Objective  In many laser industrial applications, laser beam shaping is an important process to redistribute the laser energy, which is highly essential to obtain uniform or prescribed spatial energy distribution with high efficiency. At present, there are different methods for laser beam shaping, including the grouped aspheric lenses, microlens arrays, diffractive optical elements, liquid crystal spatial light modulator and freeform optical technology. Compared with other laser beam shaping methods, the method using freeform surfaces is beneficial to make the shaping optical system more simplified and more compact. In the current freeform surface construction method for laser beam shaping, the seed curve extension algorithm in one direction has the non-negligible normal vector deviation during the generation of surface sampling points. Therefore, in this paper, a method is proposed to reduce the normal errors to improve the construction precision of freeform reflector for obtaining the highly uniform spatial energy distribution in the target plane.

  Methods  There are mainly three steps for constructing the freeform surface (Fig.2-3). At first, the incident beam and the target plane are divided in grids according to equal energy and equal area. The main purpose of this step is to obtain the one-to-one energy mapping between the light source and the target plane, which is based on the conservation of energy and Snell's law. Then, the initial constraint conditions are set according to the requirements, which are used to calculate the sampling data points of horizontal and vertical curves on the freeform surface. Finally, according to the results of previous two steps, the sample data points on the unknown freeform surface can be calculated by iteration together with normal error correction. The averaging approach of coordinates of adjacent sampling points in the orthogonal direction is applied to relieve the normal deviations, which is very useful for reducing the normal errors to obtain smooth freeform surface relatively.

  Results and Discussions   The proposed freeform surface construction method can effectively regulate a collimated Gaussian laser beam into the square or rectangular intensity distribution with high uniformity. On the target plane for a square pattern (Fig.5), the normalized irradiance uniformity is about 88.70% in the global region. Along the lines x=0 mm and y=0 mm on the target plane, the irradiance uniformity is about U_x=88.18% and U_y=86.67% respectively. Besides, the irradiance uniformity of local region (70 mm×70 mm) is about 92%. In the similar way, for a rectangular pattern on the target plane (Fig.6), the corresponding normalized irradiance uniformity is as high as about 94.30% as well as U_x=92.96% and U_y=94.07% along the lines x=0 mm and y=0 mm, which realize the laser beam shaping with high performance. On the other hand, the irradiance uniformity can also reach about 90% when the target plane has different distances for the square pattern (Fig.7-8). This indicates that the proposed method keeps robust elegantly. Further, in the aspect of surface smoothness, fitting precision and irradiance uniformity stability over a certain manufacturing error range (Fig.10-12), the freeform surface constructed by the proposed method shows great performance compared with that constructed by the traditional design method.

  Conclusions  The freeform surface design by iteration in two orthogonal directions with surface normal correction is proposed, which can effectively regulate a collimated Gaussian laser beam into the square or rectangular intensity distribution with high uniformity. The feature sampling points of the freeform reflector are calculated iteratively in two orthogonal directions based on energy conservation and Snell’s law. Meanwhile, the averaging approach of coordinates of adjacent sampling points in the orthogonal direction can relieve the normal deviations effectively. Therefore, it is very helpful for constructing the freeform surface more precisely. The capabilities of the presented method are demonstrated and verified by examples. Moreover, for the target plane with different distances within a certain range, the energy uniformity maintains 90% well. At the same time, the freeform surface designed by the proposed method not only has high fitting accuracy, but also has a more stable irradiance uniformity on target plane within the allowable machining error range. It means that the proposed freeform surface construction method keeps robust elegantly, which is very necessary and critical for laser beam shaping.