为设计单个非球面扩束(缩束)透镜，由光线折射定律矢量形式和对非球面折射特性的理论分析，提出了一种设计单个非球面扩束(缩束)透镜的新方法—全面学习策略的粒子群算法，并用此方法设计出了线度小于170 mm缩束14.16倍的单个非球面缩束透镜，用光线追迹方法模拟了缩束或扩束过程。模拟结果表明，单个非球面透镜可以起到缩束或者扩束作用，全面学习策略的粒子群算法可用于非球面缩束透镜的设计。单个非球面透镜作为扩束镜使扩束系统结构大大简化，大大提高了出射光斑的均匀性。

In order to obtain a single aspheric lens for beam shrinkage, based on the law of refraction in vector form and theoretical analyses of the refraction characteristics of an aspheric surface, a new method was presented for designing a single aspheric lens used as a beam expander or a beam compressor —the comprehensive learning strategy particle swarm optimizer. A single aspheric beam-expanding lens was designed whose length is less than 170 mm and shrinkage rate is 14.16. The process of beam-shrinking or beam-expanding was simulated by using the ray tracing method. Simulation results show that a single aspheric lens can play the role of compressing beam or expanding beam, the comprehensive learning particle swarm algorithm can be used to design an aspheric lens used as compressing beam or expanding beam. A single aspheric beam-expanding（beam-compressing）lens can greatly simplify the beam expanding（beam compressing）system, and greatly improve the uniformity of output light from the expanding lens.