The absolute testing of an optical surface with the shift-rotation method is an
effective way to obtain an optical surface with high accuracy. The
traditional shift-rotation method based on Zernike polynomials has a
large number of computations and poor fitting accuracy for high
frequency. Additionally, the number of calculations of the pixel-level
spatial frequency method in solving the test and reference error based
on each pixel is too large, which leads to poor practicability in
reality. An optimized absolute testing method of shift-rotation based
on the influence function is presented in this paper. By introducing
the concept of the influence function in adaptive optics instead of a
Zernike polynomial, the calculation accuracy of the mid-and
high-frequency surface is improved, and higher precision of the
absolute surface can be obtained. Relevant theoretical simulation and
experimental verification are carried out. The experimental results
compared with the Zernike and pixel-level methods show that the
reference and test surface can be well reconstructed by using the
proposed shift-rotation method based on the influence function.