Divergent Ray Research Articles

Differential refractometry by an integrated-optical Young interferometer

Highly sensitive refractive-index determination is used for process monitoring and quality control, e.g., in the food industry, as a detection principle for HPLC and for applications in research. Because of the large temperature dependence of the refractive index of liquids, sensitivities below 10 −5 are obtained only by differential refractometers. A new detection principle is based on the interference of two divergent rays, produced by an integrated optical splitter. These two rays pass the two flow cells and overlap on a CCD array, producing an interference pattern. The problem of ambiguity of the interference signature is overcome by using partially coherent sources, yielding a modulation of the fringe visibility. The position of fringes on the CCD array is evaluated by Fourier analysis of the intensity distribution. The spacial resolution is about a hundredth of a pixel width, resulting in a refractive-index resolution of 1×10 −7 at a measuring range of 5×10 −3. The level of signal noise (peak-to-peak) is 3×10 −8. Flow-cell volumes are in the range 15–140 μl. Tests have been performed with regard to process control and HPLC detection, showing the applicability of the system for these different areas.

On the concentration, focusing, and collimation of x-rays and neutrons using microchannel plates and configurations of holes

A new class of focusing, condensing, and collimating devices for x rays, γ rays, and neutrons is described which is based on the use of microchannel plates (MCPs) or configurations of holes. As well as providing a simple collimating action due to the absorption of severely divergent rays in the channel walls, the microchannel-plate-type structures are capable of providing a focusing and collimating action arising from the reflection of near-grazing-incidence rays at the channel walls. The focusing action is in principle controllable by mechanical bending or slump forming of the channel plates or by appropriate shaping of the channel walls and is remarkably insensitive to source location, device alignment, and wavelength. Theoretical predictions for the performance of such devices are presented via both simple model calculations and Monte Carlo simulations. These suggest that some simple scaling relations hold between key parameters, and provide a guide to the optimum performance levels achievable with such devices for a wide range of geometries. Some experimental observations of the focusing action of MCPs for 0.071-nm x rays are presented. A wide variety of x-ray and neutron optical applications is possible.

Pulsed plasma source spectrometry in the 80–8000-eV x-ray region

The general characteristics are compared for the plane, convex, and concave fixed crystal analyzers which may be applied to the spectrometry of concentrated, intense plasma sources of x radiation involved, for example, in fusion energy and x-ray laser research. The unique advantages of the elliptical analyzer for precise and absolute spectral measurements are noted and detailed descriptions of its geometrical and physical optics are presented. With a source point at one of the foci of the elliptical analyzer profile, the spectrum is Bragg reflected (45°<2θ<135°) at normal incidence upon a detection circle with its center at the second focal point, at which an effective scatter aperture and filter window is located. A primary monochromator consisting of a cylindrical, grazing-incidence mirror is placed between the source and the analyzer to provide an efficient cutoff for high-order diffracted background radiation and to focus the divergent rays so as to obtain an adjustable spectral line length at the detection circle. Photographic film may be transported along the detection circle. Linear position-sensitive electronic detection arrays or a streak camera slit window may be placed along a chord of the detection circle. Calibration procedures for absolute line and continuum intensity measurement are described and examples of calibrating spectra are presented as measured with elliptical analyzers of LiF, PET, KAP, and molecular multilayers for the 80–8000-eV photon energy region. The instrumental effects that contribute to the spectral line shape as measured by the elliptical analyzer spectrograph are defined and a simple line-shape analysis procedure is presented for the determination of the line-broadening contributions of the source. The effects of an off-axis positioning of a source point and of an extended source are analyzed and the application of the elliptical analyzer spectrograph for one- and two-dimensional imaging or an extended source at a given photon energy is discussed. Finally, methods and materials for the construction of the elliptical analyzers are described.

Constrained Optimization Algorithms for Divergent Ray Tomography

Using the projections as constraints, the reconstruction of an object from its fan beam projections is formulated and solved as a problem in constrained optimization. First a general cost criterion is optimized and the result is applied to several specific criteria. This produces a number of relationships (models) between the image and the Lagrange multipliers introduced by the Euler-Lagrange method. Utilizing these models, the ART methods are extended to fan beam projections. A non-recursive algorithm which exploits the speed of the block fast Fourier transform is given and compared with an existing convolution algorithm. The projection slice theorem for divergent ray geometry is given by introducing a new transform, the Angular Projection Transform.

A new type of x-ray absorption spectrometer

A single-crystal spectrometer for x-ray absorption and emission with a microfocus x-ray source has been set up so that the divergent rays from the source can be analyzed over a wide range of Bragg angles with a high degree of resolution. The covered energy interval depends upon the exposed width of the crystal and the geometrical setup. Preliminary experiments are presented to show the effectiveness of the spectrometer.

Direct Three-Dimensional Image Reconstruction from Divergent Rays

The solutions to the image reconstruction problem, in two and three dimensions, for both parallel and divergent ray geometries, are presented within a general linear reconstruction framework. It is shown that, with suitable parameterizations, each of these solutions reduces to a "convolve-and-backproject" algorithm. The exact solution to the three-dimensional divergent ray geometry problem is a new result and is treated in detail. This problem arises when the sensors are located around the object region in three-dimensional space, and the measurement rays diverge (i.e., fan out) from the individual sources. An approximation to the exact solution has been made in order to derive convenient and practical convolving functions for this geometry.

Some results for the lateral divergence of ray tubes

Ray tube divergence is important in determining the field strength of ionospherically propagagated radio wave. The variations of the ray equations lead to simple expressions for the lateral divergence of the ray tube when the ionospheric geometry is such that the principal ray lies in a vertical plane. However, the fact that the principal ray lies in a vertical plane does not ensure that the laterally divergent ray does. Gradients in the plane of the principal ray can cause the diverging ray to depart from a vertical plane and failure to realize this can lead to error. Collisional losses and the Earth's magnetic field are neglected. In the simple case when the ionospheric properties do not vary in the direction normal to the plane of the principal ray the lateral spreading is just δΘP′ where δΘ is the initial angle between the rays and P′is the group path to the point at which the lateral spreading is measured.

Eine Approximative Lösung des Beugungsproblems im Anisotropen Einachsigen Medium

This paper presents a problem of diffraction of light in uniaxial anisotropic medium. Under the supposition that an optical field is represented by weakly convergent (divergent) rays, from the viewpoint of geometrical optics, and that the principal direction of the ray is not too close to an optical axis of crystal, it is possible to perform a separated scalar description of the TE and TM diffraction fields. Expressions are derived for uniaxial anisotropic medium, which represent an approximative scalar description of diffraction fields, dependent on the state of the field in the aperture plane.

EFFET DU CHAMP DE FRANGE D'UN PRISME-LENTILLE MAGNÉTIQUE SUR LA POSITION DE L'IMAGE

Using measured values of the fringing-field intensity of a magnetic prism lens at a large number of points, divergent positive rays issuing from a point source may be traced by numerical calculation through the fringing field to a region within the homogeneous field of the prism. The traced rays enable a virtual source to be calculated, which then locates a virtual image by the Herzog method. The real image is found by symmetry. The method produces a theoretical image position closer to the experimentally determined position than other methods.

X-Ray Diffraction Line Shifts in the Debye-Scherrer Pattern from Wire Specimens with Preferred Orientation

In solid metal samples which have a strong texture, certain planes will favor the diffraction of the vertically divergent rays of the x-ray beam more than the parallel rays. In extreme cases this will produce a diffraction peak shift. The direction and magnitude of the shift obtained from a specimen with a prominent 〈001〉 wire texture is in good agreement with the theoretical calculations of Pike (1957).

The Significance of the Roentgen Visibility of the Horizontal Fissure

THE appearance in the roentgenogram of the chest of linear shadows corresponding to the interlobar fissures of the lung is not unusual, and by comparison of such shadows with anatomic specimens a better understanding of the anatomy of the lungs has been attained (10, 5, 24). This has permitted the more accurate localization of pathologic processes seen in the chest roentgenogram in terms of the lobes and fissures which may be involved. Particularly important has been the identification of certain previously puzzling shadows sometimes included among the “unresolved pneumonias,” and which have, in some instances, been shown to be due to effusions limited to the pulmonary fissures. The unusual and, at times, bizarre outlines of these shadows are thus easily understood. By means of its normal position in the horizontal plane, the fissure between the right upper and middle lobes has attracted primary attention in this extension of x-ray critique. Thus, it is obvious that the plane of a fissure which becomes partially radiopaque would more easily be demonstrable when its greatest diameter lay in the axis of the roentgen ray, whereas, if the ray should penetrate it perpendicularly, the result might be only a faint haziness in the area of its projection, difficult of evaluation, if even detectable. In the customary postero-anterior chest roentgenogram, the horizontal fissure is, therefore, in a position, despite its slight superior convexity, to cast its densest shadow, whereas the long or oblique fissures in front of the lower lobes, being intercepted perpendicularly by the x-ray in the greater part of their extent, are not usually noticed on the film unless they contain a considerable amount of fluid, or their walls are grossly thickened by pathologic induration. Such pathology might give rise to the unusual shadows referred to previously, correctly identified through an adequate understanding of pulmonary lobar anatomy, and by the study of the interlobar spaces, in the case in question, by unusual or special technic. At times the lateral extremity of the oblique fissure attains a plane passing anterolaterally from the hilus which permits it to be demonstrated in the usual chest radiogram as an almost vertical line or one passing slightly laterally and cephalad from the diaphragm, approximately one-fourth the distance from the lateral costal margin to the mid-line (Fig. 1). This shadow may be either unilateral or bilateral, and visualization is made possible by the occasional concurrence of the plane of the fissure and the more divergent rays from an x-ray target comparatively close to the film. A lateral projection, however, permits better demonstration of the oblique fissure of the hemithorax nearest the film, and, on the right, its relationship with the horizontal fissure (11). These demonstrations have been presented by several authors (2, 4, 10).

A Fluoroscope Attachment for Cross-section Drawing and Localization, with an Adaptation for Radiography

PALMIERI, in 1921, described the principle of an original method of obtaining a plastic model of the living heart by the aid of x-rays. Palmieri, who realized that the heart in silhouette is a record of the tangential rays, first obtained a series of films of the heart with the patient rotated at definite angles. Subsequently, these heart silhouettes were copied on cardboard and cut out. In the next stage of the procedure, he used a cutting wire, fastened to a fixed point representing the focus which followed the cardboard silhouettes in the order of their production. At the same time the wire cut off pieces of a plastic block, mounted on a turntable, to duplicate the various positions of the rotation of the patient. Thus was sculptured, for the first time, the model of a living organ. It is very simple to visualize a fluoroscopic adaptation of Palmieri's principle. There must be two synchronized turntables, one for the rotation of the patient and one for the rotation of the plastic block. Such an apparatus has been designed by Lysholm, in 1926, and by Schatzky, in 1928. For the purpose of cross-section drawing and localization, a similar apparatus has been developed. In such modifications, a writing system takes the place of the cutting system. Again the rotation of the record is synchronized with the rotation of the patient. The enveloping tangents can be produced by divergent rays exactly over the organ (Klason, 1929); the tangents can be obtained also by keeping the record in a stationary position overhead. Under such conditions the writing device moves with the fluoroscopic tube and screen which are made into a rigid system (Groedel, 1921). The fluoroscopic adaptation of Palmieri's method utilized a horizontal plane for the production of the record. Cross-section drawings are obtained overhead, with the patient in a sitting position. The entire apparatus occupies considerable space, and seems to be too elaborate when compared with its limited practical usefulness. It would seem that the development of an attachment for one's own vertical fluoroscope would be more practical than the specially built fluoroscopes mentioned. The attachment herein described was developed by the writer and built in his office. I. Attachment for the Method by Parallel Rays.—The attachment is built from maple wood, on a heavy base, 24 inches square, upon the center of which is mounted a horizontal circular turntable, 19 inches in diameters, to serve as a platform for the patient as he stands erect for the examination. Six inches from the center a vertical post is built to support the standing patient in the same position. The counterbalanced fluoroscopic screen and the recording system are mounted on a vertical frame attached to the solid base. A second turntable of similar construction is mounted perpendicular to the table which serves as a platform for the patient and as a mounting surface for the record.

A Wide Angle Magnetic Spectrometer

It is pointed out that in certain problems advantages in current intensity would be gained by having a magnetic spectrometer which would focus widely divergent ions. The usual semicircular type of spectrometer brings divergent rays to a first order focus. By making the proper variation in the intensity of the deflecting magnetic field one can obtain a second order focus. An integral equation is developed to determine the required variation of the magnetic field and a simple method of obtaining the field is given. An instrument now in use for the study of aged ions in gases is briefly described.

The Clinical Value of Roentgen Measurements of Heart Size

ROENTGEN studies of the heart have not, in the past, been looked upon by cardiologists as of any considerable value. To be sure, calcification of the pericardium, foreign bodies within the heart or immediately adjacent to it, gross aneurysmal dilatations of the aorta, dextrocardia, abnormal position of the heart, and gross enlargement have, for some time, been readily recognizable roentgenographically. However, casual observations by the roentgenologists to the effect that in certain cases film studies show an “aortic heart,” in others a “mitral heart,” etc., have not served to impress the cardiologist greatly. If, however, roentgenologists will report exact area and transverse diameter measurements under standard conditions, including heart rate at the moment of examination and perhaps arterial and venous blood pressure readings; if they will accompany their report with a true sized diagram of the heart in relation to normal landmarks, and will go so far as to compare the measurements thus obtained with predicted normal measurements for the individual in question, their efforts must soon be rewarded by the clinician's recognition of the real value of such assistance. Numerous methods have been described by various workers for determining the size of the human heart in terms of its various diameters, its area, and its relationship to chest diameter. Of these, perhaps the most widely used is the planimetric, in which a teleoroentgenogram is made at a target-film distance of 2 meters. The frontal plane silhouette and the total transverse diameter value are measured from the right border at its widest point to the midline; the left border is measured at its widest point to the midline, and correction is made for inherent distortion. Although this method has certain shortcomings, these may be easily overcome by the employment of the method known as orthodiascopy, by the addition of simple and inexpensive accessories to almost any stock fluoroscope. Orthodiascopic studies enable the examiner to combine fluoroscopic examination of the entire chest and the mediastinal structures in the various angles with careful measurements of the frontal plane silhouette. In addition, results arc immediately obtainable without the delay occasioned by the processing of photographic films. Orthodiascopy is a simple method of outlining opaque shadows in their true size without the distortion which always accompanies the x-ray projection of opaque bodies on a photographic film. This is accomplished by recording the position of the tube target when a previously determined fixed point in the x-ray beam coincides with various points along the contours of the shadow cast upon the screen. The resulting diagrams are always considerably smaller than the shadow of the opaque object as seen on the fluoroscopic screen, since the screen image produced by projection of a shadow of an opaque object lying in a beam of divergent rays is, of necessity, magnified.

A Rational Method for Demonstrating the Heart

It may seem preposterous to advocate a rational method for demonstrating the heart, since the image of this organ is one of the oldest and best-known roentgenograms. Still, when we consider the method usually employed we find two fundamental errors. In the lateral view, as you all know, the base of the heart is seen in the middle chest with the tip just touching the chest wall, the heart axis being at an angle to and not parallel to the anterior chest wall where the Film rests. In stout patients it is most difficult to approximate the upper chest snugly to the film. The same principle exists in radiating the upper teeth, where the apex is farther away from the film than the crown. But the oral roentgenologist has early overcome this distorted elongation of the root by projecting the tooth apex into the middle of the film and raising the focus, whereas many roentgenologists still adhere to the method which casts a distorted image of the heart. With this technic the central ray passes obliquely downward from the sixth dorsal rib in order to separate the heart from the dome of the diaphragm. This is possible in the average patient, but in all large and especially stout patients, weighing two hundred pounds and more, very little of the heart is seen on the roentgenogram because, with the degree of inspiration at which the exposure is taken, most of the heart shadow is hidden in the shadow of the diaphragm. However, if we lower the focal point to the tenth rib to overcome some of the distortion, still more of the heart shadow is hidden below the shadow of the diaphragm. But if we at the same time have the patient take an extremely deep breath, holding it a second with open mouth, and then make the exposure, we not only get a correct heart shadow but have it entirely separated from the shadow of the diaphragm. The central ray is above the dome and the lower divergent ray runs parallel with the front slope of the diaphragm, so that a sharp demarcation is obtained between the lower heart boundary and the shadow of the diaphragm. The lowered focus also gives a rounded, sharp outline to the tip of the heart and not the distorted one seen with the method which we formerly used. Before making the exposure the heart is studied fluoroscopically and the correct point for the central horizontal ray is noted, as is also the degree of inspiration which the patient is able to accomplish. It is anything but easy to induce a large, stout patient to take a sufficiently deep breath and to hold it long enough to insure an exposure. At first one sees only the upper part of the heart and is then surprised to see an enormous heart emerge out of the diaphragm shadow on deepest inspiration. The objection formerly raised against forced inspiration was, strange to say, the assertion that deepest inspiration narrows the heart image.

THE DIAGNOSTIC VALUE OF THE ORTHODIAGRAM IN HEART DISEASE

The orthodiagram has been a disappointment to those clinicians who had hoped to find an accurate estimation of the size of the heart of vise in diagnosis. Particularly in the field of cardiac neurosis and early myocarditis, in which the ordinary diagnostic methods fail to show any enlargement, evidence of a slight enlargement might be expected to have diagnostic or prognostic import. The roentgenogram does not give us such evidence because of the magnification of the cardiac shadow by the divergent rays and because of the lack of definition at the margin, since the heart is in active motion while the exposure is being made. The orthodiagram, however, gives perfectly definite images of a moving organ, allows of the observation of any anomaly of motion, and depends only on the skill of the operator in the interpretation of the images viewed. In addition it leaves a permanent record of