Deformation verification and surface improvement of active stressed lap for 4  m-class primary mirror fabrication

The surface shape accuracy of the active stressed lap impacts the performance of grinding and polishing in the fabrication of large mirrors. We introduce a model of active stressed lap for the fabrication of a 4 m f/1.5 mirror based on finite element analysis (FEA), and the lap surface accuracy achieves RMS<1.8  μm in the FEA method. Using the lap surface measurement system, experimental verification is put forward, and the RMS of the measured lap surface is within 2 μm in practice. A general improvement in lap surface accuracy using the Zernike polynomial is shown. After compensating the calculation errors, the lap surface accuracy is improved by 8%-23%, and achieves RMS<1.5  μm, which is appropriate for practical grinding and polishing.