Focal Circle Research Articles

Application of the diffraction phenomenon for increasing the neutrino flux density

The investigations of the neutrino physics are connected with great difficulties due to an extremely small section of the interaction of neutrino with a substance. It necessitates enlarging the volumes of a detecting substance to huge sizes. An increase in the density of low-energy neutrino at the detector entrance by several orders (to 1 MeV) is offered with the use of the diffraction phenomenon on the bent crystals in neutrino spectrometers in accordance with the inverse schemes of the methods of Johann and Cauchois. This scheme was used for investigating x-ray radiation from the source situated beyond the focal circle at an unlimited distance from the spectrometer [Trapeznikov V.A., Sapozhnikov V.P. 1970 The application of the x-ray spectrometer with a bent crystal for analyzing the radiation that is beyond the focal circle Pribory i tekhnika eksperimenta , 3 , 227]. For the neutrino investigation a large number of crystals with crystal-holders will be needed; the crystal-holders should be situated on one platform with a general direction of a cumulative neutrino beam towards one detector.

Ellipse to Hyperbola: “With This String I Thee Wed”

SummaryWe introduce a string mechanism that traces both elliptic and hyperbolic arcs having the same foci. This suggests replacing each focus by a focal circle centered at that focus, a simple step that leads to new characteristic properties of central conics that also extend to the parabola.The classical description of an ellipse and hyperbola as the locus of a point whose sum or absolute difference of focal distances is constant, is generalized to a common bifocal property, in which the sum or absolute difference of the distances to the focal circles is constant. Surprisingly, each of the sum or difference can be constant on both the ellipse and hyperbola. When the radius of one focal circle is infinite, the bifocal property becomes a new property of the parabola.We also introduce special focal circles, called circular directrices, which provide equidistance properties for central conics analogous to the classical focus-directrix property of the parabola. Those familiar with paperfolding activities for constructing an ellipse or hyperbola using a circle as a guide, will be pleased to learn that the guiding circle is, in fact, a circular directrix.

Context integration in visual processing: a computational model of center-surround suppression in the visual system

A dysfunction of GABAergic neurotransmission is hypothe-sized to be an important factor in the pathophysiology ofschizophrenia [1], depression and anxiety disorders. Find-ings of decreased center-surround suppression (CSS, i.e. themutual inhibition of a focalvisual stimulus and its sur-rounding) have been interpreted in terms of GABAergicdysfunction [2]. Consistently, strongly decreased CSS isreported in schizophrenic patients [3]. However, the under-lying mechanisms of this decrease remain unclear.MethodsWe developed a biologically inspired neural networkmodel of the human primary visual system, consisting oftwo retinas, two layers of dorso-lateral geniculatenucleus and section B and C of layer 4 of the primaryvisual cortex. The model was built using GENESIS(www.genesis-sim.org) and comprises about 150,000neurons. Three different kinds of neurons were incorpo-rated, namely thalamic relay neurons, and excitatory andinhibitory cortical neurons. The processing of input inthe retina was simply modeled as random-spike units,where the average firing rate corresponds to the inputintensity. The neurons consisted of a soma, an axon andtwo or four dendrites for relay or inhibitory and excita-tory neurons, respectively. We used different ionic chan-nels to reproduce the desired firing behaviour. Synaptictransmission was implemented using the built-in excita-tory and inhibitory synaptic channels.ResultsWe designed a protocol to explore the center-surroundsuppression capabilities of our model. The retina wasstimulated with contrast stimuli similar to those used in[2]. We compared activity in central neurons of layer 4Band 4C in response to two stimuli with a focal circle of40% Michelson contrast, where the target stimulus hada high-contrast surrounding while the reference had auniform surrounding. We found a decrease in activity of27.73% in layer 4B and one of 31.41% layer 4C whencomparing responses to the target with responses to thereference.A plausible neural network model of the human pri-mary visual system which is consistent with psychophy-sical effects previously reported in humans [2] is astarting point to further investigate the role of GABAer-gic inhibition in visual context integration. The capabil-ities of the model to explain both individual variance ofCSS strength and CSS in pathological conditions ofGABAergic neurotransmission remains to be tested. Weplan to do so on the basis of psychophysical CSS data inhumans and correspondingin vivo measurements ofGABA and Glutamate concentrations in primary visualcortex using Proton Magnetic Resonance Spectroscopy(1H-MRS).

Influence of focal spot on characteristics of very small diameter radiosurgical beams

Percentage depth dose (PDD) distributions and beam profiles of very small diameter (1.5-5 mm) megavoltage radiosurgical beams calculated with Monte Carlo (MC) technique critically depend on the diameter of the circular focal spot used in the simulation: The smaller is the field diameter, the larger is the effect. Thus, in simulations of radiosurgical fields that have diameters of the order of the focal spot size, an accurate focal spot geometry should be used. We used a simplified moving slit technique in conjunction with a diode detector for evaluation of the focal spot size and shape of a megavoltage 6 MV linac as well as for determination of the equivalent focal spot diameter of the linac for use in MC simulations. The measured total diode signal contains three components: A direct focal spot signal, a background signal, and an extra-focal radiation signal. A single profile scan of the focal spot signal is Gaussian like in shape, and its full width at half maximum is used to define the focal spot dimension for this scan. The focal spot of our 6 MV linac is approximated with a Gaussian circle, and when the geometry of the effective focal spot circle is used in MC simulations, the agreement between MC-calculated and measured PDD distributions as well as beam profiles is good even for radiosurgical fields as small as 1.5 mm in diameter. Our results also confirm that matching the penumbral areas of accurately measured large-field beam profiles to the same areas of the MC-calculated beam profiles reliably leads to a realistic effective focal spot size for use in MC simulations of very small diameter beams.

Enhanced x-ray resolving power achieved behind the focal circles of Cauchois spectrometers

Maintaining high resolving power is a primary challenge in hard x-ray spectroscopy of newly developed bright and transient x-ray sources such as laser-produced plasmas. To address this challenge, the line widths in x-ray spectra with energies in the 17 keV to 70 keV range were recorded by positioning the detectors on and behind the focal circles of Cauchois type transmission-crystal spectrometers. To analyze and understand the observed line widths, we developed a geometrical model that accounts for source broadening and various instrumental broadening mechanisms. The x-ray sources were laboratory Mo or W electron-bombarded anodes, and the spectra were recorded on photostimulable phosphor image plates. For these relatively small x-ray sources, it was found that when the detector was placed on or near the focal circle, the line widths were dominated by the effective spatial resolution of the detector. When the detector was positioned beyond the focal circle, the line widths were determined primarily by source-size broadening. Moreover, the separation between the spectral lines increased with distance behind the focal circle faster than the line widths, resulting in increased resolving power with distance. Contributions to line broadenings caused by the crystal thickness, crystal rocking curve width, geometrical aberrations, and natural widths of the x-ray transitions were in all cases smaller than detector and source broadening, but were significant for some spectrometer geometries. The various contributions to the line widths, calculated using simple analytical expressions, were in good agreement with the measured line widths for a variety of spectrometer and source conditions. These modeling and experimental results enable the design of hard x-ray spectrometers that are optimized for high resolving power and for the measurement of the x-ray source size from the line widths recorded behind the focal circle.

Crystal Spectrometers and Monochromators in Microanalysis

An x-ray spectrometer is actually a scanning monochromator because two conditions must be satisfied, namely: (1) nλ, = 2d sinθ and (2) θI{= θR to within the rocking curve of the crystal 2Δθ. Before Castaing (B.C.) there were four known types of focussing monochromators, namely: Johann, Johansson, Cauchois, and von Hamos. Castaing was fortunate in having Andre Guinier (well known for his work in x-ray crystallography) as his thesis advisor. Thus, he wisely chose to use a spectrometer of the Johansson type. Had he used a flat crystal spectrometer, the result would have been unsatisfactory and the history of microanalysis would have been significantly different. Many of the spectrometers that were used in the early instruments were either of the Johansson type, in which the crystal planes are curved to a radius of 2R and the surface has a radius of R, the focal circle radius. This is sometimes called exact focussing because rays in the plane of the focal circle converge exactly to a point focus. For simpler construction, the Johann crystal which has the surface parallel to the atomic planes (also curved to a radius of 2R) was sometimes used. While both types provide one-dimensional focussing, the Johansson type is preferred because the effective width of the crystal can be greater.In addition to the type of geometry used, early instruments developed after Castaing (A.C) also had variations in the mechanism of the crystal movement. Many used a relatively simple mechanism with the crystal and detector moving about a fixed center for the focal circle as shown in Fig. 1A. Some later instruments used curved crystals that were fixed in position, and scanning was accomplished either by rotating the crystal as in Fig. 1B or by a mechanism that flexed the crystal and changed the radius of the focal circle as in Fig. 1C. The most satisfactory arrangement and the one subsequently adopted by most manufacturers of commercial microprobes utilized a linear motion of the crystal carriage with a provision for tilting the crystal so that the focal circle always passed though the x-ray source as shown in Fig. 1D. If the detector moves so that it remains on this focal circle, its motion is along a leaf-shaped curve. With this design it is easy to have a readout proportional to wave length.

Soft x-ray emission spectrometer for undulator radiation

An experimental system for high-resolution soft x-ray emission spectroscopy was made. The experimental system is designed to be attached to the undulator beamlines. Spectrometer uses the Rowland circle geometry in which input slit, spherical grating, and multichannel detector lie on the focal circle. Three blazed holographic gratings are changeable in the vacuum. The Rowland circle radii of gratings are 5, 7, and 10 m and their line densities are 600, 1200, and 2400 lines/mm, respectively. The available photon energy is from 30 to 1200 eV. The resolution ΔE is achieved to 0.06 eV by 50 μ-input-slit width for hν=120 eV. Several experimental results measured by this system are presented.

Stigmatic spectrograph with a 2-D CCD detector for soft x-ray observations of laser produced plasmas

Stigmatic spectroscopic observations of laser produced plasma have been performed in the 50–200 Å spectral interval. The purpose was to demonstrate the good instrumental performances of an intensified bidimensional detector installed on a stigmatic soft x-ray spectrometer. The latter is the combination of a grating spectrograph in Rowland circle mount and a toroidal mirror, both working at grazing incidence. The detector is composed of a scintillator on the spectrograph focal circle, an image intensifier, and a charge coupled device. The resulting spatial and spectral resolution are of 60 μm and 1000, respectively. The observations show a marked improvement in term of dynamic range, sensitivity, ease of operation, and real-time data presentation in comparison to both traditional photographic film and photodiode array detection technique.

The reversed Müller-Lyer illusion and figure-ground organization theory.

When the shaft is shortened and reaches neither of the vertices of the two pairs of wings, a reversed Müller-Lyer illusion is observed: a shaft between inward-pointing wings appears to be longer than a shaft between the outward-pointing wings. In this paper it is examined whether this illusion can be explained in terms of figure-ground organization. A circle was used as the focal area, instead of a shaft or a pair of dots, so that the figure-ground character could be seen more definitely in this focal area. The apparent size of the focal circle was measured under different conditions with three variables (enclosure, wings direction, and depth). The focal circle appeared to be largest in the condition where the circle should appear most readily as a hole, ie in the single, wings-in, space condition. The circle appeared to be smallest in the condition where the circle should appear most readily as a disc, ie in the separate, wings-out, object condition. This is consistent with an explanation of the usual, as well as the reversed, Müller-Lyer illusion in terms of figure-ground organization theory.

Phase-space organizations in prolate and oblate potentials: Classical, semiclassical, and quantum results.

The three-dimensional trajectories of a neutron in an average deformed potential are studied for two different potentials with prolate or oblate ellipsoidal deformations. The simplest one is a simple cavity which is shown to be integrable. The motion is studied and is found to be separable in spheroidal coordinates. It is shown that the phase space of an oblate cavity may contain a separatrix which is associated with the crossing of the focal circle while the prolate phase space does contain a separatrix only for the planar trajectories. By using arguments based on a uniform semiclassical approximation, it is shown that the quantum-energy-level spectra present indeed a difference between prolate and oblate shapes corresponding to the crossing of this separatrix. The second potential studied, the Buck-Pilt potential, has a diffuse surface. When it is deformed it becomes unintegrable. For this potential Poincar\'e surfaces of section are drawn. Large regular regions are shown in which the organization of the phase space is that of the cavity. Chaos and nonlinearities are also seen. Consequences of the existence of the regular regions similar to the cavity are drawn for the energy spectrum.

Polarization and pressure dependence of 2p-1s transitions in He-like and Li-like neon recoil ions.

The pressure dependences of 2p-1s transitions in He-like and Li-like neon recoil ions produced in collisions with 1.4-MeV/amu Ar ions were studied for the purpose of assessing effects of polarization and nonstatistical population mechanisms on the relative intensities of prompt and metastable lines. A Johansson-type curved-crystal spectrometer was employed as an x-ray polarimeter by taking spectra with the plane of the focal circle oriented both parallel and perpendicular to the Ar-ion beam. The data indicate that the He-like $^{1}\mathrm{P}$ and $^{3}\mathrm{P}$ lines are only slightly polarized and that the intensity ratio I${(\mathrm{}}^{1}$P)/I${(\mathrm{}}^{3}$P) is not a linear function of pressure. Both of these results appear to be a direct consequence of serious contamination of the spectral region of interest by unresolved spectator-electron transitions.

Observation of the acoustic glory: High-frequency backscattering from an elastic sphere

Measurements of the scattering of 2.10-MHz ultrasonic bursts gave direct evidence of the acoustic glory. Echo amplitudes were measured as a function of the transverse displacement x from the backward axis; they were maximized on the axis and they manifested side lobes. Except near minima, the amplitudes were proportional to J0(kbx/zn), where b and zn are the radius of, and axial distance to, the virtual focal circles from which the echoes appeared to emanate. This dependence on x is direct evidence of axial focusing. (The principal feature of optical glories of drops and bubbles is also axial focusing.) The experiment was performed in water with a fused silica sphere having a radius a≂51.6 mm for which 2πa/λ=ka≂457. A theory is developed for certain of the echo amplitudes and focal parameters. The theory typically overestimates the amplitudes of the stronger of the echoes by 5%. Appendices describe aspects of the theory not amenable to the experiment, including: (i) a shift of focal parameters which should be significant when ka≲100, and (ii) a distortion of transients described in part by the half-order derivative operator.

An automated low-temperature Guinier X-ray diffractometer and camera

A mechanism has been constructed which is capable of cooling the rotating sample of a Guinier diffractometer down to 12.5 K with the use of a closed-cycle refrigerator. The apparatus measures intensities accurately with low background and provides high resolution. Recordings can be made in symmetrical or asymmetrical back-reflection or transmission geometry. An optical slit system allows easy adjustment to the focal circle.

Über die Entzündung eines n-Hexan-Luft-Gemisches durch Laserstrahlung

The ignition of an n-hexane-air mixture by a coherent light beam of a giant pulse laser was investigated by a statistical method. By analyzing the ignition probability and the development time from the ignition reaction to the formation of a measurable nucleus, which were calculated from the fluctuation of the ignition time-lags, the energy transferred from the light beam to the ignition reaction was estimated. The results suggest that the laser beam does not give energy directly to the developing process but only to the initiation of the ignition reaction. The development of the ignition reaction is accelerated during the breakdown process. That the quantitative effect on the ignition increases is due solely to the enlargement of the focal circle in the case of strong laser beam, while the actual energy supplied from the laser beam to the ignition reaction decreases. This means that there is an optimum energy of the laser beam for the ignition.

Application of Spherically Curved Crystals for X-Ray Fluorescence

A general purpose x-ray fluorescence spectrometer has been constructed that employs the focusing properties of large spherically curved crystals. The 10 cm X 10 cm single crystals are bent to a 63.5-cm radius of curvature, and ground to the 31.75 radius of curvature of the focal circle. A motor-driven remotely controlled interchange mechanism has positions for four of these crystals. Also provided are: interchange of gas flow proportional counter or scintillation counter, and of chromium or tungsten target x-ray tubes, and a wide range of entrance and detector slitwidth combinations. Resolution and sensitivity are greatly superior to those of flat crystal optics.

Method for least-squares analysis of gamma-ray scintillation spectra using a bent-crystal monochromator

A method is presented for determining gamma-ray relative intensities using features of the conventional least-squares analysis of a NaI pulse-height spectrum combined with the crystal-diffraction method. In studying the gamma rays from a radioactive source, a bent-crystal spectrometer is used as a gamma-ray monochromator to obtain monoenergetic gamma rays using a strong line source. The individual response functions of a NaI detector to these monoenergetic gamma rays are recorded in a multichannel analyzer. The NaI detector is then directly exposed to a second thin line source of the same source material, placed on the focal circle of the monochromator, and the composite pulse-height spectrum in the NaI detector of all gamma rays from the source is recorded. The relative intensities of the gamma rays are then determined by a least-squares adjustment of the appropriate linear combination of monochromatic response functions to obtain the best fit to the composite pulse-height spectrum. The relative intensities of gamma rays from 169Tm following electron capture of 169Yb obtained with this method show good agreement with those obtained using the crystal-diffraction method.

A Combined Focusing X-Ray Diffractometer and Nondispersive X-Ray Spectrometer for Lunar and Planetary Analysis

AbstractAn instrument is described which is intended to perform a dual purpose (elemental-structural) analysis consistent with the environmental conditions implied by lunar or planetary operation. The dififractometer section is based on a modified Seeman-Bohlin focusing principle in which a sharp-line focus target, a powdered sample, and a movable detector slit all lie on the focusing circle. The convolution of the projections on the focal circle, of a narrow receiving slit on the detector, the line focus target, combined with a high dispersion produce higher resolution and intensity than is common with Bragg focusing diflfractorneters with simitar instrumental parameters. The range of d-spacings covered is from 1 to 7 Å (chromium target). The chemical analysis section of the instrument utilizes the fluorescent X-rays produced in the specimen by the primary beam. A proportional counter and pulse-height anaiyzer accomplish detection and energy discrimination. Resolution is low, but the analysis can distinguish between elements in the range of atomic numbers 11 to 29. Data from a breadboard model is presented. The entire unit, although primarily intended to meet the requirements of space, performs equally well as a routine laboratory analyzer. The horizontal, stationary nature of the specimen holder suggests several specific applications.

Six-Meter Radius Bent-Crystal Spectrograph for Nuclear Gamma Rays

A six-meter radius bent-crystal spectrograph for the precision measurement of nuclear gamma-ray wavelengths has been designed, constructed, and placed into operation at the Massachusetts Institute of Technology. This instrument is particularly well suited for directly measuring neutron capture gamma rays produced by samples placed in the through port of the MIT research reactor. The spectrograph is designed to measure wavelengths of gamma rays in the energy region from 0.1 to 4.0 Mev with an estimated precision that varies from about 0.01% at 0.1 Mev to 0.3% at 4 Mev. Photographic methods are used to record the gamma-ray lines on the focal circle. A bent crystal is used to diffract and focus the gamma rays. Line width and efficiency data have been obtained for the (310), (003), and (006) planes of quartz. The efficiency of the instrument is quite low. In order to record a line at 2.0 Mev an exposure time of about 6000 curie hours is required.

Wavelength distribution of X-rays in the focus of a monochromator and an estimate of the influence of this distribution on precision measurements of lattice constants

Wavelength distribution in the focus of a Johansson type monochromator is computed assuming the tube focus emissivityG(α), reflection curveR(α) and wavelength distribution of the incident radiationJ(λ-λ0) are known. It is shown e.g. that the centre of gravity may be shifted in accordance with the position of the crystal on the focal circle which may considerably influence precision measurements of lattice parameters.

Point-Focusing Two-Crystal X-Ray Monochromator for X-Ray Diffraction

Crystal monochromators can provide the exceptionally fine collimation requisite for the study of small-angle diffraction phenomena. To obtain sufficient intensity and contrast it is necessary not only to bend the crystal but also to use two crystals in tandem with their focal circles mutually orthogonal. The apparatus described uses the x-ray ``weak window'' line source to illuminate the (200) planes of mica in transmission and the (101̄1) planes of a cylindrically ground, polished, and etched quartz crystal in reflection. Symmetrical couple mounts were used to minimize aberrations. The camera essentially isolates the Kα1 component and consequently reduces diffuse background and general radiation artifacts as shown by pertinent applications to collagen and feather keratin. Although operating in air and using exposure times comparable (50–250 hr) to those encountered with aperture-collimated systems, the camera has resolved the central first order of the 640-A macroperiod of collagen fibers and is capable of resolving consecutive orders of spacings as high as ca 3800 A. The Johansson, Johann, and Cauchois geometries are illustrated in a new manner to show the importance of weak and large sources of x-rays, to demonstrate the focal pattern characteristic of two-crystal point-focusing arrangements, and to show why mosaic crystals are incapable of the fine focus required.