This paper focuses on unresolved or poorly documented issues pertaining to Fresnel's diffraction theory and its various modifications. In Sec. 2 of the paper it is pointed out that all thermal sources used in practice are finite in size, so that the assumption of an infinitesimally small point source is seldom justified and errors can result from insufficient coherence of the optical field. A quarter-wave coherence criterion is applied to show that such errors can be avoided by placing the source a large distance away from the aperture plane, and in many cases it may be necessary to place it at the focus of a collimator lens 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 Rayleigh-Sommerfeld or Kirchhoff integrals must be used and that all of these are not continuously differentiable with respect to the assumed geometrical field on the source side, and therefore do not correctly describe the flow of energy through the aperture. This deficiency is remedied by constructing a new rigorous theory in which a partially reflecting screen is assumed and the diffracted field on either side of the aperture plane is expressed as the superposition of two mutually incoherent wave motions that propagate in the opposite directions of the incident geometrical field and its reflection at the screen. These field components are defined in 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.
Journal of the Optical Society of America A-Optics Image Science and Vision
Bidirectional Scalar Field, circular aperture, coherence, diffraction, half plane, near field, rigorous, slits, theory
Current Issues in Optical Diffraction Theory, Journal of the Optical Society of America A-Optics Image Science and Vision
(Accessed November 30, 2023)