In the design of a large deployable mesh reflector, high surface accuracy is one of ultimate goals since it directly determines overall performance of the reflector. Therefore, evaluation of surface accuracy is needed in many cases of design and analysis of large deployable mesh reflectors. The surface accuracy is usually specified as root-mean-square error, which measures deviation of a mesh geometry from a desired working surface. In this paper, methods of root-mean-square error calculation for large deployable mesh reflectors are reviewed. Concept of reflector gain, which describes reflector performance, and its relationship with the root-mean-square error is presented. Approaches to prediction or estimation of root-mean-square error in preliminary design of a large deployable mesh reflector are shown. Three methods of root-mean-square error calculation for large deployable mesh reflectors, namely, the nodal deviation root-mean-square error, the best-fit surface root-mean-square error, and the direct root-mean-square error, are presented. Concept of effective region is introduced. An adjusted calculation of root-mean-square error is suggested when the concept of effective region is involved. Finally, these reviewed methods of root-mean-square error calculation are applied to surface accuracy evaluation of a two-facet mesh geometry, a center-feed mesh reflector, and an offset-feed mesh reflector for demonstration and comparison.

中文翻译：

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大型可展开网格反射器的均方根误差计算方法综述

在大型可展开网格反射器的设计中，高表面精度是最终目标之一，因为它直接决定了反射器的整体性能。因此，在设计和分析大型可展开网格反射器的许多情况下，都需要评估表面精度。表面精度通常指定为均方根误差，它测量网格几何形状与所需工作表面的偏差。本文回顾了大型可展开网格反射器的均方根误差计算方法。介绍了反射器增益的概念，它描述了反射器的性能，以及它与均方根误差的关系。显示了在大型可展开网格反射器的初步设计中预测或估计均方根误差的方法。大型可展开网格反射器均方根误差计算的三种方法，即节点偏差均方根误差、最佳拟合面均方根误差和直接均方根误差，被提出。介绍了有效区域的概念。当涉及有效区域的概念时，建议对均方根误差进行调整计算。最后，将这些回顾的均方根误差计算方法应用于两面网格几何形状、中心馈电网格反射器和偏移馈电网格反射器的表面精度评估，以进行演示和比较。介绍了有效区域的概念。当涉及有效区域的概念时，建议对均方根误差进行调整计算。最后，将这些回顾的均方根误差计算方法应用于两面网格几何形状、中心馈电网格反射器和偏移馈电网格反射器的表面精度评估，以进行演示和比较。介绍了有效区域的概念。当涉及有效区域的概念时，建议对均方根误差进行调整计算。最后，将这些回顾的均方根误差计算方法应用于两面网格几何形状、中心馈电网格反射器和偏移馈电网格反射器的表面精度评估，以进行演示和比较。