An investigation of the array-tilt aberration for hexagonal, optical phased arrays is presented. The investigation begins with theoretical derivations of the far-zone radiated field, the array factor, and the far-field radiated power for the seven-element hexagonal array with array tilt present. Physical insights gained from this analysis are discussed. An analytical treatment of correlation-based array-tilt estimators is also undertaken. Two novel array-tilt estimation techniques are developed from the analysis. The new techniques are shown to be significantly more efficient computationally than the traditional estimation approach. Simulation and experimental results are presented to validate the new array-tilt estimation methods.
Milo W. Hyde, Jason E. Wyman, and Glenn A. Tyler, "Rigorous investigation of the array-tilt aberration for hexagonal, optical phased arrays," Appl. Opt. 53, 2416-2424 (2014)