In order to meet the high profile accuracy requirements of plane grating for carbon dioxide detector,the grating and its support structure were designed and analyzed.Firstly,the principles of selecting material for grating sub-assembly and the supporting form for grating were investigated.Then,the calculation method for mirror rigid body motion and surface shape error were discussed,based on the Homogenous Coordinate transformation theory and least square method.Subsequently,the surface figure precision and structural strength were analyzed with finite element method subject to thermal-structural coupling loads.A program that can directly call the surface shape error calculation program written by MATLAB was compiled using the secondary development function provide by the finite element analysis software.Simulation results show that the PV≤63 nm,RMS≤12.6 nm.To verify the sub-assembly′s dynamitic character ,the modal and harmonic response analysis were adopted.The results indicate that the fundamental frequencies of the component in three directions are 1 046.3 Hz,1 640 Hz,1 147.5 Hz,respectively.These results demonstrate that the rationality of the supporting structure and can meet the requirements.