OVERCOMING THE MULTIPLEX DISADVANTAGE BY USING MAXIMUM-LIKELIHOOD INVERSION

A maximum-likelihood estimator, derived under quantum-noise-limited me asurement conditions, is used to obtain wavenumber-ordered spectra pro duced by a model Michelson interferometer. The estimator is tested on a number of synthetic interferograms, and results are compared to simi lar spectra obtained by using the Fourier (cosine) transform. It is fo und that the maximum-likelihood inversion method does not result in wh ite noise in the spectrum estimate when the spectrum is sparse. It thu s may be used to circumvent the main disadvantage in multiplexed spect rometer measurements using quantum-noise-limited detectors for emissio n-based measurements. It is also found that maximum-likelihood inversi on methods can be used to obtain spectrum estimates with greater peak- width resolution than those found by using Fourier transforms. The met hods produce optical spectrum estimates that are relatively free of ar tifacts associated with the Fourier transform. The method is extended to include measurements with both quantum noise and additive white noi se. Results obtained by using the quantum-noise-limited and normal noi se maximum-likelihood spectrum estimation methods suggest that both th e multiplex-disadvantage and the Gibbs phenomenon effects may be reduc ed by limiting the parameter space. The main problem with the maximum- likelihood method is the relatively long times required to obtain spec trum estimates.