Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials

Fei Liu; Brian M. Robinson; Patrick J. Reardon; Joseph M. Geary

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Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials

机译：使用二维Chebyshev多项式分析矩形孔径上的光学测试数据

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摘要

We use the two-dimensional Chebyshev polynomials as the basis for decomposition of test data over rectangular apertures, particu-larly for anamorphic optics. This includes simple optics such as cylindrical lenses and mirrors as well as complex optics, such as aspheric cylindrical optics. The new basis set is strictly orthogonal over rectangles of arbitrary aspect ratio and they correspond well with the aberrations of systems containing such type of optics. An example is given that applies the new basis set to study the surface figure error of a cylindrical Schmidt cor* rector plate. It is not only an excellent fitting basis but also can be used to flag misalignment errors that are critical to fabrication.

机译：我们使用二维Chebyshev多项式作为矩形孔径上测试数据分解的基础，尤其是变形光学。这包括简单的光学器件，例如圆柱透镜和反射镜，以及复杂的光学器件，例如非球面圆柱光学器件。新的基集在任意纵横比的矩形上严格正交，并且与包含此类光学元件的系统的像差非常吻合。给出了一个使用新的基础集研究圆柱Schmidt cor *校正板的表面图形误差的示例。它不仅是出色的拟合基础，而且可以用于标记对制造至关重要的失准误差。

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来源
《Optical engineering》 |2011年第4期|p.043609.1-043609.8|共8页
作者
Fei Liu; Brian M. Robinson; Patrick J. Reardon; Joseph M. Geary;
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作者单位

The University of Alabama in Huntsvi Center for Applied Optics 301 Sparkman Drive Huntsville, Alabama 35805;

The University of Alabama in Huntsvi Center for Applied Optics 301 Sparkman Drive Huntsville, Alabama 35805;

The University of Alabama in Huntsvi Center for Applied Optics 301 Sparkman Drive Huntsville, Alabama 35805;

The University of Alabama in Huntsvi Center for Applied Optics 301 Sparkman Drive Huntsville, Alabama 35805;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
metrology; anamorphic optics; chebyshev polynomials; rectangular apertures;

机译：计量变形光学切比雪夫多项式矩形孔;

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机译：基于2-D Chebyshev多项式的子孔径调节像差，缝合干涉测量法使用计算机生成的全息图（CGH）
2. Full-aperture wavefront reconstruction from annular subaperture interferometric data by use of Zemike annular polynomials and a matrix method for testing large aspheric surfaces [J] . Xi Hou, Fan Wu, Li Yang, Applied Optics . 2006,第15期

机译：使用Zemike环形多项式和矩阵方法测试环形非孔径曲面，从环形子孔径干涉数据重建全孔径波前
3. Full-aperture wavefront reconstruction from annular subaperture interferometric data by use of Zemike annular polynomials and a matrix method for testing large aspheric surfaces [J] . Xi Hou, Fan Wu, Li Yang, Applied optics . 2006,第15期

机译：使用Zemike环形多项式和用于测试大非球面表面的矩阵方法，根据环形子孔径干涉测量数据重建全孔径波前
4. Three-Dimensional Vibration Analysis of Functionally Graded Material Rectangular Plates by Chebyshev Polynomials [C] . 第十届工程与科学中的计算方法的提高与增强国际会议（EPMESC X）论文集 . 2006

机译：Chebyshev多项式对功能梯度材料矩形板的三维振动分析
5. 2-D POLYNOMIAL AND RATIONAL MATRICES, AND THEIR APPLICATIONS FOR THE MODELING OF 2-D DYNAMICAL SYSTEMS. [D] . LEVY, BERNARD CHRISTOPHE. 1981

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6. Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials [O] . Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, -1

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7. Decision-making is the process of analyzing information about a problem situation and comparing it to a specific conclusion in order to solve a specific problematic (Yıkılmaz, 2001; Miller and Byrnes, 2001). Decision-making styles are a mechanism that is influenced by the internal and external conditions that determine the direction of the decisions of the individual, the content of the decision-making process, and the outcome of the decision-making process (Payne, Bettman and Johson, 1993; Bavol’ár and Orosová, 2015). ACT is a contemporary member of the Cognitive Behavioral Therapy family. ACT (Acceptance and commitment therapy) has both similar and different directions with Behavioral Therapies and Cognitive Therapies (Herbet and Forman, 2011; Hayes, 2004). KKT responds to classical behavioral treatments using both existential and cognitive approaches in the analysis of behavior. KKT is a science wing that tries to solve human problems with a wider perspective aimed at solving problematic human behaviors (Plumb, Stewart, Dahl and Lundgren, 2009). It is seen that there is very little research about the new approach of ACT approach when the aiming country of our country is screened and it is thought that our country will contribute to the field of psychological counseling with the work done. In the scope of the research, experimental and control groups and preliminary test, post-test and follow-up measurements of 2x3 experimental design were used. The study's study group consists of a total of 24 (12 experimental and 12 control groups) university students studying in different departments and levels, continuing their education in the academic year of 2015-2016 in Ağrı province and İbrahim Chechen University in 2015-2016 academic year. The average age of participants in the experiment and control group is 20. There were 12 participants in the experimental group, 7 female and 5 male, and 12 participants, 7 female and 5 male in the control group. Personal Information Form and Decision Making Style Scale prepared by the researcher were used in the research. In order to decide on the tests to be used in the course of analyzing the data, the scores of the participant's Decision Styles Scale pre-test, which are placed primarily in the experimental and control groups, it was analyzed whether the basic expectations of parametric tests were answered. As a result of the analysis made, the scores, skewness and kurtosis coefficients obtained from the Decision Making Styles Scale were given to the experimental and control groups. It was determined that the distribution was normal in the result of Shapiro-Wilk test, in which the skewness and kurtosis coefficients of each sub-scale were ranked between -1 and +1. 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It was determined that there was no significant difference between pre-test, post-test and follow-up scores obtained from the Spontaneous-Instant Decision Style of experiment and control groups. Thus, it can be said that this situation does not cause a significant difference in the Spontaneous-Decision-Making Style scores from the decision style sub-dimensions of the ACT-oriented psychoeducation program applied to the experimental group. The ACT -oriented psychoeducation program had a decline in the intuitive decision-making styles of the individuals, but this decrease did not create significant differences. Thus, it can be said that this situation does not make a meaningful difference in the intuitive decision style scores from the decision style sub-dimensions of the KKT oriented psychoeducation program applied to the experimental group. 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机译：决策是分析有关问题情况的信息并将其与特定结论进行比较的过程，以解决特定的问题（Yıkılmaz，2001; Miller和Byrnes，2001）。决策风格是一种机制，受到内部和外部条件的影响，确定个人决定的方向，决策过程的内容以及决策过程的结果（PAYNE，BETTMAN和BEDNE） Johson，1993;Bavol'ár和奥萨洛瓦，2015）。法案是认知行为治疗家庭的当代成员。行为（验收和承诺治疗）具有与行为疗法和认知疗法的类似和不同方向（Herbet和Forman，2011; Hayes，2004）。 KKT在分析行为中使用存在性和认知方法来响应古典行为治疗方法。 KKT是一个科学翼，试图解决人类问题，旨在解决有问题的人类行为（铅垂，斯图尔特，Dahl和Lundgren，2009）。有人认为，当我们国家的瞄准国家进行筛选时，有关行动方法的新方法几乎没有研究，并且认为我们的国家将为完成工作做出贡献的心理咨询领域。在研究的范围内，使用实验和对照组和初步测试，使用后测试和后续测量的2x3实验设计。该研究的研究小组包括共24名（12个实验和12个对照组）大学学生在不同的部门和水平上学习，在2015-2016学术上继续进行2015-2016的学术年度2015-2016学年年。实验和对照组参与者的平均年龄是20.实验组中有12名参与者，7名女性和5名男性，12名参与者，7名女性和5名男性。研究人员准备的个人信息表格和决策制定风格规模在研究中使用。为了决定在分析数据的过程中使用的测试，参与者的决策风格刻度预测的分数主要在实验和对照组中进行，分析了参数的基本期望吗？测试得到了回答。由于对实验和对照组给出了从决策曲调标度获得的分数，偏移和峰度分子系数。确定该分布是正常的在成熟的-WILK试验结果中，其中每亚级的偏差和刚度系数在-1到+1之间排名。实验和对照组的参与者;决策式预测测量的同质性测试结果表明数据是均匀的。根据毛毛环保试验的结果，已确定工作支持假设。据确定，从依赖决策风格的实验和对照组获得的预测分数之间没有显着差异，但测试组在测试后的分数内显示出较低的平均分数和后续的分数 - 测试。因此，可以说，应用于实验组的面向活动的心理教育程序减少了决策风格子维度的依赖决策风格分数，并且心理教育程序具有持久的效果。据确定，从实验和对照组自发决策风格获得的预测试，测试后和后续评分之间没有显着差异。因此，可以说这种情况不会导致从应用于实验组的活动导向的心理教育程序的决策风格分数的自发决策风格分数显着差异。行为的心理教育计划在个人直观的决策风格下降，但这种减少并没有产生显着的差异。因此，可以说，这种情况不会在从应用于实验组的KKT导向的心理教育程序的决策风格分数中产生有意义的决策风格分数。从实验和对照组的理性决策风格获得的预测分数显示后检验后和随访评分之间存在差异，但这种差异并不重要。由于分析，确定测试组的理性决策风格较高，而不是后测试和后续分数的预测分数，而对照组合理决策风格的后测试和后续测试分数显示出与预测试分数相比的减少。预测分数。决策款式扩展避免决策由于分析了预测试，测试后和后续措施的班次评分的平均分数，发现群体效应是微不足道的。确定实验和对照组从避免决策风格获得的预测评分中显着不同，但在测试后和后续测试的分数内没有显示出任何重大变化。

Analyzing optics test data on rectangular apertures using 2-D Chebyshev polynomials

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