Issues in Optical Diffraction Theory.

IF 1.5 4区 工程技术
Klaus D Mielenz
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引用次数: 1

Abstract

This paper focuses on unresolved or poorly documented issues pertaining to Fresnel's scalar diffraction theory and its modifications. In Sec. 2 it is pointed out that all thermal sources used in practice are finite in size and errors can result from insufficient coherence of the optical field. A quarter-wave criterion is applied to show how such errors can be avoided by placing the source at a large distance from the aperture plane, and it is found that in many cases it may be necessary to use collimated light as on the source side of a Fraunhofer experiment. If these precautions are not taken the theory of partial coherence may have to be used for the computations. In Sec. 3 it is recalled that for near-zone computations the Kirchhoff or Rayleigh-Sommerfeld integrals are applicable, but fail to correctly describe the energy flux across the aperture plane because they are not continuously differentiable with respect to the assumed geometrical field on the source side. This is remedied by formulating an improved theory in which the field on either side of a semi-reflecting screen is expressed as the superposition of mutually incoherent components which propagate in the opposite directions of the incident and reflected light. These components are defined as linear combinations of the Rayleigh-Sommerfeld integrals, so that they are rigorous solutions of the wave equation as well as continuously differentiable in the aperture plane. Algorithms for using the new theory for computing the diffraction patterns of circular apertures and slits at arbitrary distances z from either side of the aperture (down to z = ± 0.0003 λ) are presented, and numerical examples of the results are given. These results show that the incident geometrical field is modulated by diffraction before it reaches the aperture plane while the reflected field is spilled into the dark space. At distances from the aperture which are large compared to the wavelength λ these field expressions are reduced to the usual ones specified by Fresnel's theory. In the specific case of a diffracting half plane the numerical results obtained were practically the same as those given by Sommerfeld's rigorous theory. The modified theory developed in this paper is based on the explicit assumption that the scalar theory of light cannot explain plolarization effects. This premise is justified in Sec. 4, where it is shown that previous attempts to do so have produced dubious results.

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光学衍射理论问题。
本文的重点是关于菲涅耳标量衍射理论及其修正的未解决或文献贫乏的问题。在第二节中指出,实际使用的所有热源的尺寸都是有限的,光场的相干性不足会导致误差。应用四分之一波判据来说明如何通过将光源置于离孔径平面较远的位置来避免这种误差,并且发现在许多情况下,可能有必要像在弗劳恩霍夫实验的光源侧那样使用准直光。如果不采取这些预防措施,则可能不得不使用部分相干理论进行计算。在第3节中,我们回想起,对于近区计算,Kirchhoff或Rayleigh-Sommerfeld积分是适用的,但不能正确描述穿过孔径平面的能量通量,因为它们对源侧假定的几何场不是连续可微的。这是通过制定一个改进的理论来补救的,在这个理论中,半反射屏幕两侧的场被表示为在入射光和反射光的相反方向上传播的相互不相干分量的叠加。这些分量被定义为Rayleigh-Sommerfeld积分的线性组合,因此它们是波动方程的严格解,并且在孔径平面上连续可微。本文给出了利用新理论计算任意距离(z =±0.0003 λ)圆孔和狭缝衍射图样的算法,并给出了计算结果的数值实例。结果表明,入射的几何场在到达孔径平面之前被衍射调制,而反射的几何场则被散射到暗空间中。与波长λ相比,在距离孔径较远的地方,这些场的表达式被简化为菲涅耳理论所规定的通常表达式。在衍射半平面的具体情况下,所得到的数值结果与索默菲尔德的严格理论几乎相同。本文提出的修正理论是基于光的标量理论不能解释极化效应的明确假设。这一前提在第4节中得到了证明,在第4节中表明,以前这样做的尝试产生了可疑的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
自引率
33.30%
发文量
10
期刊介绍: The Journal of Research of the National Institute of Standards and Technology is the flagship publication of the National Institute of Standards and Technology. It has been published under various titles and forms since 1904, with its roots as Scientific Papers issued as the Bulletin of the Bureau of Standards. In 1928, the Scientific Papers were combined with Technologic Papers, which reported results of investigations of material and methods of testing. This new publication was titled the Bureau of Standards Journal of Research. The Journal of Research of NIST reports NIST research and development in metrology and related fields of physical science, engineering, applied mathematics, statistics, biotechnology, information technology.
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