基于广义惠更斯菲涅耳衍射积分和相干偏振统一理论，研究了随机电磁光束经振幅调制透镜的聚焦特性，推导出了电磁高斯谢尔模型(EGSM)在经振幅调制透镜聚焦的交叉谱密度矩阵解析式，通过数值计算分析了EGSM光束经振幅调制透镜聚焦的光强分布。研究结果表明振幅调制半径、调制位置和透射率以及空间位置和相干长度都会对EGSM光束的聚焦光强分布产生影响，当振幅调制半径在某一定值的时候，聚焦光斑存在被极度压缩的现象，此时聚焦中心光斑能量最大。通过对振幅调制半径、调制位置、透射率以及空间位置和相干长度参数的改变，可以获得不同形状的光强分布。

Based on the generalized Huygens-Fresnel diffraction integral and the unified theory of coherence and polarization, properties of stochastic electromagnetic beams focused by a modulated lens are analyzed, the analytical expressions for the cross-spectral density matrix of a class of electromagnetic Gaussian Schell-model (EGSM) beams focused by an amplitude modulated lens are derived, and intensity distribution of EGSM beams focused by an amplitude modulated lens through numerical calculations is also analyzed. It shows that focused intensity distribution of EGSM beams is influenced by radius, location, transmittance of amplitude modulation, spatial position and the coherence length. When the radius of amplitude modulation takes a certain value, it appeares that focusing spot is extremely compressed and focusing central spot has a large energy at this time. Different shapes of intensity distribution can be gotten by changing the parameters of radius, location, transmittance of amplitude modulations and spatial position, and the coherence length.