摘要
通过对LAMOST大科学工程中焦面板面型测量所遇到的问题进行后续的理论分析,给出了测量过程中的微小误差影响测量结果的几何理论的推导.由于焦面板的形状近似于一个半径为20m的截球,其采样测量面积只占焦面理论半径所构成的虚拟球面面积的两千分之一,仅采用面型上取点计算球心、半径的一般测量方法,拟合后的数据会有非常大的离散性.此时球面测量中任何一个微小的误差都将在半径和球心位置的最后测量结果中放大.误差分析从四点拟合球面的方法入手,近似计算出测量误差对最小二乘法拟合所得的球面半径值的影响,为改进测量方法、提高测量精度提供理论依据.
Some questions in the measurement of the focal plane of LAMOST were analyzed and the influence of measurement error on the result was deduced based on geometric theory. The shape of the focal plane is the section of the sphere, the diameter of the focal plane is about 20m, and the sample area is 1/2000 part of the suppositional spherical surface. The measurement data will be scattered when measuring the points on the surface to calculate the radius and center coordinate with the usual method. For this time any tiny little error in the measurement of the points will magnify the sphere radius and the center. From four-points-fit-the-sphere theory, the influence which the measurement error brought to the least square approximation of spherical fitting radius was simulated, the error regularity between the measurement area and radius to the sphere was identified by the method of least square, thus providing guidance to conduct the focal plane measurement of the LAMOST.
基金
国家"九五"重大科学工程(98BJG001)资助
