Elliptical elements are essential optical surfaces for modifying optical systems. For polishing the whole elliptical surface using doughnut-shaped MCF polishing tool with variable tilt angle, an experimental investigation was conducted in this work. Firstly, a flat workpiece was polished to determine the polishing feasibility. It was found that the middle portion of the polishing tool had optimal ability to remove materials, and the surface roughness Sa at the material removal peak was changed from 134 nm to 17.5 nm within 50 min of polishing. A smoother surface could be obtained using MCF2 slurry and MCF3 slurry, but the use of MCF1 slurry resulted in a rough surface. Then, the effects of working gap h, revolution speed of MCF polishing tool and polishing time on the polishing results were tested to study the polishing characteristics. Sa 9.6 nm and glossiness 278 Gu were obtained, and form error improved from 2.3 μm to 1.3 μm. Finally, the MCF polishing tool was dried to observe the microstructure of the MCF polishing tool after polishing. Abrasive particles were distributed evenly after polishing. It was seen that the abrasive particles were grabbed by the ferric clusters, and the α-celluloses were interleaved between the clusters.

Single-crystal sapphire (α-Al2O3) is an important material and widely used in many advanced fields. The semi-fixed abrasive grain processing method based on solid-phase reaction theory is a prominent processing method for achieving ultra-precision damage-free surfaces. In order to develop the proposed method for polishing sapphire, the basic characteristics of the semi-fixed abrasive grains polishing tool for polishing sapphire were determined. Weight analysis was used to study the influence rules of parameters on surface roughness and material removal rates using an orthogonal experiment. Then, the optimized polishing tool was obtained through a mixture of abrasive particle sizes to reduce the difficulty in molding the polishing tool. Finally, polishing experiments using different polishing tools were carried out to investigate polishing performance by considering the surface roughness, material removal rate and the surface morphology during polishing. The results showed that (1) external load affects the surface roughness and material removal rate the most, followed by abrasive particle size, sand bond ratio, revolution speed of the workpiece and he polishing tool; (2) the difficulty in manufacturing the polishing tool could be reduced by mixing larger abrasive particles with small abrasive particles; (3) the polishing tool with 200 nm and 1 μm particle sizes performed best in the first 210 min polishing.