Simulation analysis on absolute testing of spherical surfaces with shift-rotation method

The absolute testing of spherical surfaces with the shift-rotation method is an effective way to test spherical surfaces with high accuracy. In the testing, the spherical surface under test is rotated to N equally spaced positions about the optical axis and the results of testing are averaged, to obtain the rotational asymmetric component. The spherical surface is also shifted to a confocal position with a shift, to derive the rotational symmetric component. Then full surface shape information can be obtained by synthesizing the above rotational asymmetric and rotational symmetric components. The formulas of shift-rotation method are derived and a simulation of the testing is presented. The results of simulation show that the root-mean-square(RMS) of residual figure error is 5.300 0