Analysis and Numerical Modeling of Error Sources in SIM Star Light Phase Detection

The Space Interferometry Mission (SIM), scheduled to launch in 2010, will perform precision astrometry by interfering starlight beams collected by two 35 cm "collector" mirrors separated by 10m. Part of each astrometry measurement will involve accurately measuring the relative phase of the two beams at the beam combiner. This measurement will be performed by modulating the optical path of one of the beams periodically through a range of roughly one optical wavelength, while simultaneously detecting the intensity of the interference fringes using spectrometers at the two outputs of the combiner. During this process, the lengths of the optical paths traveled by both starlight beams within the interferometer will be monitored by a laser interferometer. A number of sources of error are of concern when designing this phase-detection system. Shot and read noise in the spectrometers\´ (CCD) detectors introduce errors into the phase measurement; the magnitude of these errors depends on the rate at which the CCD is read and the design resolution of the spectrometer. Vibrations in the structure of the spacecraft, produced by reaction wheels, the motion of the high gain antenna, propellant slosh, or other mechanisms, will introduce errors in the phase measurement, errors which, however, can to some extent be suppressed using measurements from the laser interferometer. Simple algorithms developed for estimating the phase of monochromatic interference fringes are computationally efficient and relatively straightforward to analyze, but have limited accuracy when used to estimate the phase of interference fringes generated by broadband starlight. This paper describes numerical simulations and other methods of analysis used to quantify the phase measurement errors introduced by a range of mechanisms, to make design decisions, to generate subsystem requirements, and to rank sources of noise or disturbances. We have developed a general simulation package which allows us to analyze th- e interference fringe detection and phase measurement processes, simulating shot and read noise either via a Monte-Carlo approach or by a method in which the corresponding variances are propagated. We are able to simulate arbitrary stellar spectra, and to calculate the effect of arbitrary vibrations. A method of suppressing vibration-induced errors has been tested using data from the microarcsecond metrology (MAM) testbed at JPL