gugllee.blogg.se

4, where it is shown that previous attempts to do so have produced dubious results. The modified theory developed in this paper is based on the explicit assumption that the scalar theory of light cannot explain plolarization effects. In the specific case of a diffracting half plane the numerical results obtained were practically the same as those given by Sommerfelds rigorous theory. At distances from the aperture which are large compared to the wavelength ? these field expressions are reduced to the usual ones specified by Fresnels theory. 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. 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? ) are presented, and numerical examples of the results are given. 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. 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. 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 cross the aperture plane because they are not continuously differentiable with respect to the assumed geometrical field on the source side. If these precautions are not taken the theory of partial coherence may have to be used for the computations. 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. 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. Abstract This paper focuses on unresolved or poorly documented issues pertaining to Fresnels scalar diffraction theory and its modifications.