Nonlinear estimation for interferometric imaging

We conduct a comparative study between two types of imaging systems for distant point sources. One is a conventional focal plane system and the other, a multiplex system based on a rotational shearing interferometer (RSI). The RSI produces linear fringes in response to each object point source, which offers functional advantages over the conventional system. A nonlinear algorithm is developed for estimating fringe parameters in an RSI that performs better than traditional Fourier methods; while an existing nonlinear algorithm is modified for use with the conventional imager. Intensity and position estimation performance of the two imaging systems is characterized using both traditional as well as nonlinear estimation in the presence of noise. In additive white gaussian noise dominated imaging, we find that the RSI is always inferior to the conventional imager by a factor that is approximately the square root of the number of detectors. However, the two imaging systems are comparable in the shot-noise limit. Simulated performances for a single monochromatic source are reported for the shot-noise limited case. The super-resolution ability of the nonlinear algorithms is studied with two monochromatic sources at various separations. The nonlinear estimator is also applied to polychromatic point sources and the simultaneous estimation of spatial and spectral data for the RSI is demonstrated.