提出了快速傅里叶变换(FFT)计算短波长激光通过短焦距聚焦系统的传输特性的方法。快速傅里叶变换方法计算聚焦光束光场分布时，如果遇到短波长激光通过短焦距聚焦系统，会出现相位随机跃变、波函数失真和采样率不够的问题。采用坐标扩展变换，突破了快速傅里叶变换计算过程中输入屏和衍射屏空间尺度必须相同、抽样格点必须等间隔的限制，使上述问题得到解决，可以得到更加详细的聚焦光束光场分布。同时，采用分两步计算的思想，避免了计算焦平面附近光场时，坐标空间的几何扩展与光束衍射极限的矛盾。

A method is proposed to calculate the focusing characteristics of short-wavelength laser beam through short-focus system. The problem of random phase jumps, wave function distortion and insufficient sampling rate will be met when the optical field distribution of a focused laser beam is calculated by fast Fourier transform method and short-wavelength laser beam passes through the short-focus system. By using coordinate transformation in the fast Fourier transform calculation, the limitation of the same input screen special scale, the same diffraction screen sptial scale and the same sampling grid spacing is broken. The optical-field distribution of a focused laser beam can be calculated in detail. At the same time, two-step calculation is used to avoid the conflict between the coordinate space of the geometric expansion and the diffraction limit when the light field near the focus is calculated.