Phase calibration on interferometric graphs

Abstract

A new (to the author’s knowledge) approach to phase calibration is proposed. The corresponding theoretical framework calls on elementary concepts of algebraic graph theory (spanning trees, cycles) and computational algebraic number theory (reduced basis, closest node). The notion of phase closure is revisited in this context. One main result of this analysis is to provide all the elements for understanding the phase calibration instabilities that may occur. The phase unwrapping problem in question can be solved, directly, by minimizing the size of certain arcs. The corresponding direct methods are often quite efficient. The problem can also be solved in an indirect manner. The bulk of the work is then to minimize the length of certain chords. The pros and cons of the related methods are considered, and a link is made with the techniques developed so far. The problem of phase averaging, which is evidently much simpler, can be dealt with in a similar manner. As the corresponding results are intuitively obvious, one then has access to a more global understanding of the matter. In practice, the implications of this approach therefore concern all the methodologies in which the notions of phase closure and phase averaging prove to play an important role: self-calibration techniques in radio imaging and in optical interferometry, redundant spacing calibration in microwave imaging by aperture synthesis, etc.