单球面透镜产生线光束的理论分析与计算

THEORETICAL ANALYSIS AND CALCULATION OF LINE BEAM PRODUCED BY A SPHERICAL LENS

基于几何光学定律和菲涅耳公式,建立了单块球面透镜产生线光束的数学模型,给出了光束出射角、像距、像散、光强分布的计算公式,通过计算机仿真计算,得出了一些有益的结论。指出了大入射角产生的大像散是单球面透镜产生线光束的原因,子午面内光束各点的反射和透射系数不等,是它使入射的细高斯光束趋于均匀化的原因。理论与实验结果吻合。

Based on the laws of geometrical optics and Fresnel formulas,the mathematical model of line beam generated by plano-spherical lens is given,the formulas of the divergent angles, imaging distances,astigmatisms as well as the distributions of light intensity of exit light beams are derived,some useful conclusions are given according to the analysis of computer simulations and numerical calculations.It is also pointed out that it is the large astigmatism due to large incident angles that contributes to the line beam generation by a single spherical lens,and the different reflective and transmitted intensity coefficients in meridian section of incident beam homogenize the intensity of incident Gaussian beam.The theory is well coinci- dent with our experimental results.