Diffraction by a sinusoidal phase screen


  • Theodore L. Beach,

  • Richard V. E. Lovelace


In order to develop computer simulations of diffraction patterns produced by scintillations, it is important to verify the simulations with examples of diffraction patterns that may be calculated analytically. One such example is classical knife-edge diffraction from a conducting half plane. Here we present another test case based on the one-dimensional sinusoidal phase screen first considered by A. Hewish. Using Huygens-Fresnel diffraction theory, we derive expressions, as a function of sinusoid scale size (Λ) and maximum phase deviation (ϕ0) for (1) the intensity, (2) the horizontal wave number spectrum of the intensity pattern, and (3) the modulation index, seen by an observer situated below a one-dimensional phase screen with an incident plane wave. Then we compare the analytic results with a computer simulation. Provided that the frequency resolution of the simulation is adequate, the simulation agrees quite well with the analytic results. Additionally, diffraction from a sinusoidal phase screen provides a case in which the influence of increasing distance from the screen on the modulation index (deviation of intensity from its mean) may be explored analytically for both weak and strong scattering.