打印方法制作菲涅耳波带片及其光学特性研究

Fabrication of Fresnel Zone Plates by a Printing Method and a Study of Their Optical Properties

摘要: 菲涅耳波带片是衍射光学元件的源头，依靠对入射波前的衍射调制实现会聚与成像，具有平面、轻量、可宽谱工作等优势。针对传统电子束直写、光刻等工艺设备昂贵、流程复杂的问题，本研究提出以激光菲林高精度打印制作振幅型菲涅耳波带片的低成本方法。基于半波带法与菲涅耳–基尔霍夫衍射积分，推导了环带半径公式与沿轴光强分布，阐明了波带片以衍射方式聚焦、具有主焦点与一系列次焦点的“一片多焦”本质。实验以氦氖激光器(632.8 nm)为光源，经扩束、衰减后照射菲林波带片，用CCD相机配合ImageJ采集并分析焦斑光强，对传统圆形与正方形波带片的多种规格(焦距40~60 cm、波带数20~160)进行测量，清晰观察到主焦点与次焦点的会聚焦斑，验证了焦点位置与理论值的一致性，并系统研究了波带数、焦距、几何构型对会聚能力的影响，同时验证了其成像能力。结果表明该方法低成本、易实现，焦距测量的相对不确定度约为1.85%，主导误差来自焦深判断，为低成本衍射光学元件的设计与应用提供了可行方案。

Abstract: The Fresnel zone plate (FZP), as the origin of diffractive optical elements, achieves focusing and imaging by diffractive modulation of the incident wavefront, offering the advantages of being planar, lightweight and broadband. To address the expensive equipment and complex procedures of traditional electron-beam direct writing and lithography, this study proposes a low-cost method of fabricating amplitude-type FZPs by high-resolution laser film printing. Based on the half-wave-zone method and the Fresnel-Kirchhoff diffraction integral, the zone-radius formula and the on-axis intensity distribution are derived, clarifying the “one plate, multiple foci” nature of the FZP with a principal focus and a series of subsidiary foci. In the experiment, a He-Ne laser (632.8 nm) was used as the light source; after beam expansion and attenuation it illuminated the film zone plate, and a CCD camera together with ImageJ was used to acquire and analyze the focal-spot intensity. Multiple specifications of circular and square zone plates (focal length 40~60 cm, zone number 20~160) were measured, and the converging spots of the principal and subsidiary foci were clearly observed, verifying the agreement between the focal positions and theory. The effects of zone number, focal length and geometry on focusing ability were studied systematically, and the imaging ability was verified. The results show that the method is low-cost and easy to implement, with a relative uncertainty of focal-length measurement of about 1.85%, dominated by depth-of-focus judgment, providing a feasible scheme for the design and application of low-cost diffractive optical elements.