Transverse differential confocal freeform surface measurement method with normal vector tracking and large linear sensing range

Freeform surfaces are widely applied in various fields, including aerospace, biomedical engineering, and optical communications. Their high degrees of design freedom facilitate the high-performance integration of complex functionalities within limited spaces. However, freeform surfaces lack rotational symmetry and exhibit significant variations in surface height and inclination angles, making it challenging for existing measurement methods to achieve high-precision measurements of surfaces with large gradient variations. In this study, we proposed a transverse differential confocal method with the capability of tracking normal vectors and a large linear sensing range for the high-precision measurement of freeform surface profiles. To adapt to the height variations of the freeform surface, a multi-element detector was adopted to transversely segment the spot and detect the intensity of the focal spots on the focal plane. Normal vector tracking based on a 2D position-sensitive detector was used to acquire angular information accurately. This method successfully balanced the range and precision of the measurements. The theoretical analyses and experimental results indicate that the sensors that were designed based on this method could represent an axial resolution of 0.5 nm, a normal resolution of 0.1°, and a maximum measurable local angle of 20°. In particular, the proposed method enables the high-precision measurement of freeform surface profiles without requiring strict initial pose adjustments. The measured peak to valley (PV) value obtained using this method differed from the result obtained using a ZYGO interferometer by only 9.5 nm. The method ensures measurement accuracy while providing higher versatility than interferometry, providing a novel and effective approach for high-precision measurement of freeform surface profiles. Owing to its excellent measurement performance and adaptability, it exhibits potential for the ultra-precision measurement of micro- or nano-structures.