Amplitude and Phase Calibration with the Aid of Beacons in Microwave Imaging Radiometry by Aperture Synthesis: Algebraic Aspects and Algorithmic Implications

In remote sensing via aperture synthesis, the complex gains of every elementary antenna have to be very well known for measuring accurate complex visibilities. The role of calibration is to estimate the instrumental and environmental variations that may affect interferometric measurements. This contribution focuses on the calibration of the effective transfer function of aperture synthesis radiometers with the aid of a radio beacon, in the same way radio-astronomers use quasi-stellar radio sources to calibrate that of radio-telescope arrays. If the amplitude calibration of complex gains does not raise any issue, it is shown that phase calibration may bring up serious challenges if it is not given special attention. Indeed, the phase of the complex visibilities cannot be roughly unwrapped as the risk of a wrong estimation of the complex gains is real and proven. This problem is overcome with the aid of a non-linear optimization algorithm for iteratively and smoothly unwrapping these phases. The performances of both amplitude and phase calibration are then assessed by means of numerical simulations with emphasis on the sensitivity of the accuracy to the inversion method as well as to various errors.