在卫星红外多光谱扫描仪模拟空间环境辐射定标试验中, 环境模拟器舱内的稳、瞬态温度场会给光学系统成像质量带来影响。以试验中的实测温度变化作为温度载荷, 借助有限元软件, 分析了定标系统中通光孔径为Φ400mm的离轴抛物面主镜的温度场分布和热弹性变形。选用在单位圆内正交的Zernike多项式为拟合基函数, 通过坐标变换, 将抛物镜表面坐标转换为完整抛物面坐标, 而后从矛盾方程组入手, 应用Householder变换, 把系数矩阵正交三角化, 求解拟合系数, 完成波面拟合。拟合前后各离散点的PV值由1.59×10-5m变为1.5626×10-5m, RMS值由3.7159×10-6m变为3.7144×10-6m。将拟合结果导入ZEMAX软件中, 导入前后, 离轴抛物面反射镜波前像差PV值由0改变为0.018λ(λ＝632.8nm)。应用该方法进行了镜面变形分析, 结果表明, 拟合精度高, 并可以分析任意面形、形状的光学表面。

In radiometric calibration test for satellite multi-spectral scanner under simulation space conditions, the steady or instantaneous temperature field brings much effect to imaging quality of optical system. The temperature of nodes collected in test is added to FEM; the distribution of temperature field and thermal deformation of off-axial paraboloidal mirror whose caliber is Φ400mm in optical system are calculated. Based on orthogonal Zernike annular polynomials used as basic functions over an unit annulus, the coordinates of off-axial paraboloidal mirror surface are transformed to the coordinates of whole paraboloidal mirror surface; Then, the matrix of inconsistent equation group is orthogonalized and triangulated by the using of the Householder transformation method, and the Zernike coefficients can be worked out by using a back substitution technique, and the wave-front fitting can be completed. Before fitting, the previous PV (peak-vale) value is 1.59×10-5m and the RMS (root-mean-square) value is 3.7159×10-6m. After fitting, they become 1.5626×10-5m and 3.7144×10-6m respectively. The fitting results are imported into ZEMAX software and the PV value of off-axial paraboloidal mirror are 0 and 0.018λ(λ＝632.8nm) respectively. Optical surfaces with any shapes can be fitted by this method and they are precise.