Fig. 1. Diagram of freeform surface construction in one direction together with its normal error

Fig. 2. Schematic of freeform surface construction method by iteration in two orthogonal directions

Fig. 3. Flow diagram of the freeform surface construction method by iteration in two orthogonal directions together with surface normal correction

Fig. 4. Laser beam shaping optical system by reflective freeform surface. (a) Source grids; (b) Target plane grids; (c) Freeform surface sampling points and its three-dimensional surface; (d) Schematic of structure of beam shaping optical system

Fig. 5. Normalized irradiance distribution in the target surface. (a) Irradiance distribution of input laser beam and the target plane along the line x = 0 mm and y = 0 mm before beam shaping; (b) Irradiance distribution of target plane along the line x = 0 mm and y = 0 mm after beam shaping

Fig. 6. Normalized irradiance distribution of rectangular pattern. (a) Irradiance distribution in the target plane after beam shaping; (b) Irradiance distribution of target plane along the line x = 0 mm and y = 0 mm after beam shaping

Fig. 7. Normalized irradiance distribution of target plane at different distances

Fig. 8. Variation of irradiance uniformity and RMS of global and local region in the target plane with different distances. (a) Irradiance uniformity; (b) The log (RMS) of irradiance

Fig. 9. Normal vector angle of adjacent data sampling points

Fig. 10. Comparison of variation of normal angle of adjacent data sampling points

Fig. 11. Comparison of freeform surface fitting errors

Fig. 12. Influence of irradiance uniformity on different freeform surface machining errors