## 1 Introduction  
Diffractive optical elements (DOEs) are new optical elements based on the principle of light diffraction. The early form of DOEs was binary optical elements, which are usually used for laser shaping. For a specific wavelength of incident laser, the microstructure of the DOE surface is designed, and the energy and phase of laser are adjusted to achieve the desired output spot pattern. After years of development, this system is now very mature and has become popular in industrial applications [1]. The Fresnel lens is a typical DOE element, and is usually a rotational symmetric element composed of a series of concentric rings. By designing a \"step\" at a specific phase mutation point, the diffraction efficiency of the optical system can be improved. The DOEs can be considered as being created by removing slabs of material that do not contribute to the bending of the light rays to a focal point. The surface profile of the DOEs, which is responsible for the optical power of the element, is preserved, but the volume and weight of the DOEs are reduced and the optical system specifications are improved, which is a common means to achieve miniaturization of optical systems. Planar substrate DOEs are usually used to build the optical path, but the quality of the system will be lost, whilst aspherical-based DOEs are often used to correct spherical aberrations in special cases [2; 3]. Especially in an infrared optical system, due to the limitations of the optional infrared material, the diversification of the surface design can not only correct the chromatic aberrations and improve the system performance, but also increase the design freedom. The optical system structure of a curve-based DOE is more simplified and has important potential applications in the fields of optical imaging systems, optical surface inspection, spectral analysis, and bionics [4]. All diffractive optics are in the geometry--the edgesof the phase transitions and the heights of the profiles. Materials enter only in determining the step height of the profile and as part of any classic optical design that incorporates a diffractive surface. Therefore, the generation, control, and measurement of the surface profiles are the keys to the design and fabrication of diffractive optics [5]. Dimensional measurements of diffractive optic structures are used both during and after the fabrication of the element. Typical measurements include lateral feature sizes, locations of the transition points across the field of the DOE, grating depths, verticality of grating side walls, rounding of edges, surface roughness, and other geometrical factors. Although the performance of the DOE can usually be inferred from the measured geometry, metrological measurements are normally used to troubleshoot and quantify problems in the fabrication process. Due to the discontinuity of the DOE surface, there are some sudden changes in the phase and depth of the surface structure, which lead to difficulties in the detection of the machining quality of the workpiece. The traditional testing equipment is mainly for continuous surfaces, so the detection of DOEs has always been difficult, which restricts precision machining. Current research shows that the measurement of DOEs remains in feature measurement, which is not capable of acquiring the specific data of the surface topography. Mechanical contact measurement is mature and widely used in surface topography measurement. The accuracy of continuous surface topography measurements can reach the nanometer level. The use of a profilometer to measure DOEs is limited by the size of the diamond probe [6; 7] and the atomic force probe [8; 9]. The profilometer can detect the position of the DOE's teeth, but there is noise in the signal, and there is also generally measuring pressure in the profilometer, which can cause damage to the workpiece. Phase-shifting interferometry has nanometer-level detection accuracy and is commonly used for non-contact measurement of DOE surface topography.