Zoom lens with high zoom ratio design based on Gaussian bracket and particle swarm optimization

In this paper, we use Gaussian brackets and a particle swarm optimization (PSO) algorithm to design a 20 × four-group zoom lens with a focus tunable lens and two moving groups. This method uses Gaussian brackets to derive the paraxial design equations of the zoom lens and determine the lens parameters. In the optimization stage, we define an objective function as a performance indicator to optimize its first-order design and implement the PSO algorithm in MATLAB to find its global optimal first-order design. The optimized 20 × zoom lens has a focal length of 4.5–90 mm and a total length of 145 mm. This method solves the difficulty of solving the initial structure of the zoom. Compared with traditional trial and error, the calculation speed is faster, the accuracy is higher, and it does not rely on the initial value. The results show that this method is suitable for the first-order design of complex optical systems.