Diffraction Patterns Of Apertures Research Articles

Theoretical simulation on Fraunhofer diffraction of arbitrarily shaped aperture

The diffraction refers to the phenomenon that when light encounters an obstacle during propagation, it will deviate from the original propagation path and propagate behind the obstacle. In the study of diffraction and the relevant, we often encounter the questions about the prediction or estimation on the diffraction patterns of apertures with various shapes. Yet the specially designed optical experiment is very time consuming and laborious for this simple purpose. In this paper, the laser far-field diffraction is studied based on Kirchhoff diffraction theory. The intensity distribution is described by using a two-dimensional matrix and then the mathematical representations of the diffraction pattern of arbitrary aperture are provided. Visualization of calculated data is achieved by computer programming, and high-precision diffraction patterns are obtained. The above theoretical analysis method presented in this paper has higher universality. When the calculation infinitesimals are small enough and the computer graphics display function is sufficient, the diffraction pattern with high resolution can be obtained efficiently compared with the experiment.

Far-field diffraction patterns of circular sectors and related apertures

In studies of scalar diffraction theory and experimental practice, the basic geometric shape of a circle is widely used as an aperture. Its Fraunhofer diffraction pattern has a simple mathematical expression easily determined by use of the Fourier-Bessel transform. However, it may require considerable mathematical effort to determine the far-field diffraction patterns of aperture shapes related to the circular geometry. From a computational point of view, the mathematical difficulties posed by other aperture geometries as well as more-general apertures with irregular shapes can be surpassed by means of optical setups or fast numerical algorithms. Unfortunately, no additional insight or information can be obtained from their exclusive application, as would be the case if mathematical formulas were available. The research presented here describes the far-field diffraction patterns of single-sector apertures as well as their extension to double symmetrical sectors and to sector wheels formed by interleaved transparent sectors of equal angular size; in each case, full or annular sectors are considered. The analytic solutions of their far-field amplitude distribution are given here in terms of a series of Bessel functions, some interesting properties are deduced from these solutions, and several examples are provided to illustrate graphically the results obtained from approximate numerical computations. Our results have been verified numerically with the fast-Fourier-transform algorithm and experimentally by means of a spherical wavefront-single-lens Fourier-transform architecture.

Diffracted field by an arbitrary aperture

Diffraction patterns of apertures on screens uniformly illuminated are standard calculations in undergraduate optics and acoustics courses. These calculations imply two-dimensional (2-D) integrations which are often performed in the far zone, at moderate angles of diffraction, i.e., using Fresnel and Fraunhofer approximations. In this note, the 2-D integration is reduced to a 1-D parametric integration over the perimeter of the aperture—resembling the Rubinowicz’s representation of the Kirchhoff diffraction integral—which allows numerical evaluation with few computational resources. The proposed formula allows mathematically exact calculation of the near-field, in the context of scalar wave theory. Explicit calculations for circular and elliptical apertures are shown.

Dispersion relations in Fraunhofer diffraction

The Fraunhofer diffraction pattern of an aperture function, which can be described in terms of the superposition of a known aperture function with a half plane, has an amplitude distribution which is real along one direction and complex along the orthogonal direction. The real and imaginary parts of the amplitude distribution are related by Hilbert transforms (dispersion relations). These dispersion relations can be used to arrive at the diffraction patterns of a variety of apertures having symmetry properties. Theoretical results are presented to illustrate the diffraction pattern of various apertures.