Wrap-type phase unwrapping utilizing arctangent operation as a differential amplifier through shifted phase maps

Abstract

This paper introduces a novel phase unwrapping algorithm based on the investigation of the arctangent function. Acting as a differential amplifier associated with nonlinear response, the arctangent operation facilitates distinguishing various wrap types. Phase jumps from two shifted-wrapped maps aligned on the same grids are combined as a pair to function as differential mode inputs. This discerns wraps from continuous and discontinuous surfaces through distinct outputs (threshold phase values). Simulations and experiments validate the feasibility of the proposed wrap-type identification. A complete mathematical form is derived to explain the effects of shifted wraps due to various causes. This paper significantly contributes to the foundational understanding of the 2π ambiguity problem in phase unwrapping.