Fig. 1. Freeform surface off-axis three-mirror optical system designed under guidance of aberration theory^[19]

Fig. 2. Freeform prism optical system designed by differential equation method^[29]

Fig. 3. 3D view of SMS design result of three freeform surfaces^[39]

Fig. 4. Flow diagram of CI-3D method^[41]

Fig. 5. Freeform optical system with three-mirror for four reflections^[54]

Fig. 6. Generalized design framework based on DNN^[61]

Fig. 7. Block diagram of fast automatic design method through system construction and correction^[72]

Fig. 8. Infrared imaging system^[48]. (a) Design layout; (b) system prototype; (c) image captured outdoors

Fig. 9. Examples of freeform imaging system. (a) Freeform off-axis three-mirror imaging system with ultra-wide field of view in meridional direction^[12]; (b) freeform off-axis three-mirror imaging system with ultra-wide field of view in sagittal direction^[82]; (c) freeform off-axis five-mirror imaging system^[51]; (d) design process of small volume freeform imaging system^[83]

Fig. 10. Performance overview of 15 different systems^[84]

Fig. 11. Design examples of freeform imaging spectrometers. (a) (b) Two freeform imaging spectrometers with different structures^[46]; (c) imaging spectrometer with single component of freeform concave grating^[88]; (d) double-pass reflective triplet spectrometer^[89]

Fig. 12. Freeform ultra-short throw catadioptric projection objective^[92]

Fig. 13. Freeform extreme ultraviolet lithography projection objective^[98]

Fig. 14. Freeform surface off-axis optical system. (a) 3D view of freeform infrared imaging system^[100]; (b) freeform off-axis three-mirror system in which primary mirror and third mirror share same surface expression^[13]; (c) spatial freeform off-axis three-mirror optical system without any symmetry^[102]; (d) off-axis reflection freeform surface optical system with spherical package^[72]

Fig. 15. Freeform surface visual imaging system. (a) Layout of OST-HMD system^[108]; (b) optical system layout of varifocal-plane OST-HMD using freeform Alvarez lenses^[109]; (c) optical layout of AR 3D HUD^[112]; (d) reflective freeform electronic viewfinder^[115]

Fig. 16. Imaging optical systems with local optical properties. (a) Oblique camera with uniform GR, designed by controlling FFL^[116]; (b) optical system equivalent to a splicing camera composed of multiple lenses^[117]; (c) imaging system with resolution distribution similar to that of human eye^[118]

Fig. 17. Freeform imaging optical system with lateral image translation function^[119]. (a) System two-dimensional structure and image translation function; (b) law of image change when freeform lens rotates at different angles around optical axis

Fig. 18. Three freeform optical systems with multiple sets of performance integrations^[120]. (a) Integrated freeform optical system with long working distance; (b) integrated freeform optical system with double fields of view; (c) integrated freeform optical system with double focal lengths

Fig. 19. Freeform infrared refractive thermal imager^[123]