Two-position spherical absolute measurement method

The positions of the traditional three-position spherical absolute measurement are the cat's eye position, the confocal position, and the confocal position rotated 180°. Rotational operation can introduce misalignment errors that affect the measurement results. In this paper, it is shown that only two measurements of cat's eye position and confocal position are necessary to obtain the absolute surface of the measured sphere through Zernike polynomial fitting. When solving the three-position spherical absolute measurement with Zernike polynomials, the number of unknowns is greater than the number of equations, resulting in the inability to solve. By analyzing the equation, the relationship between the Zernike coefficients before and after rotation can be found, resulting in a solvable system of equations.