Fig. 1. Schematic diagram of freeform off-axis reflection system

Fig. 2. Schematic diagram of the surface with different initial points and the coordinate difference. (a) Initial point is P₁₁; (b) initial point is P'₁₁; (c) difference of corresponding coordinate between two surfaces

Fig. 3. Schematic diagram of surface data points. (a) Seed curve is horizontal; (b) seed curve is vertical; (c) two sets of data points are put together

Fig. 4. Ideal freeform off-axis one-mirror system

Fig. 5. Data points of freeform surface and ideal freeform surface designed by SCE algorithm and OSCE algorithm. (a) Two sets of data points of freeform surface designed by SCE algorithm and ideal freeform surface are put together; (b) difference of the corresponding data points of surface designed by SCE algorithm and ideal freeform surface; (c) two sets of data points of freeform surface designed by OSCE algorithm and ideal freeform surface are put together; (d) difference of the corresponding data points of surface designed by OSCE algorithm and ideal freeform surface

Fig. 6. RMS error of freeform surface designed by SCE and OSCE algorithm respectively and ideal surface under 8 sets of samples

Fig. 7. Off-axis three-mirror afocal system. (a) Initial layout diagram; (b) actual light path diagram

Fig. 8. Grayscale image of wavefront error of off-axis three-mirror afocal system. (a) SCE algorithm; (b) OSCE algorithm

Fig. 9. Grayscale image of the wavefront at the zero field of view after the optimization of the off-axis three-mirror afocal system

Fig. 10. Off-axis three-mirror afocal system. (a) Full field of view light path diagram; (b) adding a paraxial lens at the exit pupil

Fig. 11. Data points obtained by OSCE algorithm and the surface after optimization. (a) Data points obtained by the OSCE algorithm and of the surface after optimization are put together; (b) difference between two sets of data points

Fig. 12. System with the field of view before and after adding the paraxial lens. (a) RMS wavefront error of the system with the field of view before adding the paraxial lens; (b) MTF at full field of view of the system after adding the paraxial lens

Fig. 13. Optical path diagram of off-axis three-mirror beam expanding afocal system

Fig. 14. Off-axis four-mirror afocal system. (a) Initial layout diagram; (b) actual light path diagram

Fig. 15. Grayscale image of wavefront error of off-axis four-mirror afocal system. (a) SCE algorithm; (b) OSCE algorithm

Fig. 16. Tolerance analysis of three freeform surfaces under 20 sets of samples. (a) RMS distribution of surface 1 with H of 0.17 μm; (b) RMS distribution of surface 2 with H of 0.08 μm; (c) RMS distribution of surface 3 with H of 0.17 μm