Dispersion in stellar interferometry: simultaneous optimization for delay tracking and visibility measurements

In long-baseline optical stellar interferometry, it is necessary to maintain optical path equality between the two arms of an interferometer in order to measure the fringe visibility. There will be errors in matching the optical paths because of a number of factors, and it is desirable to use an automatic system to monitor and correct such path errors. One type of system is a delay tracker, based on imaging of the channeled spectrum. The tracking algorithm is designed to maintain a fixed number of fringes, ideally linearly spaced, across the observed spectral band. This results in a constant optical path difference, which may be incompatible with the requirement of path equality for the measurement of fringe visibility. In a practical interferometer that uses an optical path-length compensator operating in air, there is a complication since air paths introduce differential dispersion. This dispersion can be compensated for by including dispersion correction. By modifying the operation of an appropriately designed dispersion corrector, we show that it is possible to make the optical path difference zero at the measurement wavelength and, at the same time, to produce linearly spaced channel fringes across the tracking band.