Theory Of Diffraction Optics Research Articles

Surface wave scattering from elliptical cracks for failure prediction

The scattered radiation patterns from surface cracks irradiated by acoustic surface waves are interpreted to provide estimates of crack length and aspect ratio, geometric crack parameters needed to enable failure prediction. The technique is demonstrated for circular and elliptical cracks as small as 100 μm in depth with an accuracy of about 10%. The key features are the positions and spacing of peaks and nulls in angular frequency dependence of scattered surface wave intensity. A simple model based on optical diffraction theory is demonstrated on cracks in commercial hot-pressed silicon nitride studied at 100 MHz and on spark-eroded slots in commercial aluminum studied at 2–10 MHz. The results are used to calculate the stress intensity factors and to describe the direction of crack propagation for a variety of real and simulated cracks. Implications of the technique with respect to crack closure and effects of stress and time are also discussed.

A simple approach to estimate the size of small surface cracks with the use of acoustic surface waves

The scattered radiation patterns of surface cracks irradiated by acoustic surface waves are interpreted to provide estimates of crack size. The technique is demonstrated for cracks as small as 100 μm in radius with an accuracy of about 10%.The key features are the positions and spacings of nulls in the angular dependence of the backward scattered surface-wave intensity. A simple model based on optical diffraction theory is presented and demonstrated on cracks (made with the identation technique) in commercial hot-pressed silicon nitride studied at 100 MHz and on cracklike flaws in commercial aluminum studied at 2–10 MHz.

An extension of Rusch's asymptotic physical optics diffraction theory of a paraboloid antenna

An extension of Rusch's asymptotic physical optics (APO) diffraction theory as applied to a parabolic antenna is presented. This extension provides a continuous solution throughout the shadow boundary region. The complete field expressions and the associated "new" physical optics diffraction coefficients are derived. Using the solution, the diffraction pattern for a 10-ft diameter focal plane parabola at 6 GHz is calculated.

Use of generalized theory of optical diffraction for the study of second harmonic generation

Génération de second harmonique lors de la traversée des faisceaux laser convergents (divergents) avec une distribution de l'énergie lumineuse non uniforme d'un milieu non linéaire est étudiée dans ce travail. Il est montré que la théorie de la diffraction optique dans un milieu non linéaire peut être utilisée pour la description phénoménologique. Des équations intégrales couplées sont dérivées pour le processus de la génération de la génération de second harmonique en directions de l'accord de phase en cristaux anisotropiques non linéaires pour des types différents de l'interaction non linéaire.

Concepts and Techniques of Microwave Optics

The fast-developing domain of microwave optics is surveyed, with main emphasis on those aspects of interest to optical scientists. Special attention is devoted to the newer trends in that field of research. The following aspects are covered: diffraction theory of microwave optics, microwave optical instruments, beam waveguides, and components for millimeter waves.

Application of the Sampling Theorem to Optical Diffraction Theory

The sampling theorem is applied to optical diffraction theory as a computational tool. Formulas are developed in terms of sampled values of the point spread function for the transfer function, total illuminance, line spread function and cumulative line spread function. Typical numerical examples are presented. The theory is presented for general point spread functions for slit and square apertures, but only for rotationally symmetric point spread functions for circular apertures. In the case of the slit aperture, the following question is answered: Given the real part of the incoherent transfer function, determine its imaginary part and vice versa. The theory of conjugate Fourier series and finite Hilbert transforms is introduced in order to answer this question.

Calculation of Optical Transfer Function from Lens-Design Data

A description is given of a calculation procedure for obtaining the optical transfer function of an optical system from its design data for both axial and extra-axial object points. The first part of the calculation involves determining the wave aberration of the system to the fifth order (in the classical sense), with vignetting taken into account. The second part involves calculating the optical transfer function from this aberration by the methods of physical optics (diffraction theory). A high-speed computer is required but the particular program to be written from the equations depends upon the kind of computer to be used.

Far-Field Diffraction and Boresight Error Properties of a Two-Dimensional Wedge*†

An optical diffraction theory has been developed which can be used to predict the forms of the far-field diffraction patterns and boresight error effects of a two-dimensional wedge made from two semi-infinite plane parallel plates. The solution is strictly an optical one, since the wavelength has been assumed to be small compared with the dimensions of the rectangular diffracting aperture, and also because the rectangular diffracting aperture is assumed to lie in the “near-field” of the wedge. In tracing the directly transmitted and all the multiply internally reflected wave fronts through the wedge to the plane of the diffracting aperture, amplitude losses due to reflection and absorption, phase changes due to increases in optical path, and changes in width of the various wave fronts are all evaluated in the plane of the diffracting aperture. When once the amplitude and phase distributions are known in the plane of the diffracting aperture, the Kirchhoff integrals are readily written and integrated. The UNIVAC computer can then be used to evaluate the forms of the far-field diffraction patterns characteristic of the wedge and diffracting aperture. These far-field diffraction patterns are in general non-symmetric and have forms which are functions of the plane of polarization of the incident electric vector and nine other variables. For arbitrary values of the variables, the forms of these far-field diffraction patterns cannot be understood in terms of conventional plane parallel plate theory, but in certain limiting cases plane parallel plate theory is useful. Boresight error curves have been evaluated as functions of many of the variables, and the magnitudes and signs of these errors are in agreement with the previously computed diffraction patterns. “Qualitative” checks on the theory have also been made by comparing the calculated forms of the far-field diffraction patterns for a particular glass wedge with those which were photographed experimentally. All of the calculated changes in form of these far-field diffraction patterns have been observed experimentally, and there is good reason to believe that a quantitative check might also be possible under more favorable experimental conditions.

On the diffraction theory of gaussian optics

On the diffraction theory of gaussian optics

Aerials for radar equipment

The paper presents a survey of those principles in aerial design which have come to the fore during-the war in the development of aerials for radar equipments. It is intended to serve as a co-ordinating introduction to specialist papers which willfollow. It is assumed that the reader is familiar with pre-war theory and practice in relation to aerials.On metre wavelengths the aerials are divided into those working on the “flood-lighting” and those working on the “beam” principle. The beaming in the vertical plane is seldom sufficiently sharp to avoid effects from ground reflections, which therefore play a predominant role in methods of elevation-finding.In radar direction-finding from aircraft with metre waves, use is made of overlapping “polar diagrams” provided either by self-directive aerials, or by aerials so positioned that the metal body of the aircraft causes them to have the required directive properties.With centimetre waves it is possible to produce beams so sharp that complications due to reflections from the ground can, to a large extent, be avoided. It is explained how the principles of optical diffraction theory are applied to the design of linear arrays fed from wave guides, so as to produce “fan-beams” of radiation narrow in one plane and sharp in the perpendicular one. The production of “pencil-beams,” sharp in two planes at right angles, is also discussed.Some account is given of new developments in the use of slots as aerials, in the design of wide-band aerials, and in the theory and design of end-fire arrays of the Yagi type.

X-Ray Wave-Lengths by The Dispersion in Quartz

It has been shown that the quantum theory of dispersion accounts satisfactorily for the measured refraction of x-rays. Since the x-ray wave-lengths as determined by crystals and by ruled gratings differ by 0.25 percent, the dispersion may be used to indicate which of these values is correct. Thus the quantum theory of dispersion may be written $\ensuremath{\lambda}={\ensuremath{\delta}}^{\frac{1}{2}}{\left[\frac{\ensuremath{\rho}}{W}\ifmmode\cdot\else\textperiodcentered\fi{}\frac{e}{m}\ifmmode\cdot\else\textperiodcentered\fi{}\frac{F}{2\ensuremath{\pi}}\ensuremath{\Sigma}\stackrel{s}{1}{N}_{s}\left\{1+\frac{log({x}^{2}\ensuremath{-}1)}{{x}^{2}}\ensuremath{-}\frac{2\ensuremath{\pi}q}{{x}^{3}}\right\}\right]}^{\ensuremath{-}\frac{1}{2}}$ where $\ensuremath{\delta}=1\ensuremath{-}\ensuremath{\mu}$, $\ensuremath{\rho}$ the density, $W$ the molecular weight, $\frac{e}{m}$ the ratio of the electronic charge to mass, $F$ the Faraday constant, ${N}_{s}$ the number of electrons per molecule of frequency ${\ensuremath{\nu}}_{s}$, $x=\frac{\ensuremath{\nu}}{{\ensuremath{\nu}}_{s}}$, $\ensuremath{\nu}$ the frequency of the incident radiation, $q=\frac{h}{{\ensuremath{\nu}}_{s}}$, $k$ the damping factor which can be obtained from the atomic absorption coefficient. Precise measurements of the refraction of the copper and molybdenum $K$ series in crystal quartz have been made. Both possible methods of using a prism were used. The 90\ifmmode^\circ\else\textdegree\fi{} edge of the prism was very carefully prepared. The results obtained are given in the following table. It is difficult to believe that such an agreement between the wave-lengths as determined by dispersion and by crystals is entirely fortuitous. The apparent precision obtained in the ruled grating measurements is so high that the above results must indicate a failure of the optical diffraction theory when applied to x-ray wave-lengths.

Societies and Academies

LONDON. Optical Society, October 9.—E. T. Hanson: Some problems in the theory of optical diffraction. A semi-infinite plane may be looked upon as a wedge the internal angle of which is zero. The application of KirchofFs formula in the latter case is considerably extended, it being shown that, through a region of not too small dimensions comprising the whole of the boundary of the geometrical shadow, the solution obtained is identical with the accurate solution. An expression is found for a plane wave incident at any angle upon a semi-infinite screen. An approximate expression is also found for the disturbance distributed over a straight slit due to a wave incident normally. KirchofFs formula has been applied, apparently for the first time, to an area of disturbance which is non-uniform.—W. M. Hampton: The annealing and re-annealing of glass. Relations connecting the strains present when cooling commences, strain due to gradient, and strain present after cooling, are obtained and the equations are applied to the case of slabs. The considerations affecting the temperature and conditions of annealing are discussed and tables giving annealing temperature, annealing time and rate of cooling for various kinds of glass are included.

Some problems in the theory of optical diffraction

The diffraction of waves by a perfectly reflecting wedge is now a problem of considerable celebrity. A semi-infinite plane may be looked upon as a wedge whose internal angle is zero. The application of Kirchhoff's formula in the latter case is considerably extended, it being shown that, through a region of not too small dimensions comprising the whole of the boundary of the geometrical shadow, the solution thus obtained is identical with the accurate solution. An expression is found for a plane wave incident at any angle upon a semi-infinite screen. The diffraction of waves by a straight slit in a plane screen is a problem not yet exactly solved; it is one which occupied Lord Rayleigh's mind for many years. An approximate expression is found for the disturbance distributed over the slit due to a wave incident normally, and by an application of Kirchhoff's formula an important result is obtained very readily, which is in agreement with Rayleigh's investigation by very long analysis. This appears to be the first time that an attempt has been made to apply Kirchhoff's formula to an area of disturbance which is not considered to be uniform over the area. The paper gives a brief treatment of the foregoing points of novelty and interest in these two problems which have long been and still are of some importance in mathematical physics.