Minimum Aperture Research Articles

Some Aperture-Angle Optimization Problems

Abstract. Let P and Q be two disjoint convex polygons in the plane with m and n vertices, respectively. Given a point x in P , the aperture angle of x with respect to Q is defined as the angle of the cone that: (1) contains Q , (2) has apex at x and (3) has its two rays emanating from x tangent to Q . We present algorithms with complexities O(n log m) , O(n + n log (m/n)) and O(n + m) for computing the maximum aperture angle with respect to Q when x is allowed to vary in P . To compute the minimum aperture angle we modify the latter algorithm obtaining an O(n + m) algorithm. Finally, we establish an Ω(n + n log (m/n)) time lower bound for the maximization problem and an Ω(m + n) bound for the minimization problem thereby proving the optimality of our algorithms.

Changes to regulations and the gear used in the South African commercial fishery for Jasus lalandii

Alterations to the operational fishing gear used in the South African west coast rock lobster Jasus lalandii fishery and their resultant impacts are investigated. The most important developments have been: (i) a change during the 1960s from hand-hauled hoopnets to winch-hauled traps, with a concomitant modification of vessels; (ii) the introduction of deck-grid sorters in 1975; (iii) an increase during 1984 of minimum mesh aperture from 62 to 100 mm (stretched), with a concomitant decrease in the length of the trap codend; (iv) a decrease in the minimum legal size during the early 1990s; and (v) the introduction of bottom-grid traps in 1994. Most of these alterations have been driven by a trade off between the need for greater operational efficiency and concerns surrounding the issue of how best to deal with the problem of catching and releasing specimens smaller than the minimum legal size.

The influence of accelerator physics on the magnet design of a very large hadron collider

We present a study of the influence of accelerator physics on the design of magnets for very high energy hadron colliders. The limiting specifications of a particular VLHC model are estimated, and their effect on the design of the accelerator magnets is determined using simulations and scaling laws for magnet aperture, field quality, cryogenic and vacuum properties and cost. We show that there is a maximum useful field due to synchrotron radiation power and cost, and a minimum useful aperture due to synchrotron radiation and beam-stability.

Attenuated total reflectance infrared microspectroscopy of aged carbon-filled rubbers

A number of different carbon-filled rubbers have been studied using infrared microspectroscopy with an attenuated total reflectance objective incorporating a silicon internal reflectance element (IRE). Excellent spectra were obtained of these difficult samples in a reasonable measurement time. The IRE had a contact face of 100 μm diameter which could be further apertured to improve the spatial resolution, but at the expense of the signal-to-noise ratio of the spectra. The minimum aperture size, which still produced an acceptable spectrum, was 40 μm. The spatial resolution was less than the aperture size because of the effect of the refractive index of the IRE. The method was applied to thermally aged rubbers by measuring spectra at intervals across a sectioned surface. Oxidation profiles were derived from the absorbances of oxygenated functional groups in the spectra and were found to agree with modulus profiles previously published. The IR-ATR microspectroscopic method is shown to be simple and effective because the measurement is made directly on the sectioned surface of the rubber without sacrificing the sample.

Space-based Doppler wind lidar: Modeling of edge detection and fringe imaging Doppler analyzers

Abstract Optical, noncoherent measurement of the Doppler shift of lidar backscatter is a candidate for the measurement of atmospheric wind profiles from a satellite. Commonly called “direct detection”, this method may be less difficult to implement than coherent detection systems, and can eliminate dependence on atmospheric aerosol content for Doppler wind measurements. Models presented here describe the signal shot noise limited performance of noncoherent Doppler wind lidars employing (1) location of the interference fringe of a Fabry-Perot interferometer (fringe imaging technique), and (2) measurement of the attenuation of the signal amplitude passed through the interferometer (edge technique). It is shown that there is no significant difference in sensitivity between these two direct detection techniques. The minimum receiver optical aperture required of a lidar system for space-based tropospheric wind profiling in order to meet moderately demanding spatial resolution and Doppler accuracy requirements is found to be about 2 meters, a size which may be practical with the development of deployable optical telescopes. The etalon working aperture required to match this telescope is found to be a reasonable 100 mm for the fringe imaging technique, but an impossible 500 mm for the edge technique. The edge technique etalon must also be retuned in a few milliseconds in order to observe both the outgoing laser pulse and the atmospheric signal pulse, while the fringe imager etalon can observe both at a static setting. In the absence of any performance advantage, the use of the edge technique for the spaceflight Doppler wind sounder is difficult to justify.

Thickness and spatial distributions of clastic dykes, northwest Sacramento Valley, California

The geometry and distribution of the clastic dykes of the Ono district, North Sacramento Valley are examined within stream sections. Five traverses along dry stream beds provide good exposure allowing the spacing, thickness and geometry of the dykes to be recorded. The spatial and thickness distribution of the dykes are considered using cumulative frequency plots, allowing a visual estimation of a best fit distribution. Dyke thickness conforms best to a log-normal distribution. There is also a characteristic minimum dyke thickness in a traverse and this is attributed to the minimum aperture that a fluid with sand clasts is able to exploit. Dyke spacing, however, shows a good correlation with a power-law distribution for four traverses, suggesting that there is a mechanistic control on the spatial distribution. Plotting dyke thickness against minimum dyke spacing reveals that thin dykes do not generally intrude in isolation. Unlike veins and igneous dykes, clastic dykes continue to provide preferential pathways for fluid flow, subsequent to their intrusion, thus inhibiting intrusion in the area surrounding a pre-existing dyke. A combination of this process and dyke branching provides the best model for the observed spatial and thickness distribution of clastic dykes seen in the Ono district, California.

Modeling of direct detection Doppler wind lidar I The edge technique

Analytic models, based on a convolution of a Fabry-Perot etalon transfer function with a Gaussian spectral source, are developed for the shot-noise-limited measurement precision of Doppler wind lidars based on the edge filter technique by use of either molecular or aerosol atmospheric backscatter. The Rayleigh backscatter formulation yields a map of theoretical sensitivity versus etalon parameters, permitting design optimization and showing that the optimal system will have a Doppler measurement uncertainty no better than approximately 2.4 times that of a perfect, lossless receiver. An extension of the models to include the effect of limited etalon aperture leads to a condition for the minimum aperture required to match light collection optics. It is shown that, depending on the choice of operating point, the etalon aperture finesse must be 4-15 to avoid degradation of measurement precision. A convenient, closed-form expression for the measurement precision is obtained for spectrally narrow backscatter and is shown to be useful for backscatter that is spectrally broad as well. The models are extended to include extrinsic noise, such as solar background or the Rayleigh background on an aerosol Doppler lidar. A comparison of the model predictions with experiment has not yet been possible, but a comparison with detailed instrument modeling by McGill and Spinhirne shows satisfactory agreement. The models derived here will be more conveniently implemented than McGill and Spinhirne's and more readily permit physical insights to the optimization and limitations of the double-edge technique.

The maximal angular gap among rectangular grid points

Let A = {a1, ... am} and B = {b1,...bn} be two sets of real numbers. Consider the (at most) mn rays from the origin to the points (ai, bj), and define the aperture Ap(A, B) to the largest angular gap between consecutive rays. Clearly, \({\text{Ap(}}\mathcal{A},\mathcal{B}{\text{)}} \geqslant \frac{{2\pi }}{{mn}}\). Let f(m, n) denote the minimum aperture of any m × n rectangular array, as defined above. In this paper, we show, that for sufficiently large n, \(f{\text{(}}n,n{\text{)}} < \frac{{220}}{{n^2 }}\), so that f(n, n) = Ω(n-2). We also show that \(f{\text{(}}m,n{\text{)}} = \frac{{2\pi }}{{mn}}\) only when m = 2, or n = 2 or (m, n) = (4,4), (4,6) or (6,4).

Structure of ITQ-4, a New Pure Silica Polymorph Containing Large Pores and a Large Void Volume

The new pure silica polymorph ITQ-4, structure code IFR, Si32O64, monoclinic I2/m a = 18.65243(13), b = 13.49597(8), c = 7.63109(6) Å, β = 101.9781(5)°, is a zeolitic material containing a large sinusoidal channel with 12-member ring windows as minimum apertures. Its void volume (0.21 cm3/g) is surpassed only by that of pure silica Beta among the known pure silica polymorphs. The success of the ab initio structure solution from synchrotron powder diffraction data was greatly assisted by the absence of Al and Si−OH defect groups, which generates a very high degree of crystallographic order.

A note on reflector-feed element realizability and optimality

Reflector-antenna design has reached a mature state of development. Sophisticated techniques, such as the use of array feeds for the correction of surface distortion, are now available. With sophistication, there is the danger that designers will lose sight of fundamental principles. In reviewing a manuscript submitted to the IEEE Transactions on Antennas and Propagation, on the subject of array feeds for reflector antennas, the author found that the numerical results presented in the manuscript were based on an element-pattern/spacing relationship that was unrealizable. The present note may help to avoid such difficulties, by presenting simple formulas that relate the realizability and optimality of feed antennas to reflector f/D, i.e. the ratio of focal length to diameter. The author discusses the optimality of feed elements in terms of a maximum-gain criteria for the reflector antenna, and considers the question of the realizability of an array-feed element in terms of its minimum aperture (i.e. spacing) requirement.

Minimum apertures and Fresnel zones in migration and demigration

The size of the aperture has an important influence on the results of (Kirchhoff‐type) migration and demigration. For true‐amplitude imaging, it is crucial not to have apertures below a certain size. For both the minimum migration and demigration apertures, theoretical expressions are established. Both minimum apertures depend on each other and, although a time‐domain concept, are closely related to the frequency‐dependent Fresnel zone on the searched‐for subsurface reflector. This relationship sheds new light on the role of Fresnel zones in the seismic imaging of subsurface reflectors by showing that Fresnel zones are not only important in resolution studies but also for the correct determination of migration amplitudes. It further helps to better understand the intrinsic interconnection between prestack migration and demigration as inverse procedures of the same type. In contrast to the common opinion that it is always the greatest possible aperture that yields the best signal‐to‐noise enhancement, it is in fact the selection of a minimum aperture that should be desired in order to (a) enhance the computational efficiency and reduce the cost of the summation, (b) improve the image quality by minimizing the noise on account of summing the smallest number of traces, and (c) to have a better control over boundary effects. This paper demonstrates these features rather than addressing the question of how to achieve them technically.

On the relationship between mechanical and hydraulic apertures in rough‐walled fractures

Accurate analyses of the hydrogeology of fractured rock require an understanding the flow characteristics of single fractures. It is well known that these flow characteristics are strongly controlled by fracture apertures. Recent investigations on the distribution of apertures in natural fractures suggest that the cubic law can accurately predict the fluid flux through rough‐walled fractures as long as the appropriate average fracture aperture is used. Combining the stochastic cubic law with a simple deformation model results in a nonlinear relationship between fracture hydraulic and mechanical aperture. This relationship is shown to be consistent with published experimental and numerical data above a critical minimum aperture. Below this minimum aperture, the transmissivity of the fracture is approximately constant. Results have implications for the interpretation of laboratory fracture flow data and raise important questions pertaining to the mechanics of fracture deformation below the critical minimum aperture.

Using adaptive quantization in cell-oriented holograms

This article describes the introduction of a specialized error diffusion algorithm to the quantization in cell-oriented computer generated holograms. This error diffusion quantization allows the adaptation of the calculation of the CGH to application specific requirements like minimum printable apertures.

Minimum hydrochemical conditions allowing limestone cave development

Early theoretical investigations into initiation of limestone cave development suggested that water entering small fractures approaches saturation within a short distance and thus appeared to be unable to produce much further enlargement of these fractures. The answer to this problem seems to be White's (1977) “kinetic trigger” idea, emphasizing the precipitous drop in dissolution rates as equilibrium is approached. However, minimum conditions of flow rate, passage geometry, and initial CO2 concentration may exist, below which the waters will so nearly achieve saturation that caves will be unable to develop. Modeling results indicate that under geologically reasonable PCO2 and head gradient values, the minimum initial aperture widths in which caves will develop is of the order of 100 μm. Initial apertures wider than about 500 μm will form passages very easily, even under low head gradients. There will thus be strong differential selection among initial flow paths with regard to cavern passage development.

Lunar occultation visibility

This paper presents a theoretical and observational study of the visibility of stars during lunar occultations. The theory includes the effects of varying background brightness (from scattered moonlight, night skylight, twilight, daylight, earthshine, and light pollution, as appropriate), telescope parameters (including light-collecting power, magnification, and throughput), and observer quality (based on the Snellen rating, comparative experience, and age). Our model is represented as a set of equations that predict the magnitude of the faintest star that would be visible under a given set of conditions. We report on 1739 visual observations of occultations for comparison with the theoretical model. The theoretical model is well matched by the observations with a typical uncertainty of roughly one-third of a magnitude. Thus, we have confidence that our equations are an accurate model of occultation visibility. We have four recommendations: first, observers should utilize the optimal magnification where the apparent size of the star's disk matches the eye's critical visual angle (this typically is the case for a magnification of roughly 10 power per centimeter of aperture); second, observers should record the magnification used and occultation data bases should include this information; third, occultation predictions should not list the photographic magnitudes of faint stars; and fourth, occultation predictions should routinely present the calculated minimum telescope aperture required to view the occultation as a realistic guide for observers.

The point‐spread function of a confocal microscope: its measurement and use in deconvolution of 3‐D data

SUMMARYWe have measured the point‐spread function (PSF) for an MRC‐500 confocal scanning laser microscope using subresolution fluorescent beads. PSFs were measured for two lenses of high numerical aperture—the Zeiss plan‐neofluar 63 × water immersion and Leitz plan‐apo 63 × oil immersion—at three different sizes of the confocal detector aperture. The measured PSFs are fairly symmetrical, both radially and axially. In particular there is considerably less axial asymmetry than has been demonstrated in measurements of conventional (non‐confocal) PSFs. Measurements of the peak width at half‐maximum peak height for the minimum detector aperture gave approximately 0·23 and 0·8 μm for the radial and axial resolution respectively (4·6 and 15·9 in dimensionless optical units). This increased to 0·38 and 1·5 μm (7·5 and 29·8 in dimensionless units) for the largest detector aperture examined. The resulting optical transfer functions (OTFs) were used in an iterative, constrained deconvolution procedure to process three‐dimensional confocal data sets from a biological specimen—pea root cells labelled in situ with a fluorescent probe to ribosomal genes. The deconvolution significantly improved the clarity and contrast of the data. Furthermore, the loss in resolution produced by increasing the size of the detector aperture could be restored by the deconvolution procedure. Therefore for many biological specimens which are only weakly fluorescent it may be preferable to open the detector aperture to increase the strength of the detected signal, and thus the signal‐to‐noise ratio, and then to restore the resolution by deconvolution.

Vessel Occlusions in Plants: Morphological, Functional and Evolutionary Aspects

The minimum pit aperture diameter of a vessel-parenchyma pit pair was found as the decisive wood anatomical feature for vessel occlusion by either tyloses or gums. Based on this observation, as well as on considerations and established knowledge about the functional significance of vessel occlusions, an evolutionary hypothesis is presented. In order to withstand microorganisms and embolisms, plants are able to occlude their vessels with tyloses or gums. The most primitive Angiosperms show tylosis formation. With the decreasing pit sizes in the vessel wall during plant evolution, gum formation was developed, whereas the increasing vessel sizes led in some plants to renewed tylosis formation.

Epidermal conductance, stomatal density and stomatal size among genotypes of Sorghum bicolor (L.) Moench

Abstract. The ability of a plant to survive severe water deficits depends on its ability to restrict water loss through the leaf epidermis after stomata attain minimum aperture. At this stage, the rate of water loss is regulated by the epidermal conductance (gc). Low gc would be a useful selection criterion to identify genotypes with enhanced survival capability. Consequently, variation in gc among Sorghum bicolor (L.) Moench genotypes was evaluated. Since there is little conclusive evidence linking gc with leaf waxiness, alternative hypotheses relating gc to stomatal trails were also examined. Epidermal conductance varied from 6.3 to 17.6mmol m−2 s−1 among sorghum genotypes. It was unrelated to stomatal pore length which varied with genotype and to pore depth which was similar for all genotypes measured. However, gc, increased with increasing stomatal density. This indicates that stomatal density plays a direct role in water loss even at very low conductances. The association of low stomatal density with low gc is consistent with the hypothesis that at the smallest stomata aperture, water loss from the epidermis above guard cell teichodes becomes a significant source of leaf water loss. Since low gc is directly related to crop survival under severe water deficits, it is recommended that genotypes with low gc. be selected using the selection criterion of stomatal density.

THE EFFECTS OF GLAUCOUSNESS, EPICUTICULAR WAX, LEAF AGE, PLANT HEIGHT, AND GROWTH ENVIRONMENT ON WATER LOSS RATES OF EXCISED WHEAT LEAVES

Water loss at minimum stomatal aperture (residual transpiration) from plant surfaces accounts for a substantial proportion of total transpiration during periods of water stress and at night. Its reduction by genetic selection has been suggested as a desirable objective in water-limited environments. To identify genetic and environmental sources of variation in residual transpiration of wheat (Triticum spp.), the effects of glaucousness, epicuticular wax, leaf age, plant height, and growth environment were determined using excised leaves. Glaucousness reduced residual transpiration by an average of 10%. Differing quantities of epicuticular wax and glaucousness in an isogenic pair of genotypes affected residual transpiration as well, the rate being 33% greater in the low wax, nonglaucous than in the high wax, glaucous line. Residual transpiration rate of flag leaves of field-grown plants increased with leaf age, particularly during the 7 d following ligule appearance. The rate of residual transpiration was greater in tall than in dwarf near-isogenic lines. Residual transpiration of leaves from plants grown in glasshouses was 44–66% lower than that of plants grown outdoors, which had a mean rate of 2.68 × 10−5 g H2O cm−2 min−1. Method of water application to glasshouse plants influenced residual transpiration rate. The rate for leaves of plants watered by spraying water onto the plant and soil surface was 20% greater than that of leaves of plants watered on the soil surface only. It was concluded that the increase in residual transpiration rate with leaf age was due to duration of exposure to the rigors of the exterior environment; the absence of this in controlled environments results in lower rates of residual transpiration than in the field.Key words: Cuticular transpiration, Triticum aestivum L., Triticum turgidum L. var. durum, wheat

Improved model for fluid-driven cracks in jointed rock : Shaffer, R J; Ingraffea, A R; Heuze, F E In: Research and Engineering Applications in Rocks Masses (paper to the 26th US Symposium on Rock Mechanics, Rapid City, 26–28 June 1985)V1, P333–P339. Publ Rotterdam: A. A. Balkema, 1985

The finite element model FEFFLAP (Finite Element Fracture and Flow Analysis Program) is being developed for and applied to hydrofracture analyses in support of the Unconventional Gas Recovery Program at the Lawrence Livermore National Laboratory. The major characteristics of FEFFLAP were presented earlier. Two improvements made to the model are presented here: a multiple load capability and a selection of minimum aperture for fluid flow. The results of two verification and example problems are also given. 6 refs., 7 figs.