利用Zernike多项式分析超薄镜热变形

利用圆域上正交基-Zernike多项式拟合镜面温度场,将温度场转化为较有意义的模式,采用有限元方法进行了热变形的计算,其中针对空间大口径超薄镜面建立镜面模型,且暂不考虑重力,另外因超薄镜厚度很小,也不考虑轴向温度梯度的影响。通过计算利用Zernike多项式得到温度场产生的热变形,得到了不同温度模式产生的不同像差形式:即对于不同的温度场模式—温度整体变化(平移),一端凉且一端热(倾斜),中心与边缘温度不同(离焦热模式),以及像散热模式,彗差热模式,球差热模式导致的热变形分别主要表现为像差离焦,倾斜,离焦,倾斜,倾斜,球差。不同热模式在相同温差下产生的变形有数量级的差别,能够产生较大变形量的温度模式有离焦,彗差和球差,这意味着超薄镜对这些温度场比较敏感。计算和总结表明,利用Zernike多项式分解温度场,可以对热变形规律进行有效的分析,解决了镜面温度分布随时间变化使得热分析较为不准确的困难。

Analyzing thermal deformation of ultra-thin mirror using Zernike polynomials

Thermal deformation plays an important role in large diameter optics system with ultra-thin mirror. For analysing the specific and quantitive thermal deformation of ultra-thin mirror, a simulating method of temperature distribution by Zernike polynomials is pressented. The temperature is spreaded to different thermal modes having their own meanings in thermal field. For example, the tilt thermal mode means that temperature is high in one end and low on the other end. Summing thermal deformation introduced by different thermal modes to get overall deformation based on two rules is as follows: firstly, temperature is scalar and could be summed after divided. Secondly, every thermal mode introduces small deformation which could be simply added. Considering the relative difficult of theoretical analysis in elasticity, finite element method is used. Mirror model is established for large and thin systems in space without gravity and thermal gradient along radius. The fixed point locates in the center of mirror. To demonstrate this method, some geometric parameters are used from NGST(next generation space telescope). And finally, calculation reveales that different thermal modes introduces different types of surface errors:thermal modes of piston, tilt, focus, astigmatism, coma, spherical, mainly create figure errors of focus, tilt, focus, tilt, tilt, spherical, respectively. Also, thermal deformations could be much different: focus, coma and spherical thermal mode create relative large deformation, which means mirror is sensitive to these kinds of thermal modes. With the same 2 K temperature difference across whole mirror surface, thermal mode introducing larger thermal deformation is coma(56 μm PV), spherical &; focus (18 μm PV) and focus (19 μm PV). In contrast, tilt thermal mode and coma thermal mode can create figure errors no more than 0.07 μm (PV) which almost have no effects on mirror function. Also, to find which kind of thermal mode is more possible, the environment should be put into consideration. Using Zernike polynomials to simulate mirror temperature distribution can give some meaningful findings and is proved to be useful for analysis of ultra-thin mirror.