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首页> 外文会议>SPIE Optical Engineering + Applications Conference >Chebyshev Gradient Polynomials for High Resolution Surface and Wavefront Reconstruction
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Chebyshev Gradient Polynomials for High Resolution Surface and Wavefront Reconstruction

机译：Chebyshev梯度多项式用于高分辨率表面和波前重建

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A new data processing method based on orthonormal rectangular gradient polynomials is introduced in this work. This methodology is capable of effectively reconstructing surfaces or wavefronts with data obtained from deflectometry systems, especially during fabrication and metrology of high resolution and freeform surfaces. First, we derived a complete and computationally efficient vector polynomial set, called G polynomials. These polynomials are obtained from gradients of Chebyshev polynomials of the first kind - a basis set with many qualities that are useful for modal fitting. In our approach both the scalar and vector polynomials, that are defined and manipulated easily, have a straightforward relationship due to which the polynomial coefficients of both sets are the same. This makes conversion between the two sets highly convenient. Another powerful attribute of this technique is the ability to quickly generate a very large number of polynomial terms, with high numerical efficiency. Since tens of thousands of polynomials can be generated, mid-to-high spatial frequencies of surfaces can be reconstructed from high-resolution metrology data. We will establish the strengths of our approach with examples involving simulations as well as real metrology data from the Daniel K. Inouye Solar Telescope (DKIST) primary mirror.
机译：介绍了一种基于正交矩形梯度多项式的数据处理新方法。这种方法能够利用从偏转测量系统获得的数据有效地重建表面或波前，特别是在高分辨率和自由曲面的制造和计量期间。首先，我们推导了一个完整的，计算效率高的向量多项式集，称为G多项式。这些多项式是从第一种Chebyshev多项式的梯度中获得的-一种具有多种性质的基集，可用于模态拟合。在我们的方法中，易于定义和操作的标量多项式和矢量多项式都具有直接的关系，这是因为两组的多项式系数相同。这使得两组之间的转换非常方便。该技术的另一个强大属性是能够以高数值效率快速生成大量多项式项。由于可以生成数以万计的多项式，因此可以从高分辨率度量数据中重建表面的中高空间频率。我们将通过涉及模拟以及Daniel K. Inouye太阳望远镜（DKIST）主镜的真实计量数据的示例来确立我们方法的优势。

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