Small Circular Aperture Research Articles

Reflection analysis of flanged circular waveguide radiating through small aperture into absorbing medium

A flanged circular waveguide in dominant-mode operation, radiating through a small circular aperture into an absorbing medium, has been studied from the point of view of reflections caused in the guide. The effect of varying the aperture size in modifying the reflections in amplitude and phase has been determined; the proper choice needed to realise matched conditions have been determined for a few selected media.

Qualitative and semiquantitative Fourier transformation using a noncoherent system

A number of authors have pointed out that a system of zone plates combined with a diffuse source, transparent input, lens, and focusing screen will display on the output screen the Fourier transform of the input. Strictly speaking, the transform normally displayed is the cosine transform, and the bipolar output is superimposed on a dc gray level to give a positive-only intensity variation. By phase-shifting one zone plate the sine transform is obtained. Temporal modulation is possible. It is also possible to redesign the system to accept a diffusely reflecting input at the cost of introducing a phase gradient in the output. Results are given of the sine and cosine transforms of a small circular aperture. As expected, the sine transform is a uniform gray. Both transforms show unwanted artifacts beyond 0.1 rad off-axis. An analysis shows this is due to unwanted circularly symmetrical moire patterns between the zone plates.

Electromagnetic scattering by a thin conducting flat plate with doubly periodic punched circular apertures

The problem of scattering of electromagnetic waves by a thin conducting flat plate loaded with doubly periodic small circular apertures has been theoretically investigated. An expression for the monostatic scattering cross-section has been obtained by treating the planar array of circular apertures as an array of (a) induced electric and magnetic dipoles and (b) diffracting apertures for parallel and perpendicular polarisations. The effect of punched apertures on the monostatic scattering cross-section has been presented.

A soft spherical “cap” in the field of a plane sound wave

THE PROBLEM of the scattering of a plane wave by a soft “cap” is reduced to the solution of an infinite system of linear algebraic equations of Fredholm type. In the case of Rayleigh scattering an analytic expression is obtained for the complete scattering cross-section, uniform over the aperture angle of the sphere. The perturbing action of a small circular aperture on the spectrum of the oscillations of the spherical cavity with a soft boundary is investigated.

On Image Formation with Coherent Light

Starting from linearity considerations and the Huygens-Fresnel principle, the use of ‘matched’ illumination in image formation with coherent light is described. As typical examples, the influence of a longitudinal mismatch of illumination on the images of small circular apertures is numerically studied. For comparison, the results on the defocused images of the same objects under ‘matched’ coherent illumination are also given.

A rotationally symmetric electron beam chopper for picosecond pulses

The chopper was designed for dynamic electron optical experiments where it is necessary to provide pulses of high quality with respect to both width and energy spread. The chopping action relies on the optical properties of a microwave cavity; these are exploited such that the time dependent space focusing causes a small circular aperture on the axis of rotational symmetry to transmit strongly for a single band of phase angles in each cycle of the excitation. The theoretical treatment is oriented towards computer display, and is novel in that it follows the progress of individual electron packets throughout the system. In contrast to conventional chopping and bunching theory, it is possible to analyse with ease the pulsing properties of a multicavity device.

AN AUTOMATED SKY PHOTOMETER FOR THE PALOMAR 48-INCH SCHMIDT TELESCOPE

ABSTRACT A digital sky photometer has been constructed and attached to the 48-inch Schmidt telescope at Palomar Mountain. The instrument allows plates to be automatically exposed to a predetermined level of sky density, with continuous monitoring of the sky brightness in that region of the sky and spectrum that exposes the plate. In addition to facilitating the correct exposure of the plate, the sky counts provide a calibration of the plate based on the sky density. A small circular aperture is provided for reference calibrations on standard stars.

Transmission Cross Section for Small Apertures in Black Screens

On the basis of a recently proposed theory of diffraction of light at very small apertures (of the order of a wavelength or less) in black screens, expressions are derived for the transmission cross section for diffraction of a monochromatic plane wave incident normally on a small circular aperture in a black screen. The results, which are illustrated by a set of curves, are compared with the predictions of the Kirchhoff theory. Comparisons are also made with the corresponding known results for the transmission cross section for acoustical diffraction at small apertures in hard and soft screens and for electromagnetic diffraction at apertures in conducting screens.

Diffraction at Small Apertures in Black Screens

In an earlier paper dealing with a consistent formulation of Kirchhoff’s theory, an extension of the theory was proposed which seems to be applicable to treatment of diffraction at very small apertures in black screens. The extension consists of the addition to Kirchhoff’s solution of the effect of waves arising from multiple diffraction at the edge of the aperture. In the present paper, calculations based on this modified theory are presented. Corrections to Kirchhoff’s theory are obtained for the case of a plane wave incident normally on a small circular aperture in a black screen. Appreciable departures from Kirchhoff’s theory are found only when the diameter of the aperture is small compared with the wavelength of the incident wave or when the angles of diffraction are very large. It is also shown that in the asymptotic limit ka→∞ (k is the wave number, a the radius of the aperture) our results are consistent with those obtained on the basis of Keller’s geometrical theory of diffraction.

The near field beyond a perfectly conducting plane screen with a small circular aperture

The near field beyond a perfectly conducting plane screen with a small circular aperture

A NOTE ON THE DIFFRACTION OF A SCALAR WAVE BY A SMALL CIRCULAR APERTURE

The power series solution for the diffraction of a scalar plane wave incident normally on a small circular aperture in a hard screen is extended to include terms of order α12 in the aperture field, and to terms of order α10 in the transmission coefficient (α = 2π × radius of aperture/wavelength). To do this, a set of recurrence relations is developed, and a relatively simple method of obtaining the transmission coefficient is devised.

Application of the modified vorticity transport theory to the turbulent spreading of a jet of air.

1. The turbulent spreading of a jet of air emerging from a small circular aperture has been discussed by Tollmien (1926) on the basis of Prandtl’s momentum transport theory of turbulence, by making some appropriate assumptions. He has calculated the distribution of mean velocity in the jet at distances which are sufficiently great compared with the diameter of the aperture and it has been found that the calculated distribution of mean axial velocity is in satisfactorily good agreement with observations made at Göttingen. The same problem seems to have been discussed also by L. Howarth in an unpublished paper on the basis of Taylor’s vorticity transport theory of turbulence, by assuming that not only the mean motion, but also the turbulent motion, is symmetrical about the axis of a jet. It appears, how­ever, that the agreement between Howarth’s results of calculations and the Göttingen measurements is not so good as in the case of Tollmien’s results of calculations on the momentum transport theory.

A means of increasing the light transmitted by a disappearing filament pyrometer of precision

After a short explanation of the main principles of a well-known type of disappearing filament pyrometer, it is pointed out that a fivefold (or more) increase in the brightness of the field may be obtained by substituting a slit, set parallel to the filament, for the small circular aperture placed between the erecting lens and the occular. This simple alteration facilitates the calibration of the instrument at the gold point, and extends the useful range of measurement by some 80° C. at the lower end of the scale. An addendum deals with a recent observation confirming the suggestion made in the text that the precision of a pyrometer is influenced by variations in the surface properties of the tungsten filament.

XII.Photography of diffraction patterns due to small circular apertures

XII.<i>Photography of diffraction patterns due to small circular apertures</i>

Young's Interference Experiment and the Spectrometer

IN NATURE of April 28, p. 268, Dr. R. A. Houstoun directs attention to the use of the spectrometer for Young's double-slit experiment. In a letter on “The Visibility of Interference Fringes and the Double Slit” (NATURE, July 26, 1917, vol. xcix., p. 424) the present writer made reference to a similar optical arrangement. In that letter emphasis was laid, not on the advantages of the method for observing fringes and evaluating wave-length, but on its use for studying the changes in the visibility of fringes which occur as the width of the spectrometer slit is altered. In view of Prof. Michelson's recent use of the double slit for the measurement of the angular width of distant stars, I may be pardoned for directing attention to my note of some years ago, and for pointing out the ease with which an experiment similar in method to that of Prof. Michelson may be performed by means of an ordinary spectrometer. It is true that, instead of using a source of fixed (but finite) width and a variable double slit, the converse arrangement was employed, but in principle the methods are identical. It might be worth while, however, to vary the experiment by replacing the spectrometer slit by a small circular aperture and using a double slit of variable width.

An apparatus for measurements of the defining power of objectives

The apparatus here described was devised at the National Physical Laboratory for the purpose of obtaining a numerical estimate of the goodness of definition in the image given by an optical system. It has been employed also for determining the distribution of intensity, as affected by diffraction, in the images obtained through a small circular aperture, giving results in complete agreement with the usual theory. As an object, the image of which is to be examined, is employed an "edge," forming the boundary line between a half bright, half dark, field. The distribution of intensity along a line at right angles to the edge may be represented by the broken line ABEF in fig. 1, ordinates representing intensity, and abscissæ, measured from E, distances from the edge. In the image, the intensity distribution will be given by some such curve as ADF, the light gradually falling off from full intensity at a point outside to zero at some point inside the geometrical image of the edge. The object aimed at is to obtain a series of points on, and hence to draw, this intensity curve. The whole width we are concerned with in this blurred image of the edge is extremely small, and for the measurements magnification is necessary.

Photographing Diffraction Rings—Optical Phenomenon

THE peculiar character of the photographs of an opening to the sky in the dark Cyclopean gallery at Tiryns, to which Mr. W. J. Stillman calls attention (NATURE, vol. xxiv. p. 260), finds an obvious explanation in the well-known optical phenomenon of diffraction rings, produced when a beam of light is transmitted through a small circular aperture, and viewed by means of a lens. Had your “Cecropian” correspondent examined the image of the illuminated opening by the assistance of a lens, the phenomenon of concentric coloured rings would, doubtless, have been recognisable to the eye. Hence the only point of interest in the phenomenon observed by Mr. Stillman is the significant fact that in securing the fleeting images of the rings on the gelatine plate—the actinic rays being alone effective—alternate dark and bright concentric rings are produced, as in the case of homogeneous or monochromatic light, instead of the coloured, rings seen by interposing a lens between the aperture and the eye. In other terms, the impressions on the gelatine plate being due to the action of the monochromatic actinic rays, the theory of diffraction shows that the concentric rings should be alternately dark and bright. This is an important circumstance in the applications of photography to such investigations.

On the Magnifying Power of Short Spaces illustrated by the Transmission of Light Through Minute Apertures

ABSTRACT Having described in the former papers the appearances observable when pencils of light from small circular apertures are partially intercepted by certain opaque or transparent objects of definite shape and size ; and having shown that whether shadows or illuminated spaces are thus used, they serve to exemplify the magnifying power of short intervals existing between the organ of vision and the object to be examined, inasmuch as they occupy some position in space, and have a certain form, qualities which pertain to them in common with all substances appreciable by the sense of sight, we proceed to notice the phenomena which result when exceedingly narrow linear apertures are substituted for those of a circular form. In conducting these investigations it was not unreasonable to suppose, à priori, that if the size, the quality, and the position of the object to be examined, the direction and the intensity of the light which was used, the sensitiveness and immediate response of the pupil of the eye to the minutest variation in the quantity of light impinging on the retina, and the refracting qualities of the transparent portion of the visual organ, were each and all taken into account, so that a nice and delicate adjustment of the eye to the light, and of the light as well as of the size of the objects to the eye could be insured, appearances perhaps beautiful, doubtless uncommon, and certainly interesting to the physiologist might be fairly anticipated. Such anticipations, have been so far realized as to present a strong inducement to prosecute the subject with a legitimate prospect of still greater success.