衍射追迹法模拟计算菲涅耳波带片衍射特性
Simulation of Diffraction Characteristics of Fresnel Zone Plate by Diffraction Tracing Method

大多数光学教材，对于圆孔和波带片的菲涅耳衍射特性都是基于菲涅耳半波带法，仅分析轴上点的明暗情况。本文利用标量衍射理论，相邻两面的光线传播都是基于菲涅耳衍射模型，编制程序计算了圆孔的菲涅耳衍射特性，更进一步计算了菲涅耳波带片衍射特性。计算的菲涅耳衍射图直观明了地显示观察平面近轴区的完整光强分布，不同观察平面的轴上点的明暗由露出的半波带个数决定，与半波带法分析轴上点明暗一致。菲涅耳波带片在焦距f’处和f’/3、f’/5等次焦点处都会聚成一个亮点，能量集中在轴上点，有明显的聚光效应，如同透镜成像的焦点。而在f’/2、f’/4等观察面轴上点是暗点，能量分散到其他衍射级。不同观察平面上完整的光强分布图有利于深入了解菲涅耳波带片的衍射特点，为波带片的设计与应用提供更好的理论依据。
In most optical textbooks, the Fresnel diffraction characteristics of circular holes and zone plates are based on the Fresnel half zone method, which only analyzes the light and shade of points on the axis. In this paper, based on the scalar diffraction theory, the light propagation on the adjacent two sides is based on the Fresnel diffraction model. The program is compiled to calculate the Fresnel diffraction characteristics of the circular hole and the Fresnel zone plate. The calculated Fresnel diffraction pattern can intuitively and clearly show the complete intensity distribution in the paraxial region of the observation plane. The brightness of the points on the axis of different observation planes is determined by the number of exposed half wave bands, which is consistent with the brightness of the points on the axis analyzed by the half wave band method. The Fresnel zone plate converges into a bright spot at the focal length f’ and the sub focal points such as f’/3 and f’/5, and the energy is concentrated at the point on the axis, just like the focus of lens imaging, while the point on the axis of the observation plane such as f’/2 and f’/4 is a dark point, and the energy is dispersed to other diffraction orders. The complete intensity distribution on different observation planes is conducive to deeply understanding the diffraction characteristics of Fresnel zone plate and provides a better theoretical basis for the design and application of zone plate.