Slope Contours Research Articles

Recording slope and curvature contours of flexed plates using a grating shearing interferometer

A diffraction grating shearing interferometer is presented which, depending on the recording procedure, can be used to measure directly the slopes and curvatures of specularly reflecting flexed plates. Three system arrangements are described: two for slope measurement and one for curvature. One slope arrangement yields results in real time but, in general, does not compensate for initial model curvature. The second requires an additional spatial filtering step but does compensate for the initial curvature. A diffraction theory approach is used to arrive at expressions for the complex field amplitude of the light at the output plane. This leads to expressions for the fringe values. Experimental results for three types of model are also presented. Errors of 2-4% were found for the various system arrangements. In addition, an analytical expression is derived and verified experimentally, which shows that when the system is used for measuring slope, the curvature of the model limits the measuring sensitivity. The theoretical analysis shows that this is a fundamental property of grating interferometers in general. This property is then exploited as the basis of the curvature measuring technique.

Quantitative determination of the topography of microelectronic devices by SEM micrographs.

The scanning electron microscope (SEM) is commonly used for analysis and process control of microelectronic devices, but the majority of SEM micrographs do not readily yield quantitative topographic information. It is shown how SEM micrographs have to be made and analysed in order to determine profile thicknesses as well as slope angles and/or contours. Another method is given for quick calculations of profile thickness and slope angles using a test pattern, thus obviating the need to include the magnification and the viewing angle. Whole semiconductor wafers with diameters of up to 3 in can be used without first having to be prepared. The positioning of the sample on the specimen holder while operating the SEM is explained. The method is demonstrated using micrographs of photoresist patterns and etched profiles.

Vibration Analysis of Plate and Shell by Laser Speckle Interferometry

Abstract When an optically rough structure is illuminated by laser light, speckles are created throughout the space in front of the surface covered by the reflected wavelets When the surface is under steady-state vibration these speckles also vibrate accordingly. By recording the speckles contained in a plane in front of the surface as a time average the resulting speckle interferogram will yield a variety of information upon proper Fourier filtering. One can obtain a complete anti-nodal pattern, a partial anti-nodal pattern, and partial slope contours from which bending moments can be calculated The method is applied to shell as well as plate vibration problems.

Laser speckle interferometry for plate bending problems

A method is proposed whereby the spatial speckles created in front of a plate with an optically rough surface when illuminated by a coherent laser beam is used to generate slope contour fringes. This is done by photographing the speckles contained in a parallel plane in front of the plate before and after deformation via double exposure. The resulting speckle interferogram is then optically Fourier transformed to yield the fringe pattern of slope contours. It is shown that the method is analogous to the Ligtenberg reflection moiré method with a grating of continuously variable pitch and orientation. The method can be applied to plates made of almost any material.

Surface Soil Moisture within a Watershed—Variations, Factors Influencing, and Relationship to Surface Runoff

AbstractSurface soil moisture was measured within the upper 15 cm using neutron‐scattering equipment on six soil series within a 57.8‐ha Pennsylvania watershed during the 19 May to 11 Nov. 1971 period. Surface soil moisture was responsive to individual storm events, showed discernible seasonal trends, and displayed larger fluctuations at higher moisture levels than at lower moisture levels. An analysis of variance showed that well‐drained soils had significantly different surface soil moisture levels than the more poorly drained soils and could be grouped into a hydrologic unit distinct from the more poorly drained soils. Surface soil moisture measurements along parallel transects approximately perpendicular to the slope contours showed high surface soil moisture contents proximal to the stream indicating that these areas contribute more to surface runoff in a shorter period of time than areas distant from the stream channel. Multiple regression equations using pan evaporation and surface soil moisture for each soil series were used to show the relative importance of the internal soil drainage class in predicting surface runoff.

Determination of slope and strain contours by double-exposure shearing interferometry

An interferometric technique is used to determine directly patterns of derivatives of displacements. In the case of plate models, the fringes are loci of equal slope; for specimens provided with surface gratings, one forms patterns of partial derivatives of in-plane displacements. A theory for the interpretation of the interference fringes in terms of displacements is outlined; some experimental applications illustrate the paper.

No current reversal at 10,000 B.P. in the strait of Gibraltar — A discussion

The late Quaternary pattern of sedimentary facies on the Spanish Gulf of Cadiz continental shelf results from an interaction between a number of controlling factors that are dominated by the Atlantic inflow currents flowing southeastward across the Cadiz shelf toward the Strait of Gibraltar. An inner shelf shoreface sand facies formed by shoaling waves is modified by the inflow currents to form a belt of sand dunes at 10–20 m that extends deeper and obliquely down paleo-valleys as a result of southward down-valley flow. A mid-shelf Holocene mud facies progrades offshore from river mouth sources, but Atlantic inflow currents cause extensive progradation along shelf toward the southeast. Increased inflow current speeds near the Strait of Gibraltar and the strong Mediterranean outflow currents there result in lack of mud deposition and development of a reworked transgressive sand dune facies across the entire southernmost shelf. At the outer shelf edge and underlying the mid-shelf mud and inner shelf sand facies is a late Pleistocene to Holocene transgressive sand sheet formed by the eustatic shoreline advance. The late Quaternary pattern of contourite deposits on the Spanish Gulf of Cadiz continental slope results from an interaction between linear diapiric ridges that are oblique to slope contours and the Mediterranean outflow current flowing northwestward parallel to the slope contours and down valleys between the ridges. Coincident with the northwestward decrease in outflow current speeds from the Strait there is the following northwestward gradation of contourite sediment facies: (1) upper slope sand to silt bed facies, (2) sand dune facies on the upstream mid-slope terrace, (3) large mud wave facies on the lower slope, (4) sediment drift facies banked against the diapiric ridges, and (5) valley facies between the ridges. The southeastern sediment drift facies closest to Gibraltar contains medium–fine sand beds interbedded with mud. The adjacent valley floor facies is composed of gravelly, shelly coarse to medium sand lags and large sand dunes on the valley margins. By comparison, the northwestern drift contains coarse silt interbeds and the adjacent valley floors exhibit small to medium sand dunes of fine sand. Because of the complex pattern of contour-parallel and valley-perpendicular flow paths of the Mediterranean outflow current, the larger-scale bedforms and coarser-grained sediment of valley facies trend perpendicular to the smaller-scale bedforms and finer-grained contourite deposits of adjacent sediment drift facies. Radiocarbon ages verify that the inner shelf shoreface sand facies (sedimentation rate 7.1 cm/kyr), mid-shelf mud facies (maximum rate 234 cm/kyr) and surface sandy contourite layer of 0.2–1.2 m thickness on the Cadiz slope (1–12 cm/kyr) have deposited during Holocene time when high sea level results in maximum water depth over the Gibraltar sill and full development of the Atlantic inflow and Mediterranean outflow currents. The transgressive sand sheet of the shelf, and the mud layer underlying the surface contourite sand sheet of the slope, correlate, respectively, with the late Pleistocene sea level lowstand and apparent weak Mediterranean outflow current.

Dynamic moiré methods for the bending of plates

Two approaches are proposed to extend the Ligtenberg’s reflective moire method to dynamic-bending problems of plates. Partial slope contours of two orthogonal directions can be obtained simultaneously with the proposed schemes. Vibrating modes of plates can also be obtained by the methods.

モアレ法による表面形状の測定について

A moire method is described for measuring partial slope contours of flat surfaces of transparent plates. A reference grating is projected by means of a collimated light beam on the surface of a specimen. The light beam passing through the specimen forms a distorted image of the reference grating on the surface of an identical grating, and produces moire fringes which yield partial slope contours of the specimen.A formula for obtaining the slope contour from the inclination and the spacing of the moire fringe is introduced theoretically. Experiments made with a straight line grating of 0.025 mm spacing show that this method has nearly the same precision as the optical interference method.In this paper few applications are shown. As an example, the slope contours are calculated from moire pattern produced by an acrylyte plate which is supported at both ends and loaded at mid point. And also a moire pattern produced by the fractured surface of acrylyte plate is shown.The method described in this paper is applicable for the transparent materials, but for the reflecting materials their slope contours are derived by the somewhat different moire technique.

Moiré patterns of slope contours in flexed plates

A simple method is described for the measurement of partial slopes in flexed plates. The interference of the resultant distorted reflection of a referenceline grating, projected by means of a collimated monochromatic light on the polished surface of a flexed plate, with an identical grating yields a moire pattern of the partial-slope contours of the plate.

Slope measurement by means of moir fringes

A simple method is described for the measurement of partial slopes of flat surfaces. A line reference grating is projected by means of a collimated monochromatic light beam on to the deformed lateral surface of a plane specimen loaded on its own plane. Moire fringes formed by the projection of the resultant distorted image of the grating into an identical grating yield the partial slope contours of the specimen in a direction normal to the direction of the rulings of the gratings. The method is used to determine the gradients of the sum of principal stresses of plane elastic problems and gradients of the lateral strain in the case of plane stress plasticity problems. Integration along any traverse of the specimen yields readily either the sum of principal stresses or the lateral strain distribution.

The interpretation of F2 critical frequency measurements

During winter daylight hours changes in ƒ 0F2 are almost continuous due to the presence of travelling ionospheric disturbances. It is suggested that variation in hourly values of ƒ 0F2 from day to day on magnetically quiet days is due mainly to this cause and it is shown that these values are only reliable to ± 0.5 Mc/s. The resultant error in estimated maximum usable frequencies has been determined. Critical frequencies as read from ionogram records are not true vertical incidence values but are reflected at an angle θ from the vertical because of sloping isoionic contours. This angle has been estimated as well as the amount by which average measured values of ƒ 0F2 must be decreased to give real vertical incidence values of ƒ 0F2 .

Triple splitting with the F2-region of the ionosphere at high and mid-latitudes

The occurrence of the third ( z-ray) component of the F2-trace on ionograms is investigated at high- and mid-latitudes. Diurnal variations show a systematic shift, with magnetic inclination, of the time of maximum occurrence. Seasonal variations show a winter maximum, and an inverse sunspot-cycle relationship exists. Maximum occurrence appears between a magnetic inclination of 70° and 80° with a fall-off either side. Evidence is presented to suggest a z-ray association with “Spread-F” fronts, and a possible mechanism for the recording of the z-ray trace at the transmitter site is described. This involves longitudinal propagation of the o-mode at its normal reflection level, coupling at this point, and ultimate reflection for the z-ray mode as a result of sloping ionization contours belonging to “Spread- F” fronts extending in directions perpendicular to the magnetic meridian. An association with V.L.F. emissions (“dawn-chorus”) is discussed.

SUBMARINE GEOLOGY OF BIKINI ATOLL

The program of investigations made in connection with the atomic bomb tests in the summer of 1946 at Bikini Atoll provided a rare opportunity for obtaining information on the physiography and sediments of atolls. The outer slopes around Bikini Atoll rise from a depth of about 2500 fathoms in a long gradually steepening curve. Between 0 and 200 fathoms the average slope is 25°. On the windward side, the reef at the top of the slope is bordered by a narrow 15-fathom terrace, but on the leeward side by a steep, locally vertical, cliff extending to 35 fathoms. Contours of the outer slopes reveal that a flat-topped mass having nearly the area of Bikini lagoon but below 700 fathoms extends to the northwest. The lagoon itself is saucer-shaped and has a maximum depth of 34 fathoms. Around the lagoon and bordering the inner side of the reef and islands is a 12-fathom terrace. Coral knolls rise abruptly from the lagoon floor, and some of them reach to within a few fathoms of the surface. The middle of the lagoon is floored chiefly by algal debris, whereas the shallow edges are covered by algal and foraminiferal sand. Coral comprises a relatively small percentage of the bottom materials. The outer slopes consist of algal debris grading outward to fine sand and finally to Globigerina sand.

The Transect of a Mountain Valley

The study here described was undertaken in the early part of July, 1921, and is still in progress. It was more or less preliminary in character and was handicapped by a shortage of the most-needed equipment. Briefly, its object is to confirm or deny the conclusion reached from a much more extensive study of the forest types or associations in the vicinity of the Fremont Experiment Station, Colorado, extending over a period of about ten years. This conclusion had been that the zonal distribution of the important forest trees, and the equally marked differences between the vegetative associations of opposing slopes at the same elevations, was due primarily to differences in insolation and its effects upon the surface of the soil. Unfortunately, in the extensive study no measurements whatever had been made of sunlight intensity, and for the effects of insolation upon the soil we were compelled to draw our conclusions from rather complete soil temperature data for a depth of i foot, a very few observations on surface temperature, and one season's record of surface moisture conditions, with so many variable factors entering into the results that the real importance of the primaries could be only vaguely seen. Therefore, the first opportunity was seized to measure the effects of insolation as completely as possible in the three most important forest types, and under such an arrangement that there would be the minimum of variables, such as air temperatures, precipitation, and even sunlight intensity. It will be rather readily seen that the measurement of sunlight intensity itself could not be very profitable, because of the large number of factors which would influence its effects. There was available at an extremely convenient point a valley whose axis lies almost due east and west, bounded by ridges on either side whose total distance apart is only 700 feet. A transect of this valley was therefore made, running as nearly as possible normal to the contours of both slopes, in a straight line, and on this line stations were located arbitrarily at intervals of exactly 50 feet. The illustrative diagrams show the profile of the valley, whose walls on either side attain a gradient of about 45 percent, or 25 degrees, the steepest portion, as usual, being near the middle of either slope. As to the vegetative cover in the vicinity of this transect, beginning at the top of the ridge on the north, it consists of a fairly dense stand of western