基于 Zernike 多项式的自适应包裹卡尔曼相位解缠

为了在噪声干扰下准确提取干涉图中的相位信息，提出了一种基于Zernike多项式拟合的自适应包裹卡尔曼滤波相位解缠算法。该方法将相位图建模为Zernike多项式的线性拟合，采用相位图二次差分加权策略的包裹卡尔曼滤波器准确计算拟合系数，利用预测值和量测值的新息自适应地调整量测噪声协方差矩阵且无需根据干涉图设置不同的观测噪声。实验仿真和实测结果表明，所提方法能够有效地处理干涉条纹中的噪声，并能准确地恢复出相位信息,对于受噪声干扰的干涉图的相位解缠性能优于最小二乘算法和Kalman 算法，具有鲁棒性好、无需预滤波和人工干预的优点。

Adaptive wrapped Kalman phase unwrapping algorithm based on Zernike polynomial

To accurately extract phase from the noisy interferograms, an adaptive wrapped Kalman filter phase unwrapping algorithm based on Zernike polynomial fitting is proposed in the paper. The phase map is modeled as Zernike polynomial fitting, the fitting coefficients are accurately calculated using wrapped Kalman filter with a quadratic difference weighting strategy for the phase map, and the measurement noise covariance matrix is adaptively adjusted by the innovation of the predicted and measured states without setting different observed noises according to the interferogram. The results of simulation and experiment show that the proposed method can effectively deal with the noisy interference fringe and retrieve the phase map, and is superior to the least square method and Kalman filter for phase unwrapping of noisy interferograms, which has the advantage of good robustness and no need for pre-filtering and manual intervention.