Freeform surfaces have been regarded as one of the major revolutions in the field of modern precision optics. They are expected to further promote miniaturization, lightweight and integration of optical systems due to their excellent optical and mechanical properties. The quality of machined freeform surfaces will significantly influence the performance of optical systems. Surface metrology including the measurement of surface texture and surface form errors is the important post-manufacturing part to determine which surface can be employed. In the past decades, various methods have been developed for measuring and characterizing freeform surfaces, mainly including probe-based scanning, full-aperture optical inspection, on-machine measurement technology, feature-based surface registration and multi-scale data fusion methods. Although many corresponding advances have been achieved, great challenges are posed to the quality of surface manufacturing with the complexity of freeform surfaces increasing. Moreover, the surface form error is required to be lower than 0.1 μm and the surface roughness should be less than 1 nm. It is urgent to develop a new measurement technology for achieving a higher dynamic range and a higher accuracy. Hence, it is important and necessary to summarize the existing research to guide the future development of this field more rationally.

Measurement and characterization of optical freeform surfaces are the key processes to check the quality of freeform surfaces. The widely used techniques related to these two processes are summarized. Firstly, the precision measurement methods for optical freeform surfaces are introduced, including probe-based scanning, full-aperture optical inspection and on-machine measurement. The probe-based scanning methods include nanoscale 3D coordinate measuring machine, non-contact profile scanner and swing arm profilometer. To further improve the dynamic and precision measurement performance of coordinate measuring machines, Manske's research group from Technische Universit?t Ilmenau, Germany, has conducted relatively pioneering studies by using an atomic clock-stabilized He-Ne laser via a high-stable-frequency comb. Secondly, full-aperture optical inspection methods are elaborated, including null test metrology of computer-generated holography (CGH), sub-aperture stitching test and adaptive interferometry. Subsequently, surface characterization processes such as surface registration, data fusion and error evaluation are reported. The iterative closest point (ICP) algorithm and its modified methods have been surveyed by Maiseli and Zhu. Liu and Wang from the Hong Kong Polytechnic University have engaged in plenty of studies on multi-sensor data fusion based on Gaussian processes (GP) after reliable surface registration. Jiang's team from the University of Sheffield summarized and expounded on the new application methods of characteristic parameters for complex freeform surfaces. Considering the latest application of freeform surfaces, a novel method is also presented for measuring and evaluating new freeform types called conjunctive multi-freeform surfaces. In the end, the problems and the ongoing research trends in this field are discussed, including measurement means and surface characterization techniques.

Rapid, accurate and reliable inspection technology is the core factor to judge whether the performance of an optical freeform surface meets the requirements of intelligent manufacturing. In the measurement process, the widely used point-line-based scanning measurement method can achieve high measurement accuracy and realize the measurement of micro-nano structure, large-scale surface, and local features with high steepness. However, the measurement efficiency is low and the optical surface may be scratched during contact measurement. In contrast, full-aperture measurement methods have the superiority of fast measurement and high accuracy without contacting the surface. However, the lateral resolution of these methods needs to be further improved and the dynamic range of measurement is limited. Combining the advantages of the two types of measurement technologies is a promising way to improve manufacturing efficiency. As a result, on-machine measurement technology integrating multiple measurement methods to realize the multi-sensor in-situ measurement of complex surface shapes has become the development trend of the current measurement field.

On the other hand, in the error evaluation process, ICP and its modified technologies have always been the first choice for surface registration. Although it is influenced by the initial value, the registration method combined with the inherent characteristics of optical freeform surfaces or the auxiliary datum constructed basically meets the accuracy requirements. However, the computational complexity and efficiency still need to be improved. For multi-sensor data, data fusion mostly depends on linear fitting. The associated characteristics of the fusion process remain to be further explored. The deep fusion of multi-source data may become an important direction in this field by combining with the machine learning technique. In the future, with the rapid exploration of multifunctional, micro-nano and multi-scale optical surfaces, the corresponding measurement and surface characterization methods may encounter new challenges in the manufacturing of optical freeform surfaces.