Abbe theory of image formation can be expanded from two-dimensional to three-dimensional space. It has to consider an optical system that forms an image of a grating in an object space. It is possible to introduce various inclinations of this grating relatively the optical axis round the axis in the object plane that is parallel to its slits. In this case, the minimum resolvable period and the corresponded spatial cut off frequency of the optical system may be calculated as the functions of the angle of grating inclination, the numerical apertures and the wavelength using the idea of Abbe theory. In case of axial symmetry of the optical system, the function for calculation of the spatial cut off frequencies describes a surface in the three-dimensional space of spatial frequencies that covers the three-dimensional spatial bandwidth. The spatial harmonics with spatial frequencies inside this spatial bandwidth can pass through an optical system and they participate in formation of three-dimensional images. The other spatial harmonics cannot pass through it. This approach makes understanding and explanation of formation of three-dimensional images clearer, faster and logically completed.

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阿贝成像理论可以改进吗？

阿贝成像理论可以从二维空间扩展到三维空间。它必须考虑在物空间中形成光栅图像的光学系统。可以相对于围绕物平面中平行于其狭缝的轴的光轴引入该光栅的各种倾斜度。在这种情况下，可以利用阿贝理论的思想将光学系统的最小可分辨周期和相应的空间截止频率计算为光栅倾角、数值孔径和波长的函数。在光学系统轴对称的情况下，用于计算空间截止频率的函数描述覆盖三维空间带宽的空间频率的三维空间中的表面。在该空间带宽内具有空间频率的空间谐波可以通过光学系统，并且它们参与三维图像的形成。其他空间谐波不能通过它。这种方式使得对三维图像形成的理解和解释更加清晰、快速、逻辑完整。