Astrometry with Interferometers

Astrometry, the measurement of the angle between stars can be done in a number of ways. Light from a star enters the interferometer through the two collecting apertures shown below. In order for the light to interfer, the optical path in the two arms must be equal. The paths are made equal by adjusting the position of mirrors in the optical delay line. The position of the mirrors in the delay line are measured with a laser interfrometer, with accuracies between ~10 picometers (pm) for space based interferometers and ~1 nanometer (nm) for ground based interferometers.

One interferometer, shown above measures the position of a star with respect to the baseline vector of the interferometer. Mathematically, the delay line position where stellar fringes are observed is related to the angular position of the star by X=S*B+c, where S is a unit vector to the star B is the baseline vector joining the two collectors and c is the zero point of the delay line. For the two dimensional case above, X=b*cos(theta) + c. b is the baseline length, theta is the angle between the baseline and the star.

An interferometer only measures the angle projected onto its baseline. In general stellar fringes must be observed at two or more baseline orientations to determine two angular coordinates of an astronomical object. For ground based interferometers, the baseline is fixed to the Earth and will rotate with the Earth. In space the interferometer/spacecraft must reorient the baseline to measure both angular coordinates.