Fourier transform technique for phase unwrapping with minimized boundary effects

摘要

It is proposed a quadratic cost functional for calculating a consistent gradient field from an inconsistent one. This inconsistent gradient in obtained by wrapping the first difference of the wrapped phase. The derivation of the respective Euler equations of the proposed functional is presented. A discrete Fourier transform based technique for solving the Euler equations is shown. The calculated unwrapped phase may then be calculated by integrating the consistent gradient with any integration algorithm. This fast (transform) method has the following advantages over existing Fourier technique: their transfer functions are close to one and, the boundary errors are estimated and minimized. So that the global estimation error is reduced.