Framework for freeform complex surface reconstruction by combining Zernike polynomials with radial basis function method

Freeform complex surfaces with steep variations in local areas cannot be fitted by analytical functions with high accuracy in the whole aperture in optics. A framework with a combination of Zernike polynomials as base function with radial basis function method is presented to improve reconstruction accuracy for freeform complex surfaces with circular aperture. The algorithm of the framework is analyzed, and the performance of the method is investigated and verified by numerical experiments. The proposed method is accurate and highly adaptable, which could be applied in modern optical manufacturing and measurement.