基于Gram-Schmidt算法的二阶条纹图间相位步长的计算
Computation of the phase step between two-step fringe patterns based on Gram--Schmidt algorithm
摘要：
我们提出了一个封闭形式的公式计算两个随机移位的条纹图案之间的原始步骤的评价。我们的建议扩展了条纹图的Gram-Schmidt正交归一化算法。在实验上，相移是由一个机电装置（如压电或移动支架）引入的，实际相位步长的估计允许我们改进相移装置的校准。评估包括三种情况下，代表不同的预归一化过程：首先，我们评估的方法在正交归一化过程中的准确性，估计测试步骤使用合成归一化条纹图案没有背景，恒定的振幅和不同的噪声水平。第二，我们评估的公式与一个可变的振幅函数的条纹图案，但没有背景。第三，我们评估非归一化的噪声条纹图案，包括比较预滤波过程，如Gabor滤波器组和各向同性归一化过程，以强调它们如何影响相位步长的计算。
英文摘要：
We present the evaluation of a closed form formula for the calculation of the original step between two randomly shifted fringe patterns. Our proposal extends the Gram--Schmidt orthonormalization algorithm for fringe pattern. Experimentally, the phase shift is introduced by a electro--mechanical devices (such as piezoelectric or moving mounts).The estimation of the actual phase step allows us to improve the phase shifting device calibration. The evaluation consists of three cases that represent different pre-normalization processes: First, we evaluate the accuracy of the method in the orthonormalization process by estimating the test step using synthetic normalized fringe patterns with no background, constant amplitude and different noise levels. Second, we evaluate the formula with a variable amplitude function on the fringe patterns but with no background. Third, we evaluate non-normalized noisy fringe patterns including the comparison of pre-filtering processes such as the Gabor filter banks and the isotropic normalization process, in order to emphasize how they affect in the calculation of the phase step.
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