Accurately computing the optical pathlength difference for a michelson interferometer with minimal knowledge of the source spectrum

Astrometric measurements using stellar interferometry rely on precise measurement of the central white light fringe to accurately obtain the optical pathlength difference of incoming starlight to the two arms of the interferometer. One standard approach to stellar interferometry uses a channeled spectrum to determine phases at a number of different wavelengths that are then converted to the pathlength delay. When throughput is low these channels are broadened to improve the signal-to-noise ratio. Ultimately the ability to use monochromatic models and algorithms in each of the channels to extract phase becomes problematic and knowledge of the spectrum must be incorporated to achieve the accuracies required of the astrometric measurements. To accomplish this an optimization problem is posed to estimate simultaneously the pathlength delay and spectrum of the source. Moreover, the nature of the parameterization of the spectrum that is introduced circumvents the need to solve directly for these parameters so that the optimization problem reduces to a scalar problem in just the pathlength delay variable. A number of examples are given to show the robustness of the approach.