Boundary Diffraction Wave Theory Research Articles

Uniform theory of the boundary diffraction wave

A uniform version of the potential function of the Maggi–Rubinowicz boundary diffraction wave theory is obtained by using the large argument expansion of the Fresnel integral. The derived function is obtained for the problem of diffraction of plane waves by a circular edge. The results are plotted numerically.

The relation between the boundary diffraction wave theory and physical optics

The physical optics surface integral is asymptotically reduced to a line integral along the contour of the diffracting edge. It is shown that the resultant integral can be separated into two sub-integrals which represent the reflected and transmitted diffracted fields. The integrands are transformed into the same forms with the potential function of the boundary diffraction wave theory.

MTPO based potential function of the boundary diffraction wave theory

A novel potential function is introduced by using the modified theory of physical optics integrals for a perfectly conducting half-plane. The function is valid for arbitrary aspects of observation. The line integration of these functions gives the total scattered fields. The method is applied to the problem of diffraction of plane waves by an opaque half-plane for oblique incidence.

Structure of boundary diffraction wave revisited

The physically appealing boundary diffraction wave theory which suggests that diffraction patterns arise due to interference of an undisturbed (geometrical) wave and the boundary diffraction wave generated by edge of the diffracting aperture, simplifies the solution of diffraction problems by reducing the Fresnel–Kirchhoff surface integral into a line integral over the illuminated boundary of the diffracting aperture. The present work reports experimental investigations carried out on the structure of the boundary diffraction wave. It has been shown that the boundary diffraction wave is continuous behind the diffracting aperture and apparently there does not exist any discontinuity at the geometrically light to shadow transition boundary, as is required by the theory.

The effect of impedance boundary conditions on the potential function of the boundary diffraction wave theory

A novel potential function of the boundary diffraction wave theory is obtained for the impedance surfaces by the asymptotic reduction of the modified theory of physical integrals. The function is expressed in terms of the direction vectors of the incident and scattered rays. The application of the method is performed on the problem of diffraction of plane waves by an impedance half plane for oblique incidence.

Phase knife-edge laser Schlieren diffraction interferometry with boundary diffraction wave theory

Within the framework of boundary diffraction wave theory it has been shown that the first bright fringe on either side of the central dark fringe of the phase knife-edge Fresnel diffraction pattern could be broadened to cover the whole field of view. Broadening of the first diffraction fringe, instead of conventionally modifying the spatial frequency spectrum, enhances the sensitivity of the Schlieren system. The use of phase knife-edge as viewing diaphragm in Schlieren diffraction interferometry not only enhances the fringe contrast but also avoids the loss in phase information as it lets through light from all parts of the test object and its thin interfacing makes the method suitable even for studying weak disturbances.

Knife-edge diffraction pattern as an interference phenomenon: An experimental reality

This paper demonstrates that a knife-edge diffraction pattern is, indeed, due to the interference of two superimposing waves: the geometrical wave and the boundary diffraction wave. Within the framework of boundary diffraction wave theory it is shown that this diffraction pattern can easily be broadened in such a manner that a single fringe covers the whole field of view. At this point the system converges to a schlieren diffraction interferometer and could be used for the study of phase objects using diffraction-limited optics. Experimental observations show that the method bears a similarity to that of any known two-beam interferometer, e.g. Mach-Zehnder interferometer. The experimental details have been presented and the results are compared with a two-beam holographic interferometer and a point diffraction interferometer.

Analysis of Near-Field Diffraction Pattern of a MetallicProbe Tip with the Boundary Diffraction Wave Method

The boundary diffraction wave theory is introduced to analyse anear-field diffraction (NFD) pattern of a metallic probe tip ofapertureless scanning near-field microscopy. This method is simpleand can give a clear physical picture. The polarization effect ofthe incident light and the different shapes of the metallic probetip are simulated. The results show that the NFD pattern of themetallic probe tip is directly related to those factors.

Diffraction of spherical waves at an annular aperture in the use of the boundary diffraction wave theory: A comparison of different diffraction integral approaches

The integral expression for divergent spherical waves diffracted at an annular aperture is derived based on the theory of the boundary diffraction wave. The expressions for divergent spherical waves diffracted at a circular aperture and a disk, and the axial field are treated as the special cases of our general one. Numerical calculation results for axial and transversal intensity distributions are given to compare our results with the Kirchhoff diffraction integral, first and second Rayleigh diffraction integrals. As expected, our results are in agreement with those in the use of the Kirchhoff diffraction integral, but the computer time is reduced greatly by using the boundary diffraction wave theory. The four diffraction formulae are shown to be consistent for axial and transversal intensity distributions, if the source and observation points are positioned equally from the aperture, or the observation point is located enough far from the aperture. Otherwise, the mean value of the first and second Rayleigh diffraction integrals is equal to the result of the boundary diffraction wave theory.

Experimental investigation of the boundary wave pulse

The existence of the boundary (diffraction) wave pulse is demonstrated by measuring the spectrum and the radial intensity distribution of the diffracted femtosecond pulses behind a circular aperture. Our results confirm Thomas Young’s assumption about the nature of diffraction which explains diffraction as the interference of the undisturbed (geometrical) wave and the boundary diffraction wave generated by the edge of the diffracting obstacle. It is experimentally demonstrated that two pulses propagate on the optical axis as it is predicted boundary diffraction wave theory. Because of the time (and path) difference between the geometrical pulse and the boundary wave pulse the spectrum becomes modulated. The radial intensity distribution in the vicinity of the axis can be described by the zero-order Bessel function if the two pulses do not overlap each other i.e., the time difference between the pulses is large enough compared to the pulse duration.

Focal shift in small-Fresnel-number focusing systems of different relative aperture.

Axial irradiance distribution arising from the diffraction of a uniform, converging, spherical wave at a circular aperture is studied on the basis of scalar boundary-diffraction wave theory. The combined effects of Fresnel number and angular aperture on the focal shift are evaluated, and the validity of the results is checked against the Kirchhoff boundary conditions.

Diffraction of short pulses with boundary diffraction wave theory.

The diffraction of short pulses is studied on the basis of the Miyamoto-Wolf theory of the boundary diffraction wave, which is a mathematical formulation of Young's idea about the nature of diffraction. It is pointed out that the diffracted field is given by the superposition of the boundary wave pulse (formed by interference of the elementary boundary diffraction waves) and the geometric (direct) pulse (governed by the laws of geometrical optics). The case of a circular aperture is treated in details. The diffracted field on the optical axis is calculated analytically (without any approximation) for an arbitrary temporal pulse shape. Because of the short pulse duration and the path difference the geometric and the boundary wave pulses appear separately, i.e., the boundary waves are manifested in themselves in the illuminated region (in the sense of geometrical optics). The properties of the boundary wave pulse is discussed. Its radial intensity distribution can be approximated by the Bessel function of zero order if the observation points are in the illuminated region and far from the plane of the aperture and close to the optical axis. Although the boundary wave pulse propagates on the optical axis at a speed exceeding c, it does not contradict the theory of relativity.

Boundary diffraction wave theory for rectilinear apertures

A classical problem is revisited using boundary diffraction wave theory as an alternative viewpoint to the Fourier optics treatment. Advantages and limitations of both treatments are discussed. Riassunto. Un problema classico della diffrazione è riesaminato sulla base della teoria dell'onda di bordo come punto di vista alternativo alla trattazione con i metodi dell'ottica di Fourier. Sono discussi i vantaggi e le limitazioni di entrambe le trattazioni.

Half-plane diffraction in a case of oblique incidence

Abstract The classical problem of half-plane diffraction is examined in a particular case of oblique incidence. A scalar solution to the problem is proposed using boundary diffraction wave theory and some limitations of the solution are discussed.

Imaging with photographic diffusers

A photographically made amplitude diffuser has been shown to produce in its close vicinity a system of multiple images of objects placed in front of it at a certain distance. A qualitative explanation of the formation of such images has been given in terms of pinhole imaging and boundary diffraction wave theory. A report on several interesting features of the imaging with photographic diffusers is presented.

Asymptotic representation of the boundary-diffraction wave for a three-dimensional Gaussian beam incident upon a Kirchhoff half-screen

Diffraction of a Gaussian beam with a circular spot size normally incident upon a Kirchhoff half-screen is investigated based on the boundary-diffraction-wave (BDW) theory. The evaluation of the boundary-diffraction wave by the steepest-descent method yields the uniform asymptotic representation of the total diffracted field consisting of the geometrical-optics and diffraction components. The use of complex rays to construct the diffraction component is also shown by applying the geometrical theory of diffraction (GTD) to the problem. Comparison of the representation of the diffraction component by the BDW theory with that by the GTD gives the diffraction coefficient for the Gaussian beam that ensures the continuity of the diffracted field at the shadow boundary.

Edge-On Diffraction of a Gaussian Laser Beam by a Semi-Infinite Plane

A He-Ne laser beam is used here to illuminate a razor blade at edge-on incidence. The incident light is found to be scattered into a single straight cone of circular cross section. The tip of this cone of diffracted light lies at the point of incidence, its axis coincides with the prolongation of the razor edge, and its halfangle is equal to the angle of incidence. Such cones formed by a family of diffracted rays are basic to the so-called geometrical theory of diffraction. However, the properties and geometrical laws associated with the diffracted rays are derived analytically here by application of the boundary diffraction wave theory. The experimental results are in agreement with theoretical predictions.

A Microelectronic Mask Inspection System Based on Single Spot Laser Scan Techniques

This paper introduces new techniques for automating the inspection of microcircuit mask patterns. The techniques are non-comparative, thereby eliminating the need for a reference pattern, and demonstrate an advantageous combination of simple optics and electronics to produce a system with excellent defect-sensitivity and speed. A single focussed laser spot is scanned over the mask. The resulting diffraction patterns are immobilized in the Fourier plane, where they are analyzed by a special photodetector array. Optimum designs for this array follow from a discussion, in terms of the Boundary Diffraction Wave theory, of the diffraction pattern differences between typical defects and valid mask features. The design and performance of a practical mask inspection system based on these principles is presented.

Fresnel zone plate solved by the boundary-diffraction-wave theory

The Fresnel zone plate is studied by the boundary-diffraction-wave theory (BDWT). Expressions are given for the fields in the transverse planes and along the axis; in particular, the wave amplitudes at the foci are considered in some detail. The BDWT provides a clear physical picture of the problem. The wave amplitude at any point is given by the sum of a finite number of rays determined by the number of zones in the plate. The foci are the points where the singly diffracted rays are in phase.