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Study of linear phase shift algorithms and application to deflectometry

机译：线性相移算法的研究及应用偏转测量

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For a number of optical methods, including deflectometry, information is encoded in fringe patterns. To extract the phase data from intensity values, a number of phase shift algorithms have been designed. In deflectometry, the nonlinearity of the fringe display implies that the displayed fringe pattern presents a harmonic content even if the input pattern is perfectly sinusoidal. The propagation of these harmonics through phase shift algorithms creates parasitic fringe patterns, reminiscent of the initial fringe pattern on the estimated phase. This phenomenon, known as print-through, has been identified as a serious performance limitation.In this paper, we revisit Surrel's work on harmonic insensitive phase shift algorithms and demonstrate that the class of Discrete Fourier Transform (DFT) phase shift algorithms he defines is very appropriate for the field of deflectometry. We show how to choose the most suitable one depending on the application by performing a complete modeling of the harmonic print-through phenomenon for these DFT algorithms and studying the error propagation for shot noise and temporal perturbations. In a deflectometry context, we demonstrate by means of simulations that carefully chosen DFT algorithms can simultaneously be robust to print-through and perform better with respect to noise than the state of the art nonlinear phase shift algorithms.Lastly, by comparing experimental mirror shape measurements of the matrix of the secondary mirror of the European Extremely Large Telescope made on the one hand by DFT deflectometry and on the other hand by phase shift interferometry, we demonstrate that the use of DFT algorithms can substantially improve the high spatial frequency measurement capabilities of a deflectometry setup, without the need for a calibration of the display's nonlinearities.
机译：对于许多光学方法，包括偏转测量，信息以条纹图案编码。为了从强度值中提取相位数据，已经设计了许多相移算法。在偏转测定中，边缘显示的非线性意味着即使输入图案是完全正弦的，所示的条纹图案也存在谐波含量。通过相移算法的这些谐波的传播产生寄生条纹图案，使估计阶段的初始条纹图案同意。这种现象称为印刷品，已被确定为严重的性能限制。在本文中，我们重新审视了Surrel的谐波不敏感相移算法的工作，并证明了他定义的离散傅里叶变换（DFT）相移算法非常适合偏转测量场。我们展示了如何选择最合适的方法，根据应用程序通过对这些DFT算法进行谐波打印现象的完整建模并研究射击噪声和时间扰动的错误传播。在偏转测量背景下，我们通过仿真来证明仔细选择的DFT算法可以同时稳健地打印，并且通过比较实验镜形状测量来相对于噪声而比噪声更好地执行.LASTLY。欧洲极大望远镜的二次镜子的矩阵通过DFT偏转测量，另一方面通过相移干涉测量，我们证明了DFT算法的使用可以大大提高a的高空间频率测量能力偏转量设置，无需校准显示的非线性。

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