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首页> 外文期刊>Archive for History of Exact Sciences >Kirchhoff's theory for optical diffraction, its predecessor and subsequent development: the resilience of an inconsistent theory
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Kirchhoff's theory for optical diffraction, its predecessor and subsequent development: the resilience of an inconsistent theory

机译：基尔霍夫光学衍射理论，它的前身和随后的发展：不一致理论的弹性

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Kirchhoff's 1882 theory of optical diffraction forms the centerpiece in the long-term development of wave optics, one that commenced in the 1820s when Fresnel produced an empirically successful theory based on a reinterpretation of Huygens' principle, but without working from a wave equation. Then, in 1856, Stokes demonstrated that the principle was derivable from such an equation albeit without consideration of boundary conditions. Kirchhoff's work a quarter century later marked a crucial, and widely influential, point for he produced Fresnel's results by means of Green's theorem and function under specific boundary conditions. In the late 1880s, Poincar, uncovered an inconsistency between Kirchhoff's conditions and his solution, one that seemed to imply that waves should not exist at all. Researchers nevertheless continued to use Kirchhoff's theory-even though Rayleigh, and much later Sommerfeld, developed a different and mathematically consistent formulation that, however, did not match experimental data better than Kirchhoff's theory. After all, Kirchhoff's formula worked quite well in a specific approximation regime. Finally, in 1964, Marchand and Wolf employed the transformation of Kirchhoff's surface integral that had been developed by Maggi and Rubinowicz for other purposes. The result yielded a consistent boundary condition that, while introducing a species of discontinuity, nevertheless rescued the essential structure of Kirchhoff's original formulation from Poincar,'s paradox.
机译：基尔霍夫（Kirchhoff）于1882年提出的光衍射理论是波光学长期发展的核心要素，这一理论始于1820年代，当时菲涅尔基于对惠更斯原理的重新解释提出了一种在经验上成功的理论，但没有根据波方程进行研究。然后，在1856年，斯托克斯（Stokes）证明了该原理可从这样的方程式推导，尽管不考虑边界条件。四分之一世纪之后，基尔霍夫的工作成为了关键的，广泛影响的一点，因为他根据格林定理和函数在特定边界条件下得出菲涅耳的结果。在1880年代后期，庞加莱发现了基尔霍夫的情况和他的解决方案之间的矛盾，这似乎暗示着根本不应该存在波。尽管如此，研究人员仍继续使用基尔霍夫的理论，尽管瑞利和后来的索默菲尔德开发了一种不同的，数学上一致的表述，但是与基尔霍夫的理论没有更好的匹配实验数据。毕竟，基尔霍夫的公式在特定的近似方案中效果很好。最终，在1964年，Marchand和Wolf利用了Maggi和Rubinowicz为其他目的开发的Kirchhoff表面积分的变换。结果产生了一致的边界条件，尽管引入了一种间断性，但仍从庞加（Poincar）的悖论中拯救了基希霍夫（Kirchhoff）原始公式的基本结构。

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