Convex blazed gratings, which can effectively broaden the spectral range and improve spectral resolution, have gradually evolved into a crucial optical component for lightweight and compact imaging spectroscopy instruments. Their design, processing, and testing involve multidisciplinary interdisciplinary scientific issues, and they continue to be a major area of research in imaging optics applications. This paper summarizes the effects of various grating groove shapes and structural parameters on the spectral range and diffraction efficiency of convex blazed gratings, after providing a brief introduction to the typical functions and applications of convex blazed gratings. Firstly, the latest progress in typical processing methods for convex blazed gratings is reviewed. It focuses on the current fabrication processes and reviews their capabilities in creating convex blazed gratings from three main types of technologies, namely ultra-precision machining, high-energy density beam processing, and chemically assisted fabrication processes. Secondly, the adaptability of the manufacturing process for convex blazed gratings on different scales is summarized, analyzing the adaptation of current procedures to various grating fabrication scales and their bottlenecks. Finally, the characterization methods and future feasible characterization methods for convex blazed gratings are reviewed. The development trend of efficient and precise preparation of convex blazed gratings is pointed out.

A deterministic figuring method for cylindrical surface based on abrasive belt polishing is proposed in this study in order to improve the geometric accuracy of metal shaft parts. The principal motion of material removal is performed through the axial oscillation of the abrasive belt, and the different material removal at different positions can be obtained through servo control of the machine tool spindle by removing high error spots on the cylindrical surface and finally deterministically corrects the roundness error. An abrasive belt-based deterministic figuring device was built, and the figuring experiments were performed on the surface of steel workpieces 100 mm in diameter and 130 mm in effective length. The roundness errors of the entire workpiece after twice figuring iterations decreased nearly from the initial 3 μm to 1 μm, which preliminary verified the feasibility of this method. This deterministic figuring method is expected to break the machining accuracy limit and improve the rotation precision of the precision shaft parts such as the aerostatic spindle.

The profile and concentricity of hemispherical shells affect the frequency split and quality factor of hemispherical resonators. To compensate for machining errors caused by tool wear and tool setting, an on-machine measurement (OMM) method for the profile and concentricity of hemispherical shells in ultra-precision grinding was developed without the removal of workpieces from the machine tool. The OMM utilizes an inductive lever probe to test the inner and outer surfaces of the shell. A standard sphere is utilized to calibrate the relative position of the inductive lever probe at the two different work positions. To enhance the test accuracy of the OMM, a zero-position trigger-sampling method for the inductive lever probe was developed. It was verified to achieve a stable repeatability accuracy of 0.04 μm when using the OMM to realize a single-point sampling. Hemispherical shells were tested using the proposed OMM method. The concentricity test’s accuracy was verified to achieve accuracy better than 1 μm using a coordinate measuring machine and a standard sphere. The accuracy was 0.26 μm for testing the profiles of the hemispherical shell. The proposed OMM system was integrated with an ultra-precision machine tool. It is hoped that this method can help realize the integration function of machining-measurement-compensation.

The application of ultra-precision shaft parts is widely used, such as the spindle core of the air bearing spindle in ultra-precision machine tools. The precision of the spindle core is extremely high, and it is very difficult to obtain directly by traditional Computer Numerical Control (CNC) machine tools but is mostly obtained by manual grinding, whose machining efficiency is greatly limited. Based on the deterministic figuring theory, this paper focuses on the ultra-precision roundness, optimizing the filtering parameters of the measurement error data and studying the generation mechanism of the removal function morphology; the shape of the removal function is adjusted by combining the analysis of the figuring ability and positioning error. Finally, the optimized removal function is used on an experimental steel shaft, the average roundness convergence ratio is 72% higher than that of the original removal function, and the roundness reaches a 0.1 μm level. The result shows that a reasonable filtering of measured data and the removal function adjusted for the surface feature can improve the efficiency and precision of deterministic figuring on shaft parts.

The radial error is an important parameter to evaluate the performance of ultra-precision spindles. The three-point method has not yet been well applied in nanometer-scale measurement due to its disadvantages of harmonic suppression and the complicated error separation process. In order to verify that the three-point method can realize the nanometer-scale measurement of the radial error in the machining environment, an in situ measurement and evaluation system is established. Experiments are performed using the system, and a comparative experiment is conducted to verify the accuracy of the system. The average value and standard deviation of the measurement results are 23.096 nm and 0.556 nm, respectively. The in situ measurement result was in good agreement with the Donaldson reversal method using a commercially available spindle analyzer.

In this work, based on the diffraction principle of reflective blazed grating, the structure size of the convex spherical blazed grating unit is determined, the machining accuracy of the convex spherical blazed grating is formulated, the effects of tool nose radius and Poisson burr on the diffraction efficiency of the convex spherical blazed grating are analyzed, and the performances of cutting convex gratings with microcrystalline aluminum RSA6061 and RSA6061+ chemically plated NiP for two workpiece materials are compared. A convex spherical blazed grating with a radius of curvature R = 41.104 mm, substrate diameter 14 mm, grating density 53.97 line/mm, and blaze angle of roughly 3.8° is turned by a four-axis ultra-precision machining system by adjustment of the cutting tool, workpiece material, and cutting parameters, as well as modification of the layouts of the blazed grating on the convex sphere. The results of the testing of convex spherical blazed grating elements in both layouts show that the size error of the grating period is close for both layouts, the size error of grating height is smaller in the equal-along-arc layout, the blaze angle error in the equal-along-projection layout is only 0.74%, and the average roughness of the blazed surface is less than 5 nm to meet the processing quality requirements of the reflective convex spherical blazed grating. The greater the blaze angle accuracy of the blazed grating, the higher its diffraction efficiency, so the grating element with an equal-along-projection layout has a higher diffraction efficiency than the grating element with an equal-along-arc layout. RSA6061+ chemically plated NiP material is superior to RSA6061 material in Poisson burr height and blazed surface roughness, which is more suitable for Offner-type imaging spectrometers in the spectral range 0.95–2.5 μm (SWIR).