Fig. 1. Schematic diagrams of position principle. (a) Schematic diagram of loading traditional solid screen; (b) schematic diagram of loading digital mask screen

Fig. 2. Schematic diagram of principle of adding a mask screen to a series of shadow grams collected along optical axis and searching for shadow grams located at curvature center of target ring

Fig. 3. Schematic diagram of ring belt screen mask segmentation

Fig. 4. Schematic diagram of loading ring belt screen mask and image processing

Fig. 5. Schematic diagram of testing

Fig. 6. A series of knife-edge shadow grams distributed along optical axis simulated by Zemax optical design software

Fig. 7. Schematic diagram of shadow grams processing

Fig. 8. Schematic diagrams of simulation results using Zemax and proposed method. (a) Schematic diagram of ring position simulated using Zemax; (b) surface shape calculation results simulated using proposed method when defect size is λ/2; (c) surface shape calculation results simulated using proposed method when ring defect size is λ/30

Fig. 9. Experimental system setup diagram

Fig. 10. Schematic diagram of a representative series of shadow grams collected along optical axis

Fig. 11. Comparison of testing results. (a) Interferometer testing result profile; (b) ring error relative position testing results of proposed method; (c) calculation results of curvature of ring error at different positions

Fig. 12. Schematic diagram of shadow gram processing in testing experiment

Fig. 13. Comparison of testing results. (a) Surface shape testing results of interferometer standard method; (b) surface shape testing results of proposed method

Fig. 14. Comparison of profile testing results. (a) Profile testing results of interferometer standard method; (b) profile testing results of proposed method

Fig. 15. Calculation results of surface wavefront errors when collection interval between shadow grams is 0.3 mm, and ring belt segmentation numbers are different. Ring belt segmentation numbers are (a) 50, (b) 100, and (c) 200, respectively

Fig. 16. Calculation results of surface wavefront errors corresponding to different collection intervals when number of shadow grams ring belt segmentation is 100. Collection intervals are (a) 0.3 mm, (b) 0.6 mm, and (c) 0.9 mm, respectively

Fig. 17. Schematic diagram of denoising process. (a) Knife-edge shadow gram before denoising; (b) knife-edge shadow gram after denoising; (c) schematic diagram of removed noise points