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 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 experiments are carried out concerning the recovery of the doublet power spectrum that is represented by s(x) = (s₀/2)exp(−π²x²/β)[cos(2πf₁x) + cos(2πf₂x)], where s₀ is a constant, β is the linewidth factor, and 〈f〉 = (f₁ + f₂)/2. Different values of 〈f〉, s₀, and β are considered to evaluate thoroughly the accuracy of the procedure to determine the unknown values of f₁ and f₂, the spectral linewidth, and the peak values of the spectral profiles. Our experiments show that, even for short observation times, the resonant frequencies of s(x) could be located with high accuracy over a wide range of 〈f〉 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 s(x) directly.

© 2001 Optical Society of America

[Optical Society of America ]

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

Related Journal Articles

• Remarks on the Born and Rytov scatter approximations and related exact models and probability distributions (JOSAA)
• Statistical characterization of ray propagation in a random lattice (JOSAA)
• Performance Degradation of a Michelson Interferometer Due to Random Sampling Errors (AO)
• Analog Intersatellite Communication with Frequency-Modulated Light. Part 1. Noise Theory (AO)
• Apodization Effects in the Retrieval of Volume Mixing Ratio Profiles (AO)

Related Conference Papers

• From extensional to intensional description
• From extensional to intensional description
• Quantum State Transformations, Majorization and Distinguishability
• Quantum State Transformations, Majorization and Distinguishability
• Instrument Line Shape of Fourier-Transform Spectrometers: Fast Integration and Correction Algorithms
• Signal-to-Noise Ratio Tradeoffs Associated with Coarsely Sampled Fourier Transform Spectroscopy
• New Spectral Calibration Approach Suitable for Imaging Fourier Transform Spectrometers