Thomas Young’s contributions to geometrical optics

In addition to his work on physical optics, Thomas Young (1773-1829) made several contributions to geometrical optics, most of which received little recognition in his time or since. We describe and assess some of these contributions: Young’s construction (the basis for much of his geometric work), paraxial refraction equations, oblique astigmatism and field curvature, and gradient-index optics.

Third-order theory of spectacle lenses applied to correction of peripheral refractive errors

Purpose: To demonstrate that relatively simple third-order theory can provide a framework which shows how peripheral refraction can be manipulated by altering the forms of spectacle lenses. Method: Third-order equations were used to yield lens forms that correct peripheral power errors, either for the lenses alone or in combination with typical peripheral refractions of myopic eyes. These results were compared with those of finite ray-tracing. Results: The approximate forms of spherical and conicoidal lenses provided by third-order theory were flatter over a moderate myopic range than the forms obtained by rigorous raytracing. Lenses designed to correct peripheral refractive errors produced large errors when used with foveal vision and a rotating eye. Correcting astigmatism tended to give large errors in mean oblique error and vice versa. When only spherical lens forms are used, correction of the relative hypermetropic peripheral refractions of myopic eyes which are observed experimentally, or the provision of relative myopic peripheral refractions in such eyes, seems impossible in the majority of cases. Conclusion: The third-order spectacle lens design approach can readily be used to show trends in peripheral refraction.

On selecting an optimal wavelet for detecting singularities in traffic and vehicular data

Serving as a powerful tool for extracting localized variations in non-stationary signals, applications of wavelet transforms (WTs) in traffic engineering have been introduced; however, lacking in some important theoretical fundamentals. In particular, there is little guidance provided on selecting an appropriate WT across potential transport applications. This research described in this paper contributes uniquely to the literature by first describing a numerical experiment to demonstrate the shortcomings of commonly-used data processing techniques in traffic engineering (i.e., averaging, moving averaging, second-order difference, oblique cumulative curve, and short-time Fourier transform). It then mathematically describes WT’s ability to detect singularities in traffic data. Next, selecting a suitable WT for a particular research topic in traffic engineering is discussed in detail by objectively and quantitatively comparing candidate wavelets’ performances using a numerical experiment. Finally, based on several case studies using both loop detector data and vehicle trajectories, it is shown that selecting a suitable wavelet largely depends on the specific research topic, and that the Mexican hat wavelet generally gives a satisfactory performance in detecting singularities in traffic and vehicular data.

Evaluation of coronary angiographic projections to balance the clinical yield with the radiation risk

Objective: Radiation safety principles dictate that imaging procedures should minimise the radiation risks involved, without compromising diagnostic performance. This study aims to define a core set of views that maximises clinical information yield for minimum radiation risk. Angiographers would supplement these views as clinically indicated. Methods: An algorithm was developed to combine published data detailing the quality of information derived for the major coronary artery segments through the use of a common set of views in angiography with data relating to the dose–area product and scatter radiation associated with these views. Results: The optimum view set for the left coronary system comprised four views: left anterior oblique (LAO) with cranial (Cr) tilt, shallow right anterior oblique (AP-RAO) with caudal (Ca) tilt, RAO with Ca tilt and AP-RAO with Cr tilt. For the right coronary system three views were identified: LAO with Cr tilt, RAO and AP-RAO with Cr tilt. An alternative left coronary view set including a left lateral achieved minimally superior efficiency (,5%), but with an ,8% higher radiation dose to the patient and 40% higher cardiologist dose. Conclusion: This algorithm identifies a core set of angiographic views that optimises the information yield and minimises radiation risk. This basic data set would be supplemented by additional clinically determined views selected by the angiographer for each case. The decision to use additional views for diagnostic angiography and interventions would be assisted by referencing a table of relative radiation doses for the views being considered.

Axial length changes with shifts of gaze direction in myopes and emmetropes

Purpose. The purpose of the study was to investigate the changes in axial length occurring with shifts in gaze direction. Methods. Axial length measurements were obtained from the left eye of 30 young adults (10 emmetropes, 10 low myopes, and 10 moderate myopes) through a rotating prism with 15° deviation, along the foveal axis, using a noncontact optical biometer in each of the nine different cardinal directions of gaze over 5 minutes. The subject's fellow eye fixated on an external distance (6 m) target to control accommodation, also with 15° deviation. Axial length measurements were also performed in 15° and 25° downward gaze with the biometer inclined on a tilting table, allowing gaze shifts to be achieved with either full head turn but no eye turn, or full eye turn with no head turn. Results. There was a significant influence of gaze angle and time on axial length (both P < 0.001), with the greatest axial elongation (+18 ± 8 μm) occurring with inferonasal gaze (P < 0.001) and a slight decrease in axial length in superior gaze (−12 ± 17 μm) compared with primary gaze (P < 0.001). In downward gaze, a significant axial elongation occurred when eye turn was used (P < 0.001), but not when head turn was used to shift gaze (P > 0.05). Conclusions. The angle of gaze has a small but significant short-term effect on axial length, with greatest elongation occurring in inferonasal gaze. The elongation of the eye appears to be due to the influence of the extraocular muscles, in particular the oblique muscles.

Influence of inflow turbulence in shock-wave/turbulent-boundary-layer interaction computations

The influence of inflow turbulence on the results of Favre–Reynolds-averaged Navier–Stokes computations of supersonic oblique-shock-wave/turbulent-boundary-layer interactions (shock-wave Mach-number MSW ∼2.9), using seven-equation Reynolds-stress model turbulence closures, is studied. The generation of inflow conditions (and the initialization of the flowfield) for mean flow, Reynolds stresses, and turbulence length scale, based on semi-analytic grid-independent boundary-layer profiles, is described in detail. Particular emphasis is given to freestream turbulence intensity and length scale. The influence of external-flow turbulence intensity is studied in detail both for flat-plate boundary-layer flow and for a compression-ramp interaction with large separation. It is concluded that the Reynolds-stress model correctly reproduces the effects of external flow turbulence.

25 million years to break a continent : early to middle Miocene rifting and syn-extensional magmatism in the southern Gulf of California

Cenozoic extension in western Mexico has been divided into two episodes separated by the change from convergence to oblique divergence at the plate boundary. The Gulf Extensional Province is thought to have started once subduction ended at ~12.5 Ma whereas early extension is classified as Basin and Range. Mid-Miocene volcanism of the Comondú group has been considered as a subduction-related arc, whereas post ~12.5 Ma volcanism would be extension-related. Our new integration of the continental onshore and offshore geology of the south-east Gulf region, backed by tens of Ar-Ar and U-Pb ages and geochemical studies, document an early-mid Miocene rifting and extension-related bimodal to andesitic magmatism prior to subduction termination. Between ~21 and 11 Ma a system of NNW-SSE high-angle extensional faults rifted the western side of the Sierra Madre Occidental (SMO) ignimbrite plateau. In Nayarit, rhyolitic domes and some basalts were emplaced along this extensional belt at 18-17 Ma. These rocks show strong antecrystic inheritance but an absence of Mesozoic and older xenocrysts, suggesting a genesis in the mid-upper crust triggered by extension-induced basaltic influx. In Sinaloa, large grabens were floored by huge dome complexes at ~21-17 Ma and filled by continental sediments with interlayered basalts dated at 15 Ma. Mid-Miocene volcanism, including the largely volcaniclastic Comondú strata in Baja California, was thus emplaced in rift basins and appears associated to decompression melting rather than subduction. Along the coast, flat-lying basaltic lava flows dated at 11-10 Ma are exposed just above the present sea level. Here crustal thickness is 25-20 Km, almost half that in the core of the SMO, implying significant lithosphere stretching before ~11 Ma. This mafic pulse, with relatively high Ti but still clear Nb-Ta negative spikes, may be related to the detachment of the lower part of the subducted slab, allowing asthenosphere to flow into parts of the mantle previously fluxed by subduction fluids. Very uniform OIB-like lavas appear in late Pliocene and Pleistocene, only 18 m.y. after the onset of rifting and ~9 m.y. after the end of subduction. Our study shows that rifting began much earlier than Late Miocene and progressively overwhelmed subduction in generating magmatism.

Late Oligocene to middle Miocene rifting and syn-extensional magmatism in the southwestern Sierra Madre occidental, Mexico: the beginning of the Gulf of California rift

Although Basin and Range style extension affected several areas of western Mexico since the Late Eocene, extension in the Gulf of California region (the Gulf Extensional Province GEP) is thought to have started as subduction waned and ended at ~14 12.5 Ma. A general consensus also exists in considering the mid Miocene Comondú group as a suprasubduction volcanic arc. Our new integration of the geology of the south east Gulf region, backed by 43 new Ar Ar and U Pb mineral ages and geochemical studies, document a widespread phase of extension in the southern GEP between latest Oligocene and Early Miocene that subsequently focused in the region of the future Gulf in the Middle Miocene. Upper Oligocene to Lower Miocene rocks across the southern Sierra Madre Occidental (SMO)(northern Nayarit and southern Sinaloa) were affected by major ~N S to NNW striking normal faults prior to ~21 Ma. Then, between ~21 and 11 Ma, a system of NNW-SSE high angle extensional faults continued extending the southwestern side of the SMO. Rhyolitic domes, shallow intrusive bodies, and lesser basalts were emplaced along this extensional belt at 20-17 Ma. In northern Sinaloa, large grabens were floored by huge dome complexes at ~21-17 Ma and filled by continental sediments with interlayered basalts dated at 15-14 Ma, a setting and timing very similar to Sonora. Early to Middle Miocene volcanism, including the largely volcaniclastic Comondú strata in Baja California Sur, was thus emplaced in rift basins and was likely associated to decompression melting of upper mantle (inducing crustal partial melting) rather than to fluxing by fluids from the young subducting plate. Along the Nayarit and Sinaloa coast, flatlying basaltic lava flows dated at 11-10 Ma are exposed just above the present sea level. Here, crustal thickness is almost half that in the unextended core of the SMO, implying significant lithosphere stretching before ~11 Ma. Our study shows that rifting began much earlier than Late Miocene and provided a fundamental control on the style and composition of volcanism from at least 30 Ma. We envision a sustained period of lithospheric stretching and magmatism during which the pace and breadth of extension changed at ~20-18 Ma to be narrower and likely more rapid, and again at ~12.5 Ma, when the kinematics of rifting became more oblique.

Late Oligocene to Middle Miocene rifting and synextensional magmatism in the southwestern Sierra Madre Occidental, Mexico : the beginning of the Gulf of California rift

Although Basin and Range–style extension affected large areas of western Mexico after the Late Eocene, most consider that extension in the Gulf of California region began as subduction waned and ended ca. 14–12.5 Ma. A general consensus also exists in considering Early and Middle Miocene volcanism of the Sierra Madre Occidental and Comondú Group as subduction related, whereas volcanism after ca. 12.5 Ma is extension related. Here we present a new regional geologic study of the eastern Gulf of California margin in the states of Nayarit and Sinaloa, Mexico, backed by 43 new Ar-Ar and U-Pb mineral ages, and geochemical data that document an earlier widespread phase of extension. This extension across the southern and central Gulf Extensional Province began between Late Oligocene and Early Miocene time, but was focused in the region of the future Gulf of California in the Middle Miocene. Late Oligocene to Early Miocene rocks across northern Nayarit and southern Sinaloa were affected by major approximately north-south– to north-northwest– striking normal faults prior to ca. 21 Ma. Between ca. 21 and 11 Ma, a system of north-northwest–south-southeast high angle extensional faults continued extending the southwestern side of the Sierra Madre Occidental. Rhyolitic domes, shallow intrusive bodies, and lesser basalts were emplaced along this extensional belt at 20–17 Ma. Rhyolitic rocks, in particular the domes and lavas, often show strong antecrystic inheritance but only a few Mesozoic or older xenocrysts, suggesting silicic magma generation in the mid-upper crust triggered by an extension induced basaltic infl ux. In northern Sinaloa, large grabens were occupied by huge volcanic dome complexes ca. 21–17 Ma and filled by continental sediments with interlayered basalts dated as 15–14 Ma, a stratigraphy and timing very similar to those found in central Sonora (northeastern Gulf of California margin). Early to Middle Miocene volcanism occurred thus in rift basins, and was likely associated with decompression melting of upper mantle (inducing crustal partial melting) rather than with fluxing by fluids from the young and slow subducting microplates. Along the eastern side of the Gulf of California coast, from Farallón de San Ignacio island offshore Los Mochis, Sinaloa, to San Blas, Nayarit, a strike distance of >700 km, flat lying basaltic lavas dated as ca. 11.5–10 Ma are exposed just above the present sea level. Here crustal thickness is almost half that in the unextended core of the adjacent Sierra Madre Occidental, implying signifi cant lithosphere stretching before ca. 11 Ma. This mafic pulse, with subdued Nb-Ta negative spikes, may be related to the detachment of the lower part of the subducted slab, allowing an upward asthenospheric flow into an upper mantle previously modified by fluid fluxes related to past subduction. Widespread eruption of very uniform oceanic island basalt–like lavas occurred by the late Pliocene and Pleistocene, only 20 m.y. after the onset of rifting and ~9 m.y. after the end of subduction, implying that preexisting subduction-modified mantle had now become isolated from melt source regions. Our study shows that rifting across the southern-central Gulf Extensional Province began much earlier than the Late Miocene and provided a fundamental control on the style and composition of volcanism from at least 30 Ma. We envision a sustained period of lithospheric stretching and magmatism during which the pace and breadth of extension changed ca. 20–18 Ma to be narrower, and again after ca. 12.5 Ma, when the kinematics of rifting became more oblique.

Peripheral refraction patterns out to large field angles

Purpose To investigate hyperopic shifts and the oblique (or 45-degree/135-degree) component of astigmatism at large angles in the horizontal visual field using the Hartmann-Shack technique. Methods The adult participants consisted of 6 hypermetropes, 13 emmetropes and 11 myopes. Measurements were made with a modified COAS-HD Hartmann-Shack aberrometer across T60 degrees along the horizontal visual field in 5-degree steps. Eyes were dilated with 1% cyclopentolate. Peripheral refraction was estimated as mean spherical (or spherical equivalent) refraction, with/against the rule of astigmatism and oblique astigmatism components, and as horizontal and vertical refraction components based on 3-mm major diameter elliptical pupils. Results Thirty percent of eyes showed a pattern that was a combination of type IV and type I patterns of Rempt et al. (Rempt F, Hoogerheide J, Hoogenboom WP. Peripheral retinoscopy and the skiagram. Ophthalmologica 1971;162:1Y10), which shows the characteristics of type IV (relative hypermetropia along the vertical meridian and relative myopia along the horizontal meridian) out to an angle of between 40 and 50 degrees before behaving like type I (both meridians show relative hypermetropia). We classified this pattern as type IV/I. Seven of 13 emmetropes had this pattern. As a group, there was no significant variation of the oblique component of astigmatism with angle, but about one-half of the eyes showed significant positive slopes (more positive or less negative values in the nasal field than in the temporal field) and one-fourth showed significant negative slopes. Conclusions It is often considered that a pattern of relative peripheral hypermetropia predisposes to the development of myopia. In this context, the finding of a considerable portion of emmetropes with the IV/I pattern suggests that it is unlikely that refraction at visual field angles beyond 40 degrees from fixation contributes to myopia development.

Higher-order aberrations and anisometropia

Purpose/aim Myopia incidence is increasing around the world. Myopisation is considered to be caused by a variety of factors. One consideration is whether higher-order aberrations (HOA) influence myopisation. More knowledge of optics in anisometropic eyes might give further insight into the development of refractive error. Materials and methods To analyse the possible influence of HOA on refractive error development, we compared HOA between anisometropes and isometropes. We analysed HOA up to the 4th order for both eyes of 20 anisometropes (mean age: 43 ± 17 years) and 20 isometropes (mean age: 33 ±17 years). HOA were measured with the Shack-Hartman i.Profiler (Carl Zeiss, Germany) and were recalculated for a 4 mm pupil. Mean spherical equivalent (MSE) was based on the subjective refraction. Anisometropia was defined as ≥1D interocular difference in MSE. The mean absolute differences between right and left eyes in spherical equivalent were 0.28 ± 0.21 D in the isometropic group and 2.81 ± 2.04 D in the anisometropic group. Interocular differences in HOA were compared with the interocular difference in MSE using correlations. Results For isometropes oblique trefoil, vertical coma, horizontal coma and spherical aberration showed significant correlations between the two eyes. In anisometropes all analysed higher-order aberrations correlated significantly between the two eyes except oblique secondary astigmatism and secondary astigmatism. When analysing anisometropes and isometropes separately, no significant correlations were found between interocular differences of higher-order aberrations and MSE. For isometropes and anisometropes combined, tetrafoil correlated significantly with MSE in left eyes. Conclusions The present study could not show that interocular differences of higher-order aberrations increase with increasing interocular difference in MSE.

Non-contact laser-scanning confocal microscopy of the human cornea in vivo

PURPOSE To investigate the utility of using non-contact laser-scanning confocal microscopy (NC-LSCM), compared with the more conventional contact laser-scanning confocal microscopy (C-LSCM), for examining corneal substructures in vivo. METHODS An attempt was made to capture representative images from the tear film and all layers of the cornea of a healthy, 35 year old female, using both NC-LSCM and C-LSCM, on separate days. RESULTS Using NC-LSCM, good quality images were obtained of the tear film, stroma, and a section of endothelium, but the corneal depth of the images of these various substructures could not be ascertained. Using C-LSCM, good quality, full-field images were obtained of the epithelium, subbasal nerve plexus, stroma, and endothelium, and the corneal depth of each of the captured images could be ascertained. CONCLUSIONS NC-LSCM may find general use for clinical examination of the tear film, stroma and endothelium, with the caveat that the depth of stromal images cannot be determined when using this technique. This technique also facilitates image capture of oblique sections of multiple corneal layers. The inability to clearly and consistently image thin corneal substructures - such as the tear film, subbasal nerve plexus and endothelium - is a key limitation of NC-LSCM.

Inclusion of tapered tubes in enhancing the crash performance of automotive frontal structures

This paper treats the design and analysis of an energy absorbing system. Experimental tests were conducted on a prototype, and these tests were used to validate a finite element model of the system. The model was then used to analyze the response of the system under dynamic impact loading. The response was compared with that of a similar system consisting of straight circular tubes, empty and foam-filled conical tubes. Three types of such supplementary devices were included in the energy absorbing system to examine the crush behavior and energy absorption capacity when subjected to axial and oblique impact loadings. The findings were used to develop design guidelines and recommendations for the implementation of tapered tubes in energy absorbing systems. To this end, the system was conceptual in form such that it could be adopted for a variety of applications. Nevertheless, for convenience, the approach in this study is to treat the system as a demonstrator car bumper system used to absorb impact energy during minor frontal collisions.

Structure of the magnetized sheath of a dusty plasma

A three-component fluid model for a dusty plasma-sheath in an oblique magnetic field is presented. The study is carried out for the conditions when the thermophoretic force associated with the electron temperature gradient is one of the most important forces affecting dust grains in the sheath. It is shown that the sheath properties (the sheath size, the electron, ion and dust particle densities and velocities, the electric field potential, and the forces affecting the dust particles) are functions of the neutral gas pressure and ion temperature, the dust size, the dust material density, and the electron temperature gradient. Effects of plasma-dust collisions on the sheath structure are studied. It is shown that an increase in the forces pushing dust particles to the wall is accompanied by a decrease in the sheath width. The results of this work are particularly relevant to low-temperature plasma-enabled technologies, where effective control of nano- and microsized particles near solid or liquid surfaces is required.

Porous versus porthole fuel injection in a radical farming scramjet: A numerical analysis

Numerically computed engine performance of a nominally two-dimensional radical farming scramjet with porous (permeable C/C ceramic) and porthole fuel injection is presented. Inflow conditions with Mach number, stagnation pressure, and enthalpy of 6.44, 40.2MPa, and 4.31 MJ/kg respectively, and fuel/air equivalence ratio of 0.44 were maintained, along with engine geometry. Hydrogen fuel was injected at an axial location of 92.33mm downstream of the leading edge for each investigated injection method. Results from this study show that porous fuel injection results in enhanced mixing and combustion compared to porthole fuel injection. This is particularly evident within the first half of the combustion chamber where porous fuel injection resulted in mixing and combustion efficiencies of 76% and 63% respectively. At the same location, porthole fuel injection resulted in efficiencies respectively of 58% and 46%. Key mechanisms contributing to the observed improved performance were the formation of an attached oblique fuel injection shock and associated stronger shock-expansion train ingested by the engine, enhanced spreading of the fuel in all directions and a more rapidly growing mixing layer.