Fresnel Diffraction Effects Research Articles

Coherent interference effects in SIEM and CBED

The coherent convergent incident beam produced by the field emission gun of a STEM instrument allows the observation of a number of unusual interference effects in the shadow images (SIEM) and convergent beam diffraction (CBED) patterns visible on the detector plane. Shadow images of thin crystals display the electron Ronchigrams having a form sensitive to the defocus and aberrations of the objective lens. For large crystal lattice spacings the Ronchigrams show characteristic ellipses of low contrast. CBED patterns of thin crystals show symmetries and intensities which vary with the position of the incident beam within the unit cell. Discontinuities in the specimen such as the edges of crystals show striking Fresnel diffraction effects in SIEM. In CBED patterns they give rise to the splitting of diffraction spots. If the incident beam is parallel to a smooth face of a small crystal the potential field outside the crystal gives rise to strong refraction effects.

Extension of Glauber theory to account for intratarget diffraction in multicenter scattering

A 1975 treatment of single-double multiple scattering of electrons by randomly oriented vapor-phase molecules is put on a firmer footing and extended to higher order. It is shown how to include effects of intramolecular Fresnel diffraction, as an electron scattered by one atom propagates to the next, without ever explicitly evaluating the scattered wave function in the target. Theoretically derived estimates are made of the limitations of the approach at various levels of approximation. Numerical calculations are compared as a function of energy and scattering angle with newly available high quality calculations by Kohl and Arvedson (KA). In the expected range of applicability — roughly, 10 keV and higher − the present approach yields results that are satisfactory and (unlike those of KA) inexpensive enough for use in routine electron diffraction analyses.

Modes of empty off-axis unstable resonators with rectangular mirrors

The effect of Fresnel edge diffraction on mode loss and far-field beam quality is investigated for empty offaxis unstable resonators with rectangular mirrors. For the cases investigated, mode-loss separation and beam quality of the lowest-loss mode are maximized nonconcurrently when the optical axis intersects the small convex mirror near one of its corners rather than its center. Although these properties indicate that the near-corner off-axis resonator can achieve superior beam quality to that achieved by an on-axis resonator, it is also shown that a large instability in beam quality can occur near the operating point which gives maximum mode-loss separation and superior beam quality.

Some interesting features of spherical cap transducers

Interesting features of spherical caps have been identified and investigated as a result of the availability of large computers which has overcome the problem of poor convergence of the wave‐harmonic series for spherical cap directivity at large ka. Caps which have radial velocity excitation exhibit Fresnel diffraction effects for ka ⩾ 2π. The presence of these effects has been verified experimentally with a spherical transducer which shows an axial loss of sensitivity for conditions corresponding to the 2nd Fresnel half‐period zone. Fresnel theory predicts the occurrence of directivity extrema for caps which are hemispherical or smaller. Data for prediction of diffraction effects for larger caps is presented for 2π ⩽ ka ⩽ 20π. Axially excited caps do not exhibit diffraction effects. The velocity coefficients for the wave‐harmonic series for axial velocity excitation are developed. Axially excited hemispherical caps were observed to exhibit constant directivity index for ka ⩾ 0.8π. [Work partially supported by NAVSEA and NCSC.]

Proton elastic scattering by nuclei: Fresnel and two-body correlation effects

In this paper we deal with the effects of Fresnel diffraction in the elastic scattering of 1 GeV protons by nuclei. Explicit expressions for the optical potential in58Ni and208Pb are given, showing numerically that Fresnel effects and two-body correlations are of little importance in the elastic scattering of protons by nuclei.

Water motion on a beach in the presence of a breakwater: 1. Waves

For a long breakwater on a slowly varying bottom as asymptotic theory is given which accounts for the combined effects of refraction and Fresnel diffraction of water waves. Numerical examples are given for two cases: an offshore breakwater and an isolated jetty.

Reduction of Fresnel diffraction effects by soft apertures

Reduction of Fresnel diffraction effects by soft apertures

Reduction of Fresnel diffraction effects by soft apertures

Reduction of Fresnel diffraction effects by soft apertures

Fresnel diffraction in high-energy multiple scattering

Abstract We study the effects of Fresnel diffraction on the multiple scattering of high-energy hadrons in complex nuclei. Starting from a Watson-type multiple scattering series, we approximate the free-space propagators by Fresnel propagators. By employing the unitary transformation that connects the Fresnel and eikonal propagators, we derive a closed expression for the multiple scattering amplitude which is formally similar to the corresponding Glauber expression. The Fresnel diffraction effects manifest themselves in a characteristics Dyson-type ordering of the profile operators with respect to the z -coordinates of the target nucleons. The general formulae are then applied to elastic scattering by a target nucleus represented by an independent particle model. As an example, the amplitude for nucleon-deuteron scattering is explicitly evaluated and compared with a result previously derived by Gottfried.

Fresnel diffraction effects in the design of high-power laser systems

Fresnel diffraction by circular apertures for beams commonly encountered in high-power laser systems is investigated. Striking agreement is demonstrated between experimental results and theoretical calculations for beams with uniform and Gaussian intensity profiles. It is pointed out that Fresnel diffraction patterns produced by circular apertures depend only on the incident wave front and the Fresnel number corrected for curvature of the incident beam, F = a2/λL + a2/λR. This also gives an excellent experimental method for measuring divergence. Methods are discussed for minimizing the occurrence of severe intensity variations and resulting self-focusing problems in high-power laser amplifiers.

Fresnel and Fraunhofer diffraction in nuclear processes

Angular distributions for elastic scattering and direct reactions of nuclear particles often have an oscillatory structure which is the analogue of Fraunhofer diffraction by a perfectly absorbing obstacle. It is shown that strong Coulomb interaction changes the diffraction pattern from the Fraunhofer type to the Fresnel type. Several features observed in the differential scattering and reaction cross sections of heavy charged particles are identified as Fresnel diffraction effects.

Dynamical Theory of Electron Diffraction for Finite Polyhedral Crystal III. Fresnel Diffraction Formula

Following the first paper of the same title (J. Phys. Soc. Jap. 7 1952) 397), in which Bethe's dynamical theory of electron diffraction (Ann. d. Phys. Lpz. 87 (1928) 55) was extended to the case of finite polyhedral crystal and the general expressions of wave functions for transmitted and interfracted (=reflected by crystal net plane) wave were obtained, they have been rewritten in a form of the so-called Fresnel diffraction with the purpose that we might have better understanding of electron microscope images of crystallites. From these formulae, it is concluded that the striations due to “ Pendellosung ” are observed in the just-focused images of crystallites in which Bragg reflection occurs while in defocused image they are disturbed in the neighbourhood of a crystal edge by the Fresnel diffraction effect. In a special case where the parameter indicating the deviation from the Bragg condition is very large, the present formulation applies to the phase contrast fringes due to the edge of transparent wed...

A new optical experiment and the use of a single lens for high magnification; observation of entoptic and diffraction phenomena

An interesting optical experiment may be performed with a camera and converging lens. An extension of the experiment by use of the eye in place of the camera makes possible high magnifications with a single lens, location of flaws in glass, observation and location of particles within one’s own eye and observation of Fresnel diffraction effects.