基于相位拟合的莫尔条纹局部倾角计算

Calculation of Local Fringe Direction in Moiré Patterns Based on Phase Fitting

提出了一种精确求取莫尔条纹局部倾角的图像处理方法,可用于求解在渐进多焦点镜片屈光度测量中出现的莫尔条纹局部倾角。研究了实际采集到的条纹图片特性,分析了理论推导时假设测量条件与实际测量条件的矛盾,进一步探究表明实际测量所需的莫尔条纹角度实质上是基于条纹相位场而非强度场。在此基础上,提出了基于相位拟合求取条纹局部角度的方法,该方法首先通过移相得到莫尔条纹的相位,然后对相位进行泽尼克多项式拟合,得到相位的多项式表达,最后通过求解多项式对两个方向的偏导数,计算出相应位置的条纹角度。理论分析和仿真结果表明,该方法能够避免背景光和光源振幅分布不均的影响,对条纹噪声和条纹周期变化不敏感,角度求取精度可达到0.2°。

An image processing method for accurately calculating the local fringe direction of moirépatterns was proposed that can be applied to the moirédeflectogram of a spherical progressive addition ophthalmic lens.The empirical characteristics of a collected moirépattern were used as the basis for analyzing misalignments between assumptions and actual measurement conditions during the derivation of the measurement theory.Further investigation shows that the moiréfringe angle required for actual measurement is based chiefly on the fringe phase field rather than the intensity field.Based on this,a method using phase fitting to obtain the local angle of fringes was proposed.The method first obtained the phase of the moiréfringe by phase shifting and next fitted the phase to the Zernike polynomial to obtain the polynomial expression of the phase.The method then calculated the fringe angle of the corresponding position by solving the partial derivative of the polynomial in each of two directions.Theoretical analysis and simulation results show that this method can eliminate the influence of the uneven distribution of background light and light source amplitude,making it insensitive to fringe noise and fringe period variation.Angle calculation accuracy can reach 0.2°.