Research on off-axis reflective freeform surface beam shaping using annular extension method

Laser beam shaping is widely applied in laser processing, illumination and other fields. Aiming at problems existing in previous methods, such as the difficulty in solving surface shapes, poor machinability and the difficulty in tolerance analysis, we present an entire design method for off-axis reflective freeform surface beam shaping systems. The freeform surfaces in the form of annular expansion are construct and optimized. Then, a surface tilt removal algorithm is proposed to reduce the variation amplitude of the mirror's sag, improving the machinability of the mirrors. Moreover, we established a real-time communication model between optical design software and numerical processing software, enabling the automatic statistical analysis of tolerance analysis results. The design example show that the method proposed in this paper can effectively shape Gaussian beams into circular flat-top beams. When the beam propagates from 100 mm to 500 mm, the uniformity variation range is 94.2 %–90.1 %. The surface tilt removal algorithm reduces the variation amplitude of the mirror's sag by more than 87 %. The tolerance results of irradiance uniformity at different propagation distances satisfy the demands of optical manufacture and alignment. This design method can provide valuable insight for the design, tolerance analysis and processing of freeform surface beam shaping systems.