基于离散泊松方程求解的相位解包算法

Phase Unwrapping Algorithm Based on the Solution of Discrete Poisson Equation

在光学测量中相移干涉是一种常用的测量光学镜片表面形貌的方法,但是相移干涉所提取的相位值受反正切函数的限制,被包裹在(-π,π)范围内,要想得到绝对相位就必须对提取的相位进行准确解包。基于离散泊松方程求解的相位解包算法能精确解包相位,从最小二乘损失函数开始,通过离散余弦变换在频率域得到方程的精确解,再逆变换到空间域得到方程的最小二乘解。仿真实验和真实数据实验都表明:基于离散泊松方程求解的相位解包算法能够克服路径相关方法的不一致性,抑制噪声误差,恢复绝对相位。

In optical measurement, phase-shifting interferometry is a common method to measure the surface morphology of optical lens, but the phase value extracted by phase-shifting interferometry is limited by the arctangent function and is wrapped in the range of(-π,π). In order to obtain the absolute phase, the extracted phase must be unpacked accurately. The phase unwrapping algorithm based on the solution of discrete Poisson equation can accurately unpacks phase. It starts from the least square loss function, obtains the exact solution of the equation in the frequency domain through discrete cosine transform, and then inversely transforms to the space domain to obtain the least square solution of the equation. Simulation experiments and real data experiments show that the phase unwrapping algorithm based on the solution of discrete Poisson equation can overcome the inconsistency of path correlation methods, suppress noise errors and restore absolute phase.