## 1 Introduction  
Nowadays, modern optical components with freeform surfaces are widely used since they have the advantages of excellent optical performance and functionalities [1]. Due to the high accuracy requirement and geometrical complexity of freeform surfaces, their design and manufacture are not only challenges, but their measurement is also a challenge since the measurement process needs to characterize the machined freeform surfaces to determine the conformance with the design. The coordinate measuring machine (CMM) [2] is one of the most important geometrical measurement devices. Equipped with the most widely used touch trigger probe with high repeatability, it provides traceable and accurate measurement results over a relatively large measurement range, and is well accepted in the industry for coordinate measurement due to its flexibility and accuracy [3]. For modern CMMs, after several decades of development since they were first invented, the measurement accuracy is ensured by sophisticated designed hardware and a carefully controlled environment together with specific software. Nowadays, there is a research and development trend towards multi-sensor CMMs since the measurement capability of the machines can be significantly enhanced by integrating multiple sensors [4]. This allows unique functionality comparison to be incorporated into single-sensor CMM machines. Currently, there are many commercialized multi-sensor CMMs available on the market. For instance, ZEISS O-INSPECT [5] is equipped with a contact sensor, imaging sensor and white light distance sensor, which is able to provide fast inspection by the image sensor and high-accuracy 3D (three dimensional) measurement results by the contact sensor and white light distance sensor. Werth VideoCheck [6] is designed to be equipped with many kinds of sensors such as trigger probe, fibre probe [7] and video sensor, which provide the measurement ability of small features with the help of a small-diameter fibre probe down to 20 \(\upmu\)m, as well as quick checking with a fast trigger probe and image sensor. Hexagon Optiv Classic [8] provides a vision sensor and a tough trigger probe, while Nikon [9] enhances the true three dimensional (3D) multi-sensor measurement by combining a vision sensor, laser auto-focus sensor, tactile sensor and rotary indexer. The measurement range, resolution and flexibility are largely enhanced by the complementary different characteristics of various sensors. Most multi-sensor CMMs enhance the measurement ability according to the sensor's characteristics. Although this provides high flexibility for measuring different features and samples by selecting different sensors installed on the multi-sensor CMMs, there is still plenty of room for research and development when the integration of measured datasets from different sensors is taken into account. At the current stage of surface metrology, there are studies focused on combining the datasets from different sensors to generate holistic results with improved measurement accuracy. [PERSON] et al. [10] developed a cooperative fusion method for a distributed multi-sensor large-volume metrology system which combined datasets from angular and distance measurements. However, it only worked for measurement using angular and distance sensors to determine the 3D positions of the measured points and could not be used for CMMs. [PERSON] et al. [11] used a Gaussian process modelling method to combine highly accurate low-density CMM data with low-accuracy high-density data from a laser scanner. The two datasets were linked together using a \"linkage\" model by introducing the scaling and shifting factors to correct the systematic error. The result showed that the measurement uncertainty of the fused data could be reduced as compared with the results from single measurement. This method was similar to the one proposed by [PERSON] et al. [12], but it dealt with surface metrology problems instead of mechanical material design and modelling of food processors.