectrum because the modulation term <i>s</i>(<i>x</i>) of its interferogram is below the instrumental detection limit <i>B</i>, i.e., |<i>s</i>(<i>x</i>)| < <i>B</i>, for all path difference <i>x</i> values. Extensive numerical experiments are carried out concerning the recovery of the doublet power spectrum that is represented by <i>s</i>(<i>x</i>) = (<i>s</i><sub>0</sub>/2)exp(−π<sup>2</sup><i>x</i><sup>2</sup>/β)[cos(2π<i>f</i><sub>1</sub><i>x</i>) + cos(2π<i>f</i><sub>2</sub><i>x</i>)], where <i>s</i><sub>0</sub> is a constant, β is the linewidth factor, and 〈<i>f</i>〉 = (<i>f</i><sub>1</sub> + <i>f</i><sub>2</sub>)/2. Different values of 〈<i>f</i>〉, <i>s</i><sub>0</sub>, and β are considered to evaluate thoroughly the accuracy of the procedure to determine the unknown values of <i>f</i><sub>1</sub> and <i>f</i><sub>2</sub>, the spectral linewidth, and the peak values of the spectral profiles. Our experiments show that, even for short observation times, the resonant frequencies of <i>s</i>(<i>x</i>) could be located with high accuracy over a wide range of 〈<i>f</i>〉 and β values. Signal-to-noise ratios as high as 50 are also gained for the recovered power spectra. The performance of the procedure is also analyzed with respect to another method that recovers the amplitude values of <i>s</i>(<i>x</i>) directly.
© 2001 Optical Society of America
(000.5490) General : Probability theory, stochastic processes, and statistics
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(300.6300) Spectroscopy : Spectroscopy, Fourier transforms
May Lim and Caesar Saloma, "Noise-Enhanced Measurement of Weak Doublet Spectra with a Fourier-Transform Spectrometer and a 1-Bit Analog-to-Digital Converter," Appl. Opt. 40, 1767-1775 (2001)