ELECTROMAGNETIC DIFFRACTION IN OPTICAL SYSTEMS .2. STRUCTURE OF THE IMAGE FIELD IN AN APLANATIC SYSTEM
ELECTROMAGNETIC DIFFRACTION IN OPTICAL SYSTEMS .2. STRUCTURE OF THE IMAGE FIELD IN AN APLANATIC SYSTEM
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DOI：
10.1098/rspa.1959.0200
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发表时间：
1959-01-01
影响因子：
--
通讯作者：
WOLF, E
中科院分区：
文献类型：
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作者：
RICHARDS, B;WOLF, E
对成像点源的非行星系统焦点附近的电磁场结构进行了研究。首先，研究了线偏振入射场的情况，推导了像空间中电矢量和磁矢量的表达式。然后讨论了这些公式的一些一般结果。特别注意了光场相对于焦平面的对称性，并研究了像区的偏振态。详细研究了时间平均电磁能量密度和能量流(坡印亭矢量)在焦平面内的分布，并根据电子计算机的大量计算数据，以图表和表格的形式给出了结果。文中还研究了非偏振场的情况。该解并不局限于小口径系统，计算结果实际上涵盖了像面角半孔径a在整个0≤α≤90°范围内的选取值。对极限情况α→0进行了详细的研究，结果表明，场完全由一个一般复的标量函数来刻画，这与经典的艾里、洛梅尔和斯特鲁夫的标量理论完全相同。这些结果直接关系到成像系统的分辨率；它们也有助于我们理解标量衍射理论的意义，标量衍射理论通常被用来分析小口径系统中的图像，而没有适当的理由。
An investigation is made of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source. First the case of a linearly polarized incident field is examined and expressions are derived for the electric and magnetic vectors in the image space. Some general consequences of the formulae are then discussed. In particular the symmetry properties of the field with respect to the focal plane are noted and the state of polarization of the image region is investigated. The distribution of the time-averaged electric and magnetic energy densities and of the energy flow (Poynting vector) in the focal plane is studied in detail, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor. The case of an unpolarized field is also investigated. The solution is riot restricted to systems of low aperture, and the computational results cover, in fact, selected values of the angular semi-aperture a on the image side, in the whole range 0 ≤ α ≤ 90°. The limiting case α → 0 is examined in detail and it is shown that the field is then completely characterized by a single, generally complex, scalar function, which turns out to be identical with that of the classical scalar theory of Airy, Lommel and Struve. The results have an immediate bearing on the resolving power of image forming systems; they also help our understanding of the significance of the scalar diffraction theory, which is customarily employed, without a proper justification, in the analysis of images in lowaperture systems.