Wide-band and Air Dispersion Effecting the ABCD Algorithm of Phase-Recovery in Long-baseline Interferometry

Long-baseline interferometry detects fringes created by superposition of two beams of light collected by two telescopes pointing into a common direction. The external path difference generated by pointing away from the zenith is commonly compensated by adding a variable optical path length (delay) through air for one beam such that the optical path difference between the beams remains close to zero near the detector. The ABCD formula assigns a (wrapped) phase to the amplitudes A to D of an interference pattern shifted by multiples of 90 degrees in phase. We study the interplay between a wide band pass of the optics and the dispersion of the air in the compensating delay, which leads to small deviations between the ABCD phase and the reduced, monochromatic group-delay representation of the wave packets. In essence, this adds dispersion to the effects that have been discussed for evacuated interferometers (telescopes in space) before [J. Opt. Soc. Am. A 22 (2005) 2774].