Abstract:
We investigate the mechanism of the nonparaxial propagation of the tightly focused beams in the view of Fourier optics. It shows that it is the phase of the angular spectrum which induces the interesting evolution of the tightly focused beams. Based on the theory of Fourier optics, we propose an approach on controlling and detecting the focusing spot of the tightly focused beams.

Abstract:
The heliometer of Fraunhofer in Koenigsberg (1824) is a refractor in which the lens is split into two halves to which is applied a linear displacement along the cut. Later in 1890s a variation of the heliometer has been realized in Goettingen using a beam splitting wedge: these methods were both subjected to chromatic and refractive aberrations; the second configuration being much less affected by thermal fluctuations. The mirrored version of the heliometer conceived at the Observatorio Nacional of Rio de Janeiro overcome these problems: the two halves of the vitrified ceramic mirror split at a fixed heliometric angle produce the two images of the Sun exempt of chromatisms and distortions. The heliometer of Rio is a telescope which can rotate around its axis, to measure the solar diameter at all heliolatitudes. A further development of that heliometer, now under construction, is the annular heliometer, in which the mirrors are concentric, with symmetrical Point Spread Functions. Moreover the location of the Observatory of Rio de Janeiro allows zenithal observations, with no atmospheric refraction at all heliolatitudes, in December and January.

Abstract:
The Large Binocular Telescope (LBT) is a unique telescope featuring two co-mounted optical trains with 8.4m primary mirrors. The telescope Adaptive Optics (AO) system uses two innovative key components, namely an adaptive secondary mirror with 672 actuators and a high-order pyramid wave-front sensor. During the on-sky commissioning such a system reached performances never achieved before on large ground-based optical telescopes. Images with 40mas resolution and Strehl Ratios higher than 80% have been acquired in H band (1.6 micron). Such images showed a contrast as high as 10e-4. Based on these results, we compare the performances offered by a Natural Guide Star (NGS) system upgraded with the state-of-the-art technology and those delivered by existing Laser Guide Star (LGS) systems. The comparison, in terms of sky coverage and performances, suggests rethinking the current role ascribed to NGS and LGS in the next generation of AO systems for the 8-10 meter class telescopes and Extremely Large Telescopes (ELTs).

Abstract:
Metal-dielectric layered stacks for imaging with sub-wavelength resolution are regarded as linear isoplanatic systems - a concept popular in Fourier Optics and in scalar diffraction theory. In this context, a layered flat lens is a one-dimensional spatial filter characterised by the point spread function. However, depending on the model of the source, the definition of the point spread function for multilayers with sub-wavelength resolution may be formulated in several ways. Here, a distinction is made between a soft source and hard electric or magnetic sources. Each of these definitions leads to a different meaning of perfect imaging. It is shown that some simple interpretations of the PSF, such as the relation of its width to the resolution of the imaging system are ambiguous for the multilayers with sub-wavelenth resolution. These differences must be observed in point spread function engineering of layered systems with sub-wavelength sized PSF.

Abstract:
Let $H$ and $K$ be locally compact groups and also $\tau:H\to Aut(K)$ be a continuous homomorphism and $G_\tau=H\ltimes_\tau K$ be the semi-direct product of $H$ and $K$ with respect to the continuous homomorphism $\tau$. This paper presents a novel approach to the Fourier analysis of $G_\tau$, when $K$ is abelian. We define the $\tau$-dual group $G_{\hat{\tau}}$ of $G_\tau$ as the semi-direct product $H\ltimes_{\hat{\tau}}\hat{K}$, where $\hat{\tau}:H\to Aut(\hat{K})$ defined via (\ref{A}). We prove a Ponterjagin duality Theorem and also we study $\tau$-Fourier transforms on $G_\tau$. As a concrete application we show that how these techniques apply for the affine group and also we compute the $\tau$-dual group of Euclidean groups and the Weyl-Heisenberg groups.

Abstract:
Using numerical simulations, here we demonstrate that a single sheet of graphene with properly designed inhomogeneous, nonuniform conductivity distributions can act as a convex lens for focusing and collimating the transverse-magnetic (TM) surface Plasmon polariton (SPP) surface wave propagating along the graphene. Consequently, we show that the graphene can act as a platform capable of obtaining spatial Fourier transform of infra-red (IR) SPP signals. This may lead to rebirth of the field of Fourier Optics on a one-atom-thick structure.

Abstract:
What are the historical evidence concerning the turning of the spyglass into an astronomical instrument, the telescope? In Sidereus Nuncius and in his private correspondence Galileo tells the reader what he did with the telescope, but he did not disclose the existence of a theory of the instrument. Still, the instruments which Galileo produced are extant and can be studied. With replicas of Galileo's telescopes that magnify 14 and 21 times, we have simulated and analyzed Galileos practices as he reported them in Sidereus Nuncius. On this ground, we propose a new solution to this old problem. We establish the knowledge of optics that Galileo had as it can be read off from the telescopes he constructed and the way he put them to use. Galileo addressed optical difficulties associated with illumination, resolution, field of view, and magnification. His optical knowledge was well thought through, originated as it did in a radically new optical framework.

Abstract:
The VST (VLT Survey Telescope) is a 2.6 m class Alt-Az telescope to be installed at Mount Paranal in the Atacama desert, Chile, in the European Southern Observatory (ESO) site. The VST is a wide-field imaging facility planned to supply databases for the ESO Very Large Telescope (VLT) science and carry out stand-alone observations in the UV to I spectral range. This paper will focus on the distributed control system of active optics based on CAN bus and PIC microcontrollers. Both axial and radial pads of the primary mirror will be equipped by astatic lever supports controlled by microcontroller units. The same CAN bus + microcontroller boards approach will be used for the temperature acquisition modules.

Abstract:
We propose a new algorithm for an adaptive optics system control law which allows to reduce the computational burden in the case of an Extremely Large Telescope (ELT) and to deal with non-stationary behaviors of the turbulence. This approach, using Ensemble Transform Kalman Filter and localizations by domain decomposition is called the local ETKF: the pupil of the telescope is split up into various local domains and calculations for the update estimate of the turbulent phase on each domain are performed independently. This data assimilation scheme enables parallel computation of markedly less data during this update step. This adapts the Kalman Filter to large scale systems with a non-stationary turbulence model when the explicit storage and manipulation of extremely large covariance matrices are impossible. First simulation results are given in order to assess the theoretical analysis and to demonstrate the potentiality of this new control law for complex adaptive optics systems on ELTs.

Abstract:
The trend towards ever larger telescopes and more advanced adaptive optics systems is driving the need for deformable mirrors with a large number of low cost actuators. Liquid mirrors have long been recognized a potential low cost alternative to conventional solid mirrors. By using a water or oil based ferrofluid we are able to benefit from a stronger magnetic response than is found in magnetic liquid metal amalgams and avoid the difficulty of passing a uniform current through a liquid. Depositing a thin silver colloid known as a metal liquid-like film (MELLF) on the ferrofluid surface solves the problem of low reflectivity of pure ferrofluids. This combination provides a liquid optical surface that can be precisely shaped in a magnetic field. We present experimental results obtained with a prototype deformable liquid mirror based on this combination.