Computing Fresnel integrals via modified trapezium rules

In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis. Our starting point is a method for computation of the error function of complex argument due to Matta and Reichel (J Math Phys 34:298–307, 1956) and Hunter and Regan (Math Comp 26:539–541, 1972). We construct approximations which we prove are exponentially convergent as a function of N , the number of quadrature points, obtaining explicit error bounds which show that accuracies of 10−15 uniformly on the real line are achieved with N=12 , this confirmed by computations. The approximations we obtain are attractive, additionally, in that they maintain small relative errors for small and large argument, are analytic on the real axis (echoing the analyticity of the Fresnel integrals), and are straightforward to implement.

Time-multiplexed Laguerre-Gaussian holographic optical tweezers for biological applications

A ferroelectric liquid crystal spatial light modulator is used to generate up to 24 independently controllable traps in a holographic optical tweezers system using time-multiplexed Fresnel zone plates. For use in biological applications, helical zone plates are used to generate Laguerre-Gaussian laser modes. The high speed switching of the ferroelectric device together with recent advances in computer technology enable fast, smooth movement of traps that can be independently controlled in real time. This is demonstrated by the trapping and manipulation of yeast cells and fungal spores. (c) 2006 Optical Society of America.

Integrated optics for nulling interferometry in the thermal infrared

Modal filtering is based on the capability of single-mode waveguides to transmit only one complex amplitude function to eliminate virtually any perturbation of the interfering wavefronts, thus making very high rejection ratios possible in a nulling interferometer. In the present paper we focus on the progress of Integrated Optics in the thermal infrared [6-20 mu m] range, one of the two candidate technologies for the fabrication of Modal Filters, together with fiber optics. In conclusion of the European Space Agency's (ESA) "Integrated Optics for Darwin" activity, etched layers of clialcogenide material deposited on chalcogenide glass substrates was selected among four candidates as the technology with the best potential to simultaneously meet the filtering efficiency, absolute and spectral transmission, and beam coupling requirements. ESA's new "Integrated Optics" activity started at mid-2007 with the purpose of improving the technology until compliant prototypes can be manufactured and validated, expectedly by the end of 2009. The present paper aims at introducing the project and the components requirements and functions. The selected materials and preliminary designs, as well as the experimental validation logic and test benches are presented. More details are provided on the progress of the main technology: vacuum deposition in the co-evaporation mode and subsequent etching of chalcogenide layers. In addition., preliminary investigations of an alternative technology based on burying a chalcogenide optical fiber core into a chalcogenide substrate are presented. Specific developments of anti-reflective solutions designed for the mitigation of Fresnel losses at the input and output surface of the components are also introduced.

Retrieval of mesospheric electron densities using an optimal estimation inverse method

We present a new method to determine mesospheric electron densities from partially reflected medium frequency radar pulses. The technique uses an optimal estimation inverse method and retrieves both an electron density profile and a gradient electron density profile. As well as accounting for the absorption of the two magnetoionic modes formed by ionospheric birefringence of each radar pulse, the forward model of the retrieval parameterises possible Fresnel scatter of each mode by fine electronic structure, phase changes of each mode due to Faraday rotation and the dependence of the amplitudes of the backscattered modes upon pulse width. Validation results indicate that known profiles can be retrieved and that χ2 tests upon retrieval parameters satisfy validity criteria. Application to measurements shows that retrieved electron density profiles are consistent with accepted ideas about seasonal variability of electron densities and their dependence upon nitric oxide production and transport.