Spectrum Estimation from Quantum-Limited Interferograms

A quantitative model for interferogram data collected in a quantum-limited hyperspectral imaging system is derived. This model accounts for the geometry of the interferometer, the Poisson noise, and the parameterization of the mean of the noise in terms of the autocorrelation function of the incident optical signal. The Cramér–Rao bound on the variance of unbiased spectrum estimates is derived and provides an explanation for what is often called the “multiplex disadvantage” in interferometer- based methods. Three spectrum estimation algorithms are studied: maximum likelihood via the expectation-maximization (EM) algorithm, least squares (LS), and the fast Fourier transform (FFT) with data precorrection. Extensive simulation results reveal advantages and disadvantages with all three methods in different signal-to-noise ratio (SNR) regimes.