Parallel Slits Research Articles

Far-field Diffraction Patterns of Two Slits

The diffraction of a scalar wave by two parallel slits in a plane screen is examined by a new method which uses an orthogonal set of functions and Fourier transformations. The far field is obtained for the case of normal incidence and numerical results are given for k = 0·2 − 5 and D =3 − 10, where k is the wavenumber and D is the slit separation.

Two‐dimensional multiple scattering for n slit array

AbstractA new method has been proposed to analyze 2‐dimensional multiple scattering of a plane wave by N parallel cylindrical structures. Diffraction of a plane wave incident on N parallel slits is formulated exactly via Kobayashi‐Nomura's method in an asymptotic form in which the (i+1)‐fold scattering field is given in terms of the i‐fold scattering field. The solution consists of scattering pattern functions for a single slit and their derivatives. The pattern functions are modified when applied to multiple scattering by cylindrical structures of arbitrary cross sections. Numerical solutions are presented for multiple scattering by strips.

EXTREMAL PROPERTIES OF MAPPINGS ONTO SURFACES WITH PARALLEL SLITS

In the present paper an area theorem is established for certain regular functions associated with multivalent mappings of a finitely connected domain onto a surface with parallel slits. Several consequences of this theorem generalize well-known results from the theory of univalent conformal mappings. The notion of the generalized span of a domain is introduced. It is then shown that it possesses certain properties completely analogous to the basic extremal properties of the span of a domain. Grotzsch's theorem concerning the range of the first coefficient of the regular part of the normalized Laurent expansion of a univalent function about a pole is extended to multivalent functions.Bibliography: 7 titles.

Diffraction by two parallel slits in a plane

The diffraction of scalar waves by two parallel slits in a plane screen is examined by a method which uses orthogonal functions and Fourier transformations. A solution is obtained in the case of a perfectly soft screen. Numerical results of the plane wave transmission coefficients for normal incidence are given for k=0.2∼4.0 and D=3∼10, where k is the wavenumber and D is the distance between slits.

Responses of locust visual interneurones to transiently-illuminated slits, paired spots, annuli and disc arrays

One compound eye of an immobilised locust viewed a large screen on to which could be projected a slit of variable width, parallel thin slits of variable separation, large discs or annuli, pairs of small discs or large arrays of small discs. The on-response in the contralateral cervical connective, for both the DCMD and a smaller axon group (M-spikes), was recorded over a period of 2 sec coinciding with the period of illumination. The normal spontaneous discharge of the connective is described. For a single slit the DCMD response peaked in the range 0.02–0.7° of width subtense, the most common result being 0.05°. The M-axon group showed a negative peak at a corresponding subtense. Comparing the responses to single bars and paired slits of the same overall subtense, it was found that below about 1° these were not discriminated by either type of neurone. At higher subtenses the DCMD showed preference for paired slits, the M-axons for solid bars. Comparing responses to arrays of spots with those to uniformly illuminated areas, neither the DCMD nor the M-axon group showed discrimination at angles less than 1°, but at higher angles the DCMD showed preference for arrays and the M-axons for solid areas. Annuli were more effective stimuli than were discs of the same size. Near the edge of large-area targets it was possible to detect spatial transients in excitability. Two small spots produced interaction over a wide range of separations, affording evidence for wide-range mutual inhibition affecting both types of interneurone, and for short-range facilitation for the M-axon group only.

Lyriform slit sense organs

1. In lyriform organs of arachnids several innervated cuticular slits are closely arranged in parallel. The mechanical consequences of this arrangement were studied in model experiments with regard to their importance for the organ's stimulus conducting properties (Fig. 1). 2. Groups of parallel slits were cut into plexiglass disks. On these static pressure loads were applied from varying directions. The resulting deformation of the slits was measured in terms of compression and dilatation, respectively. It was compared to that of a model with only one slit. 3. Simple models with three or five slits of equal length: A slit's deformation is drastically reduced by the presence of neighbouring slits closely arranged in parallel. Differences between various slit areas and the effect of load direction on deformation are reduced as well. The peripheral slits of a group take up much more load than the intermediate slits. In large groups they are deformed even more than a single, isolated slit. Different areas of the same peripheral slit vary markedly with regard to the effect of load direction (Figs. 2a and 5). 4. More elaborate model with seven slits copying a lyriform organ on the spider leg tibia: Again considerable differences are found in the degree of deformation. It is positively correlated with both slit length and peripheral position of the slit within the group. The majority of slits is most compressed in that area where the dendrite attaches in the original receptor. This is not always the mid portion of the slit, however (Figs. 2b, c, 6 and 7). 5. According to previous studies compression is the adequate deformation of the slit leading to nervous activity. It is most effectively achieved by loads perpendicular to its long axis.Photoelastic experiments with model tibiae show that pressure stresses roughly perpendicular to the long axes of the slits have indeed to be expected under natural stimulus conditions. They also provide a basis for understanding topographical features pertinent to the majority of the lyriform organs on the spider leg: their proximity to a joint, their location on the lateral surface of the leg, and their orientation roughly parallel to the long leg axis (Figs. 4 and 8). 6. The main physiological consequences deduced from these model studies for a close parallel arrangement of slits are: a) a considerable enlargement of the range of stimuli accessible for sensory analysis at a specific site and b) a marked stimulus intensity fractionation by different slits within the same group.

On extremal sets of parallel slits

On extremal sets of parallel slits

A multi-slit spectrograph and H? Doppler system

A multiple entrance slit spectrograph was built for time-lapse photography of the spectra of flares and other transient solar phenomena. This spectrograph employs narrow-band filters to limit the wavelength range of the spectrograph to several angstroms centered at Hα or other spectral lines. The passband of the filter, and the dispersion of the spectrograph determine the number of parallel slits through which light may be passed to achieve multiple adjacent spectral displays. By using a 7 A filter, a dispersion of 10.8 A mm−1, and 35 mm film, adjacent Hα spectra are imaged from 30 parallel slits. A system of mirrors and relay lenses transfers the slitjaw image to the same film plane as the spectral image. A 2 frame camera is used to simultaneously record both images on adjacent frames. Filtering of the reference spatial image to 1.0 A allows the observer to see the position of the slits relative to the Hα centerline structure and to match the brightness of the spatial image to the spectral display. A polarizing beamsplitter, prior to the slits, provides a prefiltered second solar image to a narrow band Hα Doppler filter for simultaneous photography in the wings of the Hα line. The multislit monochromatic spectrograph and Hα Doppler system constitute a flexible instrument in which components may be substituted to achieve different passbands width, image scales, dispersions and corresponding numbers and spacings of adjacent spectra at a selected wavelength.

Inverse problems of the plane theory of elasticity: PMM vol. 38, n≗ 6, 1974, pp. 963–979

In connection with the fact that failure of a structure ordinarily starts at sites of the most acute stress concentrations near cavitiies, it is of interest to determine the shape of the equally strong outlines of holes on which the technologically inevitable stress concentration would be least as compared with all other outlines. An effective exact solution of some inverse plane problems of the theory of elasticity concerning the determination of equally strong outlines of holes is proposed. A formulation of the problem is given first and the fundamental relationships are presented. Then the general problem for any number of holes in an infinite plane is reduced to a standard Dirichlet problem for the exterior of the same number of parallel slits on a parametric plane. An effective exact solution is found by this method for the case of one and two holes as well as for the case of periodic and doubly-periodic series of holes. The question of application of the solutions obtained to the theory of a minimum weight structure is considered.

On size effects in helium II below 1 K

The normal fluid density ρ n and the specific heatc v are calculated for helium II flowing through plane parallel slits and capillaries with a square profile at temperatures below1 K. Both functions increase over their bulk values if the thermal phonon wavelength λ becomes comparable to or larger than the smallest dimensiond of the container. The asymptotic expansions which are obtained in this paper have an overlapping range of validity, and therefore describe ρ n andc v rather accurately for all values of λ/d.

Approximate solutions of certain integral equations for the diffraction by two strips

Integral equations associated with the diffraction of obliquely incident plane waves of various kinds by two coplanar and parallel infinite strips and slits are solved approximately for low frequencies. The solutions are presented as expansions in terms of a suitable perturbation parameter.

X-ray holography of lensless Fourier-transform type

A one-dimensional X-ray hologram of lensless Fourier-transform type was made with the C Kα radiation (44.8 Å). Three parallel slits, 9 μm apart, were used as object. By the wavefront reconstruction with the He-Ne laser, images magnified by a factor 223 were obtained.

Acoustic Diffraction of a Plane Wave by Two Coplanar Parallel Perfectly Soft or Rigid Strips

The problem of diffraction of a normally incident plane acoustic wave by two parallel and coplanar infinite strips is considered. The assumed boundary conditions on the strips are the vanishing of either the total wave function or its normal derivative. Expressions are obtained for the first few terms of the series for the far-field amplitude and the scattering cross section when the wavelength is much larger than the distance between the outer edges of the strips. The corresponding results for two parallel and coplanar infinite slits in a soft or a rigid screen follow by applying Babinet's principle. This analysis also gives the transmission coefficients for the case of two infinite parallel slits in a thin conducting screen when the electric or magnetic field vectors of the incident plane monochromatic waves are polarized parallel to the edges of the slits.

Optical quality of the cat eye

The modulation transfer function (MTF) of the cat's eye was measured. The MTF was determined by projecting square-wave-gratings of differing widths onto the retina, photographing the images of these gratings with a special fundus-camera, and making a photometric recording of the film. Then with the aid of the MTF, the images on the retina were calculated for the following optical stimuli: (1) discs of various diameters, (2) contrast-border between black and white fields, (3) black bar on a light background, (4) ideal point and ideal slit, (5) double-slit. The minimum separable distance for two parallel slits was calculated as 4–5 minutes of arc. A comparison with similar data for the human eye indicates that the optical quality of the human eye is better than that of the cat's eye.

Determining the stresses in solid rock by means of load relaxation by two parallel slits

Determining the stresses in solid rock by means of load relaxation by two parallel slits

The Heart and Its Actions: Roentgenokymographic Studies

Kymography has apparently been a dead issue in the clinical practice of cardioradiology for almost 20 years. Dr. Alexander, however, presents us with a text based on ten years clinical experience with more than 3,000 patients, using a Germanbuilt kymograph based on a design by Dr. P. Strumpf published in 1931. The basic mechanism consists of a moving radiopaque plate with multiple parallel slits 0.4 mm wide at intervals of 12 mm. The plate is placed between the patient and thefilm and moves vertically or horizontally 11 mm, with the usual exposure time being 1.5 seconds. The author describes his technique and findings with many of the types of congenital heart disease which survive into adolescence and adult life, as well as the common forms of acquired heart disease. The additional information the technique affords over routine films is generously illustrated, and its limitations are also catalogued. The average stated

Photoelectric method of measuring the turbulence of high-temperature flows

Abstract : A recording method is described which permits determining the amplitude spectrum of the velocity fluctuations of a turbulent flow and to find the mean flow velocity. The investigated section of the flow with tracking particles is projected by means of an optical system onto a flat screen with two parallel slits. In the case of a low-temperature flow this section is illuminated by an intense external source, whereas at a sufficiently high temperature the self-luminescence of the particles can be used. When the image of the luminous particle strikes the slit, a voltage pulse arises at the output of a photomultiplier which is then amplified and discriminated. When the image of the luminous particle strikes the second slit a bright flash appears on the screen of the oscillograph. Since the velocity of various particles in a turbulent flow is dissimilar, the bright flashes arise at various distances from the place of triggering, grouping about a point corresponding to the most powerful transit time of the particles between the slits. (Author)

Hernia due to banding of the abdominal muscles.

SUPERIMPOSED parallel slits between bands of the internal oblique and transversus abdominis muscles occasionally open to allow formation of a hernia at the level of the semicircular line of Douglas, which enters a shallow subaponeurotic space lateral to the rectus sheath and deep to the aponeurosis of the external oblique. Zimmerman et al1noted this and described its anatomical peculiarities. Four cases, with incarceration and strangulation, show this hernia to be dangerous and misleading. Report of Cases Case 1. —A 23-year-old man, loading heavy oil drums, suddenly noticed tender, firm swelling in the left lower abdominal wall. Sharp pain rendered him helpless, and after some delay he was brought to the hospital with an oblique, oval, exquisitely tender mass, midway between the umbilicus and anterior superior iliac spine (Fig 1). During examination it quickly disappeared, with immediate cessation of pain. Because considerable time had lapsed, exploration was advised. Upon

Measurement of Parallel (Soller) Slits with a Modified Weissenberg Goniometer

Measurement of Parallel (Soller) Slits with a Modified Weissenberg Goniometer

Solution of the Dirichlet Problem in Parallel Slit Domains

Journal of Mathematics and PhysicsVolume 45, Issue 1-4 p. 77-94 Article Solution of the Dirichlet Problem in Parallel Slit Domains† Hyam L. Zuckerberg, Hyam L. Zuckerberg Yeshiva University Davidson Laboratory of Stevens Institute of Technology Brooklyn CollegeSearch for more papers by this author Hyam L. Zuckerberg, Hyam L. Zuckerberg Yeshiva University Davidson Laboratory of Stevens Institute of Technology Brooklyn CollegeSearch for more papers by this author First published: April 1966 https://doi.org/10.1002/sapm196645177 †This paper is a condensed version of a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Yeshiva University, June 1963. It was prepared under the supervision and guidance of my advisor, Dr. Bernard Epste AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume45, Issue1-4April 1966Pages 77-94 RelatedInformation