大尺寸、大数值孔径、宽波段的消色差平面透镜设计是成像技术的一个瓶颈性问题，也是近年来超构透镜研究领域的一个重要挑战，主要原因是透镜的各个参量之间存在内禀的制约关系。文中结合消色差透镜的群时延理论及透镜的相位分布，通过理论分析给出各参量之间的半定量制约关系。同时，分别通过拓扑优化和直接二值搜索的方法，设计了不同参量下的消色差超构透镜和多阶衍射透镜，发现在保持效率80%左右的前提下，透镜尺寸增加了一倍，数值孔径或波段宽度减少了一半，而透镜厚度则随尺寸成线性增长。该结果表明，这两类平面透镜具有相同的內禀参数依赖关系，即透镜尺寸与数值孔径和波段宽度呈现反相关、与透镜厚度呈现正相关的关系，这与理论预测基本一致。

The design of large scale, high numerical aperture, and broadband achromatic flat lens is a bottleneck of imaging technology and also a big challenge in metalens researches in recent years. The major reason is that there are some internal constraints between these parameters. In this paper, considering both the group dispersion theory and the phase distribution of the flat lens, the semi-quantitative relationship between these parameters was derived. Then, the achromatic flat lenses (including metalenses and multi-level diffractive lenses) with different parameters were designed by using directly binary search and topology optimization. It was found that under the condition of maintaining an efficiency of 80%, when doubling the size of flat lens (i.e., the diameter), the numerical or achromatic bandwidth was cut in half, and the thickness of lens increased linearly with lens scale. The results definitely show that these two types of flat lenses have the same internal constraint relations in parameters, that is, as that the lens size has negative correlation with the numerical aperture and achromatic bandwidth, while positive correlation with the thickness of the lenses. This result is in coincidence with the theoretical prediction.