Fig. 1. Schematic of principle and method^[22]. (a) Schematic of knife-edge instrument; (b) schematic of front and rear cutting method of knife-edge along optical axis

Fig. 2. Corresponding relationship between the ring-shaped polishing belts on the mirror to be measured and the optical axis

Fig. 3. Simulation results. (a) Knife-edge shadow grams of convex sphere before and after focal point simulated by Zemax software;(b) extraction results of the annulus

Fig. 4. Experimental optical path

Fig. 5. Experimental results using a plano-convex lens. (a) Knife-edge shadow grams collected along the optical axis; (b) images processed by gray histogram equalization algorithm for collected knife-edge shadow grams; (c) results of the ring-shaped polishing belts after gray processing of collected knife-edge shadow grams

Fig. 6. Experimental results using a concave spherical mirror. (a) Knife-edge shadow grams collected along the optical axis; (b) images processed by gray histogram equalization algorithm for the collected knife-edge shadow grams; (c) results of gray processing of the collected knife-edge shadow grams

Fig. 7. Comparison of ring-shaped polishing belt measured by proposed method and the interferometer under different ring radii. (a) 0.95r; (b) 0.80r; (c) 0.50r; (d) 0.40r

Fig. 8. A series of knife-edge shadow grams collected along the optical axis

Fig. 9. Calculation result of gradient difference sum of knife-edge shadow grams