Rahbar Kambiz, Faez Karim, Attaran Kakhki Ebrahim
J Opt Soc Am A Opt Image Sci Vis. 2013 Oct 1;30(10):1988-93. doi: 10.1364/JOSAA.30.001988.
Orthogonal polynomials can be used for representing complex surfaces on a specific domain. In optics, Zernike polynomials have widespread applications in testing optical instruments, measuring wavefront distributions, and aberration theory. This orthogonal set on the unit circle has an appropriate matching with the shape of optical system components, such as entrance and exit pupils. The existence of noise in the process of representation estimation of optical surfaces causes a reduction of precision in the process of estimation. Different strategies are developed to manage unwanted noise effects and to preserve the quality of the estimation. This article studies the modeling of phase wavefront aberrations in third-order optics by using a combination of Zernike and pseudo-Zernike polynomials and shows how this combination may increase the robustness of the estimation process of phase wavefront aberration distribution.
正交多项式可用于表示特定域上的复杂曲面。在光学领域，泽尼克多项式在测试光学仪器、测量波前分布以及像差理论方面有着广泛应用。这种在单位圆上的正交集与光学系统组件（如入射和出射光瞳）的形状具有适当的匹配性。在光学表面表示估计过程中噪声的存在会导致估计过程精度降低。人们开发了不同策略来处理不必要的噪声影响并保持估计质量。本文研究了通过结合泽尼克多项式和伪泽尼克多项式对三阶光学中的相位波前像差进行建模，并展示了这种组合如何提高相位波前像差分布估计过程的稳健性。
