Individual Rays Research Articles

Modeling and observations of an elevated, moving infrasonic source: Eigenray methods.

The acoustic ray tracing relations are extended by the inclusion of auxiliary parameters describing variations in the spatial ray coordinates and eikonal vector due to changes in the initial conditions. Computation of these parameters allows one to define the geometric spreading factor along individual ray paths and assists in identification of caustic surfaces so that phase shifts can be easily identified. A method is developed leveraging the auxiliary parameters to identify propagation paths connecting specific source-receiver geometries, termed eigenrays. The newly introduced method is found to be highly efficient in cases where propagation is non-planar due to horizontal variations in the propagation medium or the presence of cross winds. The eigenray method is utilized in analysis of infrasonic signals produced by a multi-stage sounding rocket launch with promising results for applications of tracking aeroacoustic sources in the atmosphere and specifically to analysis of motor performance during dynamic tests.

Light propagation in Swiss-cheese models of random close-packed Szekeres structures: Effects of anisotropy and comparisons with perturbative results

Light propagation in two Swiss cheese models based on anisotropic Szekeres structures is studied and compared with light propagation in Swiss cheese models based on the Szekeres models' underlying LTB models. The study shows that the anisotropy of the Szekeres models has only a small effect on quantities such as redshift-distance relations, projected shear and expansion rate along individual light rays. \newline\indent The average angular diameter distance to the last scattering surface is computed for each model. Contrary to earlier studies, the results obtained here are (mostly) in agreement with perturbative results. In particular, a small negative shift, $\delta D_A:=\frac{D_A-D_{A,bg}}{D_{A,bg}}$, in the angular diameter distance is obtained upon line-of-sight averaging in three of the four models. The results are, however, not statistically significant. In the fourth model, there is a small positive shift which has an especially small statistical significance. The line-of-sight averaged inverse magnification at $z = 1100$ is consistent with $1$ to a high level of confidence for all models, indicating that the area of the surface corresponding to $z = 1100$ is close to that of the background.

Seismic evidence for broad attenuation anomalies in the asthenosphere beneath the Pacific Ocean

We present QADR17, a global model of Rayleigh-wave attenuation based on a massive surface wave data set (372 629 frequency-dependent attenuation curves in the period range 50-260 s). We correct for focusing-defocusing effects and geometrical spreading, and perform a stringent selection to only keep robust observations. Then, data with close epicentres recorded at the same station are clustered, as they sample the same Earth's structure. After this pre-selection, our data set consists of about 35 000 curves that constrain the Rayleigh-wave intrinsic attenuation in the upper mantle. The logarithms of the attenuation along the individual rays are then inverted to obtain global maps of the logarithm of the local attenuation. After a first inversion, outliers are rejected and a second inversion yields a variance reduction of about 45 per cent. Our attenuation maps present strong agreement with surface tectonics at periods lower than 200 s, with low attenuation under continents and high attenuation under oceans. Over oceans, attenuation decreases with increasing crustal ages, but at periods sensitive to the uppermost 150 km, mid-ocean ridges are not characterized by a very localized anomaly, in contrast to what is commonly observed for seismic velocity models. Attenuation is rather well correlated with hotspots, especially in the Pacific ocean, where a strong attenuating anomaly is observed in the long wavelength component of our signal at periods sampling the oceanic asthenosphere. We suggest that this anomaly results from the horizontal spreading of several thermal plumes within the asthenosphere. Strong velocity reductions associated with high attenuation anomalies of moderate amplitudes beneath the East Pacific Rise, the Red Sea and the eastern part of Asia may require additional mechanisms, such as partial melting.

Reproductive Strategy of the Giant Electric Ray in the Southern Gulf of California

AbstractThe objective of the present study was to describe and characterize macroscopic and microscopic aspects of the reproductive biology of the Giant Electric Ray Narcine entemedor, a viviparous elasmobranch targeted by commercial fishers in Mexico. A total of 305 individual rays were captured (260 females, 45 males); all males were sexually mature. The median size at maturity for females was estimated to be 58.5 cm TL, the median size at pregnancy was 63.7 cm TL, and the median size at maternity was 66.2 cm TL. The range of ovarian follicles recorded per female was 1–69; the maximum ovarian fecundity of fully grown vitellogenic oocytes was 17, and uterine fecundity ranged from 1 to 24 embryos per female. The lengths of the oblong ovarian follicles varied significantly among months, and the largest ovarian follicles were found in July, August, and September. Median embryo size was largest in August, and the size at birth was between 12.4 and 14.5 cm TL. Histological evidence of secretions from the glandular tissue of the uterine villi indicate that this species probably has limited histotrophy as a reproductive mode. Vitellogenesis in the ovary occurred synchronously with gestation in the uterus. The Giant Electric Ray has a continuous annual reproductive cycle; a period of ovulation occurs between May and September and two peaks of parturition, one in January and one in August, occur, suggesting that embryonic diapause occurs in some individuals. These results provide useful information for the management of this important commercial species in Bahía de La Paz, Mexico, and will allow possible modification of the current Mexican regulations to enable better protection of this species.

Diffraction and polarization effects in Earth radiation budget measurements.

Thermal radiation emitted and reflected from the Earth and viewed from near-Earth orbit may be characterized by its spectral distribution, its degree of coherence, and its state of polarization. The current generation of broadband Earth radiation budget instruments has been designed to minimize the effect of diffraction and polarization on science products. We used Monte Carlo ray-trace (MCRT) models that treat individual rays as quasi-monochromatic, polarized entities to explore the possibility of improving the performance of such instruments by including measures of diffraction and polarization during calibration and operation. We have demonstrated that diffraction and polarization sensitivity associated with typical Earth radiation budget instrument design features has a negligible effect on measurements.

Secondary cosmic ray nuclei in the light of the single source model and comparison with recent AMS-02 data

Evidence for a local ‘single source’ of cosmic rays is amassing by way of the recent precise measurements of various cosmic ray energy spectra from the AMS-02 instrument. To observations of individual cosmic ray nuclei, electrons, positrons and antiprotons must now be added the determination of the boron-to-carbon ratio and the energy spectrum of lithium to 2000 GV with high precision. Our analysis leads us to claim that, with certain assumptions about propagation in the Galaxy, the results confirm our arguments regarding the presence of a local single source, perhaps, a supernova remnant (SNR). An attempt is made to determine some of the properties of this SNR and its progenitor star.

On the effects of small-scale variability on acoustic propagation in Fram Strait: The tomography forward problem

Acoustic tomography systems have been deployed in Fram Strait over the past decade to complement existing observing systems there. The observed acoustic arrival patterns are unusual, however, consisting of a single, broad arrival pulse, with no discernible repeating patterns or individual ray arrivals. The nature of these arrivals is caused by vigorous acoustic scattering from the small-scale processes that dominate ocean variability in Fram Strait. Simple models for internal wave and mesoscale variability were constructed and tailored to match the variability observed by moored thermisters in Fram Strait. The internal wave contribution to variability is weak. Acoustic propagation through a simulated ocean consisting of a climatological sound speed plus mesoscale and internal wave scintillations obtains arrival patterns that match the characteristics of those observed, i.e., pulse width and travel time variation. The scintillations cause a proliferation of acoustic ray paths, however, reminiscent of "ray chaos." This understanding of the acoustic forward problem is prerequisite to designing an inverse scheme for estimating temperature from the observed travel times.

Time series of temperature in Fram Strait determined from the 2008–2009 DAMOCLES acoustic tomography measurements and an ocean model

AbstractA pilot acoustic tomography program in Fram Strait during 2008–2009 measured a year‐long record of acoustic travel times along a 130 km range acoustic path crossing the West Spitsbergen Current. Individual ray arrivals were not observed. Rather, the arrival patterns consisted of a single, stable, broad arrival pulse of about 100 ms duration. Travel time variations of ±0.15 s recorded the vigorous mesoscale environment of the region and the seasonal cycle. To estimate ocean temperature from the tomography data an inverse scheme employed a high‐resolution ocean model for Fram Strait as the reference ocean. The information from the tomographic measurements is primarily average temperature. Estimated temperatures, averaged over 0–1000 m depth and over range, had a mean of 1.11°C and variations of ±0.33°C; the uncertainty of the tomography estimates was about 60m°C. Agreement with an alternate inverse approach based on EOFs and a Markov Chain Monte Carlo inversion scheme relying on a matched‐peak approach was excellent, indicating a robust estimate for ocean temperature. The inverse estimates for average temperature agreed with the equivalent estimates from hydrographic sections obtained along the acoustic path at the start and end of the program. Among other deficiencies, the ocean model greatly underestimated the intensity of the mesoscale fluctuations and exhibited a warm bias of about 0.38°C in section‐averaged temperature. Tomographic measurements in Fram Strait offer unique large‐scale temperature constraints for ocean models through data assimilation. It is anticipated that these constraints will lead to more accurate estimates of the circulation and transports in Fram Strait.

Hamilton’s optics

Building on work by Fermat and Huygens, Hamilton transformed the study of geometrical optics in his very first paper, presented when still in his teens. His ‘characteristic function’ was an analytical way to describe wavefronts, and in his hands a powerful tool to look at families of rays rather than isolated ones. His prediction of internal and external conical refraction in some crystals and its spectacular verification in a few months established his reputation among his contemporaries. This formulation of optics uncovered many general properties, not easy to see in the conventional method of tracing individual rays. The deepest outcome of his early optical work was a parallel view of the mechanics of particles, which played a fundamental role in the birth of quantum mechanics and continues to be the standard framework for classical mechanics up to the present time.

Geometry of Refractions and Reflections Through a Biperiodic Medium

The behavior of light rays obeying Snell's law in a medium made up of two materials with different refractive indices and which are arranged in a periodic chessboard pattern is described. The analysis is in some ways analogous to the study of rational billiards and uses a return map on one surface to prove, among other things, that the number of angles with which any individual ray intersects the lattice is bounded and that if the ratio of refractive indices is large enough, then the dynamics can be described by interval exchange maps.

Validation of a partial coherence interferometry method for estimating retinal shape.

To validate a simple partial coherence interferometry (PCI) based retinal shape method, estimates of retinal shape were determined in 60 young adults using off-axis PCI, with three stages of modeling using variants of the Le Grand model eye, and magnetic resonance imaging (MRI). Stage 1 and 2 involved a basic model eye without and with surface ray deviation, respectively and Stage 3 used model with individual ocular biometry and ray deviation at surfaces. Considering the theoretical uncertainty of MRI (12-14%), the results of the study indicate good agreement between MRI and all three stages of PCI modeling with <4% and <7% differences in retinal shapes along horizontal and vertical meridians, respectively. Stage 2 and Stage 3 gave slightly different retinal co-ordinates than Stage 1 and we recommend the intermediate Stage 2 as providing a simple and valid method of determining retinal shape from PCI data.

Studying the precision of ray tracing techniques with Szekeres models

The simplest standard ray tracing scheme employing the Born and Limber approximations and neglecting lens-lens coupling is used for computing the convergence along individual rays in mock N-body data based on Szekeres swiss cheese and onion models. The results are compared with the exact convergence computed using the exact Szekeres metric combined with the Sachs formalism. A comparison is also made with an extension of the simple ray tracing scheme which includes the Doppler convergence. The exact convergence is reproduced very precisely as the sum of the gravitational and Doppler convergences along rays in Lemaitre-Tolman-Bondi models. This is not the case when the models are based on non-symmetric Szekeres models. For such models, there is a significant deviation between the exact and ray traced paths and hence also the corresponding convergences.

Enalikter aphson is an arthropod: a reply to Struck et al . (2014)

<i>Enalikter aphson</i> is an arthropod: a reply to Struck <i>et al</i> . (2014)

Hamiltonian ray tracing in an arbitrary curvilinear coordinate system—Amplitude estimation

Acoustic ray tracing is known to be an efficient and robust numerical method to compute propagation paths of acoustic energy through the atmosphere and ocean. Over large propagation distances, a Cartesian formulation of ray tracing is known to be inadequate and a spherical or spheroidal formulation is required in order to obtain accurate propagation paths. An overview of the ray tracing equations in an arbitrary curvilinear coordinate system will be presented and compared with the known spherical coordinate formulation. Typically, coaxial ray paths are used to compute ray tube density and provide an estimation of the amplitude along the ray path. Here, the method of auxiliary parameters is used to identify the exact geometric spreading factor along individual ray paths. The implementation of the resulting ray tracing methods will be discussed including methods used to decrease computation time and planned additions to the propagation scheme.

Omnidirectional underwater camera design and calibration.

This paper presents the development of an underwater omnidirectional multi-camera system (OMS) based on a commercially available six-camera system, originally designed for land applications. A full calibration method is presented for the estimation of both the intrinsic and extrinsic parameters, which is able to cope with wide-angle lenses and non-overlapping cameras simultaneously. This method is valid for any OMS in both land or water applications. For underwater use, a customized housing is required, which often leads to strong image distortion due to refraction among the different media. This phenomena makes the basic pinhole camera model invalid for underwater cameras, especially when using wide-angle lenses, and requires the explicit modeling of the individual optical rays. To address this problem, a ray tracing approach has been adopted to create a field-of-view (FOV) simulator for underwater cameras. The simulator allows for the testing of different housing geometries and optics for the cameras to ensure a complete hemisphere coverage in underwater operation. This paper describes the design and testing of a compact custom housing for a commercial off-the-shelf OMS camera (Ladybug 3) and presents the first results of its use. A proposed three-stage calibration process allows for the estimation of all of the relevant camera parameters. Experimental results are presented, which illustrate the performance of the calibration method and validate the approach.

Further considerations of cosmic ray modulation of infra-red radiation in the atmosphere

Understanding effects of ionisation in the lower atmosphere is a new interdisciplinary area, crossing the traditionally distinct scientific boundaries between astro-particle and atmospheric physics and also requiring understanding of both heliospheric and magnetospheric influences on cosmic rays. Following the paper of Erlykin et al. (2014) we develop further the interpretation of our observed changes in long-wave (LW) radiation, Aplin and Lockwood (2013) by taking account of both cosmic ray ionisation yields and atmospheric radiative transfer. To demonstrate this, we show that the thermal structure of the whole atmosphere needs to be considered along with the vertical profile of ionisation. Allowing for, in particular, ionisation by all components of a cosmic ray shower and not just by the muons, reveals that the effect we have detected is certainly not inconsistent with laboratory observations of the LW absorption cross section. The analysis presented here, although very different from that of Erlykin et al., does come to the same conclusion that the events detected by AL were not caused by individual cosmic ray primaries – not because it is impossible on energetic grounds, but because events of the required energy are too infrequent for the 12h−1 rate at which they were seen by the AL experiment. The present paper numerically models the effect of three different scenario changes to the primary GCR spectrum which all reproduce the required magnitude of the effect observed by AL. However, they cannot solely explain the observed delay in the peak effect which, if confirmed, would appear to open up a whole new and interesting area in the study of water oligomers and their effects on LW radiation. We argue that a technical artefact in the AL experiment is highly unlikely and that our initial observations merit both a wide-ranging follow-up experiment and more rigorous, self-consistent, three-dimensional radiative transfer modelling.

Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar

Interstellar is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by somebody nearby. For this, our team at Double Negative Visual Effects, in collaboration with physicist Kip Thorne, developed a code called Double Negative Gravitational Renderer (DNGR) to solve the equations for ray-bundle (light-beam) propagation through the curved spacetime of a spinning (Kerr) black hole, and to render IMAX-quality, rapidly changing images. Our ray-bundle techniques were crucial for achieving IMAX-quality smoothness without flickering; and they differ from physicists’ image-generation techniques (which generally rely on individual light rays rather than ray bundles), and also differ from techniques previously used in the film industry’s CGI community. This paper has four purposes: (i) to describe DNGR for physicists and CGI practitioners, who may find interesting and useful some of our unconventional techniques. (ii) To present the equations we use, when the camera is in arbitrary motion at an arbitrary location near a Kerr black hole, for mapping light sources to camera images via elliptical ray bundles. (iii) To describe new insights, from DNGR, into gravitational lensing when the camera is near the spinning black hole, rather than far away as in almost all prior studies; we focus on the shapes, sizes and influence of caustics and critical curves, the creation and annihilation of stellar images, the pattern of multiple images, and the influence of almost-trapped light rays, and we find similar results to the more familiar case of a camera far from the hole. (iv) To describe how the images of the black hole Gargantua and its accretion disk, in the movie Interstellar, were generated with DNGR—including, especially, the influences of (a) colour changes due to doppler and gravitational frequency shifts, (b) intensity changes due to the frequency shifts, (c) simulated camera lens flare, and (d) decisions that the film makers made about these influences and about the Gargantua’s spin, with the goal of producing images understandable for a mass audience. There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of Interstellar interesting.

Locomotion of free-swimming ghost knifefish: anal fin kinematics during four behaviors

The maneuverability demonstrated by the weakly electric ghost knifefish (Apteronotus albifrons) is a result of its highly flexible ribbon-like anal fin, which extends nearly three-quarters the length of its body and is composed of approximately 150 individual fin rays. To understand how movement of the anal fin controls locomotion we examined kinematics of the whole fin, as well as selected individual fin rays, during four locomotor behaviors executed by free-swimming ghost knifefish: forward swimming, backward swimming, heave (vertical) motion, and hovering. We used high-speed video (1000fps) to examine the motion of the entire anal fin and we measured the three-dimensional curvature of four adjacent fin rays in the middle of the fin during each behavior to determine how individual fin rays bend along their length during swimming. Canonical discriminant analysis separated all four behaviors on anal fin kinematic variables and showed that forward and backward swimming behaviors contrasted the most: forward behaviors exhibited a large anterior wavelength and posterior amplitude while during backward locomotion the anal fin exhibited both a large posterior wavelength and anterior amplitude. Heave and hover behaviors were defined by similar kinematic variables; however, for each variable, the mean values for heave motions were generally greater than for hovering. Individual fin rays in the middle of the anal fin curved substantially along their length during swimming, and the magnitude of this curvature was nearly twice the previously measured maximum curvature for ray-finned fish fin rays during locomotion. Fin rays were often curved into the direction of motion, indicating active control of fin ray curvature, and not just passive bending in response to fluid loading.

Twenty Years’ Experience with a Novel Geometry ICPC Evacuated Solar Collector

A novel geometry ICPC evacuated tube solar collector was developed at the University of Chicago and Colorado State University in 1993. Individual evacuated tubes of this novel geometry ICPC were experimentally fabricated and tested at Colorado State University in 1994-96 and at the University of Chicago in 1996-97. In 1998 two 14 tube modules were tested on Sandia National Laboratory's two-axis tracking (AZTRAK) platform in Albuquerque New Mexico by Sandia National Laboratory and the University of Chicago. A 336 tube 100 m2 array of this collector has been in continuous operation at a demonstration project in Sacramento California since 1998. From 1998 to the present performance of the Sacramento demonstration array and single and double effect cooling systems has been monitored and evaluated by the California State University at Sacramento and Colorado State University. Optical ray tracing modelling, thermal performance modelling and collector reliability studies have been conducted by Colorado State University during the 1998 to 2013 period.Performance approaching the theoretical predictions was achieved for the individual ICPC evacuated tubes experimentally fabricated by Colorado State University and the University of Chicago. While operating in the range of 120 to 160C, daily solar collection efficiencies of nearly 0.50 and instantaneous solar collection efficiencies of about 0.60 were achieved. Daily cooling COPs of 1.1 were achieved while operating the double effect chiller with energy supplied from the ICPC solar collectors. A ray tracing simulation incorporating ray transmittance and translation, the gap between the glass tube and fin, reflectivity of the reflective surface, absorptivity of the fin and blocking and displacement of the rays by adjacent tubes has been developed. Animation of individual rays and associated summary graphics and an optical and thermal performance model of the collector have also been developed. Performance of the novel ICPC solar collector at various specified angles along the transverse and longitudinal evacuated tube directions was experimentally measured on the Sandia National Laboratory's two-axis tracking (AZTRAK) platform. Data from the Sandia tests was used to validate the ray tracing simulation performance. Data from the initial operation of the Sacramento array were used to further validate the ray tracing simulation and thermal modelling. The primacy of the two identified collector reliability failure modes was established. Details of the various testing and research activities and results are presented. Animations of the ray tracing are also included in the oral presentation.

Ultra broadband indoor channel measurements and calibrated ray tracing propagation modeling at THz frequencies

Ultra broadband communication systems operated at THz frequencies will require the thorough knowledge of the propagation channel. Therefore, an extensive measurement campaign of 50 GHz wide indoor radio channels is presented for the frequencies between 275 and 325 GHz. Individual ray paths are resolved spatially according to angle of arrival and departure. A MIMO channel is recorded in a 2×2 configuration. An advanced frequency domain ray tracing approach is used to deterministically simulate the THz indoor propagation channel. The ray tracing results are validated with the measurement data. Moreover, the measurements are utilized for the calibration of the ray tracing algorithm. Resulting ray tracing accuracies are discussed.