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.