Analytical Study of Optical Wavefront Aberrations Using Maple

This paper describes a package for analytical ray tracing of relatively simple optical systems. AESOP (An Extensible Symbolic Optics Package) enables analysis of the effects of small optical element misalignments or other perturbations. (It is possible to include two or more simultaneous independent perturbations.) Wavefront aberrations and optical path variations can be studied as functions of the perturbation parameters. The power of this approach lies in the fact that the results can be manipulated algebraically, allowing determination of misalignment tolerances as well as developing physical intuition, especially in the picometer regime of optical path length variations.Comment: To appear in MapleTech vol. 4, no. 2, pp. 52-62. 11 pages, 5 figures. PDF may also be accessed at http://aa.usno.navy.mil/AESOP

Two-dimensional beam tracing from visibility diagrams for real-time acoustic rendering

We present an extension of the fast beam-tracing method presented in the work of Antonacci et al. (2008) for the simulation of acoustic propagation in reverberant environments that accounts for diffraction and diffusion. More specifically, we show how visibility maps are suitable for modeling propagation phenomena more complex than specular reflections. We also show how the beam-tree lookup for path tracing can be entirely performed on visibility maps as well. We then contextualize such method to the two different cases of channel (point-to-point) rendering using a headset, and the rendering of a wave field based on arrays of speakers. Finally, we provide some experimental results and comparisons with real data to show the effectiveness and the accuracy of the approach in simulating the soundfield in an environment

Average luminosity distance in inhomogeneous universes

The paper studies the correction to the distance modulus induced by inhomogeneities and averaged over all directions from a given observer. The inhomogeneities are modeled as mass-compensated voids in random or regular lattices within Swiss-cheese universes. Void radii below 300 Mpc are considered, which are supported by current redshift surveys and limited by the recently observed imprint such voids leave on CMB. The averaging over all directions, performed by numerical ray tracing, is non-perturbative and includes the supernovas inside the voids. Voids aligning along a certain direction produce a cumulative gravitational lensing correction that increases with their number. Such corrections are destroyed by the averaging over all directions, even in non-randomized simple cubic void lattices. At low redshifts, the average correction is not zero but decays with the peculiar velocities and redshift. Its upper bound is provided by the maximal average correction which assumes no random cancelations between different voids. It is described well by a linear perturbation formula and, for the voids considered, is 20% of the correction corresponding to the maximal peculiar velocity. The average correction calculated in random and simple cubic void lattices is severely damped below the predicted maximal one after a single void diameter. That is traced to cancellations between the corrections from the fronts and backs of different voids. All that implies that voids cannot imitate the effect of dark energy unless they have radii and peculiar velocities much larger than the currently observed. The results obtained allow one to readily predict the redshift above which the direction-averaged fluctuation in the Hubble diagram falls below a required precision and suggest a method to extract the background Hubble constant from low redshift data without the need to correct for peculiar velocities.Comment: 34 pages, 21 figures, matches the version accepted in JCA

Dr TIM: Ray-tracer TIM, with additional specialist scientific capabilities

We describe several extensions to TIM, a raytracing program for ray-optics research. These include relativistic raytracing; simulation of the external appearance of Eaton lenses, Luneburg lenses and generalized focusing gradient-index (GGRIN) lenses, which are types of perfect imaging devices; raytracing through interfaces between spaces with different optical metrics; and refraction with generalised confocal lenslet arrays, which are particularly versatile METATOYs.Comment: 12 pages, 16 figure

Simplified broken Lefschetz fibrations and trisections of 4-manifolds

Shapes of four dimensional spaces can be studied effectively via maps to standard surfaces. We explain, and illustrate by quintessential examples, how to simplify such generic maps on 4-manifolds topologically, in order to derive simple decompositions into much better understood manifold pieces. Our methods not only allow us to produce various interesting families of examples, but also to establish a correspondence between simplified broken Lefschetz fibrations and simplified trisections of closed, oriented 4-manifolds.Comment: 17 pages, 7 figure

The theory of stochastic cosmological lensing

On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is applied to random Einstein-Straus Swiss-cheese models, allowing us to: (1) show an explicit example of the involved calculations; (2) check the validity of the method against both ray-tracing simulations and direct numerical integrations of the Langevin equation. As a byproduct, we obtain a post-Kantowski-Dyer-Roeder approximation, accounting for the effect of tidal distortions on the angular distance, in excellent agreement with numerical results. Besides, the dispersion of the angular distance is correctly reproduced in some regimes.Comment: 37+13 pages, 8 figures. A few typos corrected. Matches published versio