Virtual reference surface phase measuring deflectometry for high-precision freeform surface measurement

The phase measuring deflectometry (PMD) method has limitations in the measurement of mirror surfaces with large local curvature, such as large integration errors and overly dense fringes. This restricts its application in the detection of complex and high-precision freeform surfaces. This paper introduces a virtual reference surface phase measuring deflectometry (VRPMD) tailored for measuring complex freeform surfaces, grounded in the concept of slope difference measurement. The advantages of VRPMD over traditional PMD in highprecision measurement of large-curvature freeform surfaces are thoroughly explored through theoretical modeling, simulation analysis, and experimental validation. Furthermore, a surface self-referencing technique is proposed to address the high-precision alignment challenge between the virtual reference surface and the test surface due to the non-rotational symmetry of freeform surfaces. Comparative experiments with an interferometer and a profilometer demonstrate that the proposed method is a highly promising high-precision inspection technique for freeform surfaces.