Ray Tracing Study Research Articles

A Ray Tracing Study of Gem Quality

A computerized three-dimensional ray tracing technique is utilized to obtain the scattered pattern of light perpendicularly incident on the table of gem stones. It is then shown that a correlation exists between gem cuts considered best by the diamond trade and the reflection pattern within a cone angle of about 60°.

Angle-resolving photoelectron energy analyzer designed for synchrotron radiation spectroscopy

This paper describes design considerations, input lens analysis, ray-tracing studies, construction details and initial tests of a Kuyatt—Simpson-type photoelectron energy analyzer. The analyzer has been designed specifically for angle-resolved photoemission studies using synchrotron radiation. Design features include input and output lens systems which establish virtual slits and apertures which define the input solid angle and source region. Constant angular resolution, constant energy-resolution and constant transmission are achieved by the analyzer. The performance of the analyzer has been checked analytically using computer ray-tracing techniques and experimentally. Initial tests have verified the ray-tracing results and have shown that all the analyzer design specifications have been realized.

Three‐dimensional ray trace studies over a rough ocean bottom topography

In sea areas where long‐range acoustic propagations involves repeated bottom reflection, it is essential to consider the three‐dimensional aspect of the reflection. Computational methods by DeWitt [J. Acoust. Soc. Am. 62, S19(A), (1977)] have been extended to include horizontal changes in the sound speed profile and bottom loss at each reflection. It is now possible to study horizontal ray deflections in areas containing a mid‐ocean ridge. An area of 120 000 km2 of sea bottom is represented by triangular facets developed from a grid of bathymetric points at one km intervals. This completely describes the bottom to the degree that it is presently known from the best existing charts. Sound speed profiles can change at large zone boundaries but horizontal refraction is neglected. Bottom reflection losses are calculated as a function of grazing angle for each bottom bounce of the ray. Rays which have accumulated a loss greater than a selected threshold can then be discontinued. Illustration and conclusions of the study will be given.

Propagation through a GulfStream Ring

Previously reported ray tracing studies of fixed source and receiver propagation through a Gulf Stream Ring have been extended to several new geometries involving receivers below the SOFAR axis and sources at various ranges and depths. Particular attention is given to the variability of multipath structure as a function of source position. Results from an approximate model of horizontal refraction are also presented.

Measuring concave diffraction grating efficiencies at grazing incidence

The efficiency of a concave diffraction grating in a given order is obtained by measuring the intensities of the diffracted and incident beams and taking their ratio. A valid measurement requires that both the incident and diffracted beams be collected, in their entirety, by the detector. At grazing incidence, however, the diffracted beam may spread beyond the detector due to aberrations. In addition, the diffracted beams of consecutive orders may overlap so that unambiguous efficiency measurements cannot be made. The effect of aberrations on efficiency measurements has been studied, using ray tracing, for the geometry of the measuring instrument in use at the Naval Research Laboratory. This instrument, a reflectometer wherein the detector rotates around the grating at a given distance, is attached to a VUV monochromator which furnishes a diverging beam. The main effect of aberrations for this instrument is a spread of the diffracted beam in the direction of dispersion. The width of the diffracted beam is wavelength dependent and is minimal at the horizontal focus, spreading to longer and shorter wavelengths. Reducing the divergence of the incident beam reduces the spread but, for small radius gratings, not always sufficiently so that the entire diffracted beam can be collected by the detector. The distance from the detector to the grating can also be adjusted to aid in collecting all the diffracted beam. Some results of the ray tracing studies will be presented, and the effect of the f-number of the incident beam and the detector distance will be discussed.

PL whistlers

Simultaneous ground and satellite VLF observations together with raytracing studies clearly establishes the existence of ground observed PL whistlers. The dynamic spectrum (ƒ-ν-t shape) of observed PL whistlers may be reproduced exactly by raytracing in TLG magnetospheric models consistent with lower ionosphere, topside ionosphere and equatorial density measurements. The Transition Level Gradient (TLG) model is based on the observation that the transition level altitude increases towards the plasmapause (Titheridge, 1976). PL ground whistlers (i) are observed downgoing over large latitudinal ranges, for up to 2000 km of satellite travel, by ISIS II at 1400 km altitude, (ii) have almost the same dynamic spectrum over the entire latitudinal range observed by ISIS II, (iii) are indistinguishable from ducted whistlers over the observed frequency range (i.e. linear Q for ƒ < 10 kHz), (iv) have nose frequencies > 16 kHz, (v) at 1400 km altitude have a lower latitudinal cutoff at L ∼ 2 and a higher latitudinal cutoff between L ∼ 3 and L ∼ 4 and (vi) probably only occur at night-time during or immediately following disturbed magnetic activity.

Ray Tracing Study of Effects of Ionospheric Irregularities on HF and VHF Radio Waves

A three-dimensional ray tracing programme is used to study the effects of ionospheric irregularities on radio waves in the HF and VHF range. The electron density model used is the alpha-Chapman electron density profile. A toroidal East-West irregularity with a 150 Km by 50 Km elliptical cross section, tilted 15° with respect to the horizontal, and having a peak electron density 10% higher than the background level is taken at various heights in the F-region. The following effects are observed for low latitude north-south propagation, (a) Ray paths are significantly affected by the irregularity, the strength of the effect depending upon where the ray meets the irregularity; the phase path and ground range can change by 100 Km at 20 MHz, (b) the effect is less if the irregularity is encountered on the return path, (c) there is a focussing effect of the irregularity which may enhance the signal in certain regions, and (d) the effect on VHF signals from satellites is small but significant for such applications as interferometric position determination and radio astronomy.

The theory of VLF Doppler signatures and their relation to magnetospheric density structure

The published spectrograms of signals from ground-based VLF transmitters observed aboard satellites show a wide variation from sample to sample. In general, the observed signals are Doppler shifted by the motion of the satellite, but in some published samples there is no observed Doppler shift. A ray tracing study of differing VLF Doppler signatures observed by the Ogo 4, FR 1, and Isis 2 VLF experiments has shown that each signature can be reproduced by a distinct class of electron density gradient models. Large positive and negative Doppler shifts (∼100 Hz) are reproduced by a strong decreasing electron density gradient which interacts with the magnetic field curvature gradient between L ∼ 2 and L ∼ 3. Presence of a strong signal with no Doppler shift is shown to be a result of trapping of upgoing rays by steep density drop-offs. Merging of the spectral components in the Doppler shifted signals is interpreted in terms of scattering by small-scale field-aligned density irregularities. These results allow VLF Doppler observations to be used as a new diagnostic tool in determining magnetospheric density structure below L ∼ 3 and in estimating the effective coverage of the lower ionosphere by the ground-based VLF transmitter in the excitation hemisphere.

Non-reversibility for radio rays in the ionosphere

A recent study of the WKB solutions for radio wave propagation in the ionosphere has shown that the complex phase of the ith wave should include a term κ ∝ Γ ii dz. This has hitherto been ignored in ray tracing studies. The effect of including it is investigated and it is shown to lead to non-reversibility of the ray paths and to a small modification of the lateral deviation and bearing error. It is particularly important for frequencies less than the electron gyrofrequency in calculations that require an accurate knowledge of the phase of a wave that has traversed the ionosphere.

Experimental study of ionospheric electron density gradients and their effect on VLF propagation

Ionospheric electron density gradients in the mid-latitude ionosphere have been studied experimentally through their effect on the wave-normal direction of upgoing artificial VLF waves. From the diurnal and seasonal variations of the east-west and north-south components of the unit wave normal, the horizontal gradients of electron density are deduced. It is shown that the direction of propagation of the waves is closely related to certain broad features of the ionospheric structure, namely its variations with longitude or local time which act upon the E-W component of the wave normal and its latitudinal variations which influence the N-S component. These data shed some light on the choice of the initial wave-normal directions for use in magnetospheric ray-tracing studies.

Magnetospheric ducting of low-latitude whistlers as deduced from the rocket measurement of their wave normal directions

The measurement of wave normal directions of low-latitude sunset whistlers was carried out by means of crossed loop aerials on board a rocket. It is found that the features of whistler wave normal directions are quite consistent with the concept of a trapping cone for ducted propagation. In addition, the wave normal directions of ionospherically transmitted whistlers lend further strong support to the ducted propagation of sunset whistlers. We deduce the enhancement factor, scale and structure of sunset ducts by making use of the observed results and theoretical ray tracing studies.

Non-ducted two-hop whistlers in the inner magnetosphere deduced from rocket measurement

The non-ducted whistler propagation in the inner magnetosphere is discussed using the broad-band VLF measurement on board the K-9M-26 rocket launched at 1703 hr JST on 24 August 1969 from Kagoshima Space Center (geomagnetic lat 20°N). A large number of whistlers which seemed to be two-hop whistlers originating in the northern hemisphere were observed. The main features of these whistlers are summarized: (1) their dispersion value is widely scattered in the range 55–75 sec 1 2 , (2) their frequency spectra show a broad maximum in the frequency range 2–5 kHz and higher frequency components are likely to disappear. Attempts are made to interpret these properties in terms of ducted or non-ducted propagation. It is then found from the ray tracing studies that the measurements are satisfactorily explained by non-ducted propagation in the inner magnetospheric model with latitudinal density gradient such as the equatorial anomaly.

Digital Simulation of Sound Transmission in Reverberant Spaces

Digital computers, through their capability for accurate simulation of complex phenomena, have permitted new insights into a number of important problems arising in sound transmission in reverberant spaces: (1) Reverberation theories, based on the geometrical acoustics, are being refined by ray-tracing studies on digital computers. These studies have revealed significant discrepancies in existing reverberation-time formulas and unexpected large dependencies of the decay rate on the shape of the enclosure and the distribution of sound-absorbing materials. (2) Starting with reverberation-free speech or music signals as inputs, computers can add echoes and reverberation with specified delays, spectral content, and decay characteristics. The computer produces several output signals that—when radiated from loudspeakers in an anechoic chamber—produce, at a listener's ears, sound-pressure waves resembling those in real halls. To ensure “externalization” and proper directions of echo arrivals, the computer program is based on the measured sound diffraction around the listener's head. This digital simulation method is useful to “preaudit” architectural designs before construction and to investigate subjective correlates of a wide variety of reverberation processes. (3) Digital computers have made possible the simulation of frequency and space response of stationary sound fields and the calculation of their statistical properties. These properties are important for the design of electroacoustic systems and the evaluation of measurements in reverberant enclosures.

Ray tracing studies for the topside ionosphere

The effects of nonvertical propagation on high-altitude topside sounder data reduction are investigated. Although the extraordinary, ordinary, and Z rays exhibit significant lateral deviation in a spherically stratified ionosphere, the resultant effects on analysis accuracy are generally tolerable; however ionospheric tilts produce very large effects. The joint use of the three modes for future analyses is suggested.