Statistical Distribution of Visibilities in Digital Aperture Synthesis Radiometry

The statistical characteristics of visibilities measured by digital complex correlators in aperture synthesis radiometry are investigated. First, the analytic probability density function of visibilities is derived under the assumption that the successive samples are Gaussian distributed and statistically independent. However, in practice, the assumption may be not satisfied due to non-Nyquist sampling and quantizing. Then, to account for such impacts, an effective sample size is proposed. By compensating with it, the statistical distribution of visibilities is well represented in closed form. The experimental results by using an aperture synthesis millimeter-wave radiometer demonstrate the validity of the improved distribution. The results of this letter can be applied to sensitivity estimation and high-accuracy image reconstruction in digital aperture synthesis radiometry.