## 1 Introduction
A white light interferometer (WLI) is often used to measure the surface topography of the injected DOE and analyze the quality of the DOE injection molding process. From the measurement profile in the literature, since the principle of interferometry is limited by the numerical aperture of the objective lens, the measurement range is small, and the measurable depth is small. Therefore, it is difficult to measure the tooth of the DOE surface by using white light vertical interferometry [10]. Although the surface roughness and tooth height of a DOE can be obtained by measuring with a WLI, the complete and accurate tooth pitch cannot be obtained because of the limitations of the measuring field of view. Therefore, the method of multi-aperture stitching is used to measure the local structural feature information of a DOE, but there is a certain error in measurement data splicing and the efficiency is low [11]. The confocal microscopic measurement method has the ability to perform axial chromatography, which can measure the 3D morphology of the measured sample combined with transverse scanning. Chromatic confocal measurement is a representative confocal microscopy technique with nanoscale measurement resolution and measurement accuracy, which can be directly evaluated by spectral signal to obtain the position height information of the point along the optical axis on the surface of the workpiece [12; 13]. Nanovea, in the United States, realizes an accurate measurement of the surface topography of the DOE based on the ST400 3D non-contact surface profilometer, developed by a confocal probe, which allows the height and spacing information of the diffraction structure to be determined. However, this system is more suitable for small planar substrate DOE topography measurement. Due to the limitations of system freedom, it is difficult to measure a curve-based DOE on a structure of a larger size. Most of the systems adopt the point-by-point scanning mode, whose measurement efficiency is slow. Moreover, the measurement accuracy depends on the positioning accuracy of the scanning points [14]. In summary, because of the special structure of DOEs, there are some shortcomings in the current measurement methods, and there is a lack of high-precision measurements and evaluation of the geometric characteristics of the DOE machined surface. Motivated by this, a new measurement and evaluation strategy of DOEs is studied in this paper. We propose a novel and fast non-contact measurement method to improve the measurement speed. It is not necessary to locate each sampling point during the measurement process, and this method can realize high-precision measurements and an evaluation of the complete surface topography of DOEs on arbitrary substrates. The data processing algorithm developed by us is original. In this method, the three-dimensional morphology of DOEs is reconstructed, which is realized by registration and coordinate transformation with optimization. The confocal measurement probe is coupled with high precision and a multi-degree-of-freedom (DOF) motion mechanism to realize the measurement of the DOE feature size information at a constant contour scanning speed. The measurement method is non-point positioning, and it is not necessary to obtain system coordinates in real time, which avoids the problem of the system not being positioned with high precision. This method can also be applied well to in situ measurements because it reduces the drawbacks of real-time location acquisition in measurement. By means of the stability of the motion of each axle system of the ultra-precision machine tool, the confocal probe is integrated into the ultra-precision machine, and the feasibility of the scheme is verified by experiments. The measurement accuracy and uncertainty of the system are discussed, and an experiment is carried out to verify the feasibility of the method.