物理与工程

光学成像作为现代光学研究的核心领域，在科学探索与工程技术中具有重要应用价值。菲涅耳衍射表明，光学系统对点光源成像时，受限于光的波动性和透镜的有限孔径，会因衍射效应形成艾里斑，其尺寸决定了瑞利衍射极限。当前本科教学普遍采用菲涅耳衍射积分分析成像分辨率，本文基于傅里叶光学理论体系，通过严格理论推导点光源角谱传输揭示了传统透镜成像的衍射受限本质。通过傅里叶角谱数值求解得到圆孔衍射图样强度的第一零点，并与瑞利判据计算结果进行了对比。进一步结合负折射透镜等前沿进展，阐明了负折射率材料成像突破传统衍射极限的物理机制。本研究不仅为光学成像理论提供了新的教学视角，其分析方法对超分辨成像技术研究也具有重要参考价值，可有效衔接本科基础教学与研究生创新研究。

Optical imaging, as a cornerstone of modern optical research, bears significant application value in both scientific exploration and engineering technologies. Fresnel diffraction theory reveals that when imaging a point source through an optical system, the interplay between light's wave nature and finite lens aperture induces diffraction effects, generating an Airy disk whose spatial extent defines the Rayleigh diffraction limit. While current undergraduate curricula predominantly utilize Fresnel diffraction integrals for imaging resolution analysis, this study adopts a Fourier optics framework to rigorously derive the angular spectrum propagation of point-source radiation, thereby fundamentally unveiling the diffraction-limited nature of conventional lens systems. The first zero point of the intensity distribution in the circular aperture diffraction pattern is obtained through numerical solution based on the Fourier angular spectrum method, and the result is compared with that calculated using the Rayleigh criterion. By further integrating cutting-edge developments in negative-refraction optics, we systematically elucidate the physical principles enabling negative-index metamaterials to overcome classical diffraction constraints. This work not only establishes a novel pedagogical paradigm for optical imaging theory but also provides a critical analytical framework for super-resolution imaging research, serving as a conceptual bridge between undergraduate optics education and advanced graduate studies in photonic innovation.