By studying and discussing on the technical puzzles of the high sagitta variation rate and the seriously changed removal characteristic of lap in computer controlled optical surfacing of highly steep off-axis aspheres with large aperture

the practicable solutions are given. Decreasing the sagitta variation rate through coordinates transforming

the computer controlled manufacturing method that the lap grinds along the normal of the asphere is carried out

then

revising the figure testing result to project it on the asphere's normal

and the revised result is used in computer controlled optical manufacturing to converge the figure error more precise and effective. Finally

a manufacturing example is given in the final figure precision of PV:10.502 8 μm and RMS:0.829 3 μm during fine grind ing stage. The results show that the methods are practical and have even higher convergence efficiency.