Image formation by an optically stratified medium: optics of mirage and looming

The Askaryan Radio Array (ARA) is an ultra-high energy (> 10 17 eV) cosmic neutrino detector in phased construction near the south pole. ARA searches for radio Cherenkov emission from particle cascades induced by neutrino interactions in the ice using radio frequency antennas (∼ 150 − 800 MHz) deployed at a design depth of 200 m in the Antarctic ice. A prototype ARA Testbed station was deployed at ∼ 30 m depth in the 2010-2011 season and the first three full ARA stations were deployed in the 2011-2012 and 2012-2013 seasons. We present the first neutrino search with ARA using data taken in 2011 and 2012 with the ARA Testbed and the resulting constraints on the neutrino flux from 10 17 − 10 21 eV.

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“…Here, we provide the derivation of Eq. 1 for the exponential index of refraction model [49]. The index of refraction model is given as:…”

Section: Appendix a Appendix A: First Estimation On Ray Tracingmentioning

confidence: 99%

First constraints on the ultra-high energy neutrino flux from a prototype station of the Askaryan Radio Array

Allison

Auffenberg

Bard

et al. 2015

Astroparticle Physics

104

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“…We have seen that the usefulness of this result arises because the description is extremely accurate and because it leads to explicit ray-path solutions for a very broad range of index profiles over a spherical Earth; see Equations (13,14,24,27). This is a significant advance on earlier results in that such paths needed to be obtained by numerical integration and the resultant errors hampered image-inversion work.…”

Section: Discussionmentioning

confidence: 99%

“…A general description of this phenomenon can be found in [23, Part IV, Chapter 2]. Sodha et al [24] have quantified the phenomenon for exponential profiles. Their work needs to be extended using the results obtained above.…”

Section: Discussionmentioning

confidence: 99%

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Microwave propagation over the Earth: image inversion

Fowkes

Nener

2005

J Eng Math

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An extremely accurate but simple asymptotic description for the path of a light ray propagating over a curved Earth with steady radial variations in refractive index is derived using simple scaling arguments. It is used to determine effectively exact analytic solutions for the path of rays through refractive-index profiles described in terms of patched quadratics. Such patched quadratics can be used to accurately describe almost all refractiveindex profiles of practical interest. The results show that images generated by rays passing through a quadratic refractive-index profile are uniformly magnified in the vertical direction, and magnification and displacement observations can be used to determine the refractive-index profile parameters. For patched quadratics, observations of critical rays can be used to determine the thicknesses of the quadratic layers.An effectively exact solution is also obtained for exponential index profiles and this is used to determine the path of rays through a thin boundary layer attached to the Earth; an inferior mirage situation.

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“…In a recent paper Sodha et al (1967) developed a quantitative theory for the phenomena of mirage and looming. However, this theory of image formation in stratified media is limited to the calculation of the position and nature of the image and does not include intensity considerations.…”

Section: Introductionmentioning

confidence: 99%