Vernier interferometer performance analysis

Interferometry is as an interesting method to accurately estimate the direction of arrival signals. Its main drawback concerns the 2π-phase ambiguity removal in the presence of noise. Most phase unwrapping algorithms are limited by the assumption of a smooth varying phase. Although the Vernier approach requires 3 sensors or two frequencies, it remains an interesting technique to unwrap the interferometric phase that preserves the resolution. However this technique becomes really efficient (with the higher Vernier efficiency) when the baseline configuration is well suited. This study presents a formalism based on coprime numbers modeling the Vernier efficiency. This approach goes beyond the efficiency calculations because it justifies some general results with a direct impact on the Vernier design. For instance, it proves that phase efficiency is equal for any baselines pairs for a given interferometer configuration. The unambiguous interferometer is not necessarily the only optimal design to remove all the phase ambiguities. This study goes beyond by integrating the beamforming principle and proves all properties are simply adapted.