The least-squares calibration on the micro-arcsecond metrology test bed

The Space Interferometry Mission(SIM) will measure optical path differences (OPDs) with an accuracy of tens of picometers, requiring precise calibration of the instrument. In this article, we present a calibration approach based on fitting star light interference fringes in the interferometer using a least-squares algorithm. The algorithm is first analyzed for the case of a monochromatic light source with a monochromatic fringe model. Using fringe data measured on the Micro-Arcsecond Metrology(MAM) testbed with a laser source, the error in the determination of the wavelength is shown to be less than 10pm. By using a quasi-monochromatic fringe model, the algorithm can be extended to the case of a white light source with a narrow detection bandwidth. In SIM, because of the finite bandwidth of each CCD pixel, the effect of the fringe envelope can not be neglected, especially for the larger optical path difference range favored for the wavelength calibration. We eliminate the fringe envelope effect by "projecting away" the fringe envelope, i.e. working in a subspace orthogonal to the envelope signal. The resulting fringe envelope parameters are needed for subsequent OPD estimation in SIM. We show the sensitivities to various errors. The algorithm is validated using both simulation and the fringe data obtained on the MAM test bed.