Calibration of geometrical systematic error in high-precision spherical surface measurement

Geometric aberrations in interferometric testing system can significantly influence the measurement results in the case of high-numerical-aperture test spherical surface, in which obvious high-order aberrations introduced by wavefront defocus could be observed and they cannot be removed with the traditional calibration method. A technique based on the rigorous model for the analysis of geometric aberrations introduced by wavefront tilt and defocus, is presented for the calibration of the corresponding geometrical systematic error. The calibration method can be carried out either with or without a prior knowledge of the spherical surface under test. The feasibility of the proposed method has been demonstrated by computer simulation, and the residual error less than 0.001λ is obtained. Experimental validation is carried out by testing a high-numerical-aperture spherical surface with the ZYGO interferometer, and an accuracy RMS about 0.003λ with the proposed calibration technique is achieved. The effect of geometric aberrations on the measurement is discussed in detail. The proposed calibration method provides a feasible way to lower the requirement on the adjusting precision of mechanical device, and is of great practicality for the high-precision measurement of high-numerical-aperture spherical surface.

Research highlights
► Wavefront tilt mainly introduces Zernike tilt terms in high-NA surface testing.
► Wavefront defocus mainly introduces Zernike defocus and primary spherical terms.
► Calibration can be performed either with or without foreknowledge of test surface.
► Ultrahigh measurement precision is realized with the proposed calibration method.
► The method lowers the requirement on the adjusting precision of mechanical devices.