On Fabry P\'erot Etalon based Instruments. I. The Isotropic Case

Here we assess the spectral and imaging properties of Fabry P\'erot etalons when located in solar magnetographs. We discuss the chosen configuration (collimated or telecentric) for both ideal and real cases. For the real cases, we focus on the effects caused by the polychromatic illumination of the filter by the irregularities in the optical thickness of the etalon and by deviations from the ideal illumination in both setups. We first review the general properties of Fabry P\'erots and we then address the different sources of degradation of the spectral transmission profile. We review and extend the general treatment of defects followed by different authors. We discuss the differences between the point spread functions (PSFs) of the collimated and telecentric configurations for both monochromatic and (real) quasi-monochromatic illumination of the etalon. The PSF corresponding to collimated mounts is shown to have a better performance, although it varies from point to point due to an apodization of the image inherent to this configuration. This is in contrast to the (perfect) telecentric case, where the PSF remains constant but produces artificial velocities and magnetic field signals because of its strong spectral dependence. We find that the unavoidable presence of imperfections in the telecentrism produces a decrease of flux of photons and a shift, a broadening and a loss of symmetrization of both the spectral and PSF profiles over the field of view, thus compromising their advantages over the collimated configuration. We evaluate these effects for different apertures of the incident beam.Comment: 20 pages 22 figures 2 Appendice

BIGRE: a low cross-talk integral field unit tailored for extrasolar planets imaging spectroscopy

Integral field spectroscopy (IFS) represents a powerful technique for the detection and characterization of extrasolar planets through high contrast imaging, since it allows to obtain simultaneously a large number of monochromatic images. These can be used to calibrate and then to reduce the impact of speckles, once their chromatic dependence is taken into account. The main concern in designing integral field spectrographs for high contrast imaging is the impact of the diffraction effects and the non-common path aberrations together with an efficient use of the detector pixels. We focus our attention on integral field spectrographs based on lenslet-arrays, discussing the main features of these designs: the conditions of appropriate spatial and spectral sampling of the resulting spectrograph's slit functions and their related cross-talk terms when the system works at the diffraction limit. We present a new scheme for the integral field unit (IFU) based on a dual-lenslet device (BIGRE), that solves some of the problems related to the classical TIGER design when used for such applications. We show that BIGRE provides much lower cross-talk signals than TIGER, allowing a more efficient use of the detector pixels and a considerable saving of the overall cost of a lenslet-based integral field spectrograph.Comment: 17 pages, 18 figures, accepted for publication in Ap

Lines in Euclidean Ramsey theory

Let $\ell_m$ be a sequence of $m$ points on a line with consecutive points of distance one. For every natural number $n$, we prove the existence of a red/blue-coloring of $\mathbb{E}^n$ containing no red copy of $\ell_2$ and no blue copy of $\ell_m$ for any $m \geq 2^{cn}$. This is best possible up to the constant $c$ in the exponent. It also answers a question of Erd\H{o}s, Graham, Montgomery, Rothschild, Spencer and Straus from 1973. They asked if, for every natural number $n$, there is a set $K \subset \mathbb{E}^1$ and a red/blue-coloring of $\mathbb{E}^n$ containing no red copy of $\ell_2$ and no blue copy of $K$.Comment: 7 page

In Vivo Time- Resolved Microtomography Reveals the Mechanics of the Blowfly Flight Motor

Dipteran flies are amongst the smallest and most agile of flying animals. Their wings are driven indirectly by large power muscles, which cause cyclical deformations of the thorax that are amplified through the intricate wing hinge. Asymmetric flight manoeuvres are controlled by 13 pairs of steering muscles acting directly on the wing articulations. Collectively the steering muscles account for <3% of total flight muscle mass, raising the question of how they can modulate the vastly greater output of the power muscles during manoeuvres. Here we present the results of a synchrotron-based study performing micrometre-resolution, time-resolved microtomography on the 145 Hz wingbeat of blowflies. These data represent the first four-dimensional visualizations of an organism's internal movements on sub-millisecond and micrometre scales. This technique allows us to visualize and measure the three-dimensional movements of five of the largest steering muscles, and to place these in the context of the deforming thoracic mechanism that the muscles actuate. Our visualizations show that the steering muscles operate through a diverse range of nonlinear mechanisms, revealing several unexpected features that could not have been identified using any other technique. The tendons of some steering muscles buckle on every wingbeat to accommodate high amplitude movements of the wing hinge. Other steering muscles absorb kinetic energy from an oscillating control linkage, which rotates at low wingbeat amplitude but translates at high wingbeat amplitude. Kinetic energy is distributed differently in these two modes of oscillation, which may play a role in asymmetric power management during flight control. Structural flexibility is known to be important to the aerodynamic efficiency of insect wings, and to the function of their indirect power muscles. We show that it is integral also to the operation of the steering muscles, and so to the functional flexibility of the insect flight motor