Kirchhoff Diffraction Theory Research Articles

22 建築モデュール数値について

The sound diffraction by a semi-infinite plane screen with knife-edge was measured by AC pulses; short tones with more than 10 seccesive waves from a source at finite distances. This results shows good agreements with diffraction theory of S.W. Red fearn (phil. Mag. 7th. 1940). From the practical point of view, the anther shows that Kirchhoff's diffraction theory is so valuable as it can express the diffraction effects more simply by one parameter and one curve, and it ts applicable to a source or receiver at any distance and to any diffraction angle within ±2db approximately, taking the Fresnel's zone number N as the parameter. Above theories are calculated for a completely absorbent screen, but the experimental results measured by a screen of naked Hornogen-bord show reasonable agreement with the theoretical values, whereas the results by a screen lined with glass-wool-blanket were heigher than that values. It seems to be the term of screen surface condition does not depend on the reflection from the surface, but on the absorption at glancing incidence by screen surface, and unfortunately the factor of this absorption is never considered by any theory of diffraction. Several measurements about the effects of barrier shape were made. The results by a barrier of right angle wedge snow a curve of same form with a curve of diffraction by knife edged plane screen, but few db lower values. The results of experiments on the effects of edge width of screen on diffraction show that, when the edge width is smaller than one or a half wave length the effects of the width are negligible. But when the edge width is not smaller than wave length the measured valnes are reasonablly large.

On the Axial Phase Anomaly for Microwave Lenses*

The behavior of the phase along the axis of aberration-free microwave lenses is shown by curves of the axial phase anomaly calculated from scalar Kirchhoff diffraction theory. These curves are drawn for three different wavelengths and two typical focal lengths. Also illustrated in the calculated results are the errors introduced by the use of certain geometrical approximations commonly employed in light optics.Detailed experimental measurements have been made of the electric field along the axis in the point-source image produced by solid dielectric lenses at a wavelength of 3.2 cm. Despite the limited size of the exit pupil (radius approximately 8 wavelengths) the agreement between the measured values of the axial phase anomaly and those calculated from scalar theory is very good except within about one lens radius of the lens surface.

On the Sheen Gloss

Experiments of sheen gloss of metals and theoretical explanation of them are given. Sheen gloss is related with the specularly reflected light which appears by a incident angle above a critical angle θ c . θ c is connected with the r.m.s. roughness h as: \begin{aligned} 2h\cos\theta_{c}{=}\lambda/k\quad k{=}2{\sim}3 \end{aligned} This formula is explained by a theory similar to the Kirchhoff's diffraction theory, treating the roughness as a stationary random function given by Ornstein-Uhlenbeck process. Scattered light is separated to R - and D -comp. the former corresponds to sheen and its brightness is given as a function of incident angle ψ by \begin{aligned} \exp\left(-\frac{16\pi^{2}h^{2}}{\lambda^{2}}\cos^{2}\psi\right). \end{aligned} D - comp. is the part that represents scattered light.

金属仕上面からの反射

A wave optical theory of diffuse reflection of light from metal surfaces was given. Metal surface was represented by a probability function obeying the Ornstein-Uhlenbeck process and the reflection of light was calculated by a method similar to that of the Kirchhoff's diffraction theory. The distribution of the diffusely reflected light is given by a formula which is characterized by two constants h and β, the former being r. m. s. height and the latter being related with the average inclination of roughness peaks. The theoretical formula is well fitted with that of the experimental.

Reflection and Transmission of Sound by Thin Curved Shells

In this paper the reflection and transmission of sound by thin curved shells, as well as several related problems, are treated mathematically. First, one derives an inhomogeneous integral equation for the sound field in an infinite medium containing a thin curved shell of different material. The solution of the integral equation is then reduced, approximately, to the evaluation of a surface integral not too different from that obtained in the usual Kirchhoff diffraction theory. The integral is evaluated approximately and gives expressions for the pressure waves reflected from and transmitted through a thin curved shell. The reflection and transmission coefficients of the shell are obtained from these expressions. It is found that the reflection coefficient can be expressed as the product of a geometrical factor, a phase-cancellation factor, and a reflectivity factor. When the reflection problem for a rigid obstacle is solved with the aid of the assumptions of the Kirchhoff diffraction theory, the reflection coefficient thus obtained is the product of the geometrical and phase factors of the previous solution. The geometrical factor alone is obtained as the reflection coefficient when the reflection problem is solved exactly by geometrical acoustics. The agreement among the various solutions may be considered as a partial justification for the Kirchhoff theory as well as for geometrical acoustics. The Kirchhoff method is also applied to the problem of refraction at a curved surface. From the solutions of the reflection and refraction problems, the laws of reflection and refraction for curved surfaces are obtained. In addition, the mirror and lens laws, the conditions for point images, and the change of phase at a focus are obtained.