Fresnel diffraction

About: Fresnel diffraction is a research topic. Over the lifetime, 4094 publications have been published within this topic receiving 85335 citations.

Principles of optics : electromagnetic theory of propagation, interference and diffraction of light

Abstract: Historical introduction 1. Basic properties of the electromagnetic field 2. Electromagnetic potentials and polarization 3. Foundations of geometrical optics 4. Geometrical theory of optical imaging 5. Geometrical theory of aberrations 6. Image-forming instruments 7. Elements of the theory of interference and interferometers 8. Elements of the theory of diffraction 9. The diffraction theory of aberrations 10. Interference and diffraction with partially coherent light 11. Rigorous diffraction theory 12. Diffraction of light by ultrasonic waves 13. Scattering from inhomogeneous media 14. Optics of metals 15. Optics of crystals 16. Appendices Author index Subject index.

Geometrical Theory of Diffraction

Abstract: The geometrical theory of diffraction is an extension of geometrical optics which accounts for diffraction. It introduces diffracted rays in addition to the usual rays of geometrical optics. These rays are produced by incident rays which hit edges, corners, or vertices of boundary surfaces, or which graze such surfaces. Various laws of diffraction, analogous to the laws of reflection and refraction, are employed to characterize the diffracted rays. A modified form of Fermat’s principle, equivalent to these laws, can also be used. Diffracted wave fronts are defined, which can be found by a Huygens wavelet construction. There is an associated phase or eikonal function which satisfies the eikonal equation. In addition complex or imaginary rays are introduced. A field is associated with each ray and the total field at a point is the sum of the fields on all rays through the point. The phase of the field on a ray is proportional to the optical length of the ray from some reference point. The amplitude varies in accordance with the principle of conservation of energy in a narrow tube of rays. The initial value of the field on a diffracted ray is determined from the incident field with the aid of an appropriate diffraction coefficient. These diffraction coefficients are determined from certain canonical problems. They all vanish as the wavelength tends to zero. The theory is applied to diffraction by an aperture in a thin screen diffraction by a disk, etc., to illustrate it. Agreement is shown between the predictions of the theory and various other theoretical analyses of some of these problems. Experimental confirmation of the theory is also presented. The mathematical justification of the theory on the basis of electromagnetic theory is described. Finally, the applicability of this theory, or a modification of it, to other branches of physics is explained.

A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

Abstract: A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresenel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved wedge is continuous at shadow and reflection boundaries.

Exact solutions for nondiffracting beams. I. The scalar theory

Abstract: We present exact, nonsingular solutions of the scalar-wave equation for beams that are nondiffracting. This means that the intensity pattern in a transverse plane is unaltered by propagating in free space. These beams can have extremely narrow intensity profiles with effective widths as small as several wavelengths and yet possess an infinite depth of field. We further show (by using numerical simulations based on scalar diffraction theory) that physically realizable finite-aperture approximations to the exact solutions can also possess an extremely large depth of field.

Reconstructed Wavefronts and Communication Theory

Abstract: A two-step imaging process discovered by Gabor involves photographing the Fresnel diffraction pattern of an object and using this recorded pattern, called a hologram, to construct an image of this object. Here, the process is described from a communication-theory viewpoint. It is shown that construction of the hologram constitutes a sequence of three well-known operations: a modulation, a frequency dispersion, and a square-law detection. In the reconstruction process, the inverse-frequency-dispersion operation is carried out. The process as normally carried out results in a reconstruction in which the signal-to-noise ratio is unity. Techniques which correct this shortcoming are described and experimentally tested. Generalized holograms are discussed, in which the hologram is other than a Fresnel diffraction pattern.