摘要
本文主要研究了一种仿真分析针孔衍射波前相位及振幅分布的方法。基于该方法建立了仿真针孔衍射数学模型,编写了MATLAB仿真程序,对针孔衍射波前误差及针孔衍射的能量分布进行相应的仿真分析。主要的研究内容为：
论述了对针孔衍射波前误差的分析对于点衍射干涉检测系统的重要性。研究了针孔衍射波前误差分析方法的现状,特别是矢量衍射理论分析方法的现状。
详述了矢量衍射理论中的时域有限差分方法(Finite Difference Time Domain Method, FDTD)基于在空间和时间上的离散对麦克斯韦方程组进行数值差分求解的原理。详细分析了时域有限差分方法的算法稳定性条件及数值色散现象,并详述了吸收边界对于FDTD仿真的重要性,对吸收效果较好的完全匹配层(Perfectly Matched Layer, PML)吸收边界进行了介绍。为精确使用FDTD方法仿真分析针孔衍射波前奠定了理论基础。
综合考虑实际存在影响针孔衍射波前误差的因素及计算机的仿真效率,建立了三套仿真模型,分别为平面波入射模型、汇聚波入射模型及三维仿真模型,为对针孔衍射波前的仿真提供充分的模型。并从惠更斯原理与自由空间的格林函数出发,分别对二维、三维两种情况下的近场远推公式进行了详细的推导,得到了适用于远推大数值孔径波前的近场远推方法。
编写了MATLAB仿真程序对针孔的直径尺寸、针孔所镀膜层的厚度、入射光携带的波像差量与针孔衍射波前误差之间的关系进行了详细的仿真分析。仿真结果表明,针孔对于入射光有着很好的整形滤波作用,而且针孔的直径尺寸越小其对应的衍射波前误差越小。并对针孔衍射的能量透过率及衍射波前的强度均匀性进行了分析。仿真实验得到了详细的数据结果,可为点衍射干涉检测系统针孔的选择提供精确的数据依据。
This dissertation mainly research on a method for analyzing point-diffraction wavefront error. Based on the method, has writed a MATLAB simulation program which can be used to analyze the point diffraction wavefront error and the energy distribution. The content of this dissertation include:
After review of importance of point-diffraction wavefront error analysis, there is also a review over the current point-diffraction wavefront error analysis methods, especailly vector diffraction thoery.
The principal of Finite Difference Time Domain (FDTD) method, which can numerical solve Maxwell equation based on the discrete space and time, is detailed. Algorithm stability condition and numerical dispersion phenomenon of FDTD method is analyzed in detail. Then the importance of absorbing boundary for the FDTD simulation and Perfectly Matched Layer (PML) absorbing boundary was introduced.
Considering the impact factors of point diffraction wavefront error and efficiency of computer simulation, has established three sets of simulation models. They are the plane-wave incident model, the convergence-wave incident model and three dimensional model, respectively. Based on the Huygens principle and Green function, a new near-field to far-field method is derived, which can use for the wavefront with large numerical aperture in two-dimension or three-dimension.
The simulation of relationship between the point-diffraction error and diameter of the pinhole, the thickness of pinhole, the aberration amount of incident light, has been carried out by the MATLAB simulation program. Simulation results show that the pinhole has a very good role in shaping wavefront, and diffraction wavefront error is smaller, when the pinhole has the smaller diameter. And transmission of energy and the intensity uniformity of diffraction wavefront have been analyzed. The analysis of point-diffraction wavefront error and engry distribution with FDTD method provides theoretical basis for choosing dimension of pinhole in the experiments and testing with point-diffraction interferometer.
引文
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