Mapping error correction of large off-axis aspheric surface in null test

Testing a large off-axis aspheric surface in null configuration, the measured image lost symmetry due to spherical aberration brought by null compensator. The mapping relation was not determinated like testing sphere with linear transform, but was nonlinear depending on the test configuration. In this paper, an interval method was proposed to trace all intersections, and polynomials or spline method was presented to correct the nonlinear mapping error. This will improve and accelerate process-cycle. Then experimental study on off-axis aspheric surface with 720 mm aperture, 400 mm off-axis magnitude proved the validity and efficiency of the method. The fluctuated curve of surface error shows a tendency of low efficiency and slow convergency in the beginning polishing cycles without correction method. Using nonlinear correction, the surface error decreased monotonously to pv = 0.550λ, rms = 0.049λ in same polishing cycles.