Detection noise bias and variance in the power spectrum and bispectrum in optical interferometry

The researchers seek a formalism to allow the construction of bias-free estimators of the bispectrum and power spectrum, and to estimate their variances, under less restrictive conditions, which include both unevenly-sampled data and measurements affected by a combination of noise sources with Poisson and Gaussian statistics. They used a method based on the moments of the noise distributions to derive formulae for the biases introduced to the power spectrum and bispectrum when the complex fringe amplitude is derived from an arbitrary linear combination of a set of discrete interferogram measurements. They have derived formulae for bias-free estimators of the power spectrum and bispectrum, which can be used with any linear estimator of the fringe complex amplitude. They have demonstrated the importance of bias-free estimators for the case of the detection of faint companions (for example exoplanets) using closure phase nulling.